Research ArticleAlgorithm Development for the Optimum Rainfall EstimationUsing Polarimetric Variables in Korea

Cheol-Hwan You1 and Dong-In Lee2

1Atmospheric Environmental Research Institute Pukyong National University Yongso-ro Nam-gu Busan 608-737 Republic of Korea2Department of Environmental Atmospheric Sciences Pukyong National University Yongso-ro Nam-guBusan 608-737 Republic of Korea

Correspondence should be addressed to Dong-In Lee leedipknuackr

Received 17 October 2014 Accepted 3 May 2015

Academic Editor Anthony R Lupo

Copyright copy 2015 C-H You and D-I Lee This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

In this study to get an optimum rainfall estimation using polarimetric variables observed from Bislsan radar which is the firstpolarimetric radar in Korea rainfall cases for 84 hours caused by different conditions which are Changma front and typhoonChangma front only and typhoon only occurred in 2011 were analyzed And rainfall algorithms were developed by using longperiod drop size distributions with six different raindrop axis ratio relations The combination of the relations between 119877 and 119885119885DR 119877 and 119870DP 119885DR and 119877 and 119870DP with different rainfall intensity would be an optimum rainfall algorithm if the reference ofrainfall would be defined correctly In the case the reference is not defined adequately the relation between 119877 and 119885 119885DR119870DP119860119867and 119877 and 119885119870DP 119860119867 can be used as a representative rainfall relation Particularly if the qualified 119885DR is not available the relationbetween 119877 and 119885 119870DP 119860119867 can be used as an optimum rainfall relation in Korea

1 Introduction

Measurement of drop size distributions (DSDs) have beenextensively used to calculate both radar reflectivity and rainrate for conventional radar and there is no unique relationbetween horizontal reflectivity (119885) and rain rate (119877) (here-inafter 119877(119885)) in the world because DSDs could vary fromstorm to storm and within the storm itself [1 2] Calculationsof polarimetric parameters such as 119885 differential reflectivity(119885DR) differential phase shift (ΦDP) cross correlation coef-ficients (120588

ℎ120592) specific differential phase (119870DP) and specific

attenuation (119860119867) could be obtained usingT-matrix scattering

techniques derived byWaterman [3] and later developed fur-ther by Mishchenko et al [4] The raindrop axis is one of theparameters for calculating polarimetric variables of T-matrixsimulation The variations of raindrop axis ratio in natureare intensively related to the oscillating of raindrop andhence are also connected to the polarimetric variables Thereare many researches on the investigation of raindrop shapeby laboratory study [5 6] field measurements [7 8] andmodeling [9 10]

Many researchers noticed that radar rainfall estimationis contaminated by a number of uncertainties such as hard-ware calibration partial beam filling rain attenuation andnonweather echoes [11 12] To mitigate these problems theparticle identification algorithm using polarimetric parame-ters for improving data quality control and rainfall estimatesby the discrimination of nonmeteorological artifacts such asanomalous propagation birds insects and second trip echowas developed [13ndash15] And improvement of quantitativeprecipitation estimation (QPE) accuracy is one of the majorpoints of polarization radar [16ndash20] Ryzhkov et al [21] com-pared the rainfall relations with different drop shape assump-tions and developed rainfall algorithm using polarimetricradar for the prototype WSR-88D Cifelli et al [22] com-pared the two rainfall algorithms CSU-HIDRO (ColoradoState University-Hydrometeor IDentification of Rainfall) andJPOLE- (Joint Polarization Experiment-) like in the highplains environment Recently Ryzhkov et al [23] investigatedthe potential utilization of 119860

119867for rainfall estimation using

X-band and S-band radar They found that 119877(119860) method

Hindawi Publishing CorporationAdvances in MeteorologyVolume 2015 Article ID 395937 15 pageshttpdxdoiorg1011552015395937

2 Advances in Meteorology

POSS

BISL

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Latit

ude (

nort

h)

Latit

ude (

nort

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Longitude (east)Longitude (east)122 124 126 128 130 132

122 123 125 127 129124 126 128 130 131

123 125 127 129 131

132

35

3550

36

3650

35

3550

36

3650

12750 128 12850 129 12950

12750 128 12850 129 12950

100 km

100 km

Figure 1The location of a Bislsan radar (solid rectangle) a POSS disdrometer (open rectangle) and rain gages (plus sign) distributed within100 km of radar coverage

yields robust estimates of rain rates and rain totals even at Sband which has very small attenuation

There have been also many researches on polarimetricradar to implement it into operational uses Based on thesetheoretical and other experimental researches many coun-tries are replacing ormodifying their radars into polarimetricradar for operational use There are three major agenciesMinistry of National Defense (MND) Ministry of LandInfrastructure and Transportation (MOLIT) and KoreaMeteorological Administration (KMA) which operate radarsto monitor and forecast severe weather and flash flood oper-ationally in Korea Among these agencies MOLIT installedpolarimetric radars in 2009 and 2012 for the first time inKorea KMA has installed the S-band polarimetric radar atthe most northwestern part of Korea in 2014 For successfulimplementation of their radars for the purpose of operationaluses many researches on rainfall estimation hydrometeorclassification and DSDs retrieval are required Howeverthere are few studies on these polarimetric related issuesexcept for getting relationships using long period disdrom-eter data and assessment of each relation after applying avery simple quality control for differential phase shift [24]They found that the accuracy of rainfall estimation using119877(119885 119885DR) obtained by DSDs of Busan area in Korea wasthe best one comparing with relations calculated by onesof Oklahoma in US And the quality control and unfoldingof ΦDP for calculating 119870DP were applied to the rainfallestimation [25]The above two studies used only 84574 sam-ples of DSDs excluding winter rainfall events two and fourraindrop shapes for calculation of rainfall relations

This paper discussed how to improve the accuracy ofthe rainfall estimation using all polarimetric variables withdifferent raindrop shapes and get optimum rainfall algorithmfor Korean S-band polarimetric radar In Section 2 rain gage

DSDs and radar dataset calculation of rainfall relationsraindrop axis ratio relations and the method of validationare described Section 3 provides the optimum rainfall algo-rithms with and without rainfall category followed by the cal-culation of119860

119867using observedΦDP and119885 and the validations

of rainfall estimation Finally we provide some conclusionsand derived results are summarized in Section 4

2 Data and Methodology

21 Rain Gage and Radar Dataset The rainfall data from raingages operated by the KMA were used to evaluate the accu-racy of radar rainfall Rain gages located from 5 km to 95 kmwithin radar coverage are included in the analysis Figure 1shows the location of all instruments used in this study Thecircle means the radar coverage solid rectangle is the centerof Bislsan radar plus sign shows the distributed rain gageswithin radar coverage and open rectangle is the location of aPOSS (PrecipitationOccurrence Sensor System) disdrometerthat was installed around 82 km away from radar

Radar data were collected by Bislsan polarimetric radarthat was installed and operated by MOLIT in Korea since2009The specifications of Bislsan polarimetric radar and thequality control algorithm of BDP were shown by You et al[24 25]

22 Calculations of Polarimetric Variables and ValidationThe relations for converting radar variables into rain rateare required to get rainfall because radar could not observethe rainfall directly In order to calculate these relations dis-drometer data which canmeasure theDSDs are needed One-minute DSDs obtained by POSS (Precipitation OccurrenceSensor System) from 2001 to 2004 were used and processedto remove the unreliable data as shown by You et al [25]

Advances in Meteorology 3

Total DSDs

Diameter (mm)034 054 078 105 137 176 226 292 415

Slope 819Shape 552Intercept (log) 538Median dia 128

Num

ber c

onc(m

m6m

m3)lowast

log 1

0

0

2

4

6

8

(a)

Rain rate distribution (POSS)

0 50 100 150 200Rain rate (mmh)

Occ

urre

nce f

requ

ency

10minus1

100

101

104

105

106

102

103

Min 010mmh

Max 19934mmh

Avg 247mmh

Med 108mmh

(b)

Figure 2 Histogram of (a) total number concentration with respect to the drop size and gamma parameters and (b) rain rate calculated using114105 samples of 1-minute DSD after quality control

DSDs data for calculations of relationships were 114105samples after quality control and removal of negative 119870DPThe total number concentration with respect to the dropsize and the averaged parameters of gamma distributionswas shown in Figure 2(a) The slope shape and interceptfor gamma model were 82 55 and 10

54 respectivelyand median diameter was 13mm Most of the data aredistributed in awide rangewith amaximum rain rate of about1993mmhminus1 and the average was 247mmhminus1 (Figure 2(b))

Polarimetric variables were calculated using T-matrixscattering techniques derived by Waterman [3] and laterdeveloped further by Mishchenko et al [4] To get thevariables using DSDs six raindrop shape assumptions areused

The first raindrop axis ratio used in this study has slightlymodified the relation proposed by Pruppacher and Beard [5]and will be called DS1

119887

119886=

10 0 le 119863 le 03mm

103 minus 0062119863 119863 ge 03mm

(1)

where 119886 119887 and 119863 are the major axis minor axis andequivolume diameter of raindrop in mm respectively

119887

119886= 10048+ 0500057119863minus 0026281198632

+ 00036821198633

minus 000016771198634

(2)

Equation (2) is for equilibrium axis ratio derived fromthe numerical model of Beard and Chuang [9] which is ingood agreement with the results from wind tunnel measure-ments (hereinafter DS2)The practical shapes of raindrops inturbulent flow are expected to be different shapes from theequilibrium shapes due to the drop oscillations Oscillatingdrops appear to be more spherical on average than the dropswith equilibrium shapes as shown by Andsager et al [10] inlaboratory studiesThey figured out that the raindropsrsquo shapebetween 11 and 44mm is better explained by the followingformula

119887

119886= 1012minus 001445119863minus 0010281198632

(3)

Bringi et al [26] suggested using (3) for drops with sizessmaller than 44mmand (2) for larger sizes (hereinafterDS3)The shape-diameter relation that combines the observationsof different authors was recently proposed by Brandes et al[27 hereinafter DS4]

119887

119886= 09951+ 0025119863minus 0036441198632

+ 00053031198633

minus 000024921198634

(4)

The relations of raindrop axis ratio (DS5) proposed byBeard and Kubesh [28] andThurai et al [29] were combinedgiven by

119887

119886=

10 119863 le 07mm

1173 minus 05165119863 + 046981198632 minus 013171198633 minus 000851198633 07 lt 119863 le 15mm

1065 minus 00625119863 minus 0003991198632 minus 00007661198633 minus 000040951198634 119863 gt 15mm

(5)

4 Advances in Meteorology

Korea Meteorological Administration (KMA)

20∘E

30∘E

40∘E

20∘E

30∘E

40∘E

50∘E

90∘E 100

∘E 110∘E 120

∘E 130∘E 140

∘E

110∘E 120

∘E 130∘E 140

∘E

150∘E 160

∘E15 UTC June 24 2011 (00 KST June 25 2011)

(a)

Korea Meteorological Administration (KMA)

20∘E

30∘E

40∘E

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30∘E

40∘E

50∘E

90∘E 100

∘E 110∘E 120

∘E 130∘E 140

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∘E 130∘E 140

∘E

150∘E 160

∘E00 UTC June 26 2011 (09 KST June 26 2011)

(b)

Korea Meteorological Administration (KMA)

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30∘E

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∘E03 UTC July 9 2011 (12 KST July 9 2011)

(c)

Korea Meteorological Administration (KMA)

20∘E

30∘E

40∘E

20∘E

30∘E

40∘E

50∘E

90∘E 100

∘E 110∘E 120

∘E 130∘E 140

∘E

110∘E 120

∘E 130∘E 140

∘E

150∘E 160

∘E15 UTC August 7 2011 (00 KST August 8 2011)

(d)

Figure 3 The surface weather chart (a) 0000 LST June 25 (b) 0900 LST June 26 (c) 1200 LST July 9 and (d) 0000 LST August 8 in 2011

The relation of raindrop axis ratio that slightly modifiedthe relation proposed by Goddard et al [30] was used(hereinafter DS6)

119887

119886

=

10 119863 le 10mm

1075 minus 0065119863 minus 000361198632 + 000041198633 119863 gt 10mm

(6)

Another parameter in the T-matrix calculations is thetemperature which is assumed to be 20∘C in this study Itis also necessary to take the canting angle into considerationof the T-matrix simulation because it can account for a 6reduction in the coefficient of the 119877(119870DP) relation [31] and

may cause small negative biases of the estimators [32] Thedistribution of canting angles of raindrops is Gaussian with amean of 0∘ and a standard deviation of 7∘ which have beenrecently determined by Huang et al [33]

23 Validations Because the rainfall in Korea is mostlyaccompanied with Changma front and Typhoon three rain-fall cases which are caused by Changma front and typhoonChangma front only and typhoon only were used forvalidations (Table 1)

Figure 3 shows the surface weather chart of each caseThetyphoon MAERI was located at the eastern ocean of Taiwanand the Changma front was elongated from eastern Chinacontinent to the central Japan through the southern part of

Advances in Meteorology 5

0

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Aver

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ainf

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nt (m

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1 3 6 9 12 15 18 21 00 3 6 9 12 15 18 21 24

(c)

Figure 4 Time series of averaged rainfall amount which was accompanied with (a) Changma front and typhoon (b) Changma front onlyand (c) typhoon only averaged rainfall from all rain gages within radar coverage

Table 1 Rainfall cases with different sources for the study

Period Sources

2011 6 25 0900 LSTsim6 26 1400 LST Changma frontand typhoon

2011 7 09 0000 LSTsim7 10 2200 LST Changma front2011 8 07 1800 LSTsim8 08 0300 LST Typhoon

Korea on 0000 LST June 25 (Figure 3(a))TheMAERImovedto the north located at the southern west sea of Korea andmade rainfall in the Korean peninsula on 0900 LST June 26 in2011 (Figure 3(b)) Changma frontwas located at the southernpart of Korea and brought rainfall at the analyzed area on1200 LST July 9 in 2011 (Figure 3(c))The rainfall was affectedby Changma front all the time during case 2 The typhoonMUIFAwas located at the southwestern sea of Korea on 0000LST August 8 in 2011 and caused rainfall at the target area(Figure 3(d))

Figure 4 shows the time series of averaged rainfall amountobserved on the ground rain gages within radar coveragefrom 5 km to 95 km Averaged rainfall amount refers to thatobtained by averaging the amount of rainfall observed by raingages within the radius of the radar There are three peaksof rainfall in case of Changma front and typhoon the firsttwo peaks were due to Changma front and the third one wasdue to the influence of the typhoon There are three peaksof rainfall accompanied with Changma front in the secondrainfall eventThe third event was also caused by typhoon butwas relatively shortThe period of the selected rainfall was 84hours 29 hours for Changma front and typhoon 46 hours forChangma front only and 9 hours for typhoon only

The normalized error (NE) fractional root mean squareerror (RMSE) and correlation coefficients (CC) of rainfallrelations and 121 gages were used to investigate the perfor-mance of each rainfall relation

NE =(1119873)sum

119873

119894=1 (1003816100381610038161003816119877119877119894 minus 119877

119866119894

1003816100381610038161003816)

119877119866

6 Advances in Meteorology

Beard and Chuang 1987

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Standard

Average 2620deviation 838

(a)

Andsager et al 1999

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Standard

Average 2616deviation 837

(b)

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Goddard et al 1995

Standard

Average 2616deviation 839

(c)

Freq

uenc

y

Beard and Chuang 1987

00 05 10 15 20 25 30 35000002004006008010012014

Standard deviation 063Average 091

ZDR (dB)

(d)

Andsager et al 1999

Standard deviation 061Average 080

Freq

uenc

y

00 05 10 15 20 25 30 35000002004006008010012014

ZDR (dB)

(e)

Goddard et al 1995

Standard deviation 066Average 082

Freq

uenc

y

00 05 10 15 20 25 30 35000002004006008010012014

ZDR (dB)

(f)

Freq

uenc

y

Beard and Chuang 1987

000 005 010 015 020000

010

020

030

040

050Standard deviation 0107

Average 0037

KDP (degkm)

(g)

Freq

uenc

y

000 005 010 015 020000

010

020

030

040

050

KDP (degkm)

Andsager et al 1999

Standard deviation 0092Average 0031

(h)

Freq

uenc

y

000 005 010 015 020000

010

020

030

040

050

KDP (degkm)

Goddard et al 1995

Standard deviation 0096Average 0030

(i)

Figure 5 The occurrence frequency of (a) 119885 with DS1 (b) 119885 with DS3 (c) 119885 with DS6 (d) 119885DR with DS1 (e) 119885DR with DS3 (f) 119885DR withDS6 (g) 119870DP with DS1 (h) 119870DP with DS3 and (i) 119870DP with DS6

RMSE = [1119873

119873

sum

119894=1(119877119877119894

minus119877119866119894

)2]

12

CC =

sum119873

119894=1 (119877119877119894

minus 119877119877) (119877119866119894

minus 119877119866)

[sum119873

119894=1 (119877119877119894

minus 119877119877)2]

12[sum119873

119894=1 (119877119866119894

minus 119877119866)2]

12

(7)

where 119873 is the number of the RR and RG pairs and 119877119877and

119877119866are the averaged rain rate of radar and gage for an hour

respectively The above statistical variables are calculatedusing 1-hour rainfall amount of radar and gage at the pointThe point rainfall of radar was obtained by averaging rainfallover a small area (1 km times 1∘) centered on each rain gage

3 Results

31 Rainfall Relations with Different Raindrop Axis Ratios

311 The Characteristics of 119885 119885119863119877

and 119870119863119875

with DifferentDrop Shapes The histograms of occurrence frequency forpolarimetric variables 119885 119885DR and 119870DP calculated by DSDsdata for 4 years in Busan with different raindrop axis ratiorelations DS1 DS3 and DS6 were shown in Figure 5

The averages and modes of 119885 were around 262 dBZ and32sim33 dBZ for all raindrop axis assumptions (Figures 5(a)sim5(c)) It means that the reflectivity is not sensitive to the dropaxis relation In case of 119885DR there were two modes of occur-rence for all cases The averages and standard deviation ofeach relation were 063 dB and 091 dB for DS1 061 dB and08 dB for DS3 and 066 dB and 082 dB for DS6The low and

Advances in Meteorology 7

Table 2 The rainfall relations of 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) with different raindrop shape assumptions

DS 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) 119877(119870DP 119885DR)

DS1 R = 00273119885060 R = 029119885DR527 R = 445119870DP

0942 R = 00161198850889119885DRminus494 R = 537119870DP

0857119885DRminus148

DS2 R = 00277119885059 R = 038119885DR487 R = 533119870DP

0913 R = 00141198850852119885DRminus408 R = 752119870DP

0855119885DRminus198

DS3 R = 00277119885060 R = 042119885DR498 R = 615119870DP

0908 R = 00151198850818119885DRminus372 R = 822119870DP

0855119885DRminus198

DS4 R = 00277119885060 R = 041119885DR498 R = 599119870DP

0896 R = 00141198850844119885DRminus406 R = 674119870DP

0785119885DRminus213

DS5 R = 00277119885060 R = 040119885DR503 R = 562119870DP

0897 R = 00131198850861119885DRminus43 R = 847119870DP

0840119885DRminus238

DS6 R = 00280119885059 R = 043119885DR469 R = 563119870DP

0857 R = 00131198850857119885DRminus40 R = 150119870DP

0483119885DRminus077

R(Z

ZD

R)

(mm

h)

R = 001589085Z08927

ZDRminus49936

NB = 1300

RMSE = 2776

CC = 0965

R (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

(a)

R = 13428687294KDP08991

ZDRminus26757

NB = 188

RMSE = 2593

CC = 0967

R (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(K

DPZ

DR)

(mm

h)

(b)

Figure 6 The scatter plots of rainfall obtained by DSDs and (a) 119877(119885 119885DR) and (b) 119877(119870DP 119885DR) using 119885 for DS3 119885DR for DS1 and 119870DP forDS3

high modes of 119885DR with DS1 DS3 and DS6 were 02sim03 dBand 17sim18 dB 02sim03 dB and 16sim17 dB and 00sim01 dB and17sim18 dB respectively The occurrence frequencies of lowmode for each raindrop axis ratio were significantly differentfrom each other (Figures 5(d)sim5(f)) The averages and stan-dard deviation of119870DPwith different raindrop shapeswere 011and 004 009 and 003 and 01 and 003 respectively Themodes of all drop shapes were the same but the occurrencefrequencies were different (Figures 5(g)sim5(i))

312 The Statistics of Rainfall Relations with Different Rain-drop Axis Ratios Because the occurrence frequencies of119885DRand 119870DP with different raindrop axis ratios were differentfrom each other the rainfall relations using those variablesshould be different with drop shape assumptions Table 2shows the rainfall relations obtained by using different rain-drop shape assumptions The coefficients of 119877(119885) were notsignificantly different with drop shape assumptions howeverthose of other relations were different with each drop shape

Table 3 shows the cross correlations (hereinafter CC) andRMSEs (root mean square errors) of rainfall relations 119877(119885)119877(119885DR) 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) obtained bycalculations using DSDs data with different raindrop shapes

The statistics of 119877(119885) and 119877(119885DR) were not significantlydifferent with raindrop shapesThe CC and RMSE of 119877(119885DR)and 119877(119885 119885DR) were the worst and the best among theother rainfall relations The statistics of 119877(119870DR) 119877(119885 119885DR)and 119877(119870DP 119885DR) were much more variable with differentraindrop axis ratios than the ones of 119877(119885) and 119877(119885DR) TheRMSEs of 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) with rain-drop shapes were distributed from 3030 to 3828mm 2965to 3523mm and 3151 to 5412mm respectivelyThe best per-formance of each relation occurred at DS3 for 119877(119885) DS1 for119877(119885DR) DS1 for 119877(119870DP) DS1 for 119877(119885 119885DR) and DS3 for119877(119870DP 119885DR)

In order to calculate more accurate 119877(119885 119885DR) and119877(119870DP 119885DR) the 119885 and 119885DR with the best performance werechosen Figure 6 shows the scatter plots of rainfall obtainedby DSDs and 119877(119885 119885DR) and 119877(119870DP 119885DR) using the beststatistics among raindrop axis ratio 119885 119885DR and 119870DP werechosen from DS3 DS1 and DS1 respectively Comparingwith 119877(119885 119885DR) and 119877(119870DP 119885DR) of single raindrop axisratio relations having the best performance new combinedrelations had better RMSE and CC The RMSEs of new rela-tions 119877(119885 119885DR) and 119877(119870DP 119885DR) had better score as muchas around 02mm and 06mm respectively Even though

8 Advances in Meteorology

Table 3 The correlation coefficients and RMSEs (mm) of rainfall obtained by rainfall relations and DSDs CC means cross correlation

DS 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) 119877(119870DP 119885DR)

CC RMSE CC RMSE CC RMSE CC RMSE CC RMSEDS1 0913 4705 0572 6241 0875 3030 0964 2965 0951 3313DS2 0913 4709 0569 6248 0861 3198 0956 3272 0956 3222DS3 0914 4704 0562 6261 0861 3178 0949 3523 0960 3151DS4 0913 4706 0569 6249 0828 3549 0954 3334 0931 3882DS5 0913 4706 0572 6243 0849 3326 0957 3210 0950 3348DS6 0913 4713 0572 6244 0795 3828 0956 3239 0814 5412

Table 4The rainfall relations NE RMSE and CC of each raindropaxis ratio relation

DropShape Relation NE RMSE CC

DS1119877(119870DP) = 445119870DP

0942 052 4996 082119877(119885 119885DR) = 001571198850889119885DR

minus494 031 4802 097119877(119870DP 119885DR) = 537119870DP

0857119885DRminus148 056 5262 088

DS2119877(119870DP) = 530119870DP

0913 052 4645 078119877(119885 119885DR) = 001411198850853119885DR

minus408 036 3793 073119877(119870DP 119885DR) = 752119870DP

0855119885DRminus198 060 5146 073

DS3119877(119870DP) = 615119870DP

0908 055 4698 078119877(119885 119885DR) = 001481198850818119885DR

minus372 043 4479 089119877(119870DP 119885DR) = 822119870DP

0855119885DRminus198 063 5247 073

DS4119877(119870DP) = 599119870DP

0896 054 4673 078119877(119885 119885DR) = 001361198850840119885DR

minus406 040 4134 089119877(119870DP 119885DR) = 674119870DP

0785119885DRminus213 060 5249 073

DS5119877(119870DP) = 562119870DP

0897 053 4625 078119877(119885 119885DR) = 001331198850861119885DR

minus431 037 3900 088119877(119870DP 119885DR) = 847119870DP

0840119885DRminus238 065 5390 071

DS6119877(119870DP) = 563119870DP

0857 054 4647 078119877(119885 119885DR) = 001251198850857119885DR

minus399 038 3967 089119877(119870DP 119885DR) = 150119870DP

0483119885DRminus077 065 7141 076

the CC and RMSE of 119877(119885) and 119877(119885DR) with different dropshapes were not significant the combined relations had betterperformance

32 Validations of Rainfall Relations with Different RaindropAxis Ratio Relations To investigate the performance ofrainfall relationsNE (normalized error) RMSE andCCwerecalculated using rainfall from each relation with six raindropshapes and that of gage rainfall

Table 4 summarizes the relations and the statistics suchas NE RMSE and CC The NEs and RMSEs of 119877(119870DR)calculated by each raindrop axis were distributed from 052 to055 and from 4625 to 4996 respectively The 119877(119870DR) withassumption of DS5 was the best score of RMSE in other rain-drop shapes In case of119877(119885 119885DR) the distribution ofNEs andRMSEs was from 031 to 043 and from 3793 to 4602 respec-tively The best RMSE score of 119877(119885 119885DR) was from DS2The NEs and RMSEs of 119877(119870DP 119885DR) occurred from 055 to065 and from 5146 to 7141 respectively The performance of

119877(119870DP 119885DR) was the worst score and 119877(119885 119885DR) had the bestscore in all raindrop axis ratio relations The performancesof validation were different from that of rainfall relationcalculation It would be caused by the variations of DSDs inthis study

To compare the performance between new combined119877(119870DP 119885DR) and 119877(119885 119885DR) the statistics were also calcu-lated Figure 7 shows the scatter plots rainfall from rainfallrelation and gage rainfall with some statistics The NEand RMSE of two relations from single raindrop shapeassumption showed better results However it seems that the119877(119885 119885DR)with two-raindrop axis ratio was more close to thegage rainfall in the range of weaker than 20mmh and the119877(119870DP 119885DR) with two drop shapes was more accurate in therainfall of higher than 20mmh

33 Rainfall Estimation Using Specific Attenuation331 Calculation of Specific Attenuation The 119860

119867can be

calculated from the radial profile of the attenuated reflectivity119885119886and the two-way PIA (Path Integrated Attenuation) along

the propagation path (1199031 1199032) proposed by Meneghini and

Nakamura [34]

119860 (119903) =119886 (119903) [119885119886]

119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(8)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

119886 (119904) [119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

119886 (119904) [119885119886 (119904)]119887119889119904

(9)

If 119886 is not dependent on range then (8) becomes

119860 (119903) =[119885119886]119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(10)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

[119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

[119885119886 (119904)]119887119889119904

(11)

119862 (119887PIA) = exp (023119887PIA) minus 1 (12)

Advances in Meteorology 9

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 036

RMSE = 3793

CC = 0888

Rada

r tot

alR

(ZZ

DR)

BC

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 060

RMSE = 5146

CC = 0732

Rada

r tot

alR

(KD

PZ

DR)

BC

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 032

RMSE = 5194

CC = 0818

Rada

r tot

alR

(ZZ

DR)

best

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 092

RMSE = 7302

CC = 0695

Rada

r tot

alR

(KD

PZ

DR)

best

(d)

Figure 7The scatter plot of rainfall from gage and (a) 119877(119885 119885DR) (b) 119877(119870DP 119885DR)with single raindrop axis ratio relation (c) 119877(119885 119885DR) and(d) 119877(119870DP 119885DR) with two-raindrop axis ratio relation

Bringi et al [35] recommended estimating PIA usingΦDPby

PIA (1199031 1199032) = 120572 [ΦDP (1199032) minusΦDP (1199031)] = 120572ΔΦDP (13)

and Testud et al [36] used (10) and (12) to obtain radialprofiles of 119860

119867at C-band In this study 119860

119867was calculated

by the method proposed by Ryzhkov et al [23] The constant

119887 was set by 06 and 120572 was by 0027 calculated by the ratio of119860119867to 119870DP obtained from DSDsFigure 8 shows the scatter plot of rainfall from 119877(119885)

119877(119870DP) and 119877(119860119867) and rainfall from DSDs and an PPIs

(Plan Position Indicators) at 05 degree elevation angle of gagerainfall and rainfall from 119877(119870DP) and 119877(119860

119867) at 0251 KST on

the 8th of August in 2011The 119877(119860

119867) relation had much better fit to the rainfall of

DSDs than that of119877(119870DP) and119877(119885) relation Comparingwith

10 Advances in Meteorology

Beard and Chuang 1987

Rain rate DSD (mmh)

R(Z

) (m

mh

)

10minus1

100

101

102

103

10minus1

100

101

102

103

R = 00277Z05994

NB = minus2122

RMSE = 4709

CC = 0913

(a)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

NB = minus1295136

RMSE = 3198

CC = 0861

R = 533039KDP091341

R(K

DP)

(mm

h)

(b)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(A

H)

(mm

h)

R = 337359AH10194

NB = 327

RMSE = 3667

CC = 0984

(c)

150100705040302015107310500

R(KDP) (mmh)

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(d)

R(AH) (mmh)

150100705040302015107310500

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(e)

Figure 8 The scatter plot of (a) 119877(119885) (b) 119877(119870DP) and (c) 119877(119860119867) with statistics and the rainfall distribution of 119877(119870DP) and 119877(119860

119867) at 0251

KST on the 8th of August in 2001

Advances in Meteorology 11

Table 5 The rainfall relations of 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assumptions

DS 119877(119885119870DP 119860119867) 119877(119885 119885DR 119870DP 119860119867)

DS1 119877 = 1527119885minus004119870DP0327

119860119867

0713119877 = 310Z012

119885DRminus083

119870DP0304

119860119867

0677

DS2 119877 = 12012119885minus024119870DP0551

119860119867

0685119877 = 4947Zminus015119885DR

minus026119870DP

0468119860119867

0681

DS3 119877 = 17211119885minus027119870DP0619

119860119867

0650119877 = 4502Z014

119885DRminus039

119870DP0486

119860119867

0653

DS4 119877 = 10798119885minus019119870DP0403

119860119867

0778119877 = 193Z018

119885DRminus111

119870DP0114

119860119867

0702

DS5 119877 = 20275119885minus027119870DP0543

119860119867

0720119877 = 24Z037

119885DRminus147

119870DPminus0025

119860119867

0656

DS6 119877 = 397119885minus011119870DP0044

119860119867

0808119877 = 571Z007

119885DRminus092

119870DP0238

119860119867

0687

the distribution of rainfall obtained by 119877(119870DP) and 119877(119860119867)

119877(119860119867) has better spatial resolution and more homogeneous

pattern than those of 119877(119870DP)

332 Validations of 119877(119860119867) 119877(119885119870

119863119875 119860119867) and 119877(119885 119885

119863119877

119870119863119875

119860119867) Relations As mentioned in the previous section

119877(119860119867) has the potential to be the best choice for estimating

rainfall using polarimetric variables To verify the accuracy119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) relations

were obtained and the accuracy of 119877(119860119867) 119877(119885119870DP 119860119867)

and 119877(119885 119885DR 119870DP 119860119867) which had the best performance inthe relations calculated by the six raindrop axis ratio relationswere examined by comparing with 119877(119870DP)

Figure 9 shows the scatter plot of rainfall from gagerainfall and 119877(119870DP) 119877(119860

119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR

119870DP 119860119867) for 84 hours The accuracy of 119877(119885 119885DR 119870DP 119860119867)was the best and119877(119885119870DP 119860119867)was the second in 4 relations119877(119860119867)was not better than 119877(119870DP) in whole range of rainfall

However in the range of higher rainfall it seems that 119877(119860119867)

was closer to the gage rainfall The error of 119877(119860119867) would be

caused by the missing radial profile ofΦDP along the rayThemissing has occurred if the difference of ΦDP between thestarting and end gate is negative According to the results119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) would compensatefor this region

34 Optimum Rainfall Algorithm To find out the optimumrainfall algorithm for Korean S-band polarimetric radar thegage rainfall amount was categorized by three steps 0 to5mmh assigned as light rain 5 to 30mmh as medium rainand higher than 30mmh as high rain In previous sectionthe relations have different accuracy not only for the raindropaxis ratio relation but also for rainfall amount The samplenumbers for each category were 3322 samples 1980 samplesand 92 samples respectively

Figure 10 shows the RMSEs of 119877(119870DP) 119877(119885 119885DR)119877(119870DP 119885DR) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) withdifferent rainfall categories defined in three steps All rela-tions have different RMSEs with respect to the raindrop axisratio relations 119877(119870DP) with DS3 119877(119885 119885DR) with DS2 and119877(119870DP 119885DR) with DS3 have the best score at the high rainfallregime at the low rainfall regime and at the medium rainfallregime respectively Even though 119877(119885 119885DR) has the bestperformance among other relations in total rainfall eventsusing different rainfall relations with different rainfall regimewould be an optimum rainfall algorithm for Korean S-band

polarimetric radar A possible optimum polarimetric rainfallalgorithm can be expressed by

119877 = 00141198850852119885DRminus408 0 lt Rainfall lt 5mmhminus1

119877 = 822119870DP0855

119885DRminus198

5 lt Rainfall lt 30mmhminus1

119877 = 615119870DP0908 30mmhminus1 lt Rainfall

(14)

Table 5 shows the rainfall relations of 119877(119885119870DP 119860119867) and119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assump-tions The coefficients of each relation with respect to thedrop shapes were much different comparing with relationsobtained by combining two polarimetric variables

In case of rainfall relations combined with119860119867 119877(119885 119885DR

119870DP 119860119867) has better score than 119877(119885119870DP 119860119867) Both119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with DS3 showedbetter result than other raindrop shape assumptions119877(119885 119885DR 119870DP 119860119867) at the low medium and high rainfallregimes has similar RMSE to 119877(119885 119885DR) 119877(119870DP 119885DR) and119877(119870DP) respectively

Equations (14) would be an optimum rainfall algorithmbut there is still a problem to solve how the rainfall categoriesare defined using radar and gage Gage does not have goodspatial resolution to cover radar resolution like 125m or 1 kmand each rainfall relation has its own error at certain rainfallregime Therefore 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867)withDS3 can be used regardless rainfall intensity And in case119885DR bias calibration is not available or does not have enoughquality for quantitative use 119877(119885119870DP 119860119867) with DS3 can beused as a representative rainfall estimation

4 Summary and Conclusions

Polarimetric radars will be main tools to monitor andforecast severe weather and flash flooding within severalyears in Korea To get an optimum rainfall algorithm usingpolarimetric variables observed from Bislsan radar which isthe first polarimetric radar in Korea rainfall cases for 84hours caused by different conditions which are Changmafront and typhoon Changma front only and typhoon onlythat occurred in 2011 were analyzed And rainfall relationswere obtained by using long period DSDs with six differentraindrop axis ratio relations

In the analysis of 119885 119885DR and119870DP occurrence frequencythere were two modes of 119885DR occurrence frequency and

12 Advances in Meteorology

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100Ra

dar t

otal

R(K

DP)

BC

NE = 052

RMSE = 4645

CC = 0778

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 051

RMSE = 5005

CC = 0797

Rada

r tot

al R

(AH

) AS

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100NE = 046

RMSE = 4374

CC = 0820

Rada

r tot

al R

(ZK

DPA

H) A

S

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 045

RMSE = 4368

CC = 0852

Rada

r tot

al R

(ZZ

DRK

DPA

H) A

S

(d)

Figure 9 The scatter plot of gage rainfall and 119877(119870DP) 119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DP 119870DP 119860119867) rainfall for 84 hours

the variations of 119870DP and 119885DR histograms were higherthan that of 119885 with raindrop ratio relations According tothese variations the combined relations of 119877(119885 119885DR) and119877(119870DP 119885DR) using 119885 with DS3 119885DR with DS1 and 119870DP withDS1 were closer to the rainfall of DSDs

To examine the performance of each rainfall relationNE RMSE CC were calculated using rainfall recorded at121 gages within radar coverage for 84 hours The statisticsof each rainfall relation were different with raindrop shape

assumptions and rainfall intensity119877(119870DP 119885DR)had theworstperformance and119877(119885 119885DR) had the best score in all raindropshapes 119860

119867was calculated by observed ΦDP and 119885 using the

method by Ryzhkov et al [23] and the rainfall relations using119860119867were also calculated and analyzedThe performance of rainfall relations were comparedwith

three different rainfall categories to findout an optimumrain-fall relation for the S-band polarimetric in Korea 119877(119885 119885DR)119877(119870DP 119885DR) and 119877(119870DP) had the best RMSE at the light

Advances in Meteorology 13

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP) with drop shape

(a)

0

5

10

15

20

Drop shape

25

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(Z ZDR) with drop shape

(b)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP ZDR) with drop shape

(c)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(ZKDP AH) with drop shape

(d)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

0ndash5mm5ndash30mmOver 30mm

RMSE of R(Z ZDR KDP AH) with drop shape

(e)

Figure 10The RMSEs of (a) 119877(119870DP) (b) 119877(119885 119885DP) (c) 119877(119870DP 119885DP) (d) 119877(119885119870DP 119860119867) and (e) 119877(119885 119885DP 119870DP 119860119867)with raindrop axis ratiorelations in the three rainfall categories

14 Advances in Meteorology

rain medium rain and high rainfall regimes respectively119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) showed relativelygood performance in all rainfall regimesThe combination of119877(119885 119885DR) 119877(119870DP 119885DR) and 119877(119870DP) with rainfall intensitywould be an optimum rainfall algorithm if the referenceof rainfall would be defined correctly Regardless of rainfallintensity 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) obtainedby assuming DS3 can be used as a representative rainfall rela-tion without consideration of rainfall intensity regime Par-ticularly if the qualified 119885DR is not available 119877(119885119870DP 119860119867)with DS3 drop shape assumption can be used as an optimumrainfall relation in Korea

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge providing radar data weatherchart and AWS data for this work from the Ministry ofLand Infrastructure Transport and Korea MeteorologicalAdministration The authors also acknowledge providingcodes for scattering simulation from Professor V N Bringi atColorado StateUniversityThisworkwas funded by theKoreaMeteorological Industry Promotion Agency under GrantKMIPA 2015-1050

References

[1] E Campos and I Zawadzki ldquoInstrumental uncertainties in Z-R relationsrdquo Journal of Applied Meteorology vol 39 no 7 pp1088ndash1102 2000

[2] C-H You D-I Lee S-M Jang et al ldquoCharacteristics ofrainfall systems accompanied with Changma front at Chujadoin Koreardquo Asia-Pacific Journal of Atmospheric Sciences vol 46no 1 pp 41ndash51 2010

[3] P CWaterman ldquoSymmetry unitarity and geometry in electro-magnetic scatteringrdquo Physical Review D vol 3 no 4 pp 825ndash839 1971

[4] M IMishchenko LD Travis andDWMackowski ldquoT-matrixcomputations of light scattering by nonspherical particles areviewrdquo Journal of Quantitative Spectroscopy and RadiativeTransfer vol 55 no 5 pp 535ndash575 1996

[5] H R Pruppacher and K V Beard ldquoA wind tunnel investigationof the internal circulation and shape of water drops fallingat terminal velocity in airrdquo Quarterly Journal of the RoyalMeteorological Society vol 96 no 408 pp 247ndash256 1970

[6] D C Blanchard ldquoThe behavior of water drops at terminalvelocity in airrdquo EOS vol 31 no 6 pp 836ndash842 1950

[7] G-J Huang V N Bringi M Schonhuber et al ldquoDrop shapeand canting angle distributions in rain from2-Dvideo disdrom-eterrdquo in Proceedings of the 33rd Conference on Radar Meteorol-ogy Extended Abstract P8A8 Cairns Australia August 2007

[8] M Thurai V N Bringi and W A Petersen ldquoRain microstruc-ture retrievals using 2-D video disdrometer and C-band polari-metric radarrdquo Advances in Geosciences vol 20 pp 13ndash18 2009

[9] K V Beard and C Chuang ldquoA new model for the equilibriumshape of raindropsrdquo Journal of the Atmospheric Sciences vol 44pp 1509ndash1524 1987

[10] K Andsager K V Beard and N S Laird ldquoA laboratory studyof oscillations and axis ratios for large raindropsrdquo Journal of theAtmospheric Sciences vol 55 pp 208ndash226 1999

[11] J W Wilson and E A Brandes ldquoRadar measurement of rain-fallmdasha summaryrdquo Bulletin AmericanMeteorological Society vol60 no 9 pp 1048ndash1058 1979

[12] P M Austin ldquoRelation betweenmeasured radar reflectivity andsurface rainfallrdquo Monthly Weather Review vol 115 no 5 pp1053ndash1070 1987

[13] J Vivekanandan D S Zrnic S M Ellis R Oye A V Ryzhkovand J Straka ldquoCloud microphysics retrieval using S-band dual-polarization radar measurementsrdquo Bulletin of the AmericanMeteorological Society vol 80 no 3 pp 381ndash388 1999

[14] A V Ryzhkov and D S Zrnic ldquoDiscrimination between rainand snow with a polarimetric radarrdquo Journal of Applied Meteo-rology vol 37 no 10 pp 1228ndash1240 1998

[15] S E Giangrande and A V Ryzhkov ldquoEstimation of rainfallbased on the results of polarimetric echo classificationrdquo Journalof AppliedMeteorology and Climatology vol 47 no 9 pp 2445ndash2462 2008

[16] A V Ryzhkov and D S Zrnic ldquoAssessment of rainfall measure-ment that uses specific differential phaserdquo Journal of AppliedMeteorology vol 35 no 11 pp 2080ndash2090 1996

[17] P T May T D Keenan D S Zrnic L D Carey and S ARutledge ldquoPolarimetric radar measurements of tropical rain ata 5-cm wavelengthrdquo Journal of Applied Meteorology vol 38 no6 pp 750ndash765 1999

[18] V N Bringi and V Chandrasekar ldquoThe polarimetric basis forcharacterizing precipitationrdquo in Polarimetric Doppler WeatherRadar Principles and Applications pp 378ndash533 CambridgeUniversity Press Cambridge UK 2001

[19] E A Brandes G Zhang and J Vivekanandan ldquoExperiments inrainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[20] A V Ryzhkov T J Schuur D W Burgess P L Heinselman SE Giangrande and D S Zrnic ldquoThe joint polarization exper-iment polarimetric rainfall measurements and hydrometeorclassificationrdquo Bulletin of the American Meteorological Societyvol 86 no 6 pp 809ndash824 2005

[21] A V Ryzhkov S E Giangrande and T J Schuur ldquoRainfall esti-mation with a polarimetric prototype of WSR-88Drdquo Journal ofApplied Meteorology vol 44 no 4 pp 502ndash515 2005

[22] R Cifelli V Chandrasekar S Lim P C Kennedy Y Wang andS A Rutledge ldquoA new dual-polarization radar rainfall algo-rithm application in Colorado precipitation eventsrdquo Journal ofAtmospheric andOceanic Technology vol 28 no 3 pp 352ndash3642011

[23] A Ryzhkov M Diederich P Zhang and C Simmer ldquoPotentialutilization of specific attenuation for rainfall estimationmitiga-tion of partial beam blockage and radar networkingrdquo Journal ofAtmospheric and Oceanic Technology vol 31 no 3 pp 599ndash6192014

[24] C-H You M-Y Kang D-I Lee and H Uyeda ldquoRainfallestimation by S-band polarimetric radar in Korea Part Ipreprocessing and preliminary resultsrdquoMeteorological Applica-tions vol 21 no 4 pp 975ndash983 2014

[25] C-H You D-I Lee andM-Y Kang ldquoRainfall estimation usingspecific differential phase for the first operational polarimetricradar in Koreardquo Advances in Meteorology vol 2014 Article ID413717 10 pages 2014

Advances in Meteorology 15

[26] V N Bringi V Chandrasekar J Hubbert E Gorgucci W LRandeu and M Schoenhuber ldquoRaindrop size distribution indifferent climatic regimes from disdrometer and dual-polarizedradar analysisrdquo Journal of the Atmospheric Sciences vol 60 no2 pp 354ndash365 2003

[27] E A Brandes G Zhang and J Vivekanandan ldquoExperimentsin rainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[28] K V Beard and R J Kubesh ldquoLaboratory measurements ofsmall raindrop distortion Part 2 oscillation frequencies andmodesrdquo Journal of the Atmospheric Sciences vol 48 no 20 pp2245ndash2264 1991

[29] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[30] J W F Goddard K L Morgan A Illingworth and HSauvageot ldquoDual-wavelength polarization measurements inprecipitation using the CAMRA and Rabelias radarsrdquo in Pro-ceedings of the 27th Conference on Radar Meteorology pp 196ndash198 American Meteorology Society Vail Colo USA 1995

[31] A V Ryzhkov D S Zrnic J C Hubbert V N Bringi JVivekanandan and E A Brandes ldquoPolarimetric radar obser-vations and interpretation of co-cross-polar correlation coeffi-cientsrdquo Journal of Atmospheric and Oceanic Technology vol 19no 3 pp 340ndash354 2002

[32] S YMatrosov KAClark B EMartner andA Tokay ldquoX-bandpolarimetric radar measurements of rainfallrdquo Journal of AppliedMeteorology vol 41 no 9 pp 941ndash952 2002

[33] G-J Huang V N Bringi and M Thurai ldquoOrientation angledistributions of drops after an 80-m fall using a 2D videodisdrometerrdquo Journal of Atmospheric and Oceanic Technologyvol 25 no 9 pp 1717ndash1723 2008

[34] R Meneghini and K Nakamura ldquoRange profiling of the rainrate by an airborne weather radarrdquo Remote Sensing of Environ-ment vol 31 no 3 pp 193ndash209 1990

[35] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onpolarimetric variables at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[36] J Testud E L Bouar E Obligis and M Ali-Mehenni ldquoTherain profiling algorithm applied to polarimetric weather radarrdquoJournal of Atmospheric andOceanic Technology vol 17 no 3 pp332ndash356 2000

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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2 Advances in Meteorology

POSS

BISL

32

33

34

35

36

37

39

38

40

32

33

34

35

36

37

39

38

40

Latit

ude (

nort

h)

Latit

ude (

nort

h)

Longitude (east)Longitude (east)122 124 126 128 130 132

122 123 125 127 129124 126 128 130 131

123 125 127 129 131

132

35

3550

36

3650

35

3550

36

3650

12750 128 12850 129 12950

12750 128 12850 129 12950

100 km

100 km

Figure 1The location of a Bislsan radar (solid rectangle) a POSS disdrometer (open rectangle) and rain gages (plus sign) distributed within100 km of radar coverage

yields robust estimates of rain rates and rain totals even at Sband which has very small attenuation

There have been also many researches on polarimetricradar to implement it into operational uses Based on thesetheoretical and other experimental researches many coun-tries are replacing ormodifying their radars into polarimetricradar for operational use There are three major agenciesMinistry of National Defense (MND) Ministry of LandInfrastructure and Transportation (MOLIT) and KoreaMeteorological Administration (KMA) which operate radarsto monitor and forecast severe weather and flash flood oper-ationally in Korea Among these agencies MOLIT installedpolarimetric radars in 2009 and 2012 for the first time inKorea KMA has installed the S-band polarimetric radar atthe most northwestern part of Korea in 2014 For successfulimplementation of their radars for the purpose of operationaluses many researches on rainfall estimation hydrometeorclassification and DSDs retrieval are required Howeverthere are few studies on these polarimetric related issuesexcept for getting relationships using long period disdrom-eter data and assessment of each relation after applying avery simple quality control for differential phase shift [24]They found that the accuracy of rainfall estimation using119877(119885 119885DR) obtained by DSDs of Busan area in Korea wasthe best one comparing with relations calculated by onesof Oklahoma in US And the quality control and unfoldingof ΦDP for calculating 119870DP were applied to the rainfallestimation [25]The above two studies used only 84574 sam-ples of DSDs excluding winter rainfall events two and fourraindrop shapes for calculation of rainfall relations

This paper discussed how to improve the accuracy ofthe rainfall estimation using all polarimetric variables withdifferent raindrop shapes and get optimum rainfall algorithmfor Korean S-band polarimetric radar In Section 2 rain gage

DSDs and radar dataset calculation of rainfall relationsraindrop axis ratio relations and the method of validationare described Section 3 provides the optimum rainfall algo-rithms with and without rainfall category followed by the cal-culation of119860

119867using observedΦDP and119885 and the validations

of rainfall estimation Finally we provide some conclusionsand derived results are summarized in Section 4

2 Data and Methodology

21 Rain Gage and Radar Dataset The rainfall data from raingages operated by the KMA were used to evaluate the accu-racy of radar rainfall Rain gages located from 5 km to 95 kmwithin radar coverage are included in the analysis Figure 1shows the location of all instruments used in this study Thecircle means the radar coverage solid rectangle is the centerof Bislsan radar plus sign shows the distributed rain gageswithin radar coverage and open rectangle is the location of aPOSS (PrecipitationOccurrence Sensor System) disdrometerthat was installed around 82 km away from radar

Radar data were collected by Bislsan polarimetric radarthat was installed and operated by MOLIT in Korea since2009The specifications of Bislsan polarimetric radar and thequality control algorithm of BDP were shown by You et al[24 25]

22 Calculations of Polarimetric Variables and ValidationThe relations for converting radar variables into rain rateare required to get rainfall because radar could not observethe rainfall directly In order to calculate these relations dis-drometer data which canmeasure theDSDs are needed One-minute DSDs obtained by POSS (Precipitation OccurrenceSensor System) from 2001 to 2004 were used and processedto remove the unreliable data as shown by You et al [25]

Advances in Meteorology 3

Total DSDs

Diameter (mm)034 054 078 105 137 176 226 292 415

Slope 819Shape 552Intercept (log) 538Median dia 128

Num

ber c

onc(m

m6m

m3)lowast

log 1

0

0

2

4

6

8

(a)

Rain rate distribution (POSS)

0 50 100 150 200Rain rate (mmh)

Occ

urre

nce f

requ

ency

10minus1

100

101

104

105

106

102

103

Min 010mmh

Max 19934mmh

Avg 247mmh

Med 108mmh

(b)

Figure 2 Histogram of (a) total number concentration with respect to the drop size and gamma parameters and (b) rain rate calculated using114105 samples of 1-minute DSD after quality control

DSDs data for calculations of relationships were 114105samples after quality control and removal of negative 119870DPThe total number concentration with respect to the dropsize and the averaged parameters of gamma distributionswas shown in Figure 2(a) The slope shape and interceptfor gamma model were 82 55 and 10

54 respectivelyand median diameter was 13mm Most of the data aredistributed in awide rangewith amaximum rain rate of about1993mmhminus1 and the average was 247mmhminus1 (Figure 2(b))

Polarimetric variables were calculated using T-matrixscattering techniques derived by Waterman [3] and laterdeveloped further by Mishchenko et al [4] To get thevariables using DSDs six raindrop shape assumptions areused

The first raindrop axis ratio used in this study has slightlymodified the relation proposed by Pruppacher and Beard [5]and will be called DS1

119887

119886=

10 0 le 119863 le 03mm

103 minus 0062119863 119863 ge 03mm

(1)

where 119886 119887 and 119863 are the major axis minor axis andequivolume diameter of raindrop in mm respectively

119887

119886= 10048+ 0500057119863minus 0026281198632

+ 00036821198633

minus 000016771198634

(2)

Equation (2) is for equilibrium axis ratio derived fromthe numerical model of Beard and Chuang [9] which is ingood agreement with the results from wind tunnel measure-ments (hereinafter DS2)The practical shapes of raindrops inturbulent flow are expected to be different shapes from theequilibrium shapes due to the drop oscillations Oscillatingdrops appear to be more spherical on average than the dropswith equilibrium shapes as shown by Andsager et al [10] inlaboratory studiesThey figured out that the raindropsrsquo shapebetween 11 and 44mm is better explained by the followingformula

119887

119886= 1012minus 001445119863minus 0010281198632

(3)

Bringi et al [26] suggested using (3) for drops with sizessmaller than 44mmand (2) for larger sizes (hereinafterDS3)The shape-diameter relation that combines the observationsof different authors was recently proposed by Brandes et al[27 hereinafter DS4]

119887

119886= 09951+ 0025119863minus 0036441198632

+ 00053031198633

minus 000024921198634

(4)

The relations of raindrop axis ratio (DS5) proposed byBeard and Kubesh [28] andThurai et al [29] were combinedgiven by

119887

119886=

10 119863 le 07mm

1173 minus 05165119863 + 046981198632 minus 013171198633 minus 000851198633 07 lt 119863 le 15mm

1065 minus 00625119863 minus 0003991198632 minus 00007661198633 minus 000040951198634 119863 gt 15mm

(5)

4 Advances in Meteorology

Korea Meteorological Administration (KMA)

20∘E

30∘E

40∘E

20∘E

30∘E

40∘E

50∘E

90∘E 100

∘E 110∘E 120

∘E 130∘E 140

∘E

110∘E 120

∘E 130∘E 140

∘E

150∘E 160

∘E15 UTC June 24 2011 (00 KST June 25 2011)

(a)

Korea Meteorological Administration (KMA)

20∘E

30∘E

40∘E

20∘E

30∘E

40∘E

50∘E

90∘E 100

∘E 110∘E 120

∘E 130∘E 140

∘E

110∘E 120

∘E 130∘E 140

∘E

150∘E 160

∘E00 UTC June 26 2011 (09 KST June 26 2011)

(b)

Korea Meteorological Administration (KMA)

20∘E

30∘E

40∘E

20∘E

30∘E

40∘E

50∘E

90∘E 100

∘E 110∘E 120

∘E 130∘E 140

∘E

110∘E 120

∘E 130∘E 140

∘E

150∘E 160

∘E03 UTC July 9 2011 (12 KST July 9 2011)

(c)

Korea Meteorological Administration (KMA)

20∘E

30∘E

40∘E

20∘E

30∘E

40∘E

50∘E

90∘E 100

∘E 110∘E 120

∘E 130∘E 140

∘E

110∘E 120

∘E 130∘E 140

∘E

150∘E 160

∘E15 UTC August 7 2011 (00 KST August 8 2011)

(d)

Figure 3 The surface weather chart (a) 0000 LST June 25 (b) 0900 LST June 26 (c) 1200 LST July 9 and (d) 0000 LST August 8 in 2011

The relation of raindrop axis ratio that slightly modifiedthe relation proposed by Goddard et al [30] was used(hereinafter DS6)

119887

119886

=

10 119863 le 10mm

1075 minus 0065119863 minus 000361198632 + 000041198633 119863 gt 10mm

(6)

Another parameter in the T-matrix calculations is thetemperature which is assumed to be 20∘C in this study Itis also necessary to take the canting angle into considerationof the T-matrix simulation because it can account for a 6reduction in the coefficient of the 119877(119870DP) relation [31] and

may cause small negative biases of the estimators [32] Thedistribution of canting angles of raindrops is Gaussian with amean of 0∘ and a standard deviation of 7∘ which have beenrecently determined by Huang et al [33]

23 Validations Because the rainfall in Korea is mostlyaccompanied with Changma front and Typhoon three rain-fall cases which are caused by Changma front and typhoonChangma front only and typhoon only were used forvalidations (Table 1)

Figure 3 shows the surface weather chart of each caseThetyphoon MAERI was located at the eastern ocean of Taiwanand the Changma front was elongated from eastern Chinacontinent to the central Japan through the southern part of

Advances in Meteorology 5

0

5

10

15

20

Time (hour LST)

Aver

age r

ainf

all a

mou

nt (m

m)

1 3 6 9 12 15 18 21 00 3 6 9 12 15 18 21 24

(a)

0

5

10

15

20

Time (hour LST)

Aver

age r

ainf

all a

mou

nt (m

m)

1 3 6 9 12 15 18 21 00 3 6 9 12 15 18 21 24

(b)

0

5

10

15

20

Time (hour LST)

Aver

age r

ainf

all a

mou

nt (m

m)

1 3 6 9 12 15 18 21 00 3 6 9 12 15 18 21 24

(c)

Figure 4 Time series of averaged rainfall amount which was accompanied with (a) Changma front and typhoon (b) Changma front onlyand (c) typhoon only averaged rainfall from all rain gages within radar coverage

Table 1 Rainfall cases with different sources for the study

Period Sources

2011 6 25 0900 LSTsim6 26 1400 LST Changma frontand typhoon

2011 7 09 0000 LSTsim7 10 2200 LST Changma front2011 8 07 1800 LSTsim8 08 0300 LST Typhoon

Korea on 0000 LST June 25 (Figure 3(a))TheMAERImovedto the north located at the southern west sea of Korea andmade rainfall in the Korean peninsula on 0900 LST June 26 in2011 (Figure 3(b)) Changma frontwas located at the southernpart of Korea and brought rainfall at the analyzed area on1200 LST July 9 in 2011 (Figure 3(c))The rainfall was affectedby Changma front all the time during case 2 The typhoonMUIFAwas located at the southwestern sea of Korea on 0000LST August 8 in 2011 and caused rainfall at the target area(Figure 3(d))

Figure 4 shows the time series of averaged rainfall amountobserved on the ground rain gages within radar coveragefrom 5 km to 95 km Averaged rainfall amount refers to thatobtained by averaging the amount of rainfall observed by raingages within the radius of the radar There are three peaksof rainfall in case of Changma front and typhoon the firsttwo peaks were due to Changma front and the third one wasdue to the influence of the typhoon There are three peaksof rainfall accompanied with Changma front in the secondrainfall eventThe third event was also caused by typhoon butwas relatively shortThe period of the selected rainfall was 84hours 29 hours for Changma front and typhoon 46 hours forChangma front only and 9 hours for typhoon only

The normalized error (NE) fractional root mean squareerror (RMSE) and correlation coefficients (CC) of rainfallrelations and 121 gages were used to investigate the perfor-mance of each rainfall relation

NE =(1119873)sum

119873

119894=1 (1003816100381610038161003816119877119877119894 minus 119877

119866119894

1003816100381610038161003816)

119877119866

6 Advances in Meteorology

Beard and Chuang 1987

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Standard

Average 2620deviation 838

(a)

Andsager et al 1999

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Standard

Average 2616deviation 837

(b)

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Goddard et al 1995

Standard

Average 2616deviation 839

(c)

Freq

uenc

y

Beard and Chuang 1987

00 05 10 15 20 25 30 35000002004006008010012014

Standard deviation 063Average 091

ZDR (dB)

(d)

Andsager et al 1999

Standard deviation 061Average 080

Freq

uenc

y

00 05 10 15 20 25 30 35000002004006008010012014

ZDR (dB)

(e)

Goddard et al 1995

Standard deviation 066Average 082

Freq

uenc

y

00 05 10 15 20 25 30 35000002004006008010012014

ZDR (dB)

(f)

Freq

uenc

y

Beard and Chuang 1987

000 005 010 015 020000

010

020

030

040

050Standard deviation 0107

Average 0037

KDP (degkm)

(g)

Freq

uenc

y

000 005 010 015 020000

010

020

030

040

050

KDP (degkm)

Andsager et al 1999

Standard deviation 0092Average 0031

(h)

Freq

uenc

y

000 005 010 015 020000

010

020

030

040

050

KDP (degkm)

Goddard et al 1995

Standard deviation 0096Average 0030

(i)

Figure 5 The occurrence frequency of (a) 119885 with DS1 (b) 119885 with DS3 (c) 119885 with DS6 (d) 119885DR with DS1 (e) 119885DR with DS3 (f) 119885DR withDS6 (g) 119870DP with DS1 (h) 119870DP with DS3 and (i) 119870DP with DS6

RMSE = [1119873

119873

sum

119894=1(119877119877119894

minus119877119866119894

)2]

12

CC =

sum119873

119894=1 (119877119877119894

minus 119877119877) (119877119866119894

minus 119877119866)

[sum119873

119894=1 (119877119877119894

minus 119877119877)2]

12[sum119873

119894=1 (119877119866119894

minus 119877119866)2]

12

(7)

where 119873 is the number of the RR and RG pairs and 119877119877and

119877119866are the averaged rain rate of radar and gage for an hour

respectively The above statistical variables are calculatedusing 1-hour rainfall amount of radar and gage at the pointThe point rainfall of radar was obtained by averaging rainfallover a small area (1 km times 1∘) centered on each rain gage

3 Results

31 Rainfall Relations with Different Raindrop Axis Ratios

311 The Characteristics of 119885 119885119863119877

and 119870119863119875

with DifferentDrop Shapes The histograms of occurrence frequency forpolarimetric variables 119885 119885DR and 119870DP calculated by DSDsdata for 4 years in Busan with different raindrop axis ratiorelations DS1 DS3 and DS6 were shown in Figure 5

The averages and modes of 119885 were around 262 dBZ and32sim33 dBZ for all raindrop axis assumptions (Figures 5(a)sim5(c)) It means that the reflectivity is not sensitive to the dropaxis relation In case of 119885DR there were two modes of occur-rence for all cases The averages and standard deviation ofeach relation were 063 dB and 091 dB for DS1 061 dB and08 dB for DS3 and 066 dB and 082 dB for DS6The low and

Advances in Meteorology 7

Table 2 The rainfall relations of 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) with different raindrop shape assumptions

DS 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) 119877(119870DP 119885DR)

DS1 R = 00273119885060 R = 029119885DR527 R = 445119870DP

0942 R = 00161198850889119885DRminus494 R = 537119870DP

0857119885DRminus148

DS2 R = 00277119885059 R = 038119885DR487 R = 533119870DP

0913 R = 00141198850852119885DRminus408 R = 752119870DP

0855119885DRminus198

DS3 R = 00277119885060 R = 042119885DR498 R = 615119870DP

0908 R = 00151198850818119885DRminus372 R = 822119870DP

0855119885DRminus198

DS4 R = 00277119885060 R = 041119885DR498 R = 599119870DP

0896 R = 00141198850844119885DRminus406 R = 674119870DP

0785119885DRminus213

DS5 R = 00277119885060 R = 040119885DR503 R = 562119870DP

0897 R = 00131198850861119885DRminus43 R = 847119870DP

0840119885DRminus238

DS6 R = 00280119885059 R = 043119885DR469 R = 563119870DP

0857 R = 00131198850857119885DRminus40 R = 150119870DP

0483119885DRminus077

R(Z

ZD

R)

(mm

h)

R = 001589085Z08927

ZDRminus49936

NB = 1300

RMSE = 2776

CC = 0965

R (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

(a)

R = 13428687294KDP08991

ZDRminus26757

NB = 188

RMSE = 2593

CC = 0967

R (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(K

DPZ

DR)

(mm

h)

(b)

Figure 6 The scatter plots of rainfall obtained by DSDs and (a) 119877(119885 119885DR) and (b) 119877(119870DP 119885DR) using 119885 for DS3 119885DR for DS1 and 119870DP forDS3

high modes of 119885DR with DS1 DS3 and DS6 were 02sim03 dBand 17sim18 dB 02sim03 dB and 16sim17 dB and 00sim01 dB and17sim18 dB respectively The occurrence frequencies of lowmode for each raindrop axis ratio were significantly differentfrom each other (Figures 5(d)sim5(f)) The averages and stan-dard deviation of119870DPwith different raindrop shapeswere 011and 004 009 and 003 and 01 and 003 respectively Themodes of all drop shapes were the same but the occurrencefrequencies were different (Figures 5(g)sim5(i))

312 The Statistics of Rainfall Relations with Different Rain-drop Axis Ratios Because the occurrence frequencies of119885DRand 119870DP with different raindrop axis ratios were differentfrom each other the rainfall relations using those variablesshould be different with drop shape assumptions Table 2shows the rainfall relations obtained by using different rain-drop shape assumptions The coefficients of 119877(119885) were notsignificantly different with drop shape assumptions howeverthose of other relations were different with each drop shape

Table 3 shows the cross correlations (hereinafter CC) andRMSEs (root mean square errors) of rainfall relations 119877(119885)119877(119885DR) 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) obtained bycalculations using DSDs data with different raindrop shapes

The statistics of 119877(119885) and 119877(119885DR) were not significantlydifferent with raindrop shapesThe CC and RMSE of 119877(119885DR)and 119877(119885 119885DR) were the worst and the best among theother rainfall relations The statistics of 119877(119870DR) 119877(119885 119885DR)and 119877(119870DP 119885DR) were much more variable with differentraindrop axis ratios than the ones of 119877(119885) and 119877(119885DR) TheRMSEs of 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) with rain-drop shapes were distributed from 3030 to 3828mm 2965to 3523mm and 3151 to 5412mm respectivelyThe best per-formance of each relation occurred at DS3 for 119877(119885) DS1 for119877(119885DR) DS1 for 119877(119870DP) DS1 for 119877(119885 119885DR) and DS3 for119877(119870DP 119885DR)

In order to calculate more accurate 119877(119885 119885DR) and119877(119870DP 119885DR) the 119885 and 119885DR with the best performance werechosen Figure 6 shows the scatter plots of rainfall obtainedby DSDs and 119877(119885 119885DR) and 119877(119870DP 119885DR) using the beststatistics among raindrop axis ratio 119885 119885DR and 119870DP werechosen from DS3 DS1 and DS1 respectively Comparingwith 119877(119885 119885DR) and 119877(119870DP 119885DR) of single raindrop axisratio relations having the best performance new combinedrelations had better RMSE and CC The RMSEs of new rela-tions 119877(119885 119885DR) and 119877(119870DP 119885DR) had better score as muchas around 02mm and 06mm respectively Even though

8 Advances in Meteorology

Table 3 The correlation coefficients and RMSEs (mm) of rainfall obtained by rainfall relations and DSDs CC means cross correlation

DS 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) 119877(119870DP 119885DR)

CC RMSE CC RMSE CC RMSE CC RMSE CC RMSEDS1 0913 4705 0572 6241 0875 3030 0964 2965 0951 3313DS2 0913 4709 0569 6248 0861 3198 0956 3272 0956 3222DS3 0914 4704 0562 6261 0861 3178 0949 3523 0960 3151DS4 0913 4706 0569 6249 0828 3549 0954 3334 0931 3882DS5 0913 4706 0572 6243 0849 3326 0957 3210 0950 3348DS6 0913 4713 0572 6244 0795 3828 0956 3239 0814 5412

Table 4The rainfall relations NE RMSE and CC of each raindropaxis ratio relation

DropShape Relation NE RMSE CC

DS1119877(119870DP) = 445119870DP

0942 052 4996 082119877(119885 119885DR) = 001571198850889119885DR

minus494 031 4802 097119877(119870DP 119885DR) = 537119870DP

0857119885DRminus148 056 5262 088

DS2119877(119870DP) = 530119870DP

0913 052 4645 078119877(119885 119885DR) = 001411198850853119885DR

minus408 036 3793 073119877(119870DP 119885DR) = 752119870DP

0855119885DRminus198 060 5146 073

DS3119877(119870DP) = 615119870DP

0908 055 4698 078119877(119885 119885DR) = 001481198850818119885DR

minus372 043 4479 089119877(119870DP 119885DR) = 822119870DP

0855119885DRminus198 063 5247 073

DS4119877(119870DP) = 599119870DP

0896 054 4673 078119877(119885 119885DR) = 001361198850840119885DR

minus406 040 4134 089119877(119870DP 119885DR) = 674119870DP

0785119885DRminus213 060 5249 073

DS5119877(119870DP) = 562119870DP

0897 053 4625 078119877(119885 119885DR) = 001331198850861119885DR

minus431 037 3900 088119877(119870DP 119885DR) = 847119870DP

0840119885DRminus238 065 5390 071

DS6119877(119870DP) = 563119870DP

0857 054 4647 078119877(119885 119885DR) = 001251198850857119885DR

minus399 038 3967 089119877(119870DP 119885DR) = 150119870DP

0483119885DRminus077 065 7141 076

the CC and RMSE of 119877(119885) and 119877(119885DR) with different dropshapes were not significant the combined relations had betterperformance

32 Validations of Rainfall Relations with Different RaindropAxis Ratio Relations To investigate the performance ofrainfall relationsNE (normalized error) RMSE andCCwerecalculated using rainfall from each relation with six raindropshapes and that of gage rainfall

Table 4 summarizes the relations and the statistics suchas NE RMSE and CC The NEs and RMSEs of 119877(119870DR)calculated by each raindrop axis were distributed from 052 to055 and from 4625 to 4996 respectively The 119877(119870DR) withassumption of DS5 was the best score of RMSE in other rain-drop shapes In case of119877(119885 119885DR) the distribution ofNEs andRMSEs was from 031 to 043 and from 3793 to 4602 respec-tively The best RMSE score of 119877(119885 119885DR) was from DS2The NEs and RMSEs of 119877(119870DP 119885DR) occurred from 055 to065 and from 5146 to 7141 respectively The performance of

119877(119870DP 119885DR) was the worst score and 119877(119885 119885DR) had the bestscore in all raindrop axis ratio relations The performancesof validation were different from that of rainfall relationcalculation It would be caused by the variations of DSDs inthis study

To compare the performance between new combined119877(119870DP 119885DR) and 119877(119885 119885DR) the statistics were also calcu-lated Figure 7 shows the scatter plots rainfall from rainfallrelation and gage rainfall with some statistics The NEand RMSE of two relations from single raindrop shapeassumption showed better results However it seems that the119877(119885 119885DR)with two-raindrop axis ratio was more close to thegage rainfall in the range of weaker than 20mmh and the119877(119870DP 119885DR) with two drop shapes was more accurate in therainfall of higher than 20mmh

33 Rainfall Estimation Using Specific Attenuation331 Calculation of Specific Attenuation The 119860

119867can be

calculated from the radial profile of the attenuated reflectivity119885119886and the two-way PIA (Path Integrated Attenuation) along

the propagation path (1199031 1199032) proposed by Meneghini and

Nakamura [34]

119860 (119903) =119886 (119903) [119885119886]

119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(8)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

119886 (119904) [119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

119886 (119904) [119885119886 (119904)]119887119889119904

(9)

If 119886 is not dependent on range then (8) becomes

119860 (119903) =[119885119886]119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(10)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

[119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

[119885119886 (119904)]119887119889119904

(11)

119862 (119887PIA) = exp (023119887PIA) minus 1 (12)

Advances in Meteorology 9

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 036

RMSE = 3793

CC = 0888

Rada

r tot

alR

(ZZ

DR)

BC

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 060

RMSE = 5146

CC = 0732

Rada

r tot

alR

(KD

PZ

DR)

BC

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 032

RMSE = 5194

CC = 0818

Rada

r tot

alR

(ZZ

DR)

best

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 092

RMSE = 7302

CC = 0695

Rada

r tot

alR

(KD

PZ

DR)

best

(d)

Figure 7The scatter plot of rainfall from gage and (a) 119877(119885 119885DR) (b) 119877(119870DP 119885DR)with single raindrop axis ratio relation (c) 119877(119885 119885DR) and(d) 119877(119870DP 119885DR) with two-raindrop axis ratio relation

Bringi et al [35] recommended estimating PIA usingΦDPby

PIA (1199031 1199032) = 120572 [ΦDP (1199032) minusΦDP (1199031)] = 120572ΔΦDP (13)

and Testud et al [36] used (10) and (12) to obtain radialprofiles of 119860

119867at C-band In this study 119860

119867was calculated

by the method proposed by Ryzhkov et al [23] The constant

119887 was set by 06 and 120572 was by 0027 calculated by the ratio of119860119867to 119870DP obtained from DSDsFigure 8 shows the scatter plot of rainfall from 119877(119885)

119877(119870DP) and 119877(119860119867) and rainfall from DSDs and an PPIs

(Plan Position Indicators) at 05 degree elevation angle of gagerainfall and rainfall from 119877(119870DP) and 119877(119860

119867) at 0251 KST on

the 8th of August in 2011The 119877(119860

119867) relation had much better fit to the rainfall of

DSDs than that of119877(119870DP) and119877(119885) relation Comparingwith

10 Advances in Meteorology

Beard and Chuang 1987

Rain rate DSD (mmh)

R(Z

) (m

mh

)

10minus1

100

101

102

103

10minus1

100

101

102

103

R = 00277Z05994

NB = minus2122

RMSE = 4709

CC = 0913

(a)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

NB = minus1295136

RMSE = 3198

CC = 0861

R = 533039KDP091341

R(K

DP)

(mm

h)

(b)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(A

H)

(mm

h)

R = 337359AH10194

NB = 327

RMSE = 3667

CC = 0984

(c)

150100705040302015107310500

R(KDP) (mmh)

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(d)

R(AH) (mmh)

150100705040302015107310500

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(e)

Figure 8 The scatter plot of (a) 119877(119885) (b) 119877(119870DP) and (c) 119877(119860119867) with statistics and the rainfall distribution of 119877(119870DP) and 119877(119860

119867) at 0251

KST on the 8th of August in 2001

Advances in Meteorology 11

Table 5 The rainfall relations of 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assumptions

DS 119877(119885119870DP 119860119867) 119877(119885 119885DR 119870DP 119860119867)

DS1 119877 = 1527119885minus004119870DP0327

119860119867

0713119877 = 310Z012

119885DRminus083

119870DP0304

119860119867

0677

DS2 119877 = 12012119885minus024119870DP0551

119860119867

0685119877 = 4947Zminus015119885DR

minus026119870DP

0468119860119867

0681

DS3 119877 = 17211119885minus027119870DP0619

119860119867

0650119877 = 4502Z014

119885DRminus039

119870DP0486

119860119867

0653

DS4 119877 = 10798119885minus019119870DP0403

119860119867

0778119877 = 193Z018

119885DRminus111

119870DP0114

119860119867

0702

DS5 119877 = 20275119885minus027119870DP0543

119860119867

0720119877 = 24Z037

119885DRminus147

119870DPminus0025

119860119867

0656

DS6 119877 = 397119885minus011119870DP0044

119860119867

0808119877 = 571Z007

119885DRminus092

119870DP0238

119860119867

0687

the distribution of rainfall obtained by 119877(119870DP) and 119877(119860119867)

119877(119860119867) has better spatial resolution and more homogeneous

pattern than those of 119877(119870DP)

332 Validations of 119877(119860119867) 119877(119885119870

119863119875 119860119867) and 119877(119885 119885

119863119877

119870119863119875

119860119867) Relations As mentioned in the previous section

119877(119860119867) has the potential to be the best choice for estimating

rainfall using polarimetric variables To verify the accuracy119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) relations

were obtained and the accuracy of 119877(119860119867) 119877(119885119870DP 119860119867)

and 119877(119885 119885DR 119870DP 119860119867) which had the best performance inthe relations calculated by the six raindrop axis ratio relationswere examined by comparing with 119877(119870DP)

Figure 9 shows the scatter plot of rainfall from gagerainfall and 119877(119870DP) 119877(119860

119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR

119870DP 119860119867) for 84 hours The accuracy of 119877(119885 119885DR 119870DP 119860119867)was the best and119877(119885119870DP 119860119867)was the second in 4 relations119877(119860119867)was not better than 119877(119870DP) in whole range of rainfall

However in the range of higher rainfall it seems that 119877(119860119867)

was closer to the gage rainfall The error of 119877(119860119867) would be

caused by the missing radial profile ofΦDP along the rayThemissing has occurred if the difference of ΦDP between thestarting and end gate is negative According to the results119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) would compensatefor this region

34 Optimum Rainfall Algorithm To find out the optimumrainfall algorithm for Korean S-band polarimetric radar thegage rainfall amount was categorized by three steps 0 to5mmh assigned as light rain 5 to 30mmh as medium rainand higher than 30mmh as high rain In previous sectionthe relations have different accuracy not only for the raindropaxis ratio relation but also for rainfall amount The samplenumbers for each category were 3322 samples 1980 samplesand 92 samples respectively

Figure 10 shows the RMSEs of 119877(119870DP) 119877(119885 119885DR)119877(119870DP 119885DR) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) withdifferent rainfall categories defined in three steps All rela-tions have different RMSEs with respect to the raindrop axisratio relations 119877(119870DP) with DS3 119877(119885 119885DR) with DS2 and119877(119870DP 119885DR) with DS3 have the best score at the high rainfallregime at the low rainfall regime and at the medium rainfallregime respectively Even though 119877(119885 119885DR) has the bestperformance among other relations in total rainfall eventsusing different rainfall relations with different rainfall regimewould be an optimum rainfall algorithm for Korean S-band

polarimetric radar A possible optimum polarimetric rainfallalgorithm can be expressed by

119877 = 00141198850852119885DRminus408 0 lt Rainfall lt 5mmhminus1

119877 = 822119870DP0855

119885DRminus198

5 lt Rainfall lt 30mmhminus1

119877 = 615119870DP0908 30mmhminus1 lt Rainfall

(14)

Table 5 shows the rainfall relations of 119877(119885119870DP 119860119867) and119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assump-tions The coefficients of each relation with respect to thedrop shapes were much different comparing with relationsobtained by combining two polarimetric variables

In case of rainfall relations combined with119860119867 119877(119885 119885DR

119870DP 119860119867) has better score than 119877(119885119870DP 119860119867) Both119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with DS3 showedbetter result than other raindrop shape assumptions119877(119885 119885DR 119870DP 119860119867) at the low medium and high rainfallregimes has similar RMSE to 119877(119885 119885DR) 119877(119870DP 119885DR) and119877(119870DP) respectively

Equations (14) would be an optimum rainfall algorithmbut there is still a problem to solve how the rainfall categoriesare defined using radar and gage Gage does not have goodspatial resolution to cover radar resolution like 125m or 1 kmand each rainfall relation has its own error at certain rainfallregime Therefore 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867)withDS3 can be used regardless rainfall intensity And in case119885DR bias calibration is not available or does not have enoughquality for quantitative use 119877(119885119870DP 119860119867) with DS3 can beused as a representative rainfall estimation

4 Summary and Conclusions

Polarimetric radars will be main tools to monitor andforecast severe weather and flash flooding within severalyears in Korea To get an optimum rainfall algorithm usingpolarimetric variables observed from Bislsan radar which isthe first polarimetric radar in Korea rainfall cases for 84hours caused by different conditions which are Changmafront and typhoon Changma front only and typhoon onlythat occurred in 2011 were analyzed And rainfall relationswere obtained by using long period DSDs with six differentraindrop axis ratio relations

In the analysis of 119885 119885DR and119870DP occurrence frequencythere were two modes of 119885DR occurrence frequency and

12 Advances in Meteorology

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100Ra

dar t

otal

R(K

DP)

BC

NE = 052

RMSE = 4645

CC = 0778

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 051

RMSE = 5005

CC = 0797

Rada

r tot

al R

(AH

) AS

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100NE = 046

RMSE = 4374

CC = 0820

Rada

r tot

al R

(ZK

DPA

H) A

S

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 045

RMSE = 4368

CC = 0852

Rada

r tot

al R

(ZZ

DRK

DPA

H) A

S

(d)

Figure 9 The scatter plot of gage rainfall and 119877(119870DP) 119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DP 119870DP 119860119867) rainfall for 84 hours

the variations of 119870DP and 119885DR histograms were higherthan that of 119885 with raindrop ratio relations According tothese variations the combined relations of 119877(119885 119885DR) and119877(119870DP 119885DR) using 119885 with DS3 119885DR with DS1 and 119870DP withDS1 were closer to the rainfall of DSDs

To examine the performance of each rainfall relationNE RMSE CC were calculated using rainfall recorded at121 gages within radar coverage for 84 hours The statisticsof each rainfall relation were different with raindrop shape

assumptions and rainfall intensity119877(119870DP 119885DR)had theworstperformance and119877(119885 119885DR) had the best score in all raindropshapes 119860

119867was calculated by observed ΦDP and 119885 using the

method by Ryzhkov et al [23] and the rainfall relations using119860119867were also calculated and analyzedThe performance of rainfall relations were comparedwith

three different rainfall categories to findout an optimumrain-fall relation for the S-band polarimetric in Korea 119877(119885 119885DR)119877(119870DP 119885DR) and 119877(119870DP) had the best RMSE at the light

Advances in Meteorology 13

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP) with drop shape

(a)

0

5

10

15

20

Drop shape

25

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(Z ZDR) with drop shape

(b)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP ZDR) with drop shape

(c)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(ZKDP AH) with drop shape

(d)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

0ndash5mm5ndash30mmOver 30mm

RMSE of R(Z ZDR KDP AH) with drop shape

(e)

Figure 10The RMSEs of (a) 119877(119870DP) (b) 119877(119885 119885DP) (c) 119877(119870DP 119885DP) (d) 119877(119885119870DP 119860119867) and (e) 119877(119885 119885DP 119870DP 119860119867)with raindrop axis ratiorelations in the three rainfall categories

14 Advances in Meteorology

rain medium rain and high rainfall regimes respectively119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) showed relativelygood performance in all rainfall regimesThe combination of119877(119885 119885DR) 119877(119870DP 119885DR) and 119877(119870DP) with rainfall intensitywould be an optimum rainfall algorithm if the referenceof rainfall would be defined correctly Regardless of rainfallintensity 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) obtainedby assuming DS3 can be used as a representative rainfall rela-tion without consideration of rainfall intensity regime Par-ticularly if the qualified 119885DR is not available 119877(119885119870DP 119860119867)with DS3 drop shape assumption can be used as an optimumrainfall relation in Korea

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge providing radar data weatherchart and AWS data for this work from the Ministry ofLand Infrastructure Transport and Korea MeteorologicalAdministration The authors also acknowledge providingcodes for scattering simulation from Professor V N Bringi atColorado StateUniversityThisworkwas funded by theKoreaMeteorological Industry Promotion Agency under GrantKMIPA 2015-1050

References

[1] E Campos and I Zawadzki ldquoInstrumental uncertainties in Z-R relationsrdquo Journal of Applied Meteorology vol 39 no 7 pp1088ndash1102 2000

[2] C-H You D-I Lee S-M Jang et al ldquoCharacteristics ofrainfall systems accompanied with Changma front at Chujadoin Koreardquo Asia-Pacific Journal of Atmospheric Sciences vol 46no 1 pp 41ndash51 2010

[3] P CWaterman ldquoSymmetry unitarity and geometry in electro-magnetic scatteringrdquo Physical Review D vol 3 no 4 pp 825ndash839 1971

[4] M IMishchenko LD Travis andDWMackowski ldquoT-matrixcomputations of light scattering by nonspherical particles areviewrdquo Journal of Quantitative Spectroscopy and RadiativeTransfer vol 55 no 5 pp 535ndash575 1996

[5] H R Pruppacher and K V Beard ldquoA wind tunnel investigationof the internal circulation and shape of water drops fallingat terminal velocity in airrdquo Quarterly Journal of the RoyalMeteorological Society vol 96 no 408 pp 247ndash256 1970

[6] D C Blanchard ldquoThe behavior of water drops at terminalvelocity in airrdquo EOS vol 31 no 6 pp 836ndash842 1950

[7] G-J Huang V N Bringi M Schonhuber et al ldquoDrop shapeand canting angle distributions in rain from2-Dvideo disdrom-eterrdquo in Proceedings of the 33rd Conference on Radar Meteorol-ogy Extended Abstract P8A8 Cairns Australia August 2007

[8] M Thurai V N Bringi and W A Petersen ldquoRain microstruc-ture retrievals using 2-D video disdrometer and C-band polari-metric radarrdquo Advances in Geosciences vol 20 pp 13ndash18 2009

[9] K V Beard and C Chuang ldquoA new model for the equilibriumshape of raindropsrdquo Journal of the Atmospheric Sciences vol 44pp 1509ndash1524 1987

[10] K Andsager K V Beard and N S Laird ldquoA laboratory studyof oscillations and axis ratios for large raindropsrdquo Journal of theAtmospheric Sciences vol 55 pp 208ndash226 1999

[11] J W Wilson and E A Brandes ldquoRadar measurement of rain-fallmdasha summaryrdquo Bulletin AmericanMeteorological Society vol60 no 9 pp 1048ndash1058 1979

[12] P M Austin ldquoRelation betweenmeasured radar reflectivity andsurface rainfallrdquo Monthly Weather Review vol 115 no 5 pp1053ndash1070 1987

[13] J Vivekanandan D S Zrnic S M Ellis R Oye A V Ryzhkovand J Straka ldquoCloud microphysics retrieval using S-band dual-polarization radar measurementsrdquo Bulletin of the AmericanMeteorological Society vol 80 no 3 pp 381ndash388 1999

[14] A V Ryzhkov and D S Zrnic ldquoDiscrimination between rainand snow with a polarimetric radarrdquo Journal of Applied Meteo-rology vol 37 no 10 pp 1228ndash1240 1998

[15] S E Giangrande and A V Ryzhkov ldquoEstimation of rainfallbased on the results of polarimetric echo classificationrdquo Journalof AppliedMeteorology and Climatology vol 47 no 9 pp 2445ndash2462 2008

[16] A V Ryzhkov and D S Zrnic ldquoAssessment of rainfall measure-ment that uses specific differential phaserdquo Journal of AppliedMeteorology vol 35 no 11 pp 2080ndash2090 1996

[17] P T May T D Keenan D S Zrnic L D Carey and S ARutledge ldquoPolarimetric radar measurements of tropical rain ata 5-cm wavelengthrdquo Journal of Applied Meteorology vol 38 no6 pp 750ndash765 1999

[18] V N Bringi and V Chandrasekar ldquoThe polarimetric basis forcharacterizing precipitationrdquo in Polarimetric Doppler WeatherRadar Principles and Applications pp 378ndash533 CambridgeUniversity Press Cambridge UK 2001

[19] E A Brandes G Zhang and J Vivekanandan ldquoExperiments inrainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[20] A V Ryzhkov T J Schuur D W Burgess P L Heinselman SE Giangrande and D S Zrnic ldquoThe joint polarization exper-iment polarimetric rainfall measurements and hydrometeorclassificationrdquo Bulletin of the American Meteorological Societyvol 86 no 6 pp 809ndash824 2005

[21] A V Ryzhkov S E Giangrande and T J Schuur ldquoRainfall esti-mation with a polarimetric prototype of WSR-88Drdquo Journal ofApplied Meteorology vol 44 no 4 pp 502ndash515 2005

[22] R Cifelli V Chandrasekar S Lim P C Kennedy Y Wang andS A Rutledge ldquoA new dual-polarization radar rainfall algo-rithm application in Colorado precipitation eventsrdquo Journal ofAtmospheric andOceanic Technology vol 28 no 3 pp 352ndash3642011

[23] A Ryzhkov M Diederich P Zhang and C Simmer ldquoPotentialutilization of specific attenuation for rainfall estimationmitiga-tion of partial beam blockage and radar networkingrdquo Journal ofAtmospheric and Oceanic Technology vol 31 no 3 pp 599ndash6192014

[24] C-H You M-Y Kang D-I Lee and H Uyeda ldquoRainfallestimation by S-band polarimetric radar in Korea Part Ipreprocessing and preliminary resultsrdquoMeteorological Applica-tions vol 21 no 4 pp 975ndash983 2014

[25] C-H You D-I Lee andM-Y Kang ldquoRainfall estimation usingspecific differential phase for the first operational polarimetricradar in Koreardquo Advances in Meteorology vol 2014 Article ID413717 10 pages 2014

Advances in Meteorology 15

[26] V N Bringi V Chandrasekar J Hubbert E Gorgucci W LRandeu and M Schoenhuber ldquoRaindrop size distribution indifferent climatic regimes from disdrometer and dual-polarizedradar analysisrdquo Journal of the Atmospheric Sciences vol 60 no2 pp 354ndash365 2003

[27] E A Brandes G Zhang and J Vivekanandan ldquoExperimentsin rainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[28] K V Beard and R J Kubesh ldquoLaboratory measurements ofsmall raindrop distortion Part 2 oscillation frequencies andmodesrdquo Journal of the Atmospheric Sciences vol 48 no 20 pp2245ndash2264 1991

[29] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[30] J W F Goddard K L Morgan A Illingworth and HSauvageot ldquoDual-wavelength polarization measurements inprecipitation using the CAMRA and Rabelias radarsrdquo in Pro-ceedings of the 27th Conference on Radar Meteorology pp 196ndash198 American Meteorology Society Vail Colo USA 1995

[31] A V Ryzhkov D S Zrnic J C Hubbert V N Bringi JVivekanandan and E A Brandes ldquoPolarimetric radar obser-vations and interpretation of co-cross-polar correlation coeffi-cientsrdquo Journal of Atmospheric and Oceanic Technology vol 19no 3 pp 340ndash354 2002

[32] S YMatrosov KAClark B EMartner andA Tokay ldquoX-bandpolarimetric radar measurements of rainfallrdquo Journal of AppliedMeteorology vol 41 no 9 pp 941ndash952 2002

[33] G-J Huang V N Bringi and M Thurai ldquoOrientation angledistributions of drops after an 80-m fall using a 2D videodisdrometerrdquo Journal of Atmospheric and Oceanic Technologyvol 25 no 9 pp 1717ndash1723 2008

[34] R Meneghini and K Nakamura ldquoRange profiling of the rainrate by an airborne weather radarrdquo Remote Sensing of Environ-ment vol 31 no 3 pp 193ndash209 1990

[35] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onpolarimetric variables at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[36] J Testud E L Bouar E Obligis and M Ali-Mehenni ldquoTherain profiling algorithm applied to polarimetric weather radarrdquoJournal of Atmospheric andOceanic Technology vol 17 no 3 pp332ndash356 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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EarthquakesJournal of

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Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

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International Journal of

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OceanographyInternational Journal of

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GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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MineralogyInternational Journal of

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MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Advances in Meteorology 3

Total DSDs

Diameter (mm)034 054 078 105 137 176 226 292 415

Slope 819Shape 552Intercept (log) 538Median dia 128

Num

ber c

onc(m

m6m

m3)lowast

log 1

0

0

2

4

6

8

(a)

Rain rate distribution (POSS)

0 50 100 150 200Rain rate (mmh)

Occ

urre

nce f

requ

ency

10minus1

100

101

104

105

106

102

103

Min 010mmh

Max 19934mmh

Avg 247mmh

Med 108mmh

(b)

Figure 2 Histogram of (a) total number concentration with respect to the drop size and gamma parameters and (b) rain rate calculated using114105 samples of 1-minute DSD after quality control

DSDs data for calculations of relationships were 114105samples after quality control and removal of negative 119870DPThe total number concentration with respect to the dropsize and the averaged parameters of gamma distributionswas shown in Figure 2(a) The slope shape and interceptfor gamma model were 82 55 and 10

54 respectivelyand median diameter was 13mm Most of the data aredistributed in awide rangewith amaximum rain rate of about1993mmhminus1 and the average was 247mmhminus1 (Figure 2(b))

Polarimetric variables were calculated using T-matrixscattering techniques derived by Waterman [3] and laterdeveloped further by Mishchenko et al [4] To get thevariables using DSDs six raindrop shape assumptions areused

The first raindrop axis ratio used in this study has slightlymodified the relation proposed by Pruppacher and Beard [5]and will be called DS1

119887

119886=

10 0 le 119863 le 03mm

103 minus 0062119863 119863 ge 03mm

(1)

where 119886 119887 and 119863 are the major axis minor axis andequivolume diameter of raindrop in mm respectively

119887

119886= 10048+ 0500057119863minus 0026281198632

+ 00036821198633

minus 000016771198634

(2)

Equation (2) is for equilibrium axis ratio derived fromthe numerical model of Beard and Chuang [9] which is ingood agreement with the results from wind tunnel measure-ments (hereinafter DS2)The practical shapes of raindrops inturbulent flow are expected to be different shapes from theequilibrium shapes due to the drop oscillations Oscillatingdrops appear to be more spherical on average than the dropswith equilibrium shapes as shown by Andsager et al [10] inlaboratory studiesThey figured out that the raindropsrsquo shapebetween 11 and 44mm is better explained by the followingformula

119887

119886= 1012minus 001445119863minus 0010281198632

(3)

Bringi et al [26] suggested using (3) for drops with sizessmaller than 44mmand (2) for larger sizes (hereinafterDS3)The shape-diameter relation that combines the observationsof different authors was recently proposed by Brandes et al[27 hereinafter DS4]

119887

119886= 09951+ 0025119863minus 0036441198632

+ 00053031198633

minus 000024921198634

(4)

The relations of raindrop axis ratio (DS5) proposed byBeard and Kubesh [28] andThurai et al [29] were combinedgiven by

119887

119886=

10 119863 le 07mm

1173 minus 05165119863 + 046981198632 minus 013171198633 minus 000851198633 07 lt 119863 le 15mm

1065 minus 00625119863 minus 0003991198632 minus 00007661198633 minus 000040951198634 119863 gt 15mm

(5)

4 Advances in Meteorology

Korea Meteorological Administration (KMA)

20∘E

30∘E

40∘E

20∘E

30∘E

40∘E

50∘E

90∘E 100

∘E 110∘E 120

∘E 130∘E 140

∘E

110∘E 120

∘E 130∘E 140

∘E

150∘E 160

∘E15 UTC June 24 2011 (00 KST June 25 2011)

(a)

Korea Meteorological Administration (KMA)

20∘E

30∘E

40∘E

20∘E

30∘E

40∘E

50∘E

90∘E 100

∘E 110∘E 120

∘E 130∘E 140

∘E

110∘E 120

∘E 130∘E 140

∘E

150∘E 160

∘E00 UTC June 26 2011 (09 KST June 26 2011)

(b)

Korea Meteorological Administration (KMA)

20∘E

30∘E

40∘E

20∘E

30∘E

40∘E

50∘E

90∘E 100

∘E 110∘E 120

∘E 130∘E 140

∘E

110∘E 120

∘E 130∘E 140

∘E

150∘E 160

∘E03 UTC July 9 2011 (12 KST July 9 2011)

(c)

Korea Meteorological Administration (KMA)

20∘E

30∘E

40∘E

20∘E

30∘E

40∘E

50∘E

90∘E 100

∘E 110∘E 120

∘E 130∘E 140

∘E

110∘E 120

∘E 130∘E 140

∘E

150∘E 160

∘E15 UTC August 7 2011 (00 KST August 8 2011)

(d)

Figure 3 The surface weather chart (a) 0000 LST June 25 (b) 0900 LST June 26 (c) 1200 LST July 9 and (d) 0000 LST August 8 in 2011

The relation of raindrop axis ratio that slightly modifiedthe relation proposed by Goddard et al [30] was used(hereinafter DS6)

119887

119886

=

10 119863 le 10mm

1075 minus 0065119863 minus 000361198632 + 000041198633 119863 gt 10mm

(6)

Another parameter in the T-matrix calculations is thetemperature which is assumed to be 20∘C in this study Itis also necessary to take the canting angle into considerationof the T-matrix simulation because it can account for a 6reduction in the coefficient of the 119877(119870DP) relation [31] and

may cause small negative biases of the estimators [32] Thedistribution of canting angles of raindrops is Gaussian with amean of 0∘ and a standard deviation of 7∘ which have beenrecently determined by Huang et al [33]

23 Validations Because the rainfall in Korea is mostlyaccompanied with Changma front and Typhoon three rain-fall cases which are caused by Changma front and typhoonChangma front only and typhoon only were used forvalidations (Table 1)

Figure 3 shows the surface weather chart of each caseThetyphoon MAERI was located at the eastern ocean of Taiwanand the Changma front was elongated from eastern Chinacontinent to the central Japan through the southern part of

Advances in Meteorology 5

0

5

10

15

20

Time (hour LST)

Aver

age r

ainf

all a

mou

nt (m

m)

1 3 6 9 12 15 18 21 00 3 6 9 12 15 18 21 24

(a)

0

5

10

15

20

Time (hour LST)

Aver

age r

ainf

all a

mou

nt (m

m)

1 3 6 9 12 15 18 21 00 3 6 9 12 15 18 21 24

(b)

0

5

10

15

20

Time (hour LST)

Aver

age r

ainf

all a

mou

nt (m

m)

1 3 6 9 12 15 18 21 00 3 6 9 12 15 18 21 24

(c)

Figure 4 Time series of averaged rainfall amount which was accompanied with (a) Changma front and typhoon (b) Changma front onlyand (c) typhoon only averaged rainfall from all rain gages within radar coverage

Table 1 Rainfall cases with different sources for the study

Period Sources

2011 6 25 0900 LSTsim6 26 1400 LST Changma frontand typhoon

2011 7 09 0000 LSTsim7 10 2200 LST Changma front2011 8 07 1800 LSTsim8 08 0300 LST Typhoon

Korea on 0000 LST June 25 (Figure 3(a))TheMAERImovedto the north located at the southern west sea of Korea andmade rainfall in the Korean peninsula on 0900 LST June 26 in2011 (Figure 3(b)) Changma frontwas located at the southernpart of Korea and brought rainfall at the analyzed area on1200 LST July 9 in 2011 (Figure 3(c))The rainfall was affectedby Changma front all the time during case 2 The typhoonMUIFAwas located at the southwestern sea of Korea on 0000LST August 8 in 2011 and caused rainfall at the target area(Figure 3(d))

Figure 4 shows the time series of averaged rainfall amountobserved on the ground rain gages within radar coveragefrom 5 km to 95 km Averaged rainfall amount refers to thatobtained by averaging the amount of rainfall observed by raingages within the radius of the radar There are three peaksof rainfall in case of Changma front and typhoon the firsttwo peaks were due to Changma front and the third one wasdue to the influence of the typhoon There are three peaksof rainfall accompanied with Changma front in the secondrainfall eventThe third event was also caused by typhoon butwas relatively shortThe period of the selected rainfall was 84hours 29 hours for Changma front and typhoon 46 hours forChangma front only and 9 hours for typhoon only

The normalized error (NE) fractional root mean squareerror (RMSE) and correlation coefficients (CC) of rainfallrelations and 121 gages were used to investigate the perfor-mance of each rainfall relation

NE =(1119873)sum

119873

119894=1 (1003816100381610038161003816119877119877119894 minus 119877

119866119894

1003816100381610038161003816)

119877119866

6 Advances in Meteorology

Beard and Chuang 1987

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Standard

Average 2620deviation 838

(a)

Andsager et al 1999

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Standard

Average 2616deviation 837

(b)

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Goddard et al 1995

Standard

Average 2616deviation 839

(c)

Freq

uenc

y

Beard and Chuang 1987

00 05 10 15 20 25 30 35000002004006008010012014

Standard deviation 063Average 091

ZDR (dB)

(d)

Andsager et al 1999

Standard deviation 061Average 080

Freq

uenc

y

00 05 10 15 20 25 30 35000002004006008010012014

ZDR (dB)

(e)

Goddard et al 1995

Standard deviation 066Average 082

Freq

uenc

y

00 05 10 15 20 25 30 35000002004006008010012014

ZDR (dB)

(f)

Freq

uenc

y

Beard and Chuang 1987

000 005 010 015 020000

010

020

030

040

050Standard deviation 0107

Average 0037

KDP (degkm)

(g)

Freq

uenc

y

000 005 010 015 020000

010

020

030

040

050

KDP (degkm)

Andsager et al 1999

Standard deviation 0092Average 0031

(h)

Freq

uenc

y

000 005 010 015 020000

010

020

030

040

050

KDP (degkm)

Goddard et al 1995

Standard deviation 0096Average 0030

(i)

Figure 5 The occurrence frequency of (a) 119885 with DS1 (b) 119885 with DS3 (c) 119885 with DS6 (d) 119885DR with DS1 (e) 119885DR with DS3 (f) 119885DR withDS6 (g) 119870DP with DS1 (h) 119870DP with DS3 and (i) 119870DP with DS6

RMSE = [1119873

119873

sum

119894=1(119877119877119894

minus119877119866119894

)2]

12

CC =

sum119873

119894=1 (119877119877119894

minus 119877119877) (119877119866119894

minus 119877119866)

[sum119873

119894=1 (119877119877119894

minus 119877119877)2]

12[sum119873

119894=1 (119877119866119894

minus 119877119866)2]

12

(7)

where 119873 is the number of the RR and RG pairs and 119877119877and

119877119866are the averaged rain rate of radar and gage for an hour

respectively The above statistical variables are calculatedusing 1-hour rainfall amount of radar and gage at the pointThe point rainfall of radar was obtained by averaging rainfallover a small area (1 km times 1∘) centered on each rain gage

3 Results

31 Rainfall Relations with Different Raindrop Axis Ratios

311 The Characteristics of 119885 119885119863119877

and 119870119863119875

with DifferentDrop Shapes The histograms of occurrence frequency forpolarimetric variables 119885 119885DR and 119870DP calculated by DSDsdata for 4 years in Busan with different raindrop axis ratiorelations DS1 DS3 and DS6 were shown in Figure 5

The averages and modes of 119885 were around 262 dBZ and32sim33 dBZ for all raindrop axis assumptions (Figures 5(a)sim5(c)) It means that the reflectivity is not sensitive to the dropaxis relation In case of 119885DR there were two modes of occur-rence for all cases The averages and standard deviation ofeach relation were 063 dB and 091 dB for DS1 061 dB and08 dB for DS3 and 066 dB and 082 dB for DS6The low and

Advances in Meteorology 7

Table 2 The rainfall relations of 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) with different raindrop shape assumptions

DS 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) 119877(119870DP 119885DR)

DS1 R = 00273119885060 R = 029119885DR527 R = 445119870DP

0942 R = 00161198850889119885DRminus494 R = 537119870DP

0857119885DRminus148

DS2 R = 00277119885059 R = 038119885DR487 R = 533119870DP

0913 R = 00141198850852119885DRminus408 R = 752119870DP

0855119885DRminus198

DS3 R = 00277119885060 R = 042119885DR498 R = 615119870DP

0908 R = 00151198850818119885DRminus372 R = 822119870DP

0855119885DRminus198

DS4 R = 00277119885060 R = 041119885DR498 R = 599119870DP

0896 R = 00141198850844119885DRminus406 R = 674119870DP

0785119885DRminus213

DS5 R = 00277119885060 R = 040119885DR503 R = 562119870DP

0897 R = 00131198850861119885DRminus43 R = 847119870DP

0840119885DRminus238

DS6 R = 00280119885059 R = 043119885DR469 R = 563119870DP

0857 R = 00131198850857119885DRminus40 R = 150119870DP

0483119885DRminus077

R(Z

ZD

R)

(mm

h)

R = 001589085Z08927

ZDRminus49936

NB = 1300

RMSE = 2776

CC = 0965

R (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

(a)

R = 13428687294KDP08991

ZDRminus26757

NB = 188

RMSE = 2593

CC = 0967

R (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(K

DPZ

DR)

(mm

h)

(b)

Figure 6 The scatter plots of rainfall obtained by DSDs and (a) 119877(119885 119885DR) and (b) 119877(119870DP 119885DR) using 119885 for DS3 119885DR for DS1 and 119870DP forDS3

high modes of 119885DR with DS1 DS3 and DS6 were 02sim03 dBand 17sim18 dB 02sim03 dB and 16sim17 dB and 00sim01 dB and17sim18 dB respectively The occurrence frequencies of lowmode for each raindrop axis ratio were significantly differentfrom each other (Figures 5(d)sim5(f)) The averages and stan-dard deviation of119870DPwith different raindrop shapeswere 011and 004 009 and 003 and 01 and 003 respectively Themodes of all drop shapes were the same but the occurrencefrequencies were different (Figures 5(g)sim5(i))

312 The Statistics of Rainfall Relations with Different Rain-drop Axis Ratios Because the occurrence frequencies of119885DRand 119870DP with different raindrop axis ratios were differentfrom each other the rainfall relations using those variablesshould be different with drop shape assumptions Table 2shows the rainfall relations obtained by using different rain-drop shape assumptions The coefficients of 119877(119885) were notsignificantly different with drop shape assumptions howeverthose of other relations were different with each drop shape

Table 3 shows the cross correlations (hereinafter CC) andRMSEs (root mean square errors) of rainfall relations 119877(119885)119877(119885DR) 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) obtained bycalculations using DSDs data with different raindrop shapes

The statistics of 119877(119885) and 119877(119885DR) were not significantlydifferent with raindrop shapesThe CC and RMSE of 119877(119885DR)and 119877(119885 119885DR) were the worst and the best among theother rainfall relations The statistics of 119877(119870DR) 119877(119885 119885DR)and 119877(119870DP 119885DR) were much more variable with differentraindrop axis ratios than the ones of 119877(119885) and 119877(119885DR) TheRMSEs of 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) with rain-drop shapes were distributed from 3030 to 3828mm 2965to 3523mm and 3151 to 5412mm respectivelyThe best per-formance of each relation occurred at DS3 for 119877(119885) DS1 for119877(119885DR) DS1 for 119877(119870DP) DS1 for 119877(119885 119885DR) and DS3 for119877(119870DP 119885DR)

In order to calculate more accurate 119877(119885 119885DR) and119877(119870DP 119885DR) the 119885 and 119885DR with the best performance werechosen Figure 6 shows the scatter plots of rainfall obtainedby DSDs and 119877(119885 119885DR) and 119877(119870DP 119885DR) using the beststatistics among raindrop axis ratio 119885 119885DR and 119870DP werechosen from DS3 DS1 and DS1 respectively Comparingwith 119877(119885 119885DR) and 119877(119870DP 119885DR) of single raindrop axisratio relations having the best performance new combinedrelations had better RMSE and CC The RMSEs of new rela-tions 119877(119885 119885DR) and 119877(119870DP 119885DR) had better score as muchas around 02mm and 06mm respectively Even though

8 Advances in Meteorology

Table 3 The correlation coefficients and RMSEs (mm) of rainfall obtained by rainfall relations and DSDs CC means cross correlation

DS 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) 119877(119870DP 119885DR)

CC RMSE CC RMSE CC RMSE CC RMSE CC RMSEDS1 0913 4705 0572 6241 0875 3030 0964 2965 0951 3313DS2 0913 4709 0569 6248 0861 3198 0956 3272 0956 3222DS3 0914 4704 0562 6261 0861 3178 0949 3523 0960 3151DS4 0913 4706 0569 6249 0828 3549 0954 3334 0931 3882DS5 0913 4706 0572 6243 0849 3326 0957 3210 0950 3348DS6 0913 4713 0572 6244 0795 3828 0956 3239 0814 5412

Table 4The rainfall relations NE RMSE and CC of each raindropaxis ratio relation

DropShape Relation NE RMSE CC

DS1119877(119870DP) = 445119870DP

0942 052 4996 082119877(119885 119885DR) = 001571198850889119885DR

minus494 031 4802 097119877(119870DP 119885DR) = 537119870DP

0857119885DRminus148 056 5262 088

DS2119877(119870DP) = 530119870DP

0913 052 4645 078119877(119885 119885DR) = 001411198850853119885DR

minus408 036 3793 073119877(119870DP 119885DR) = 752119870DP

0855119885DRminus198 060 5146 073

DS3119877(119870DP) = 615119870DP

0908 055 4698 078119877(119885 119885DR) = 001481198850818119885DR

minus372 043 4479 089119877(119870DP 119885DR) = 822119870DP

0855119885DRminus198 063 5247 073

DS4119877(119870DP) = 599119870DP

0896 054 4673 078119877(119885 119885DR) = 001361198850840119885DR

minus406 040 4134 089119877(119870DP 119885DR) = 674119870DP

0785119885DRminus213 060 5249 073

DS5119877(119870DP) = 562119870DP

0897 053 4625 078119877(119885 119885DR) = 001331198850861119885DR

minus431 037 3900 088119877(119870DP 119885DR) = 847119870DP

0840119885DRminus238 065 5390 071

DS6119877(119870DP) = 563119870DP

0857 054 4647 078119877(119885 119885DR) = 001251198850857119885DR

minus399 038 3967 089119877(119870DP 119885DR) = 150119870DP

0483119885DRminus077 065 7141 076

the CC and RMSE of 119877(119885) and 119877(119885DR) with different dropshapes were not significant the combined relations had betterperformance

32 Validations of Rainfall Relations with Different RaindropAxis Ratio Relations To investigate the performance ofrainfall relationsNE (normalized error) RMSE andCCwerecalculated using rainfall from each relation with six raindropshapes and that of gage rainfall

Table 4 summarizes the relations and the statistics suchas NE RMSE and CC The NEs and RMSEs of 119877(119870DR)calculated by each raindrop axis were distributed from 052 to055 and from 4625 to 4996 respectively The 119877(119870DR) withassumption of DS5 was the best score of RMSE in other rain-drop shapes In case of119877(119885 119885DR) the distribution ofNEs andRMSEs was from 031 to 043 and from 3793 to 4602 respec-tively The best RMSE score of 119877(119885 119885DR) was from DS2The NEs and RMSEs of 119877(119870DP 119885DR) occurred from 055 to065 and from 5146 to 7141 respectively The performance of

119877(119870DP 119885DR) was the worst score and 119877(119885 119885DR) had the bestscore in all raindrop axis ratio relations The performancesof validation were different from that of rainfall relationcalculation It would be caused by the variations of DSDs inthis study

To compare the performance between new combined119877(119870DP 119885DR) and 119877(119885 119885DR) the statistics were also calcu-lated Figure 7 shows the scatter plots rainfall from rainfallrelation and gage rainfall with some statistics The NEand RMSE of two relations from single raindrop shapeassumption showed better results However it seems that the119877(119885 119885DR)with two-raindrop axis ratio was more close to thegage rainfall in the range of weaker than 20mmh and the119877(119870DP 119885DR) with two drop shapes was more accurate in therainfall of higher than 20mmh

33 Rainfall Estimation Using Specific Attenuation331 Calculation of Specific Attenuation The 119860

119867can be

calculated from the radial profile of the attenuated reflectivity119885119886and the two-way PIA (Path Integrated Attenuation) along

the propagation path (1199031 1199032) proposed by Meneghini and

Nakamura [34]

119860 (119903) =119886 (119903) [119885119886]

119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(8)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

119886 (119904) [119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

119886 (119904) [119885119886 (119904)]119887119889119904

(9)

If 119886 is not dependent on range then (8) becomes

119860 (119903) =[119885119886]119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(10)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

[119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

[119885119886 (119904)]119887119889119904

(11)

119862 (119887PIA) = exp (023119887PIA) minus 1 (12)

Advances in Meteorology 9

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 036

RMSE = 3793

CC = 0888

Rada

r tot

alR

(ZZ

DR)

BC

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 060

RMSE = 5146

CC = 0732

Rada

r tot

alR

(KD

PZ

DR)

BC

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 032

RMSE = 5194

CC = 0818

Rada

r tot

alR

(ZZ

DR)

best

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 092

RMSE = 7302

CC = 0695

Rada

r tot

alR

(KD

PZ

DR)

best

(d)

Figure 7The scatter plot of rainfall from gage and (a) 119877(119885 119885DR) (b) 119877(119870DP 119885DR)with single raindrop axis ratio relation (c) 119877(119885 119885DR) and(d) 119877(119870DP 119885DR) with two-raindrop axis ratio relation

Bringi et al [35] recommended estimating PIA usingΦDPby

PIA (1199031 1199032) = 120572 [ΦDP (1199032) minusΦDP (1199031)] = 120572ΔΦDP (13)

and Testud et al [36] used (10) and (12) to obtain radialprofiles of 119860

119867at C-band In this study 119860

119867was calculated

by the method proposed by Ryzhkov et al [23] The constant

119887 was set by 06 and 120572 was by 0027 calculated by the ratio of119860119867to 119870DP obtained from DSDsFigure 8 shows the scatter plot of rainfall from 119877(119885)

119877(119870DP) and 119877(119860119867) and rainfall from DSDs and an PPIs

(Plan Position Indicators) at 05 degree elevation angle of gagerainfall and rainfall from 119877(119870DP) and 119877(119860

119867) at 0251 KST on

the 8th of August in 2011The 119877(119860

119867) relation had much better fit to the rainfall of

DSDs than that of119877(119870DP) and119877(119885) relation Comparingwith

10 Advances in Meteorology

Beard and Chuang 1987

Rain rate DSD (mmh)

R(Z

) (m

mh

)

10minus1

100

101

102

103

10minus1

100

101

102

103

R = 00277Z05994

NB = minus2122

RMSE = 4709

CC = 0913

(a)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

NB = minus1295136

RMSE = 3198

CC = 0861

R = 533039KDP091341

R(K

DP)

(mm

h)

(b)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(A

H)

(mm

h)

R = 337359AH10194

NB = 327

RMSE = 3667

CC = 0984

(c)

150100705040302015107310500

R(KDP) (mmh)

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(d)

R(AH) (mmh)

150100705040302015107310500

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(e)

Figure 8 The scatter plot of (a) 119877(119885) (b) 119877(119870DP) and (c) 119877(119860119867) with statistics and the rainfall distribution of 119877(119870DP) and 119877(119860

119867) at 0251

KST on the 8th of August in 2001

Advances in Meteorology 11

Table 5 The rainfall relations of 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assumptions

DS 119877(119885119870DP 119860119867) 119877(119885 119885DR 119870DP 119860119867)

DS1 119877 = 1527119885minus004119870DP0327

119860119867

0713119877 = 310Z012

119885DRminus083

119870DP0304

119860119867

0677

DS2 119877 = 12012119885minus024119870DP0551

119860119867

0685119877 = 4947Zminus015119885DR

minus026119870DP

0468119860119867

0681

DS3 119877 = 17211119885minus027119870DP0619

119860119867

0650119877 = 4502Z014

119885DRminus039

119870DP0486

119860119867

0653

DS4 119877 = 10798119885minus019119870DP0403

119860119867

0778119877 = 193Z018

119885DRminus111

119870DP0114

119860119867

0702

DS5 119877 = 20275119885minus027119870DP0543

119860119867

0720119877 = 24Z037

119885DRminus147

119870DPminus0025

119860119867

0656

DS6 119877 = 397119885minus011119870DP0044

119860119867

0808119877 = 571Z007

119885DRminus092

119870DP0238

119860119867

0687

the distribution of rainfall obtained by 119877(119870DP) and 119877(119860119867)

119877(119860119867) has better spatial resolution and more homogeneous

pattern than those of 119877(119870DP)

332 Validations of 119877(119860119867) 119877(119885119870

119863119875 119860119867) and 119877(119885 119885

119863119877

119870119863119875

119860119867) Relations As mentioned in the previous section

119877(119860119867) has the potential to be the best choice for estimating

rainfall using polarimetric variables To verify the accuracy119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) relations

were obtained and the accuracy of 119877(119860119867) 119877(119885119870DP 119860119867)

and 119877(119885 119885DR 119870DP 119860119867) which had the best performance inthe relations calculated by the six raindrop axis ratio relationswere examined by comparing with 119877(119870DP)

Figure 9 shows the scatter plot of rainfall from gagerainfall and 119877(119870DP) 119877(119860

119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR

119870DP 119860119867) for 84 hours The accuracy of 119877(119885 119885DR 119870DP 119860119867)was the best and119877(119885119870DP 119860119867)was the second in 4 relations119877(119860119867)was not better than 119877(119870DP) in whole range of rainfall

However in the range of higher rainfall it seems that 119877(119860119867)

was closer to the gage rainfall The error of 119877(119860119867) would be

caused by the missing radial profile ofΦDP along the rayThemissing has occurred if the difference of ΦDP between thestarting and end gate is negative According to the results119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) would compensatefor this region

34 Optimum Rainfall Algorithm To find out the optimumrainfall algorithm for Korean S-band polarimetric radar thegage rainfall amount was categorized by three steps 0 to5mmh assigned as light rain 5 to 30mmh as medium rainand higher than 30mmh as high rain In previous sectionthe relations have different accuracy not only for the raindropaxis ratio relation but also for rainfall amount The samplenumbers for each category were 3322 samples 1980 samplesand 92 samples respectively

Figure 10 shows the RMSEs of 119877(119870DP) 119877(119885 119885DR)119877(119870DP 119885DR) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) withdifferent rainfall categories defined in three steps All rela-tions have different RMSEs with respect to the raindrop axisratio relations 119877(119870DP) with DS3 119877(119885 119885DR) with DS2 and119877(119870DP 119885DR) with DS3 have the best score at the high rainfallregime at the low rainfall regime and at the medium rainfallregime respectively Even though 119877(119885 119885DR) has the bestperformance among other relations in total rainfall eventsusing different rainfall relations with different rainfall regimewould be an optimum rainfall algorithm for Korean S-band

polarimetric radar A possible optimum polarimetric rainfallalgorithm can be expressed by

119877 = 00141198850852119885DRminus408 0 lt Rainfall lt 5mmhminus1

119877 = 822119870DP0855

119885DRminus198

5 lt Rainfall lt 30mmhminus1

119877 = 615119870DP0908 30mmhminus1 lt Rainfall

(14)

Table 5 shows the rainfall relations of 119877(119885119870DP 119860119867) and119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assump-tions The coefficients of each relation with respect to thedrop shapes were much different comparing with relationsobtained by combining two polarimetric variables

In case of rainfall relations combined with119860119867 119877(119885 119885DR

119870DP 119860119867) has better score than 119877(119885119870DP 119860119867) Both119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with DS3 showedbetter result than other raindrop shape assumptions119877(119885 119885DR 119870DP 119860119867) at the low medium and high rainfallregimes has similar RMSE to 119877(119885 119885DR) 119877(119870DP 119885DR) and119877(119870DP) respectively

Equations (14) would be an optimum rainfall algorithmbut there is still a problem to solve how the rainfall categoriesare defined using radar and gage Gage does not have goodspatial resolution to cover radar resolution like 125m or 1 kmand each rainfall relation has its own error at certain rainfallregime Therefore 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867)withDS3 can be used regardless rainfall intensity And in case119885DR bias calibration is not available or does not have enoughquality for quantitative use 119877(119885119870DP 119860119867) with DS3 can beused as a representative rainfall estimation

4 Summary and Conclusions

Polarimetric radars will be main tools to monitor andforecast severe weather and flash flooding within severalyears in Korea To get an optimum rainfall algorithm usingpolarimetric variables observed from Bislsan radar which isthe first polarimetric radar in Korea rainfall cases for 84hours caused by different conditions which are Changmafront and typhoon Changma front only and typhoon onlythat occurred in 2011 were analyzed And rainfall relationswere obtained by using long period DSDs with six differentraindrop axis ratio relations

In the analysis of 119885 119885DR and119870DP occurrence frequencythere were two modes of 119885DR occurrence frequency and

12 Advances in Meteorology

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100Ra

dar t

otal

R(K

DP)

BC

NE = 052

RMSE = 4645

CC = 0778

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 051

RMSE = 5005

CC = 0797

Rada

r tot

al R

(AH

) AS

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100NE = 046

RMSE = 4374

CC = 0820

Rada

r tot

al R

(ZK

DPA

H) A

S

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 045

RMSE = 4368

CC = 0852

Rada

r tot

al R

(ZZ

DRK

DPA

H) A

S

(d)

Figure 9 The scatter plot of gage rainfall and 119877(119870DP) 119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DP 119870DP 119860119867) rainfall for 84 hours

the variations of 119870DP and 119885DR histograms were higherthan that of 119885 with raindrop ratio relations According tothese variations the combined relations of 119877(119885 119885DR) and119877(119870DP 119885DR) using 119885 with DS3 119885DR with DS1 and 119870DP withDS1 were closer to the rainfall of DSDs

To examine the performance of each rainfall relationNE RMSE CC were calculated using rainfall recorded at121 gages within radar coverage for 84 hours The statisticsof each rainfall relation were different with raindrop shape

assumptions and rainfall intensity119877(119870DP 119885DR)had theworstperformance and119877(119885 119885DR) had the best score in all raindropshapes 119860

119867was calculated by observed ΦDP and 119885 using the

method by Ryzhkov et al [23] and the rainfall relations using119860119867were also calculated and analyzedThe performance of rainfall relations were comparedwith

three different rainfall categories to findout an optimumrain-fall relation for the S-band polarimetric in Korea 119877(119885 119885DR)119877(119870DP 119885DR) and 119877(119870DP) had the best RMSE at the light

Advances in Meteorology 13

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP) with drop shape

(a)

0

5

10

15

20

Drop shape

25

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(Z ZDR) with drop shape

(b)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP ZDR) with drop shape

(c)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(ZKDP AH) with drop shape

(d)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

0ndash5mm5ndash30mmOver 30mm

RMSE of R(Z ZDR KDP AH) with drop shape

(e)

Figure 10The RMSEs of (a) 119877(119870DP) (b) 119877(119885 119885DP) (c) 119877(119870DP 119885DP) (d) 119877(119885119870DP 119860119867) and (e) 119877(119885 119885DP 119870DP 119860119867)with raindrop axis ratiorelations in the three rainfall categories

14 Advances in Meteorology

rain medium rain and high rainfall regimes respectively119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) showed relativelygood performance in all rainfall regimesThe combination of119877(119885 119885DR) 119877(119870DP 119885DR) and 119877(119870DP) with rainfall intensitywould be an optimum rainfall algorithm if the referenceof rainfall would be defined correctly Regardless of rainfallintensity 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) obtainedby assuming DS3 can be used as a representative rainfall rela-tion without consideration of rainfall intensity regime Par-ticularly if the qualified 119885DR is not available 119877(119885119870DP 119860119867)with DS3 drop shape assumption can be used as an optimumrainfall relation in Korea

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge providing radar data weatherchart and AWS data for this work from the Ministry ofLand Infrastructure Transport and Korea MeteorologicalAdministration The authors also acknowledge providingcodes for scattering simulation from Professor V N Bringi atColorado StateUniversityThisworkwas funded by theKoreaMeteorological Industry Promotion Agency under GrantKMIPA 2015-1050

References

[1] E Campos and I Zawadzki ldquoInstrumental uncertainties in Z-R relationsrdquo Journal of Applied Meteorology vol 39 no 7 pp1088ndash1102 2000

[2] C-H You D-I Lee S-M Jang et al ldquoCharacteristics ofrainfall systems accompanied with Changma front at Chujadoin Koreardquo Asia-Pacific Journal of Atmospheric Sciences vol 46no 1 pp 41ndash51 2010

[3] P CWaterman ldquoSymmetry unitarity and geometry in electro-magnetic scatteringrdquo Physical Review D vol 3 no 4 pp 825ndash839 1971

[4] M IMishchenko LD Travis andDWMackowski ldquoT-matrixcomputations of light scattering by nonspherical particles areviewrdquo Journal of Quantitative Spectroscopy and RadiativeTransfer vol 55 no 5 pp 535ndash575 1996

[5] H R Pruppacher and K V Beard ldquoA wind tunnel investigationof the internal circulation and shape of water drops fallingat terminal velocity in airrdquo Quarterly Journal of the RoyalMeteorological Society vol 96 no 408 pp 247ndash256 1970

[6] D C Blanchard ldquoThe behavior of water drops at terminalvelocity in airrdquo EOS vol 31 no 6 pp 836ndash842 1950

[7] G-J Huang V N Bringi M Schonhuber et al ldquoDrop shapeand canting angle distributions in rain from2-Dvideo disdrom-eterrdquo in Proceedings of the 33rd Conference on Radar Meteorol-ogy Extended Abstract P8A8 Cairns Australia August 2007

[8] M Thurai V N Bringi and W A Petersen ldquoRain microstruc-ture retrievals using 2-D video disdrometer and C-band polari-metric radarrdquo Advances in Geosciences vol 20 pp 13ndash18 2009

[9] K V Beard and C Chuang ldquoA new model for the equilibriumshape of raindropsrdquo Journal of the Atmospheric Sciences vol 44pp 1509ndash1524 1987

[10] K Andsager K V Beard and N S Laird ldquoA laboratory studyof oscillations and axis ratios for large raindropsrdquo Journal of theAtmospheric Sciences vol 55 pp 208ndash226 1999

[11] J W Wilson and E A Brandes ldquoRadar measurement of rain-fallmdasha summaryrdquo Bulletin AmericanMeteorological Society vol60 no 9 pp 1048ndash1058 1979

[12] P M Austin ldquoRelation betweenmeasured radar reflectivity andsurface rainfallrdquo Monthly Weather Review vol 115 no 5 pp1053ndash1070 1987

[13] J Vivekanandan D S Zrnic S M Ellis R Oye A V Ryzhkovand J Straka ldquoCloud microphysics retrieval using S-band dual-polarization radar measurementsrdquo Bulletin of the AmericanMeteorological Society vol 80 no 3 pp 381ndash388 1999

[14] A V Ryzhkov and D S Zrnic ldquoDiscrimination between rainand snow with a polarimetric radarrdquo Journal of Applied Meteo-rology vol 37 no 10 pp 1228ndash1240 1998

[15] S E Giangrande and A V Ryzhkov ldquoEstimation of rainfallbased on the results of polarimetric echo classificationrdquo Journalof AppliedMeteorology and Climatology vol 47 no 9 pp 2445ndash2462 2008

[16] A V Ryzhkov and D S Zrnic ldquoAssessment of rainfall measure-ment that uses specific differential phaserdquo Journal of AppliedMeteorology vol 35 no 11 pp 2080ndash2090 1996

[17] P T May T D Keenan D S Zrnic L D Carey and S ARutledge ldquoPolarimetric radar measurements of tropical rain ata 5-cm wavelengthrdquo Journal of Applied Meteorology vol 38 no6 pp 750ndash765 1999

[18] V N Bringi and V Chandrasekar ldquoThe polarimetric basis forcharacterizing precipitationrdquo in Polarimetric Doppler WeatherRadar Principles and Applications pp 378ndash533 CambridgeUniversity Press Cambridge UK 2001

[19] E A Brandes G Zhang and J Vivekanandan ldquoExperiments inrainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[20] A V Ryzhkov T J Schuur D W Burgess P L Heinselman SE Giangrande and D S Zrnic ldquoThe joint polarization exper-iment polarimetric rainfall measurements and hydrometeorclassificationrdquo Bulletin of the American Meteorological Societyvol 86 no 6 pp 809ndash824 2005

[21] A V Ryzhkov S E Giangrande and T J Schuur ldquoRainfall esti-mation with a polarimetric prototype of WSR-88Drdquo Journal ofApplied Meteorology vol 44 no 4 pp 502ndash515 2005

[22] R Cifelli V Chandrasekar S Lim P C Kennedy Y Wang andS A Rutledge ldquoA new dual-polarization radar rainfall algo-rithm application in Colorado precipitation eventsrdquo Journal ofAtmospheric andOceanic Technology vol 28 no 3 pp 352ndash3642011

[23] A Ryzhkov M Diederich P Zhang and C Simmer ldquoPotentialutilization of specific attenuation for rainfall estimationmitiga-tion of partial beam blockage and radar networkingrdquo Journal ofAtmospheric and Oceanic Technology vol 31 no 3 pp 599ndash6192014

[24] C-H You M-Y Kang D-I Lee and H Uyeda ldquoRainfallestimation by S-band polarimetric radar in Korea Part Ipreprocessing and preliminary resultsrdquoMeteorological Applica-tions vol 21 no 4 pp 975ndash983 2014

[25] C-H You D-I Lee andM-Y Kang ldquoRainfall estimation usingspecific differential phase for the first operational polarimetricradar in Koreardquo Advances in Meteorology vol 2014 Article ID413717 10 pages 2014

Advances in Meteorology 15

[26] V N Bringi V Chandrasekar J Hubbert E Gorgucci W LRandeu and M Schoenhuber ldquoRaindrop size distribution indifferent climatic regimes from disdrometer and dual-polarizedradar analysisrdquo Journal of the Atmospheric Sciences vol 60 no2 pp 354ndash365 2003

[27] E A Brandes G Zhang and J Vivekanandan ldquoExperimentsin rainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[28] K V Beard and R J Kubesh ldquoLaboratory measurements ofsmall raindrop distortion Part 2 oscillation frequencies andmodesrdquo Journal of the Atmospheric Sciences vol 48 no 20 pp2245ndash2264 1991

[29] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[30] J W F Goddard K L Morgan A Illingworth and HSauvageot ldquoDual-wavelength polarization measurements inprecipitation using the CAMRA and Rabelias radarsrdquo in Pro-ceedings of the 27th Conference on Radar Meteorology pp 196ndash198 American Meteorology Society Vail Colo USA 1995

[31] A V Ryzhkov D S Zrnic J C Hubbert V N Bringi JVivekanandan and E A Brandes ldquoPolarimetric radar obser-vations and interpretation of co-cross-polar correlation coeffi-cientsrdquo Journal of Atmospheric and Oceanic Technology vol 19no 3 pp 340ndash354 2002

[32] S YMatrosov KAClark B EMartner andA Tokay ldquoX-bandpolarimetric radar measurements of rainfallrdquo Journal of AppliedMeteorology vol 41 no 9 pp 941ndash952 2002

[33] G-J Huang V N Bringi and M Thurai ldquoOrientation angledistributions of drops after an 80-m fall using a 2D videodisdrometerrdquo Journal of Atmospheric and Oceanic Technologyvol 25 no 9 pp 1717ndash1723 2008

[34] R Meneghini and K Nakamura ldquoRange profiling of the rainrate by an airborne weather radarrdquo Remote Sensing of Environ-ment vol 31 no 3 pp 193ndash209 1990

[35] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onpolarimetric variables at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[36] J Testud E L Bouar E Obligis and M Ali-Mehenni ldquoTherain profiling algorithm applied to polarimetric weather radarrdquoJournal of Atmospheric andOceanic Technology vol 17 no 3 pp332ndash356 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

4 Advances in Meteorology

Korea Meteorological Administration (KMA)

20∘E

30∘E

40∘E

20∘E

30∘E

40∘E

50∘E

90∘E 100

∘E 110∘E 120

∘E 130∘E 140

∘E

110∘E 120

∘E 130∘E 140

∘E

150∘E 160

∘E15 UTC June 24 2011 (00 KST June 25 2011)

(a)

Korea Meteorological Administration (KMA)

20∘E

30∘E

40∘E

20∘E

30∘E

40∘E

50∘E

90∘E 100

∘E 110∘E 120

∘E 130∘E 140

∘E

110∘E 120

∘E 130∘E 140

∘E

150∘E 160

∘E00 UTC June 26 2011 (09 KST June 26 2011)

(b)

Korea Meteorological Administration (KMA)

20∘E

30∘E

40∘E

20∘E

30∘E

40∘E

50∘E

90∘E 100

∘E 110∘E 120

∘E 130∘E 140

∘E

110∘E 120

∘E 130∘E 140

∘E

150∘E 160

∘E03 UTC July 9 2011 (12 KST July 9 2011)

(c)

Korea Meteorological Administration (KMA)

20∘E

30∘E

40∘E

20∘E

30∘E

40∘E

50∘E

90∘E 100

∘E 110∘E 120

∘E 130∘E 140

∘E

110∘E 120

∘E 130∘E 140

∘E

150∘E 160

∘E15 UTC August 7 2011 (00 KST August 8 2011)

(d)

Figure 3 The surface weather chart (a) 0000 LST June 25 (b) 0900 LST June 26 (c) 1200 LST July 9 and (d) 0000 LST August 8 in 2011

The relation of raindrop axis ratio that slightly modifiedthe relation proposed by Goddard et al [30] was used(hereinafter DS6)

119887

119886

=

10 119863 le 10mm

1075 minus 0065119863 minus 000361198632 + 000041198633 119863 gt 10mm

(6)

Another parameter in the T-matrix calculations is thetemperature which is assumed to be 20∘C in this study Itis also necessary to take the canting angle into considerationof the T-matrix simulation because it can account for a 6reduction in the coefficient of the 119877(119870DP) relation [31] and

may cause small negative biases of the estimators [32] Thedistribution of canting angles of raindrops is Gaussian with amean of 0∘ and a standard deviation of 7∘ which have beenrecently determined by Huang et al [33]

23 Validations Because the rainfall in Korea is mostlyaccompanied with Changma front and Typhoon three rain-fall cases which are caused by Changma front and typhoonChangma front only and typhoon only were used forvalidations (Table 1)

Figure 3 shows the surface weather chart of each caseThetyphoon MAERI was located at the eastern ocean of Taiwanand the Changma front was elongated from eastern Chinacontinent to the central Japan through the southern part of

Advances in Meteorology 5

0

5

10

15

20

Time (hour LST)

Aver

age r

ainf

all a

mou

nt (m

m)

1 3 6 9 12 15 18 21 00 3 6 9 12 15 18 21 24

(a)

0

5

10

15

20

Time (hour LST)

Aver

age r

ainf

all a

mou

nt (m

m)

1 3 6 9 12 15 18 21 00 3 6 9 12 15 18 21 24

(b)

0

5

10

15

20

Time (hour LST)

Aver

age r

ainf

all a

mou

nt (m

m)

1 3 6 9 12 15 18 21 00 3 6 9 12 15 18 21 24

(c)

Figure 4 Time series of averaged rainfall amount which was accompanied with (a) Changma front and typhoon (b) Changma front onlyand (c) typhoon only averaged rainfall from all rain gages within radar coverage

Table 1 Rainfall cases with different sources for the study

Period Sources

2011 6 25 0900 LSTsim6 26 1400 LST Changma frontand typhoon

2011 7 09 0000 LSTsim7 10 2200 LST Changma front2011 8 07 1800 LSTsim8 08 0300 LST Typhoon

Korea on 0000 LST June 25 (Figure 3(a))TheMAERImovedto the north located at the southern west sea of Korea andmade rainfall in the Korean peninsula on 0900 LST June 26 in2011 (Figure 3(b)) Changma frontwas located at the southernpart of Korea and brought rainfall at the analyzed area on1200 LST July 9 in 2011 (Figure 3(c))The rainfall was affectedby Changma front all the time during case 2 The typhoonMUIFAwas located at the southwestern sea of Korea on 0000LST August 8 in 2011 and caused rainfall at the target area(Figure 3(d))

Figure 4 shows the time series of averaged rainfall amountobserved on the ground rain gages within radar coveragefrom 5 km to 95 km Averaged rainfall amount refers to thatobtained by averaging the amount of rainfall observed by raingages within the radius of the radar There are three peaksof rainfall in case of Changma front and typhoon the firsttwo peaks were due to Changma front and the third one wasdue to the influence of the typhoon There are three peaksof rainfall accompanied with Changma front in the secondrainfall eventThe third event was also caused by typhoon butwas relatively shortThe period of the selected rainfall was 84hours 29 hours for Changma front and typhoon 46 hours forChangma front only and 9 hours for typhoon only

The normalized error (NE) fractional root mean squareerror (RMSE) and correlation coefficients (CC) of rainfallrelations and 121 gages were used to investigate the perfor-mance of each rainfall relation

NE =(1119873)sum

119873

119894=1 (1003816100381610038161003816119877119877119894 minus 119877

119866119894

1003816100381610038161003816)

119877119866

6 Advances in Meteorology

Beard and Chuang 1987

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Standard

Average 2620deviation 838

(a)

Andsager et al 1999

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Standard

Average 2616deviation 837

(b)

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Goddard et al 1995

Standard

Average 2616deviation 839

(c)

Freq

uenc

y

Beard and Chuang 1987

00 05 10 15 20 25 30 35000002004006008010012014

Standard deviation 063Average 091

ZDR (dB)

(d)

Andsager et al 1999

Standard deviation 061Average 080

Freq

uenc

y

00 05 10 15 20 25 30 35000002004006008010012014

ZDR (dB)

(e)

Goddard et al 1995

Standard deviation 066Average 082

Freq

uenc

y

00 05 10 15 20 25 30 35000002004006008010012014

ZDR (dB)

(f)

Freq

uenc

y

Beard and Chuang 1987

000 005 010 015 020000

010

020

030

040

050Standard deviation 0107

Average 0037

KDP (degkm)

(g)

Freq

uenc

y

000 005 010 015 020000

010

020

030

040

050

KDP (degkm)

Andsager et al 1999

Standard deviation 0092Average 0031

(h)

Freq

uenc

y

000 005 010 015 020000

010

020

030

040

050

KDP (degkm)

Goddard et al 1995

Standard deviation 0096Average 0030

(i)

Figure 5 The occurrence frequency of (a) 119885 with DS1 (b) 119885 with DS3 (c) 119885 with DS6 (d) 119885DR with DS1 (e) 119885DR with DS3 (f) 119885DR withDS6 (g) 119870DP with DS1 (h) 119870DP with DS3 and (i) 119870DP with DS6

RMSE = [1119873

119873

sum

119894=1(119877119877119894

minus119877119866119894

)2]

12

CC =

sum119873

119894=1 (119877119877119894

minus 119877119877) (119877119866119894

minus 119877119866)

[sum119873

119894=1 (119877119877119894

minus 119877119877)2]

12[sum119873

119894=1 (119877119866119894

minus 119877119866)2]

12

(7)

where 119873 is the number of the RR and RG pairs and 119877119877and

119877119866are the averaged rain rate of radar and gage for an hour

respectively The above statistical variables are calculatedusing 1-hour rainfall amount of radar and gage at the pointThe point rainfall of radar was obtained by averaging rainfallover a small area (1 km times 1∘) centered on each rain gage

3 Results

31 Rainfall Relations with Different Raindrop Axis Ratios

311 The Characteristics of 119885 119885119863119877

and 119870119863119875

with DifferentDrop Shapes The histograms of occurrence frequency forpolarimetric variables 119885 119885DR and 119870DP calculated by DSDsdata for 4 years in Busan with different raindrop axis ratiorelations DS1 DS3 and DS6 were shown in Figure 5

The averages and modes of 119885 were around 262 dBZ and32sim33 dBZ for all raindrop axis assumptions (Figures 5(a)sim5(c)) It means that the reflectivity is not sensitive to the dropaxis relation In case of 119885DR there were two modes of occur-rence for all cases The averages and standard deviation ofeach relation were 063 dB and 091 dB for DS1 061 dB and08 dB for DS3 and 066 dB and 082 dB for DS6The low and

Advances in Meteorology 7

Table 2 The rainfall relations of 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) with different raindrop shape assumptions

DS 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) 119877(119870DP 119885DR)

DS1 R = 00273119885060 R = 029119885DR527 R = 445119870DP

0942 R = 00161198850889119885DRminus494 R = 537119870DP

0857119885DRminus148

DS2 R = 00277119885059 R = 038119885DR487 R = 533119870DP

0913 R = 00141198850852119885DRminus408 R = 752119870DP

0855119885DRminus198

DS3 R = 00277119885060 R = 042119885DR498 R = 615119870DP

0908 R = 00151198850818119885DRminus372 R = 822119870DP

0855119885DRminus198

DS4 R = 00277119885060 R = 041119885DR498 R = 599119870DP

0896 R = 00141198850844119885DRminus406 R = 674119870DP

0785119885DRminus213

DS5 R = 00277119885060 R = 040119885DR503 R = 562119870DP

0897 R = 00131198850861119885DRminus43 R = 847119870DP

0840119885DRminus238

DS6 R = 00280119885059 R = 043119885DR469 R = 563119870DP

0857 R = 00131198850857119885DRminus40 R = 150119870DP

0483119885DRminus077

R(Z

ZD

R)

(mm

h)

R = 001589085Z08927

ZDRminus49936

NB = 1300

RMSE = 2776

CC = 0965

R (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

(a)

R = 13428687294KDP08991

ZDRminus26757

NB = 188

RMSE = 2593

CC = 0967

R (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(K

DPZ

DR)

(mm

h)

(b)

Figure 6 The scatter plots of rainfall obtained by DSDs and (a) 119877(119885 119885DR) and (b) 119877(119870DP 119885DR) using 119885 for DS3 119885DR for DS1 and 119870DP forDS3

high modes of 119885DR with DS1 DS3 and DS6 were 02sim03 dBand 17sim18 dB 02sim03 dB and 16sim17 dB and 00sim01 dB and17sim18 dB respectively The occurrence frequencies of lowmode for each raindrop axis ratio were significantly differentfrom each other (Figures 5(d)sim5(f)) The averages and stan-dard deviation of119870DPwith different raindrop shapeswere 011and 004 009 and 003 and 01 and 003 respectively Themodes of all drop shapes were the same but the occurrencefrequencies were different (Figures 5(g)sim5(i))

312 The Statistics of Rainfall Relations with Different Rain-drop Axis Ratios Because the occurrence frequencies of119885DRand 119870DP with different raindrop axis ratios were differentfrom each other the rainfall relations using those variablesshould be different with drop shape assumptions Table 2shows the rainfall relations obtained by using different rain-drop shape assumptions The coefficients of 119877(119885) were notsignificantly different with drop shape assumptions howeverthose of other relations were different with each drop shape

Table 3 shows the cross correlations (hereinafter CC) andRMSEs (root mean square errors) of rainfall relations 119877(119885)119877(119885DR) 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) obtained bycalculations using DSDs data with different raindrop shapes

The statistics of 119877(119885) and 119877(119885DR) were not significantlydifferent with raindrop shapesThe CC and RMSE of 119877(119885DR)and 119877(119885 119885DR) were the worst and the best among theother rainfall relations The statistics of 119877(119870DR) 119877(119885 119885DR)and 119877(119870DP 119885DR) were much more variable with differentraindrop axis ratios than the ones of 119877(119885) and 119877(119885DR) TheRMSEs of 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) with rain-drop shapes were distributed from 3030 to 3828mm 2965to 3523mm and 3151 to 5412mm respectivelyThe best per-formance of each relation occurred at DS3 for 119877(119885) DS1 for119877(119885DR) DS1 for 119877(119870DP) DS1 for 119877(119885 119885DR) and DS3 for119877(119870DP 119885DR)

In order to calculate more accurate 119877(119885 119885DR) and119877(119870DP 119885DR) the 119885 and 119885DR with the best performance werechosen Figure 6 shows the scatter plots of rainfall obtainedby DSDs and 119877(119885 119885DR) and 119877(119870DP 119885DR) using the beststatistics among raindrop axis ratio 119885 119885DR and 119870DP werechosen from DS3 DS1 and DS1 respectively Comparingwith 119877(119885 119885DR) and 119877(119870DP 119885DR) of single raindrop axisratio relations having the best performance new combinedrelations had better RMSE and CC The RMSEs of new rela-tions 119877(119885 119885DR) and 119877(119870DP 119885DR) had better score as muchas around 02mm and 06mm respectively Even though

8 Advances in Meteorology

Table 3 The correlation coefficients and RMSEs (mm) of rainfall obtained by rainfall relations and DSDs CC means cross correlation

DS 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) 119877(119870DP 119885DR)

CC RMSE CC RMSE CC RMSE CC RMSE CC RMSEDS1 0913 4705 0572 6241 0875 3030 0964 2965 0951 3313DS2 0913 4709 0569 6248 0861 3198 0956 3272 0956 3222DS3 0914 4704 0562 6261 0861 3178 0949 3523 0960 3151DS4 0913 4706 0569 6249 0828 3549 0954 3334 0931 3882DS5 0913 4706 0572 6243 0849 3326 0957 3210 0950 3348DS6 0913 4713 0572 6244 0795 3828 0956 3239 0814 5412

Table 4The rainfall relations NE RMSE and CC of each raindropaxis ratio relation

DropShape Relation NE RMSE CC

DS1119877(119870DP) = 445119870DP

0942 052 4996 082119877(119885 119885DR) = 001571198850889119885DR

minus494 031 4802 097119877(119870DP 119885DR) = 537119870DP

0857119885DRminus148 056 5262 088

DS2119877(119870DP) = 530119870DP

0913 052 4645 078119877(119885 119885DR) = 001411198850853119885DR

minus408 036 3793 073119877(119870DP 119885DR) = 752119870DP

0855119885DRminus198 060 5146 073

DS3119877(119870DP) = 615119870DP

0908 055 4698 078119877(119885 119885DR) = 001481198850818119885DR

minus372 043 4479 089119877(119870DP 119885DR) = 822119870DP

0855119885DRminus198 063 5247 073

DS4119877(119870DP) = 599119870DP

0896 054 4673 078119877(119885 119885DR) = 001361198850840119885DR

minus406 040 4134 089119877(119870DP 119885DR) = 674119870DP

0785119885DRminus213 060 5249 073

DS5119877(119870DP) = 562119870DP

0897 053 4625 078119877(119885 119885DR) = 001331198850861119885DR

minus431 037 3900 088119877(119870DP 119885DR) = 847119870DP

0840119885DRminus238 065 5390 071

DS6119877(119870DP) = 563119870DP

0857 054 4647 078119877(119885 119885DR) = 001251198850857119885DR

minus399 038 3967 089119877(119870DP 119885DR) = 150119870DP

0483119885DRminus077 065 7141 076

the CC and RMSE of 119877(119885) and 119877(119885DR) with different dropshapes were not significant the combined relations had betterperformance

32 Validations of Rainfall Relations with Different RaindropAxis Ratio Relations To investigate the performance ofrainfall relationsNE (normalized error) RMSE andCCwerecalculated using rainfall from each relation with six raindropshapes and that of gage rainfall

Table 4 summarizes the relations and the statistics suchas NE RMSE and CC The NEs and RMSEs of 119877(119870DR)calculated by each raindrop axis were distributed from 052 to055 and from 4625 to 4996 respectively The 119877(119870DR) withassumption of DS5 was the best score of RMSE in other rain-drop shapes In case of119877(119885 119885DR) the distribution ofNEs andRMSEs was from 031 to 043 and from 3793 to 4602 respec-tively The best RMSE score of 119877(119885 119885DR) was from DS2The NEs and RMSEs of 119877(119870DP 119885DR) occurred from 055 to065 and from 5146 to 7141 respectively The performance of

119877(119870DP 119885DR) was the worst score and 119877(119885 119885DR) had the bestscore in all raindrop axis ratio relations The performancesof validation were different from that of rainfall relationcalculation It would be caused by the variations of DSDs inthis study

To compare the performance between new combined119877(119870DP 119885DR) and 119877(119885 119885DR) the statistics were also calcu-lated Figure 7 shows the scatter plots rainfall from rainfallrelation and gage rainfall with some statistics The NEand RMSE of two relations from single raindrop shapeassumption showed better results However it seems that the119877(119885 119885DR)with two-raindrop axis ratio was more close to thegage rainfall in the range of weaker than 20mmh and the119877(119870DP 119885DR) with two drop shapes was more accurate in therainfall of higher than 20mmh

33 Rainfall Estimation Using Specific Attenuation331 Calculation of Specific Attenuation The 119860

119867can be

calculated from the radial profile of the attenuated reflectivity119885119886and the two-way PIA (Path Integrated Attenuation) along

the propagation path (1199031 1199032) proposed by Meneghini and

Nakamura [34]

119860 (119903) =119886 (119903) [119885119886]

119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(8)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

119886 (119904) [119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

119886 (119904) [119885119886 (119904)]119887119889119904

(9)

If 119886 is not dependent on range then (8) becomes

119860 (119903) =[119885119886]119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(10)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

[119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

[119885119886 (119904)]119887119889119904

(11)

119862 (119887PIA) = exp (023119887PIA) minus 1 (12)

Advances in Meteorology 9

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 036

RMSE = 3793

CC = 0888

Rada

r tot

alR

(ZZ

DR)

BC

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 060

RMSE = 5146

CC = 0732

Rada

r tot

alR

(KD

PZ

DR)

BC

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 032

RMSE = 5194

CC = 0818

Rada

r tot

alR

(ZZ

DR)

best

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 092

RMSE = 7302

CC = 0695

Rada

r tot

alR

(KD

PZ

DR)

best

(d)

Figure 7The scatter plot of rainfall from gage and (a) 119877(119885 119885DR) (b) 119877(119870DP 119885DR)with single raindrop axis ratio relation (c) 119877(119885 119885DR) and(d) 119877(119870DP 119885DR) with two-raindrop axis ratio relation

Bringi et al [35] recommended estimating PIA usingΦDPby

PIA (1199031 1199032) = 120572 [ΦDP (1199032) minusΦDP (1199031)] = 120572ΔΦDP (13)

and Testud et al [36] used (10) and (12) to obtain radialprofiles of 119860

119867at C-band In this study 119860

119867was calculated

by the method proposed by Ryzhkov et al [23] The constant

119887 was set by 06 and 120572 was by 0027 calculated by the ratio of119860119867to 119870DP obtained from DSDsFigure 8 shows the scatter plot of rainfall from 119877(119885)

119877(119870DP) and 119877(119860119867) and rainfall from DSDs and an PPIs

(Plan Position Indicators) at 05 degree elevation angle of gagerainfall and rainfall from 119877(119870DP) and 119877(119860

119867) at 0251 KST on

the 8th of August in 2011The 119877(119860

119867) relation had much better fit to the rainfall of

DSDs than that of119877(119870DP) and119877(119885) relation Comparingwith

10 Advances in Meteorology

Beard and Chuang 1987

Rain rate DSD (mmh)

R(Z

) (m

mh

)

10minus1

100

101

102

103

10minus1

100

101

102

103

R = 00277Z05994

NB = minus2122

RMSE = 4709

CC = 0913

(a)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

NB = minus1295136

RMSE = 3198

CC = 0861

R = 533039KDP091341

R(K

DP)

(mm

h)

(b)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(A

H)

(mm

h)

R = 337359AH10194

NB = 327

RMSE = 3667

CC = 0984

(c)

150100705040302015107310500

R(KDP) (mmh)

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(d)

R(AH) (mmh)

150100705040302015107310500

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(e)

Figure 8 The scatter plot of (a) 119877(119885) (b) 119877(119870DP) and (c) 119877(119860119867) with statistics and the rainfall distribution of 119877(119870DP) and 119877(119860

119867) at 0251

KST on the 8th of August in 2001

Advances in Meteorology 11

Table 5 The rainfall relations of 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assumptions

DS 119877(119885119870DP 119860119867) 119877(119885 119885DR 119870DP 119860119867)

DS1 119877 = 1527119885minus004119870DP0327

119860119867

0713119877 = 310Z012

119885DRminus083

119870DP0304

119860119867

0677

DS2 119877 = 12012119885minus024119870DP0551

119860119867

0685119877 = 4947Zminus015119885DR

minus026119870DP

0468119860119867

0681

DS3 119877 = 17211119885minus027119870DP0619

119860119867

0650119877 = 4502Z014

119885DRminus039

119870DP0486

119860119867

0653

DS4 119877 = 10798119885minus019119870DP0403

119860119867

0778119877 = 193Z018

119885DRminus111

119870DP0114

119860119867

0702

DS5 119877 = 20275119885minus027119870DP0543

119860119867

0720119877 = 24Z037

119885DRminus147

119870DPminus0025

119860119867

0656

DS6 119877 = 397119885minus011119870DP0044

119860119867

0808119877 = 571Z007

119885DRminus092

119870DP0238

119860119867

0687

the distribution of rainfall obtained by 119877(119870DP) and 119877(119860119867)

119877(119860119867) has better spatial resolution and more homogeneous

pattern than those of 119877(119870DP)

332 Validations of 119877(119860119867) 119877(119885119870

119863119875 119860119867) and 119877(119885 119885

119863119877

119870119863119875

119860119867) Relations As mentioned in the previous section

119877(119860119867) has the potential to be the best choice for estimating

rainfall using polarimetric variables To verify the accuracy119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) relations

were obtained and the accuracy of 119877(119860119867) 119877(119885119870DP 119860119867)

and 119877(119885 119885DR 119870DP 119860119867) which had the best performance inthe relations calculated by the six raindrop axis ratio relationswere examined by comparing with 119877(119870DP)

Figure 9 shows the scatter plot of rainfall from gagerainfall and 119877(119870DP) 119877(119860

119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR

119870DP 119860119867) for 84 hours The accuracy of 119877(119885 119885DR 119870DP 119860119867)was the best and119877(119885119870DP 119860119867)was the second in 4 relations119877(119860119867)was not better than 119877(119870DP) in whole range of rainfall

However in the range of higher rainfall it seems that 119877(119860119867)

was closer to the gage rainfall The error of 119877(119860119867) would be

caused by the missing radial profile ofΦDP along the rayThemissing has occurred if the difference of ΦDP between thestarting and end gate is negative According to the results119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) would compensatefor this region

34 Optimum Rainfall Algorithm To find out the optimumrainfall algorithm for Korean S-band polarimetric radar thegage rainfall amount was categorized by three steps 0 to5mmh assigned as light rain 5 to 30mmh as medium rainand higher than 30mmh as high rain In previous sectionthe relations have different accuracy not only for the raindropaxis ratio relation but also for rainfall amount The samplenumbers for each category were 3322 samples 1980 samplesand 92 samples respectively

Figure 10 shows the RMSEs of 119877(119870DP) 119877(119885 119885DR)119877(119870DP 119885DR) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) withdifferent rainfall categories defined in three steps All rela-tions have different RMSEs with respect to the raindrop axisratio relations 119877(119870DP) with DS3 119877(119885 119885DR) with DS2 and119877(119870DP 119885DR) with DS3 have the best score at the high rainfallregime at the low rainfall regime and at the medium rainfallregime respectively Even though 119877(119885 119885DR) has the bestperformance among other relations in total rainfall eventsusing different rainfall relations with different rainfall regimewould be an optimum rainfall algorithm for Korean S-band

polarimetric radar A possible optimum polarimetric rainfallalgorithm can be expressed by

119877 = 00141198850852119885DRminus408 0 lt Rainfall lt 5mmhminus1

119877 = 822119870DP0855

119885DRminus198

5 lt Rainfall lt 30mmhminus1

119877 = 615119870DP0908 30mmhminus1 lt Rainfall

(14)

Table 5 shows the rainfall relations of 119877(119885119870DP 119860119867) and119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assump-tions The coefficients of each relation with respect to thedrop shapes were much different comparing with relationsobtained by combining two polarimetric variables

In case of rainfall relations combined with119860119867 119877(119885 119885DR

119870DP 119860119867) has better score than 119877(119885119870DP 119860119867) Both119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with DS3 showedbetter result than other raindrop shape assumptions119877(119885 119885DR 119870DP 119860119867) at the low medium and high rainfallregimes has similar RMSE to 119877(119885 119885DR) 119877(119870DP 119885DR) and119877(119870DP) respectively

Equations (14) would be an optimum rainfall algorithmbut there is still a problem to solve how the rainfall categoriesare defined using radar and gage Gage does not have goodspatial resolution to cover radar resolution like 125m or 1 kmand each rainfall relation has its own error at certain rainfallregime Therefore 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867)withDS3 can be used regardless rainfall intensity And in case119885DR bias calibration is not available or does not have enoughquality for quantitative use 119877(119885119870DP 119860119867) with DS3 can beused as a representative rainfall estimation

4 Summary and Conclusions

Polarimetric radars will be main tools to monitor andforecast severe weather and flash flooding within severalyears in Korea To get an optimum rainfall algorithm usingpolarimetric variables observed from Bislsan radar which isthe first polarimetric radar in Korea rainfall cases for 84hours caused by different conditions which are Changmafront and typhoon Changma front only and typhoon onlythat occurred in 2011 were analyzed And rainfall relationswere obtained by using long period DSDs with six differentraindrop axis ratio relations

In the analysis of 119885 119885DR and119870DP occurrence frequencythere were two modes of 119885DR occurrence frequency and

12 Advances in Meteorology

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100Ra

dar t

otal

R(K

DP)

BC

NE = 052

RMSE = 4645

CC = 0778

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 051

RMSE = 5005

CC = 0797

Rada

r tot

al R

(AH

) AS

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100NE = 046

RMSE = 4374

CC = 0820

Rada

r tot

al R

(ZK

DPA

H) A

S

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 045

RMSE = 4368

CC = 0852

Rada

r tot

al R

(ZZ

DRK

DPA

H) A

S

(d)

Figure 9 The scatter plot of gage rainfall and 119877(119870DP) 119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DP 119870DP 119860119867) rainfall for 84 hours

the variations of 119870DP and 119885DR histograms were higherthan that of 119885 with raindrop ratio relations According tothese variations the combined relations of 119877(119885 119885DR) and119877(119870DP 119885DR) using 119885 with DS3 119885DR with DS1 and 119870DP withDS1 were closer to the rainfall of DSDs

To examine the performance of each rainfall relationNE RMSE CC were calculated using rainfall recorded at121 gages within radar coverage for 84 hours The statisticsof each rainfall relation were different with raindrop shape

assumptions and rainfall intensity119877(119870DP 119885DR)had theworstperformance and119877(119885 119885DR) had the best score in all raindropshapes 119860

119867was calculated by observed ΦDP and 119885 using the

method by Ryzhkov et al [23] and the rainfall relations using119860119867were also calculated and analyzedThe performance of rainfall relations were comparedwith

three different rainfall categories to findout an optimumrain-fall relation for the S-band polarimetric in Korea 119877(119885 119885DR)119877(119870DP 119885DR) and 119877(119870DP) had the best RMSE at the light

Advances in Meteorology 13

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP) with drop shape

(a)

0

5

10

15

20

Drop shape

25

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(Z ZDR) with drop shape

(b)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP ZDR) with drop shape

(c)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(ZKDP AH) with drop shape

(d)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

0ndash5mm5ndash30mmOver 30mm

RMSE of R(Z ZDR KDP AH) with drop shape

(e)

Figure 10The RMSEs of (a) 119877(119870DP) (b) 119877(119885 119885DP) (c) 119877(119870DP 119885DP) (d) 119877(119885119870DP 119860119867) and (e) 119877(119885 119885DP 119870DP 119860119867)with raindrop axis ratiorelations in the three rainfall categories

14 Advances in Meteorology

rain medium rain and high rainfall regimes respectively119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) showed relativelygood performance in all rainfall regimesThe combination of119877(119885 119885DR) 119877(119870DP 119885DR) and 119877(119870DP) with rainfall intensitywould be an optimum rainfall algorithm if the referenceof rainfall would be defined correctly Regardless of rainfallintensity 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) obtainedby assuming DS3 can be used as a representative rainfall rela-tion without consideration of rainfall intensity regime Par-ticularly if the qualified 119885DR is not available 119877(119885119870DP 119860119867)with DS3 drop shape assumption can be used as an optimumrainfall relation in Korea

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge providing radar data weatherchart and AWS data for this work from the Ministry ofLand Infrastructure Transport and Korea MeteorologicalAdministration The authors also acknowledge providingcodes for scattering simulation from Professor V N Bringi atColorado StateUniversityThisworkwas funded by theKoreaMeteorological Industry Promotion Agency under GrantKMIPA 2015-1050

References

[1] E Campos and I Zawadzki ldquoInstrumental uncertainties in Z-R relationsrdquo Journal of Applied Meteorology vol 39 no 7 pp1088ndash1102 2000

[2] C-H You D-I Lee S-M Jang et al ldquoCharacteristics ofrainfall systems accompanied with Changma front at Chujadoin Koreardquo Asia-Pacific Journal of Atmospheric Sciences vol 46no 1 pp 41ndash51 2010

[3] P CWaterman ldquoSymmetry unitarity and geometry in electro-magnetic scatteringrdquo Physical Review D vol 3 no 4 pp 825ndash839 1971

[4] M IMishchenko LD Travis andDWMackowski ldquoT-matrixcomputations of light scattering by nonspherical particles areviewrdquo Journal of Quantitative Spectroscopy and RadiativeTransfer vol 55 no 5 pp 535ndash575 1996

[5] H R Pruppacher and K V Beard ldquoA wind tunnel investigationof the internal circulation and shape of water drops fallingat terminal velocity in airrdquo Quarterly Journal of the RoyalMeteorological Society vol 96 no 408 pp 247ndash256 1970

[6] D C Blanchard ldquoThe behavior of water drops at terminalvelocity in airrdquo EOS vol 31 no 6 pp 836ndash842 1950

[7] G-J Huang V N Bringi M Schonhuber et al ldquoDrop shapeand canting angle distributions in rain from2-Dvideo disdrom-eterrdquo in Proceedings of the 33rd Conference on Radar Meteorol-ogy Extended Abstract P8A8 Cairns Australia August 2007

[8] M Thurai V N Bringi and W A Petersen ldquoRain microstruc-ture retrievals using 2-D video disdrometer and C-band polari-metric radarrdquo Advances in Geosciences vol 20 pp 13ndash18 2009

[9] K V Beard and C Chuang ldquoA new model for the equilibriumshape of raindropsrdquo Journal of the Atmospheric Sciences vol 44pp 1509ndash1524 1987

[10] K Andsager K V Beard and N S Laird ldquoA laboratory studyof oscillations and axis ratios for large raindropsrdquo Journal of theAtmospheric Sciences vol 55 pp 208ndash226 1999

[11] J W Wilson and E A Brandes ldquoRadar measurement of rain-fallmdasha summaryrdquo Bulletin AmericanMeteorological Society vol60 no 9 pp 1048ndash1058 1979

[12] P M Austin ldquoRelation betweenmeasured radar reflectivity andsurface rainfallrdquo Monthly Weather Review vol 115 no 5 pp1053ndash1070 1987

[13] J Vivekanandan D S Zrnic S M Ellis R Oye A V Ryzhkovand J Straka ldquoCloud microphysics retrieval using S-band dual-polarization radar measurementsrdquo Bulletin of the AmericanMeteorological Society vol 80 no 3 pp 381ndash388 1999

[14] A V Ryzhkov and D S Zrnic ldquoDiscrimination between rainand snow with a polarimetric radarrdquo Journal of Applied Meteo-rology vol 37 no 10 pp 1228ndash1240 1998

[15] S E Giangrande and A V Ryzhkov ldquoEstimation of rainfallbased on the results of polarimetric echo classificationrdquo Journalof AppliedMeteorology and Climatology vol 47 no 9 pp 2445ndash2462 2008

[16] A V Ryzhkov and D S Zrnic ldquoAssessment of rainfall measure-ment that uses specific differential phaserdquo Journal of AppliedMeteorology vol 35 no 11 pp 2080ndash2090 1996

[17] P T May T D Keenan D S Zrnic L D Carey and S ARutledge ldquoPolarimetric radar measurements of tropical rain ata 5-cm wavelengthrdquo Journal of Applied Meteorology vol 38 no6 pp 750ndash765 1999

[18] V N Bringi and V Chandrasekar ldquoThe polarimetric basis forcharacterizing precipitationrdquo in Polarimetric Doppler WeatherRadar Principles and Applications pp 378ndash533 CambridgeUniversity Press Cambridge UK 2001

[19] E A Brandes G Zhang and J Vivekanandan ldquoExperiments inrainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[20] A V Ryzhkov T J Schuur D W Burgess P L Heinselman SE Giangrande and D S Zrnic ldquoThe joint polarization exper-iment polarimetric rainfall measurements and hydrometeorclassificationrdquo Bulletin of the American Meteorological Societyvol 86 no 6 pp 809ndash824 2005

[21] A V Ryzhkov S E Giangrande and T J Schuur ldquoRainfall esti-mation with a polarimetric prototype of WSR-88Drdquo Journal ofApplied Meteorology vol 44 no 4 pp 502ndash515 2005

[22] R Cifelli V Chandrasekar S Lim P C Kennedy Y Wang andS A Rutledge ldquoA new dual-polarization radar rainfall algo-rithm application in Colorado precipitation eventsrdquo Journal ofAtmospheric andOceanic Technology vol 28 no 3 pp 352ndash3642011

[23] A Ryzhkov M Diederich P Zhang and C Simmer ldquoPotentialutilization of specific attenuation for rainfall estimationmitiga-tion of partial beam blockage and radar networkingrdquo Journal ofAtmospheric and Oceanic Technology vol 31 no 3 pp 599ndash6192014

[24] C-H You M-Y Kang D-I Lee and H Uyeda ldquoRainfallestimation by S-band polarimetric radar in Korea Part Ipreprocessing and preliminary resultsrdquoMeteorological Applica-tions vol 21 no 4 pp 975ndash983 2014

[25] C-H You D-I Lee andM-Y Kang ldquoRainfall estimation usingspecific differential phase for the first operational polarimetricradar in Koreardquo Advances in Meteorology vol 2014 Article ID413717 10 pages 2014

Advances in Meteorology 15

[26] V N Bringi V Chandrasekar J Hubbert E Gorgucci W LRandeu and M Schoenhuber ldquoRaindrop size distribution indifferent climatic regimes from disdrometer and dual-polarizedradar analysisrdquo Journal of the Atmospheric Sciences vol 60 no2 pp 354ndash365 2003

[27] E A Brandes G Zhang and J Vivekanandan ldquoExperimentsin rainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[28] K V Beard and R J Kubesh ldquoLaboratory measurements ofsmall raindrop distortion Part 2 oscillation frequencies andmodesrdquo Journal of the Atmospheric Sciences vol 48 no 20 pp2245ndash2264 1991

[29] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[30] J W F Goddard K L Morgan A Illingworth and HSauvageot ldquoDual-wavelength polarization measurements inprecipitation using the CAMRA and Rabelias radarsrdquo in Pro-ceedings of the 27th Conference on Radar Meteorology pp 196ndash198 American Meteorology Society Vail Colo USA 1995

[31] A V Ryzhkov D S Zrnic J C Hubbert V N Bringi JVivekanandan and E A Brandes ldquoPolarimetric radar obser-vations and interpretation of co-cross-polar correlation coeffi-cientsrdquo Journal of Atmospheric and Oceanic Technology vol 19no 3 pp 340ndash354 2002

[32] S YMatrosov KAClark B EMartner andA Tokay ldquoX-bandpolarimetric radar measurements of rainfallrdquo Journal of AppliedMeteorology vol 41 no 9 pp 941ndash952 2002

[33] G-J Huang V N Bringi and M Thurai ldquoOrientation angledistributions of drops after an 80-m fall using a 2D videodisdrometerrdquo Journal of Atmospheric and Oceanic Technologyvol 25 no 9 pp 1717ndash1723 2008

[34] R Meneghini and K Nakamura ldquoRange profiling of the rainrate by an airborne weather radarrdquo Remote Sensing of Environ-ment vol 31 no 3 pp 193ndash209 1990

[35] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onpolarimetric variables at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[36] J Testud E L Bouar E Obligis and M Ali-Mehenni ldquoTherain profiling algorithm applied to polarimetric weather radarrdquoJournal of Atmospheric andOceanic Technology vol 17 no 3 pp332ndash356 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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EarthquakesJournal of

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Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

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MineralogyInternational Journal of

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ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Advances in Meteorology 5

0

5

10

15

20

Time (hour LST)

Aver

age r

ainf

all a

mou

nt (m

m)

1 3 6 9 12 15 18 21 00 3 6 9 12 15 18 21 24

(a)

0

5

10

15

20

Time (hour LST)

Aver

age r

ainf

all a

mou

nt (m

m)

1 3 6 9 12 15 18 21 00 3 6 9 12 15 18 21 24

(b)

0

5

10

15

20

Time (hour LST)

Aver

age r

ainf

all a

mou

nt (m

m)

1 3 6 9 12 15 18 21 00 3 6 9 12 15 18 21 24

(c)

Figure 4 Time series of averaged rainfall amount which was accompanied with (a) Changma front and typhoon (b) Changma front onlyand (c) typhoon only averaged rainfall from all rain gages within radar coverage

Table 1 Rainfall cases with different sources for the study

Period Sources

2011 6 25 0900 LSTsim6 26 1400 LST Changma frontand typhoon

2011 7 09 0000 LSTsim7 10 2200 LST Changma front2011 8 07 1800 LSTsim8 08 0300 LST Typhoon

Korea on 0000 LST June 25 (Figure 3(a))TheMAERImovedto the north located at the southern west sea of Korea andmade rainfall in the Korean peninsula on 0900 LST June 26 in2011 (Figure 3(b)) Changma frontwas located at the southernpart of Korea and brought rainfall at the analyzed area on1200 LST July 9 in 2011 (Figure 3(c))The rainfall was affectedby Changma front all the time during case 2 The typhoonMUIFAwas located at the southwestern sea of Korea on 0000LST August 8 in 2011 and caused rainfall at the target area(Figure 3(d))

Figure 4 shows the time series of averaged rainfall amountobserved on the ground rain gages within radar coveragefrom 5 km to 95 km Averaged rainfall amount refers to thatobtained by averaging the amount of rainfall observed by raingages within the radius of the radar There are three peaksof rainfall in case of Changma front and typhoon the firsttwo peaks were due to Changma front and the third one wasdue to the influence of the typhoon There are three peaksof rainfall accompanied with Changma front in the secondrainfall eventThe third event was also caused by typhoon butwas relatively shortThe period of the selected rainfall was 84hours 29 hours for Changma front and typhoon 46 hours forChangma front only and 9 hours for typhoon only

The normalized error (NE) fractional root mean squareerror (RMSE) and correlation coefficients (CC) of rainfallrelations and 121 gages were used to investigate the perfor-mance of each rainfall relation

NE =(1119873)sum

119873

119894=1 (1003816100381610038161003816119877119877119894 minus 119877

119866119894

1003816100381610038161003816)

119877119866

6 Advances in Meteorology

Beard and Chuang 1987

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Standard

Average 2620deviation 838

(a)

Andsager et al 1999

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Standard

Average 2616deviation 837

(b)

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Goddard et al 1995

Standard

Average 2616deviation 839

(c)

Freq

uenc

y

Beard and Chuang 1987

00 05 10 15 20 25 30 35000002004006008010012014

Standard deviation 063Average 091

ZDR (dB)

(d)

Andsager et al 1999

Standard deviation 061Average 080

Freq

uenc

y

00 05 10 15 20 25 30 35000002004006008010012014

ZDR (dB)

(e)

Goddard et al 1995

Standard deviation 066Average 082

Freq

uenc

y

00 05 10 15 20 25 30 35000002004006008010012014

ZDR (dB)

(f)

Freq

uenc

y

Beard and Chuang 1987

000 005 010 015 020000

010

020

030

040

050Standard deviation 0107

Average 0037

KDP (degkm)

(g)

Freq

uenc

y

000 005 010 015 020000

010

020

030

040

050

KDP (degkm)

Andsager et al 1999

Standard deviation 0092Average 0031

(h)

Freq

uenc

y

000 005 010 015 020000

010

020

030

040

050

KDP (degkm)

Goddard et al 1995

Standard deviation 0096Average 0030

(i)

Figure 5 The occurrence frequency of (a) 119885 with DS1 (b) 119885 with DS3 (c) 119885 with DS6 (d) 119885DR with DS1 (e) 119885DR with DS3 (f) 119885DR withDS6 (g) 119870DP with DS1 (h) 119870DP with DS3 and (i) 119870DP with DS6

RMSE = [1119873

119873

sum

119894=1(119877119877119894

minus119877119866119894

)2]

12

CC =

sum119873

119894=1 (119877119877119894

minus 119877119877) (119877119866119894

minus 119877119866)

[sum119873

119894=1 (119877119877119894

minus 119877119877)2]

12[sum119873

119894=1 (119877119866119894

minus 119877119866)2]

12

(7)

where 119873 is the number of the RR and RG pairs and 119877119877and

119877119866are the averaged rain rate of radar and gage for an hour

respectively The above statistical variables are calculatedusing 1-hour rainfall amount of radar and gage at the pointThe point rainfall of radar was obtained by averaging rainfallover a small area (1 km times 1∘) centered on each rain gage

3 Results

31 Rainfall Relations with Different Raindrop Axis Ratios

311 The Characteristics of 119885 119885119863119877

and 119870119863119875

with DifferentDrop Shapes The histograms of occurrence frequency forpolarimetric variables 119885 119885DR and 119870DP calculated by DSDsdata for 4 years in Busan with different raindrop axis ratiorelations DS1 DS3 and DS6 were shown in Figure 5

The averages and modes of 119885 were around 262 dBZ and32sim33 dBZ for all raindrop axis assumptions (Figures 5(a)sim5(c)) It means that the reflectivity is not sensitive to the dropaxis relation In case of 119885DR there were two modes of occur-rence for all cases The averages and standard deviation ofeach relation were 063 dB and 091 dB for DS1 061 dB and08 dB for DS3 and 066 dB and 082 dB for DS6The low and

Advances in Meteorology 7

Table 2 The rainfall relations of 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) with different raindrop shape assumptions

DS 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) 119877(119870DP 119885DR)

DS1 R = 00273119885060 R = 029119885DR527 R = 445119870DP

0942 R = 00161198850889119885DRminus494 R = 537119870DP

0857119885DRminus148

DS2 R = 00277119885059 R = 038119885DR487 R = 533119870DP

0913 R = 00141198850852119885DRminus408 R = 752119870DP

0855119885DRminus198

DS3 R = 00277119885060 R = 042119885DR498 R = 615119870DP

0908 R = 00151198850818119885DRminus372 R = 822119870DP

0855119885DRminus198

DS4 R = 00277119885060 R = 041119885DR498 R = 599119870DP

0896 R = 00141198850844119885DRminus406 R = 674119870DP

0785119885DRminus213

DS5 R = 00277119885060 R = 040119885DR503 R = 562119870DP

0897 R = 00131198850861119885DRminus43 R = 847119870DP

0840119885DRminus238

DS6 R = 00280119885059 R = 043119885DR469 R = 563119870DP

0857 R = 00131198850857119885DRminus40 R = 150119870DP

0483119885DRminus077

R(Z

ZD

R)

(mm

h)

R = 001589085Z08927

ZDRminus49936

NB = 1300

RMSE = 2776

CC = 0965

R (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

(a)

R = 13428687294KDP08991

ZDRminus26757

NB = 188

RMSE = 2593

CC = 0967

R (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(K

DPZ

DR)

(mm

h)

(b)

Figure 6 The scatter plots of rainfall obtained by DSDs and (a) 119877(119885 119885DR) and (b) 119877(119870DP 119885DR) using 119885 for DS3 119885DR for DS1 and 119870DP forDS3

high modes of 119885DR with DS1 DS3 and DS6 were 02sim03 dBand 17sim18 dB 02sim03 dB and 16sim17 dB and 00sim01 dB and17sim18 dB respectively The occurrence frequencies of lowmode for each raindrop axis ratio were significantly differentfrom each other (Figures 5(d)sim5(f)) The averages and stan-dard deviation of119870DPwith different raindrop shapeswere 011and 004 009 and 003 and 01 and 003 respectively Themodes of all drop shapes were the same but the occurrencefrequencies were different (Figures 5(g)sim5(i))

312 The Statistics of Rainfall Relations with Different Rain-drop Axis Ratios Because the occurrence frequencies of119885DRand 119870DP with different raindrop axis ratios were differentfrom each other the rainfall relations using those variablesshould be different with drop shape assumptions Table 2shows the rainfall relations obtained by using different rain-drop shape assumptions The coefficients of 119877(119885) were notsignificantly different with drop shape assumptions howeverthose of other relations were different with each drop shape

Table 3 shows the cross correlations (hereinafter CC) andRMSEs (root mean square errors) of rainfall relations 119877(119885)119877(119885DR) 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) obtained bycalculations using DSDs data with different raindrop shapes

The statistics of 119877(119885) and 119877(119885DR) were not significantlydifferent with raindrop shapesThe CC and RMSE of 119877(119885DR)and 119877(119885 119885DR) were the worst and the best among theother rainfall relations The statistics of 119877(119870DR) 119877(119885 119885DR)and 119877(119870DP 119885DR) were much more variable with differentraindrop axis ratios than the ones of 119877(119885) and 119877(119885DR) TheRMSEs of 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) with rain-drop shapes were distributed from 3030 to 3828mm 2965to 3523mm and 3151 to 5412mm respectivelyThe best per-formance of each relation occurred at DS3 for 119877(119885) DS1 for119877(119885DR) DS1 for 119877(119870DP) DS1 for 119877(119885 119885DR) and DS3 for119877(119870DP 119885DR)

In order to calculate more accurate 119877(119885 119885DR) and119877(119870DP 119885DR) the 119885 and 119885DR with the best performance werechosen Figure 6 shows the scatter plots of rainfall obtainedby DSDs and 119877(119885 119885DR) and 119877(119870DP 119885DR) using the beststatistics among raindrop axis ratio 119885 119885DR and 119870DP werechosen from DS3 DS1 and DS1 respectively Comparingwith 119877(119885 119885DR) and 119877(119870DP 119885DR) of single raindrop axisratio relations having the best performance new combinedrelations had better RMSE and CC The RMSEs of new rela-tions 119877(119885 119885DR) and 119877(119870DP 119885DR) had better score as muchas around 02mm and 06mm respectively Even though

8 Advances in Meteorology

Table 3 The correlation coefficients and RMSEs (mm) of rainfall obtained by rainfall relations and DSDs CC means cross correlation

DS 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) 119877(119870DP 119885DR)

CC RMSE CC RMSE CC RMSE CC RMSE CC RMSEDS1 0913 4705 0572 6241 0875 3030 0964 2965 0951 3313DS2 0913 4709 0569 6248 0861 3198 0956 3272 0956 3222DS3 0914 4704 0562 6261 0861 3178 0949 3523 0960 3151DS4 0913 4706 0569 6249 0828 3549 0954 3334 0931 3882DS5 0913 4706 0572 6243 0849 3326 0957 3210 0950 3348DS6 0913 4713 0572 6244 0795 3828 0956 3239 0814 5412

Table 4The rainfall relations NE RMSE and CC of each raindropaxis ratio relation

DropShape Relation NE RMSE CC

DS1119877(119870DP) = 445119870DP

0942 052 4996 082119877(119885 119885DR) = 001571198850889119885DR

minus494 031 4802 097119877(119870DP 119885DR) = 537119870DP

0857119885DRminus148 056 5262 088

DS2119877(119870DP) = 530119870DP

0913 052 4645 078119877(119885 119885DR) = 001411198850853119885DR

minus408 036 3793 073119877(119870DP 119885DR) = 752119870DP

0855119885DRminus198 060 5146 073

DS3119877(119870DP) = 615119870DP

0908 055 4698 078119877(119885 119885DR) = 001481198850818119885DR

minus372 043 4479 089119877(119870DP 119885DR) = 822119870DP

0855119885DRminus198 063 5247 073

DS4119877(119870DP) = 599119870DP

0896 054 4673 078119877(119885 119885DR) = 001361198850840119885DR

minus406 040 4134 089119877(119870DP 119885DR) = 674119870DP

0785119885DRminus213 060 5249 073

DS5119877(119870DP) = 562119870DP

0897 053 4625 078119877(119885 119885DR) = 001331198850861119885DR

minus431 037 3900 088119877(119870DP 119885DR) = 847119870DP

0840119885DRminus238 065 5390 071

DS6119877(119870DP) = 563119870DP

0857 054 4647 078119877(119885 119885DR) = 001251198850857119885DR

minus399 038 3967 089119877(119870DP 119885DR) = 150119870DP

0483119885DRminus077 065 7141 076

the CC and RMSE of 119877(119885) and 119877(119885DR) with different dropshapes were not significant the combined relations had betterperformance

32 Validations of Rainfall Relations with Different RaindropAxis Ratio Relations To investigate the performance ofrainfall relationsNE (normalized error) RMSE andCCwerecalculated using rainfall from each relation with six raindropshapes and that of gage rainfall

Table 4 summarizes the relations and the statistics suchas NE RMSE and CC The NEs and RMSEs of 119877(119870DR)calculated by each raindrop axis were distributed from 052 to055 and from 4625 to 4996 respectively The 119877(119870DR) withassumption of DS5 was the best score of RMSE in other rain-drop shapes In case of119877(119885 119885DR) the distribution ofNEs andRMSEs was from 031 to 043 and from 3793 to 4602 respec-tively The best RMSE score of 119877(119885 119885DR) was from DS2The NEs and RMSEs of 119877(119870DP 119885DR) occurred from 055 to065 and from 5146 to 7141 respectively The performance of

119877(119870DP 119885DR) was the worst score and 119877(119885 119885DR) had the bestscore in all raindrop axis ratio relations The performancesof validation were different from that of rainfall relationcalculation It would be caused by the variations of DSDs inthis study

To compare the performance between new combined119877(119870DP 119885DR) and 119877(119885 119885DR) the statistics were also calcu-lated Figure 7 shows the scatter plots rainfall from rainfallrelation and gage rainfall with some statistics The NEand RMSE of two relations from single raindrop shapeassumption showed better results However it seems that the119877(119885 119885DR)with two-raindrop axis ratio was more close to thegage rainfall in the range of weaker than 20mmh and the119877(119870DP 119885DR) with two drop shapes was more accurate in therainfall of higher than 20mmh

33 Rainfall Estimation Using Specific Attenuation331 Calculation of Specific Attenuation The 119860

119867can be

calculated from the radial profile of the attenuated reflectivity119885119886and the two-way PIA (Path Integrated Attenuation) along

the propagation path (1199031 1199032) proposed by Meneghini and

Nakamura [34]

119860 (119903) =119886 (119903) [119885119886]

119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(8)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

119886 (119904) [119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

119886 (119904) [119885119886 (119904)]119887119889119904

(9)

If 119886 is not dependent on range then (8) becomes

119860 (119903) =[119885119886]119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(10)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

[119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

[119885119886 (119904)]119887119889119904

(11)

119862 (119887PIA) = exp (023119887PIA) minus 1 (12)

Advances in Meteorology 9

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 036

RMSE = 3793

CC = 0888

Rada

r tot

alR

(ZZ

DR)

BC

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 060

RMSE = 5146

CC = 0732

Rada

r tot

alR

(KD

PZ

DR)

BC

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 032

RMSE = 5194

CC = 0818

Rada

r tot

alR

(ZZ

DR)

best

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 092

RMSE = 7302

CC = 0695

Rada

r tot

alR

(KD

PZ

DR)

best

(d)

Figure 7The scatter plot of rainfall from gage and (a) 119877(119885 119885DR) (b) 119877(119870DP 119885DR)with single raindrop axis ratio relation (c) 119877(119885 119885DR) and(d) 119877(119870DP 119885DR) with two-raindrop axis ratio relation

Bringi et al [35] recommended estimating PIA usingΦDPby

PIA (1199031 1199032) = 120572 [ΦDP (1199032) minusΦDP (1199031)] = 120572ΔΦDP (13)

and Testud et al [36] used (10) and (12) to obtain radialprofiles of 119860

119867at C-band In this study 119860

119867was calculated

by the method proposed by Ryzhkov et al [23] The constant

119887 was set by 06 and 120572 was by 0027 calculated by the ratio of119860119867to 119870DP obtained from DSDsFigure 8 shows the scatter plot of rainfall from 119877(119885)

119877(119870DP) and 119877(119860119867) and rainfall from DSDs and an PPIs

(Plan Position Indicators) at 05 degree elevation angle of gagerainfall and rainfall from 119877(119870DP) and 119877(119860

119867) at 0251 KST on

the 8th of August in 2011The 119877(119860

119867) relation had much better fit to the rainfall of

DSDs than that of119877(119870DP) and119877(119885) relation Comparingwith

10 Advances in Meteorology

Beard and Chuang 1987

Rain rate DSD (mmh)

R(Z

) (m

mh

)

10minus1

100

101

102

103

10minus1

100

101

102

103

R = 00277Z05994

NB = minus2122

RMSE = 4709

CC = 0913

(a)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

NB = minus1295136

RMSE = 3198

CC = 0861

R = 533039KDP091341

R(K

DP)

(mm

h)

(b)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(A

H)

(mm

h)

R = 337359AH10194

NB = 327

RMSE = 3667

CC = 0984

(c)

150100705040302015107310500

R(KDP) (mmh)

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(d)

R(AH) (mmh)

150100705040302015107310500

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(e)

Figure 8 The scatter plot of (a) 119877(119885) (b) 119877(119870DP) and (c) 119877(119860119867) with statistics and the rainfall distribution of 119877(119870DP) and 119877(119860

119867) at 0251

KST on the 8th of August in 2001

Advances in Meteorology 11

Table 5 The rainfall relations of 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assumptions

DS 119877(119885119870DP 119860119867) 119877(119885 119885DR 119870DP 119860119867)

DS1 119877 = 1527119885minus004119870DP0327

119860119867

0713119877 = 310Z012

119885DRminus083

119870DP0304

119860119867

0677

DS2 119877 = 12012119885minus024119870DP0551

119860119867

0685119877 = 4947Zminus015119885DR

minus026119870DP

0468119860119867

0681

DS3 119877 = 17211119885minus027119870DP0619

119860119867

0650119877 = 4502Z014

119885DRminus039

119870DP0486

119860119867

0653

DS4 119877 = 10798119885minus019119870DP0403

119860119867

0778119877 = 193Z018

119885DRminus111

119870DP0114

119860119867

0702

DS5 119877 = 20275119885minus027119870DP0543

119860119867

0720119877 = 24Z037

119885DRminus147

119870DPminus0025

119860119867

0656

DS6 119877 = 397119885minus011119870DP0044

119860119867

0808119877 = 571Z007

119885DRminus092

119870DP0238

119860119867

0687

the distribution of rainfall obtained by 119877(119870DP) and 119877(119860119867)

119877(119860119867) has better spatial resolution and more homogeneous

pattern than those of 119877(119870DP)

332 Validations of 119877(119860119867) 119877(119885119870

119863119875 119860119867) and 119877(119885 119885

119863119877

119870119863119875

119860119867) Relations As mentioned in the previous section

119877(119860119867) has the potential to be the best choice for estimating

rainfall using polarimetric variables To verify the accuracy119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) relations

were obtained and the accuracy of 119877(119860119867) 119877(119885119870DP 119860119867)

and 119877(119885 119885DR 119870DP 119860119867) which had the best performance inthe relations calculated by the six raindrop axis ratio relationswere examined by comparing with 119877(119870DP)

Figure 9 shows the scatter plot of rainfall from gagerainfall and 119877(119870DP) 119877(119860

119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR

119870DP 119860119867) for 84 hours The accuracy of 119877(119885 119885DR 119870DP 119860119867)was the best and119877(119885119870DP 119860119867)was the second in 4 relations119877(119860119867)was not better than 119877(119870DP) in whole range of rainfall

However in the range of higher rainfall it seems that 119877(119860119867)

was closer to the gage rainfall The error of 119877(119860119867) would be

caused by the missing radial profile ofΦDP along the rayThemissing has occurred if the difference of ΦDP between thestarting and end gate is negative According to the results119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) would compensatefor this region

34 Optimum Rainfall Algorithm To find out the optimumrainfall algorithm for Korean S-band polarimetric radar thegage rainfall amount was categorized by three steps 0 to5mmh assigned as light rain 5 to 30mmh as medium rainand higher than 30mmh as high rain In previous sectionthe relations have different accuracy not only for the raindropaxis ratio relation but also for rainfall amount The samplenumbers for each category were 3322 samples 1980 samplesand 92 samples respectively

Figure 10 shows the RMSEs of 119877(119870DP) 119877(119885 119885DR)119877(119870DP 119885DR) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) withdifferent rainfall categories defined in three steps All rela-tions have different RMSEs with respect to the raindrop axisratio relations 119877(119870DP) with DS3 119877(119885 119885DR) with DS2 and119877(119870DP 119885DR) with DS3 have the best score at the high rainfallregime at the low rainfall regime and at the medium rainfallregime respectively Even though 119877(119885 119885DR) has the bestperformance among other relations in total rainfall eventsusing different rainfall relations with different rainfall regimewould be an optimum rainfall algorithm for Korean S-band

polarimetric radar A possible optimum polarimetric rainfallalgorithm can be expressed by

119877 = 00141198850852119885DRminus408 0 lt Rainfall lt 5mmhminus1

119877 = 822119870DP0855

119885DRminus198

5 lt Rainfall lt 30mmhminus1

119877 = 615119870DP0908 30mmhminus1 lt Rainfall

(14)

Table 5 shows the rainfall relations of 119877(119885119870DP 119860119867) and119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assump-tions The coefficients of each relation with respect to thedrop shapes were much different comparing with relationsobtained by combining two polarimetric variables

In case of rainfall relations combined with119860119867 119877(119885 119885DR

119870DP 119860119867) has better score than 119877(119885119870DP 119860119867) Both119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with DS3 showedbetter result than other raindrop shape assumptions119877(119885 119885DR 119870DP 119860119867) at the low medium and high rainfallregimes has similar RMSE to 119877(119885 119885DR) 119877(119870DP 119885DR) and119877(119870DP) respectively

Equations (14) would be an optimum rainfall algorithmbut there is still a problem to solve how the rainfall categoriesare defined using radar and gage Gage does not have goodspatial resolution to cover radar resolution like 125m or 1 kmand each rainfall relation has its own error at certain rainfallregime Therefore 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867)withDS3 can be used regardless rainfall intensity And in case119885DR bias calibration is not available or does not have enoughquality for quantitative use 119877(119885119870DP 119860119867) with DS3 can beused as a representative rainfall estimation

4 Summary and Conclusions

Polarimetric radars will be main tools to monitor andforecast severe weather and flash flooding within severalyears in Korea To get an optimum rainfall algorithm usingpolarimetric variables observed from Bislsan radar which isthe first polarimetric radar in Korea rainfall cases for 84hours caused by different conditions which are Changmafront and typhoon Changma front only and typhoon onlythat occurred in 2011 were analyzed And rainfall relationswere obtained by using long period DSDs with six differentraindrop axis ratio relations

In the analysis of 119885 119885DR and119870DP occurrence frequencythere were two modes of 119885DR occurrence frequency and

12 Advances in Meteorology

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100Ra

dar t

otal

R(K

DP)

BC

NE = 052

RMSE = 4645

CC = 0778

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 051

RMSE = 5005

CC = 0797

Rada

r tot

al R

(AH

) AS

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100NE = 046

RMSE = 4374

CC = 0820

Rada

r tot

al R

(ZK

DPA

H) A

S

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 045

RMSE = 4368

CC = 0852

Rada

r tot

al R

(ZZ

DRK

DPA

H) A

S

(d)

Figure 9 The scatter plot of gage rainfall and 119877(119870DP) 119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DP 119870DP 119860119867) rainfall for 84 hours

the variations of 119870DP and 119885DR histograms were higherthan that of 119885 with raindrop ratio relations According tothese variations the combined relations of 119877(119885 119885DR) and119877(119870DP 119885DR) using 119885 with DS3 119885DR with DS1 and 119870DP withDS1 were closer to the rainfall of DSDs

To examine the performance of each rainfall relationNE RMSE CC were calculated using rainfall recorded at121 gages within radar coverage for 84 hours The statisticsof each rainfall relation were different with raindrop shape

assumptions and rainfall intensity119877(119870DP 119885DR)had theworstperformance and119877(119885 119885DR) had the best score in all raindropshapes 119860

119867was calculated by observed ΦDP and 119885 using the

method by Ryzhkov et al [23] and the rainfall relations using119860119867were also calculated and analyzedThe performance of rainfall relations were comparedwith

three different rainfall categories to findout an optimumrain-fall relation for the S-band polarimetric in Korea 119877(119885 119885DR)119877(119870DP 119885DR) and 119877(119870DP) had the best RMSE at the light

Advances in Meteorology 13

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP) with drop shape

(a)

0

5

10

15

20

Drop shape

25

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(Z ZDR) with drop shape

(b)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP ZDR) with drop shape

(c)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(ZKDP AH) with drop shape

(d)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

0ndash5mm5ndash30mmOver 30mm

RMSE of R(Z ZDR KDP AH) with drop shape

(e)

Figure 10The RMSEs of (a) 119877(119870DP) (b) 119877(119885 119885DP) (c) 119877(119870DP 119885DP) (d) 119877(119885119870DP 119860119867) and (e) 119877(119885 119885DP 119870DP 119860119867)with raindrop axis ratiorelations in the three rainfall categories

14 Advances in Meteorology

rain medium rain and high rainfall regimes respectively119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) showed relativelygood performance in all rainfall regimesThe combination of119877(119885 119885DR) 119877(119870DP 119885DR) and 119877(119870DP) with rainfall intensitywould be an optimum rainfall algorithm if the referenceof rainfall would be defined correctly Regardless of rainfallintensity 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) obtainedby assuming DS3 can be used as a representative rainfall rela-tion without consideration of rainfall intensity regime Par-ticularly if the qualified 119885DR is not available 119877(119885119870DP 119860119867)with DS3 drop shape assumption can be used as an optimumrainfall relation in Korea

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge providing radar data weatherchart and AWS data for this work from the Ministry ofLand Infrastructure Transport and Korea MeteorologicalAdministration The authors also acknowledge providingcodes for scattering simulation from Professor V N Bringi atColorado StateUniversityThisworkwas funded by theKoreaMeteorological Industry Promotion Agency under GrantKMIPA 2015-1050

References

[1] E Campos and I Zawadzki ldquoInstrumental uncertainties in Z-R relationsrdquo Journal of Applied Meteorology vol 39 no 7 pp1088ndash1102 2000

[2] C-H You D-I Lee S-M Jang et al ldquoCharacteristics ofrainfall systems accompanied with Changma front at Chujadoin Koreardquo Asia-Pacific Journal of Atmospheric Sciences vol 46no 1 pp 41ndash51 2010

[3] P CWaterman ldquoSymmetry unitarity and geometry in electro-magnetic scatteringrdquo Physical Review D vol 3 no 4 pp 825ndash839 1971

[4] M IMishchenko LD Travis andDWMackowski ldquoT-matrixcomputations of light scattering by nonspherical particles areviewrdquo Journal of Quantitative Spectroscopy and RadiativeTransfer vol 55 no 5 pp 535ndash575 1996

[5] H R Pruppacher and K V Beard ldquoA wind tunnel investigationof the internal circulation and shape of water drops fallingat terminal velocity in airrdquo Quarterly Journal of the RoyalMeteorological Society vol 96 no 408 pp 247ndash256 1970

[6] D C Blanchard ldquoThe behavior of water drops at terminalvelocity in airrdquo EOS vol 31 no 6 pp 836ndash842 1950

[7] G-J Huang V N Bringi M Schonhuber et al ldquoDrop shapeand canting angle distributions in rain from2-Dvideo disdrom-eterrdquo in Proceedings of the 33rd Conference on Radar Meteorol-ogy Extended Abstract P8A8 Cairns Australia August 2007

[8] M Thurai V N Bringi and W A Petersen ldquoRain microstruc-ture retrievals using 2-D video disdrometer and C-band polari-metric radarrdquo Advances in Geosciences vol 20 pp 13ndash18 2009

[9] K V Beard and C Chuang ldquoA new model for the equilibriumshape of raindropsrdquo Journal of the Atmospheric Sciences vol 44pp 1509ndash1524 1987

[10] K Andsager K V Beard and N S Laird ldquoA laboratory studyof oscillations and axis ratios for large raindropsrdquo Journal of theAtmospheric Sciences vol 55 pp 208ndash226 1999

[11] J W Wilson and E A Brandes ldquoRadar measurement of rain-fallmdasha summaryrdquo Bulletin AmericanMeteorological Society vol60 no 9 pp 1048ndash1058 1979

[12] P M Austin ldquoRelation betweenmeasured radar reflectivity andsurface rainfallrdquo Monthly Weather Review vol 115 no 5 pp1053ndash1070 1987

[13] J Vivekanandan D S Zrnic S M Ellis R Oye A V Ryzhkovand J Straka ldquoCloud microphysics retrieval using S-band dual-polarization radar measurementsrdquo Bulletin of the AmericanMeteorological Society vol 80 no 3 pp 381ndash388 1999

[14] A V Ryzhkov and D S Zrnic ldquoDiscrimination between rainand snow with a polarimetric radarrdquo Journal of Applied Meteo-rology vol 37 no 10 pp 1228ndash1240 1998

[15] S E Giangrande and A V Ryzhkov ldquoEstimation of rainfallbased on the results of polarimetric echo classificationrdquo Journalof AppliedMeteorology and Climatology vol 47 no 9 pp 2445ndash2462 2008

[16] A V Ryzhkov and D S Zrnic ldquoAssessment of rainfall measure-ment that uses specific differential phaserdquo Journal of AppliedMeteorology vol 35 no 11 pp 2080ndash2090 1996

[17] P T May T D Keenan D S Zrnic L D Carey and S ARutledge ldquoPolarimetric radar measurements of tropical rain ata 5-cm wavelengthrdquo Journal of Applied Meteorology vol 38 no6 pp 750ndash765 1999

[18] V N Bringi and V Chandrasekar ldquoThe polarimetric basis forcharacterizing precipitationrdquo in Polarimetric Doppler WeatherRadar Principles and Applications pp 378ndash533 CambridgeUniversity Press Cambridge UK 2001

[19] E A Brandes G Zhang and J Vivekanandan ldquoExperiments inrainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[20] A V Ryzhkov T J Schuur D W Burgess P L Heinselman SE Giangrande and D S Zrnic ldquoThe joint polarization exper-iment polarimetric rainfall measurements and hydrometeorclassificationrdquo Bulletin of the American Meteorological Societyvol 86 no 6 pp 809ndash824 2005

[21] A V Ryzhkov S E Giangrande and T J Schuur ldquoRainfall esti-mation with a polarimetric prototype of WSR-88Drdquo Journal ofApplied Meteorology vol 44 no 4 pp 502ndash515 2005

[22] R Cifelli V Chandrasekar S Lim P C Kennedy Y Wang andS A Rutledge ldquoA new dual-polarization radar rainfall algo-rithm application in Colorado precipitation eventsrdquo Journal ofAtmospheric andOceanic Technology vol 28 no 3 pp 352ndash3642011

[23] A Ryzhkov M Diederich P Zhang and C Simmer ldquoPotentialutilization of specific attenuation for rainfall estimationmitiga-tion of partial beam blockage and radar networkingrdquo Journal ofAtmospheric and Oceanic Technology vol 31 no 3 pp 599ndash6192014

[24] C-H You M-Y Kang D-I Lee and H Uyeda ldquoRainfallestimation by S-band polarimetric radar in Korea Part Ipreprocessing and preliminary resultsrdquoMeteorological Applica-tions vol 21 no 4 pp 975ndash983 2014

[25] C-H You D-I Lee andM-Y Kang ldquoRainfall estimation usingspecific differential phase for the first operational polarimetricradar in Koreardquo Advances in Meteorology vol 2014 Article ID413717 10 pages 2014

Advances in Meteorology 15

[26] V N Bringi V Chandrasekar J Hubbert E Gorgucci W LRandeu and M Schoenhuber ldquoRaindrop size distribution indifferent climatic regimes from disdrometer and dual-polarizedradar analysisrdquo Journal of the Atmospheric Sciences vol 60 no2 pp 354ndash365 2003

[27] E A Brandes G Zhang and J Vivekanandan ldquoExperimentsin rainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[28] K V Beard and R J Kubesh ldquoLaboratory measurements ofsmall raindrop distortion Part 2 oscillation frequencies andmodesrdquo Journal of the Atmospheric Sciences vol 48 no 20 pp2245ndash2264 1991

[29] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[30] J W F Goddard K L Morgan A Illingworth and HSauvageot ldquoDual-wavelength polarization measurements inprecipitation using the CAMRA and Rabelias radarsrdquo in Pro-ceedings of the 27th Conference on Radar Meteorology pp 196ndash198 American Meteorology Society Vail Colo USA 1995

[31] A V Ryzhkov D S Zrnic J C Hubbert V N Bringi JVivekanandan and E A Brandes ldquoPolarimetric radar obser-vations and interpretation of co-cross-polar correlation coeffi-cientsrdquo Journal of Atmospheric and Oceanic Technology vol 19no 3 pp 340ndash354 2002

[32] S YMatrosov KAClark B EMartner andA Tokay ldquoX-bandpolarimetric radar measurements of rainfallrdquo Journal of AppliedMeteorology vol 41 no 9 pp 941ndash952 2002

[33] G-J Huang V N Bringi and M Thurai ldquoOrientation angledistributions of drops after an 80-m fall using a 2D videodisdrometerrdquo Journal of Atmospheric and Oceanic Technologyvol 25 no 9 pp 1717ndash1723 2008

[34] R Meneghini and K Nakamura ldquoRange profiling of the rainrate by an airborne weather radarrdquo Remote Sensing of Environ-ment vol 31 no 3 pp 193ndash209 1990

[35] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onpolarimetric variables at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[36] J Testud E L Bouar E Obligis and M Ali-Mehenni ldquoTherain profiling algorithm applied to polarimetric weather radarrdquoJournal of Atmospheric andOceanic Technology vol 17 no 3 pp332ndash356 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

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Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

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MineralogyInternational Journal of

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MeteorologyAdvances in

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Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

6 Advances in Meteorology

Beard and Chuang 1987

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Standard

Average 2620deviation 838

(a)

Andsager et al 1999

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Standard

Average 2616deviation 837

(b)

0 10 20 30 40 50Z (dBZ)

000

001

002

003

004

Freq

uenc

y

Goddard et al 1995

Standard

Average 2616deviation 839

(c)

Freq

uenc

y

Beard and Chuang 1987

00 05 10 15 20 25 30 35000002004006008010012014

Standard deviation 063Average 091

ZDR (dB)

(d)

Andsager et al 1999

Standard deviation 061Average 080

Freq

uenc

y

00 05 10 15 20 25 30 35000002004006008010012014

ZDR (dB)

(e)

Goddard et al 1995

Standard deviation 066Average 082

Freq

uenc

y

00 05 10 15 20 25 30 35000002004006008010012014

ZDR (dB)

(f)

Freq

uenc

y

Beard and Chuang 1987

000 005 010 015 020000

010

020

030

040

050Standard deviation 0107

Average 0037

KDP (degkm)

(g)

Freq

uenc

y

000 005 010 015 020000

010

020

030

040

050

KDP (degkm)

Andsager et al 1999

Standard deviation 0092Average 0031

(h)

Freq

uenc

y

000 005 010 015 020000

010

020

030

040

050

KDP (degkm)

Goddard et al 1995

Standard deviation 0096Average 0030

(i)

Figure 5 The occurrence frequency of (a) 119885 with DS1 (b) 119885 with DS3 (c) 119885 with DS6 (d) 119885DR with DS1 (e) 119885DR with DS3 (f) 119885DR withDS6 (g) 119870DP with DS1 (h) 119870DP with DS3 and (i) 119870DP with DS6

RMSE = [1119873

119873

sum

119894=1(119877119877119894

minus119877119866119894

)2]

12

CC =

sum119873

119894=1 (119877119877119894

minus 119877119877) (119877119866119894

minus 119877119866)

[sum119873

119894=1 (119877119877119894

minus 119877119877)2]

12[sum119873

119894=1 (119877119866119894

minus 119877119866)2]

12

(7)

where 119873 is the number of the RR and RG pairs and 119877119877and

119877119866are the averaged rain rate of radar and gage for an hour

respectively The above statistical variables are calculatedusing 1-hour rainfall amount of radar and gage at the pointThe point rainfall of radar was obtained by averaging rainfallover a small area (1 km times 1∘) centered on each rain gage

3 Results

31 Rainfall Relations with Different Raindrop Axis Ratios

311 The Characteristics of 119885 119885119863119877

and 119870119863119875

with DifferentDrop Shapes The histograms of occurrence frequency forpolarimetric variables 119885 119885DR and 119870DP calculated by DSDsdata for 4 years in Busan with different raindrop axis ratiorelations DS1 DS3 and DS6 were shown in Figure 5

The averages and modes of 119885 were around 262 dBZ and32sim33 dBZ for all raindrop axis assumptions (Figures 5(a)sim5(c)) It means that the reflectivity is not sensitive to the dropaxis relation In case of 119885DR there were two modes of occur-rence for all cases The averages and standard deviation ofeach relation were 063 dB and 091 dB for DS1 061 dB and08 dB for DS3 and 066 dB and 082 dB for DS6The low and

Advances in Meteorology 7

Table 2 The rainfall relations of 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) with different raindrop shape assumptions

DS 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) 119877(119870DP 119885DR)

DS1 R = 00273119885060 R = 029119885DR527 R = 445119870DP

0942 R = 00161198850889119885DRminus494 R = 537119870DP

0857119885DRminus148

DS2 R = 00277119885059 R = 038119885DR487 R = 533119870DP

0913 R = 00141198850852119885DRminus408 R = 752119870DP

0855119885DRminus198

DS3 R = 00277119885060 R = 042119885DR498 R = 615119870DP

0908 R = 00151198850818119885DRminus372 R = 822119870DP

0855119885DRminus198

DS4 R = 00277119885060 R = 041119885DR498 R = 599119870DP

0896 R = 00141198850844119885DRminus406 R = 674119870DP

0785119885DRminus213

DS5 R = 00277119885060 R = 040119885DR503 R = 562119870DP

0897 R = 00131198850861119885DRminus43 R = 847119870DP

0840119885DRminus238

DS6 R = 00280119885059 R = 043119885DR469 R = 563119870DP

0857 R = 00131198850857119885DRminus40 R = 150119870DP

0483119885DRminus077

R(Z

ZD

R)

(mm

h)

R = 001589085Z08927

ZDRminus49936

NB = 1300

RMSE = 2776

CC = 0965

R (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

(a)

R = 13428687294KDP08991

ZDRminus26757

NB = 188

RMSE = 2593

CC = 0967

R (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(K

DPZ

DR)

(mm

h)

(b)

Figure 6 The scatter plots of rainfall obtained by DSDs and (a) 119877(119885 119885DR) and (b) 119877(119870DP 119885DR) using 119885 for DS3 119885DR for DS1 and 119870DP forDS3

high modes of 119885DR with DS1 DS3 and DS6 were 02sim03 dBand 17sim18 dB 02sim03 dB and 16sim17 dB and 00sim01 dB and17sim18 dB respectively The occurrence frequencies of lowmode for each raindrop axis ratio were significantly differentfrom each other (Figures 5(d)sim5(f)) The averages and stan-dard deviation of119870DPwith different raindrop shapeswere 011and 004 009 and 003 and 01 and 003 respectively Themodes of all drop shapes were the same but the occurrencefrequencies were different (Figures 5(g)sim5(i))

312 The Statistics of Rainfall Relations with Different Rain-drop Axis Ratios Because the occurrence frequencies of119885DRand 119870DP with different raindrop axis ratios were differentfrom each other the rainfall relations using those variablesshould be different with drop shape assumptions Table 2shows the rainfall relations obtained by using different rain-drop shape assumptions The coefficients of 119877(119885) were notsignificantly different with drop shape assumptions howeverthose of other relations were different with each drop shape

Table 3 shows the cross correlations (hereinafter CC) andRMSEs (root mean square errors) of rainfall relations 119877(119885)119877(119885DR) 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) obtained bycalculations using DSDs data with different raindrop shapes

The statistics of 119877(119885) and 119877(119885DR) were not significantlydifferent with raindrop shapesThe CC and RMSE of 119877(119885DR)and 119877(119885 119885DR) were the worst and the best among theother rainfall relations The statistics of 119877(119870DR) 119877(119885 119885DR)and 119877(119870DP 119885DR) were much more variable with differentraindrop axis ratios than the ones of 119877(119885) and 119877(119885DR) TheRMSEs of 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) with rain-drop shapes were distributed from 3030 to 3828mm 2965to 3523mm and 3151 to 5412mm respectivelyThe best per-formance of each relation occurred at DS3 for 119877(119885) DS1 for119877(119885DR) DS1 for 119877(119870DP) DS1 for 119877(119885 119885DR) and DS3 for119877(119870DP 119885DR)

In order to calculate more accurate 119877(119885 119885DR) and119877(119870DP 119885DR) the 119885 and 119885DR with the best performance werechosen Figure 6 shows the scatter plots of rainfall obtainedby DSDs and 119877(119885 119885DR) and 119877(119870DP 119885DR) using the beststatistics among raindrop axis ratio 119885 119885DR and 119870DP werechosen from DS3 DS1 and DS1 respectively Comparingwith 119877(119885 119885DR) and 119877(119870DP 119885DR) of single raindrop axisratio relations having the best performance new combinedrelations had better RMSE and CC The RMSEs of new rela-tions 119877(119885 119885DR) and 119877(119870DP 119885DR) had better score as muchas around 02mm and 06mm respectively Even though

8 Advances in Meteorology

Table 3 The correlation coefficients and RMSEs (mm) of rainfall obtained by rainfall relations and DSDs CC means cross correlation

DS 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) 119877(119870DP 119885DR)

CC RMSE CC RMSE CC RMSE CC RMSE CC RMSEDS1 0913 4705 0572 6241 0875 3030 0964 2965 0951 3313DS2 0913 4709 0569 6248 0861 3198 0956 3272 0956 3222DS3 0914 4704 0562 6261 0861 3178 0949 3523 0960 3151DS4 0913 4706 0569 6249 0828 3549 0954 3334 0931 3882DS5 0913 4706 0572 6243 0849 3326 0957 3210 0950 3348DS6 0913 4713 0572 6244 0795 3828 0956 3239 0814 5412

Table 4The rainfall relations NE RMSE and CC of each raindropaxis ratio relation

DropShape Relation NE RMSE CC

DS1119877(119870DP) = 445119870DP

0942 052 4996 082119877(119885 119885DR) = 001571198850889119885DR

minus494 031 4802 097119877(119870DP 119885DR) = 537119870DP

0857119885DRminus148 056 5262 088

DS2119877(119870DP) = 530119870DP

0913 052 4645 078119877(119885 119885DR) = 001411198850853119885DR

minus408 036 3793 073119877(119870DP 119885DR) = 752119870DP

0855119885DRminus198 060 5146 073

DS3119877(119870DP) = 615119870DP

0908 055 4698 078119877(119885 119885DR) = 001481198850818119885DR

minus372 043 4479 089119877(119870DP 119885DR) = 822119870DP

0855119885DRminus198 063 5247 073

DS4119877(119870DP) = 599119870DP

0896 054 4673 078119877(119885 119885DR) = 001361198850840119885DR

minus406 040 4134 089119877(119870DP 119885DR) = 674119870DP

0785119885DRminus213 060 5249 073

DS5119877(119870DP) = 562119870DP

0897 053 4625 078119877(119885 119885DR) = 001331198850861119885DR

minus431 037 3900 088119877(119870DP 119885DR) = 847119870DP

0840119885DRminus238 065 5390 071

DS6119877(119870DP) = 563119870DP

0857 054 4647 078119877(119885 119885DR) = 001251198850857119885DR

minus399 038 3967 089119877(119870DP 119885DR) = 150119870DP

0483119885DRminus077 065 7141 076

the CC and RMSE of 119877(119885) and 119877(119885DR) with different dropshapes were not significant the combined relations had betterperformance

32 Validations of Rainfall Relations with Different RaindropAxis Ratio Relations To investigate the performance ofrainfall relationsNE (normalized error) RMSE andCCwerecalculated using rainfall from each relation with six raindropshapes and that of gage rainfall

Table 4 summarizes the relations and the statistics suchas NE RMSE and CC The NEs and RMSEs of 119877(119870DR)calculated by each raindrop axis were distributed from 052 to055 and from 4625 to 4996 respectively The 119877(119870DR) withassumption of DS5 was the best score of RMSE in other rain-drop shapes In case of119877(119885 119885DR) the distribution ofNEs andRMSEs was from 031 to 043 and from 3793 to 4602 respec-tively The best RMSE score of 119877(119885 119885DR) was from DS2The NEs and RMSEs of 119877(119870DP 119885DR) occurred from 055 to065 and from 5146 to 7141 respectively The performance of

119877(119870DP 119885DR) was the worst score and 119877(119885 119885DR) had the bestscore in all raindrop axis ratio relations The performancesof validation were different from that of rainfall relationcalculation It would be caused by the variations of DSDs inthis study

To compare the performance between new combined119877(119870DP 119885DR) and 119877(119885 119885DR) the statistics were also calcu-lated Figure 7 shows the scatter plots rainfall from rainfallrelation and gage rainfall with some statistics The NEand RMSE of two relations from single raindrop shapeassumption showed better results However it seems that the119877(119885 119885DR)with two-raindrop axis ratio was more close to thegage rainfall in the range of weaker than 20mmh and the119877(119870DP 119885DR) with two drop shapes was more accurate in therainfall of higher than 20mmh

33 Rainfall Estimation Using Specific Attenuation331 Calculation of Specific Attenuation The 119860

119867can be

calculated from the radial profile of the attenuated reflectivity119885119886and the two-way PIA (Path Integrated Attenuation) along

the propagation path (1199031 1199032) proposed by Meneghini and

Nakamura [34]

119860 (119903) =119886 (119903) [119885119886]

119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(8)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

119886 (119904) [119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

119886 (119904) [119885119886 (119904)]119887119889119904

(9)

If 119886 is not dependent on range then (8) becomes

119860 (119903) =[119885119886]119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(10)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

[119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

[119885119886 (119904)]119887119889119904

(11)

119862 (119887PIA) = exp (023119887PIA) minus 1 (12)

Advances in Meteorology 9

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 036

RMSE = 3793

CC = 0888

Rada

r tot

alR

(ZZ

DR)

BC

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 060

RMSE = 5146

CC = 0732

Rada

r tot

alR

(KD

PZ

DR)

BC

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 032

RMSE = 5194

CC = 0818

Rada

r tot

alR

(ZZ

DR)

best

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 092

RMSE = 7302

CC = 0695

Rada

r tot

alR

(KD

PZ

DR)

best

(d)

Figure 7The scatter plot of rainfall from gage and (a) 119877(119885 119885DR) (b) 119877(119870DP 119885DR)with single raindrop axis ratio relation (c) 119877(119885 119885DR) and(d) 119877(119870DP 119885DR) with two-raindrop axis ratio relation

Bringi et al [35] recommended estimating PIA usingΦDPby

PIA (1199031 1199032) = 120572 [ΦDP (1199032) minusΦDP (1199031)] = 120572ΔΦDP (13)

and Testud et al [36] used (10) and (12) to obtain radialprofiles of 119860

119867at C-band In this study 119860

119867was calculated

by the method proposed by Ryzhkov et al [23] The constant

119887 was set by 06 and 120572 was by 0027 calculated by the ratio of119860119867to 119870DP obtained from DSDsFigure 8 shows the scatter plot of rainfall from 119877(119885)

119877(119870DP) and 119877(119860119867) and rainfall from DSDs and an PPIs

(Plan Position Indicators) at 05 degree elevation angle of gagerainfall and rainfall from 119877(119870DP) and 119877(119860

119867) at 0251 KST on

the 8th of August in 2011The 119877(119860

119867) relation had much better fit to the rainfall of

DSDs than that of119877(119870DP) and119877(119885) relation Comparingwith

10 Advances in Meteorology

Beard and Chuang 1987

Rain rate DSD (mmh)

R(Z

) (m

mh

)

10minus1

100

101

102

103

10minus1

100

101

102

103

R = 00277Z05994

NB = minus2122

RMSE = 4709

CC = 0913

(a)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

NB = minus1295136

RMSE = 3198

CC = 0861

R = 533039KDP091341

R(K

DP)

(mm

h)

(b)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(A

H)

(mm

h)

R = 337359AH10194

NB = 327

RMSE = 3667

CC = 0984

(c)

150100705040302015107310500

R(KDP) (mmh)

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(d)

R(AH) (mmh)

150100705040302015107310500

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(e)

Figure 8 The scatter plot of (a) 119877(119885) (b) 119877(119870DP) and (c) 119877(119860119867) with statistics and the rainfall distribution of 119877(119870DP) and 119877(119860

119867) at 0251

KST on the 8th of August in 2001

Advances in Meteorology 11

Table 5 The rainfall relations of 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assumptions

DS 119877(119885119870DP 119860119867) 119877(119885 119885DR 119870DP 119860119867)

DS1 119877 = 1527119885minus004119870DP0327

119860119867

0713119877 = 310Z012

119885DRminus083

119870DP0304

119860119867

0677

DS2 119877 = 12012119885minus024119870DP0551

119860119867

0685119877 = 4947Zminus015119885DR

minus026119870DP

0468119860119867

0681

DS3 119877 = 17211119885minus027119870DP0619

119860119867

0650119877 = 4502Z014

119885DRminus039

119870DP0486

119860119867

0653

DS4 119877 = 10798119885minus019119870DP0403

119860119867

0778119877 = 193Z018

119885DRminus111

119870DP0114

119860119867

0702

DS5 119877 = 20275119885minus027119870DP0543

119860119867

0720119877 = 24Z037

119885DRminus147

119870DPminus0025

119860119867

0656

DS6 119877 = 397119885minus011119870DP0044

119860119867

0808119877 = 571Z007

119885DRminus092

119870DP0238

119860119867

0687

the distribution of rainfall obtained by 119877(119870DP) and 119877(119860119867)

119877(119860119867) has better spatial resolution and more homogeneous

pattern than those of 119877(119870DP)

332 Validations of 119877(119860119867) 119877(119885119870

119863119875 119860119867) and 119877(119885 119885

119863119877

119870119863119875

119860119867) Relations As mentioned in the previous section

119877(119860119867) has the potential to be the best choice for estimating

rainfall using polarimetric variables To verify the accuracy119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) relations

were obtained and the accuracy of 119877(119860119867) 119877(119885119870DP 119860119867)

and 119877(119885 119885DR 119870DP 119860119867) which had the best performance inthe relations calculated by the six raindrop axis ratio relationswere examined by comparing with 119877(119870DP)

Figure 9 shows the scatter plot of rainfall from gagerainfall and 119877(119870DP) 119877(119860

119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR

119870DP 119860119867) for 84 hours The accuracy of 119877(119885 119885DR 119870DP 119860119867)was the best and119877(119885119870DP 119860119867)was the second in 4 relations119877(119860119867)was not better than 119877(119870DP) in whole range of rainfall

However in the range of higher rainfall it seems that 119877(119860119867)

was closer to the gage rainfall The error of 119877(119860119867) would be

caused by the missing radial profile ofΦDP along the rayThemissing has occurred if the difference of ΦDP between thestarting and end gate is negative According to the results119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) would compensatefor this region

34 Optimum Rainfall Algorithm To find out the optimumrainfall algorithm for Korean S-band polarimetric radar thegage rainfall amount was categorized by three steps 0 to5mmh assigned as light rain 5 to 30mmh as medium rainand higher than 30mmh as high rain In previous sectionthe relations have different accuracy not only for the raindropaxis ratio relation but also for rainfall amount The samplenumbers for each category were 3322 samples 1980 samplesand 92 samples respectively

Figure 10 shows the RMSEs of 119877(119870DP) 119877(119885 119885DR)119877(119870DP 119885DR) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) withdifferent rainfall categories defined in three steps All rela-tions have different RMSEs with respect to the raindrop axisratio relations 119877(119870DP) with DS3 119877(119885 119885DR) with DS2 and119877(119870DP 119885DR) with DS3 have the best score at the high rainfallregime at the low rainfall regime and at the medium rainfallregime respectively Even though 119877(119885 119885DR) has the bestperformance among other relations in total rainfall eventsusing different rainfall relations with different rainfall regimewould be an optimum rainfall algorithm for Korean S-band

polarimetric radar A possible optimum polarimetric rainfallalgorithm can be expressed by

119877 = 00141198850852119885DRminus408 0 lt Rainfall lt 5mmhminus1

119877 = 822119870DP0855

119885DRminus198

5 lt Rainfall lt 30mmhminus1

119877 = 615119870DP0908 30mmhminus1 lt Rainfall

(14)

Table 5 shows the rainfall relations of 119877(119885119870DP 119860119867) and119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assump-tions The coefficients of each relation with respect to thedrop shapes were much different comparing with relationsobtained by combining two polarimetric variables

In case of rainfall relations combined with119860119867 119877(119885 119885DR

119870DP 119860119867) has better score than 119877(119885119870DP 119860119867) Both119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with DS3 showedbetter result than other raindrop shape assumptions119877(119885 119885DR 119870DP 119860119867) at the low medium and high rainfallregimes has similar RMSE to 119877(119885 119885DR) 119877(119870DP 119885DR) and119877(119870DP) respectively

Equations (14) would be an optimum rainfall algorithmbut there is still a problem to solve how the rainfall categoriesare defined using radar and gage Gage does not have goodspatial resolution to cover radar resolution like 125m or 1 kmand each rainfall relation has its own error at certain rainfallregime Therefore 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867)withDS3 can be used regardless rainfall intensity And in case119885DR bias calibration is not available or does not have enoughquality for quantitative use 119877(119885119870DP 119860119867) with DS3 can beused as a representative rainfall estimation

4 Summary and Conclusions

Polarimetric radars will be main tools to monitor andforecast severe weather and flash flooding within severalyears in Korea To get an optimum rainfall algorithm usingpolarimetric variables observed from Bislsan radar which isthe first polarimetric radar in Korea rainfall cases for 84hours caused by different conditions which are Changmafront and typhoon Changma front only and typhoon onlythat occurred in 2011 were analyzed And rainfall relationswere obtained by using long period DSDs with six differentraindrop axis ratio relations

In the analysis of 119885 119885DR and119870DP occurrence frequencythere were two modes of 119885DR occurrence frequency and

12 Advances in Meteorology

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100Ra

dar t

otal

R(K

DP)

BC

NE = 052

RMSE = 4645

CC = 0778

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 051

RMSE = 5005

CC = 0797

Rada

r tot

al R

(AH

) AS

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100NE = 046

RMSE = 4374

CC = 0820

Rada

r tot

al R

(ZK

DPA

H) A

S

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 045

RMSE = 4368

CC = 0852

Rada

r tot

al R

(ZZ

DRK

DPA

H) A

S

(d)

Figure 9 The scatter plot of gage rainfall and 119877(119870DP) 119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DP 119870DP 119860119867) rainfall for 84 hours

the variations of 119870DP and 119885DR histograms were higherthan that of 119885 with raindrop ratio relations According tothese variations the combined relations of 119877(119885 119885DR) and119877(119870DP 119885DR) using 119885 with DS3 119885DR with DS1 and 119870DP withDS1 were closer to the rainfall of DSDs

To examine the performance of each rainfall relationNE RMSE CC were calculated using rainfall recorded at121 gages within radar coverage for 84 hours The statisticsof each rainfall relation were different with raindrop shape

assumptions and rainfall intensity119877(119870DP 119885DR)had theworstperformance and119877(119885 119885DR) had the best score in all raindropshapes 119860

119867was calculated by observed ΦDP and 119885 using the

method by Ryzhkov et al [23] and the rainfall relations using119860119867were also calculated and analyzedThe performance of rainfall relations were comparedwith

three different rainfall categories to findout an optimumrain-fall relation for the S-band polarimetric in Korea 119877(119885 119885DR)119877(119870DP 119885DR) and 119877(119870DP) had the best RMSE at the light

Advances in Meteorology 13

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP) with drop shape

(a)

0

5

10

15

20

Drop shape

25

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(Z ZDR) with drop shape

(b)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP ZDR) with drop shape

(c)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(ZKDP AH) with drop shape

(d)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

0ndash5mm5ndash30mmOver 30mm

RMSE of R(Z ZDR KDP AH) with drop shape

(e)

Figure 10The RMSEs of (a) 119877(119870DP) (b) 119877(119885 119885DP) (c) 119877(119870DP 119885DP) (d) 119877(119885119870DP 119860119867) and (e) 119877(119885 119885DP 119870DP 119860119867)with raindrop axis ratiorelations in the three rainfall categories

14 Advances in Meteorology

rain medium rain and high rainfall regimes respectively119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) showed relativelygood performance in all rainfall regimesThe combination of119877(119885 119885DR) 119877(119870DP 119885DR) and 119877(119870DP) with rainfall intensitywould be an optimum rainfall algorithm if the referenceof rainfall would be defined correctly Regardless of rainfallintensity 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) obtainedby assuming DS3 can be used as a representative rainfall rela-tion without consideration of rainfall intensity regime Par-ticularly if the qualified 119885DR is not available 119877(119885119870DP 119860119867)with DS3 drop shape assumption can be used as an optimumrainfall relation in Korea

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge providing radar data weatherchart and AWS data for this work from the Ministry ofLand Infrastructure Transport and Korea MeteorologicalAdministration The authors also acknowledge providingcodes for scattering simulation from Professor V N Bringi atColorado StateUniversityThisworkwas funded by theKoreaMeteorological Industry Promotion Agency under GrantKMIPA 2015-1050

References

[1] E Campos and I Zawadzki ldquoInstrumental uncertainties in Z-R relationsrdquo Journal of Applied Meteorology vol 39 no 7 pp1088ndash1102 2000

[2] C-H You D-I Lee S-M Jang et al ldquoCharacteristics ofrainfall systems accompanied with Changma front at Chujadoin Koreardquo Asia-Pacific Journal of Atmospheric Sciences vol 46no 1 pp 41ndash51 2010

[3] P CWaterman ldquoSymmetry unitarity and geometry in electro-magnetic scatteringrdquo Physical Review D vol 3 no 4 pp 825ndash839 1971

[4] M IMishchenko LD Travis andDWMackowski ldquoT-matrixcomputations of light scattering by nonspherical particles areviewrdquo Journal of Quantitative Spectroscopy and RadiativeTransfer vol 55 no 5 pp 535ndash575 1996

[5] H R Pruppacher and K V Beard ldquoA wind tunnel investigationof the internal circulation and shape of water drops fallingat terminal velocity in airrdquo Quarterly Journal of the RoyalMeteorological Society vol 96 no 408 pp 247ndash256 1970

[6] D C Blanchard ldquoThe behavior of water drops at terminalvelocity in airrdquo EOS vol 31 no 6 pp 836ndash842 1950

[7] G-J Huang V N Bringi M Schonhuber et al ldquoDrop shapeand canting angle distributions in rain from2-Dvideo disdrom-eterrdquo in Proceedings of the 33rd Conference on Radar Meteorol-ogy Extended Abstract P8A8 Cairns Australia August 2007

[8] M Thurai V N Bringi and W A Petersen ldquoRain microstruc-ture retrievals using 2-D video disdrometer and C-band polari-metric radarrdquo Advances in Geosciences vol 20 pp 13ndash18 2009

[9] K V Beard and C Chuang ldquoA new model for the equilibriumshape of raindropsrdquo Journal of the Atmospheric Sciences vol 44pp 1509ndash1524 1987

[10] K Andsager K V Beard and N S Laird ldquoA laboratory studyof oscillations and axis ratios for large raindropsrdquo Journal of theAtmospheric Sciences vol 55 pp 208ndash226 1999

[11] J W Wilson and E A Brandes ldquoRadar measurement of rain-fallmdasha summaryrdquo Bulletin AmericanMeteorological Society vol60 no 9 pp 1048ndash1058 1979

[12] P M Austin ldquoRelation betweenmeasured radar reflectivity andsurface rainfallrdquo Monthly Weather Review vol 115 no 5 pp1053ndash1070 1987

[13] J Vivekanandan D S Zrnic S M Ellis R Oye A V Ryzhkovand J Straka ldquoCloud microphysics retrieval using S-band dual-polarization radar measurementsrdquo Bulletin of the AmericanMeteorological Society vol 80 no 3 pp 381ndash388 1999

[14] A V Ryzhkov and D S Zrnic ldquoDiscrimination between rainand snow with a polarimetric radarrdquo Journal of Applied Meteo-rology vol 37 no 10 pp 1228ndash1240 1998

[15] S E Giangrande and A V Ryzhkov ldquoEstimation of rainfallbased on the results of polarimetric echo classificationrdquo Journalof AppliedMeteorology and Climatology vol 47 no 9 pp 2445ndash2462 2008

[16] A V Ryzhkov and D S Zrnic ldquoAssessment of rainfall measure-ment that uses specific differential phaserdquo Journal of AppliedMeteorology vol 35 no 11 pp 2080ndash2090 1996

[17] P T May T D Keenan D S Zrnic L D Carey and S ARutledge ldquoPolarimetric radar measurements of tropical rain ata 5-cm wavelengthrdquo Journal of Applied Meteorology vol 38 no6 pp 750ndash765 1999

[18] V N Bringi and V Chandrasekar ldquoThe polarimetric basis forcharacterizing precipitationrdquo in Polarimetric Doppler WeatherRadar Principles and Applications pp 378ndash533 CambridgeUniversity Press Cambridge UK 2001

[19] E A Brandes G Zhang and J Vivekanandan ldquoExperiments inrainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[20] A V Ryzhkov T J Schuur D W Burgess P L Heinselman SE Giangrande and D S Zrnic ldquoThe joint polarization exper-iment polarimetric rainfall measurements and hydrometeorclassificationrdquo Bulletin of the American Meteorological Societyvol 86 no 6 pp 809ndash824 2005

[21] A V Ryzhkov S E Giangrande and T J Schuur ldquoRainfall esti-mation with a polarimetric prototype of WSR-88Drdquo Journal ofApplied Meteorology vol 44 no 4 pp 502ndash515 2005

[22] R Cifelli V Chandrasekar S Lim P C Kennedy Y Wang andS A Rutledge ldquoA new dual-polarization radar rainfall algo-rithm application in Colorado precipitation eventsrdquo Journal ofAtmospheric andOceanic Technology vol 28 no 3 pp 352ndash3642011

[23] A Ryzhkov M Diederich P Zhang and C Simmer ldquoPotentialutilization of specific attenuation for rainfall estimationmitiga-tion of partial beam blockage and radar networkingrdquo Journal ofAtmospheric and Oceanic Technology vol 31 no 3 pp 599ndash6192014

[24] C-H You M-Y Kang D-I Lee and H Uyeda ldquoRainfallestimation by S-band polarimetric radar in Korea Part Ipreprocessing and preliminary resultsrdquoMeteorological Applica-tions vol 21 no 4 pp 975ndash983 2014

[25] C-H You D-I Lee andM-Y Kang ldquoRainfall estimation usingspecific differential phase for the first operational polarimetricradar in Koreardquo Advances in Meteorology vol 2014 Article ID413717 10 pages 2014

Advances in Meteorology 15

[26] V N Bringi V Chandrasekar J Hubbert E Gorgucci W LRandeu and M Schoenhuber ldquoRaindrop size distribution indifferent climatic regimes from disdrometer and dual-polarizedradar analysisrdquo Journal of the Atmospheric Sciences vol 60 no2 pp 354ndash365 2003

[27] E A Brandes G Zhang and J Vivekanandan ldquoExperimentsin rainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[28] K V Beard and R J Kubesh ldquoLaboratory measurements ofsmall raindrop distortion Part 2 oscillation frequencies andmodesrdquo Journal of the Atmospheric Sciences vol 48 no 20 pp2245ndash2264 1991

[29] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[30] J W F Goddard K L Morgan A Illingworth and HSauvageot ldquoDual-wavelength polarization measurements inprecipitation using the CAMRA and Rabelias radarsrdquo in Pro-ceedings of the 27th Conference on Radar Meteorology pp 196ndash198 American Meteorology Society Vail Colo USA 1995

[31] A V Ryzhkov D S Zrnic J C Hubbert V N Bringi JVivekanandan and E A Brandes ldquoPolarimetric radar obser-vations and interpretation of co-cross-polar correlation coeffi-cientsrdquo Journal of Atmospheric and Oceanic Technology vol 19no 3 pp 340ndash354 2002

[32] S YMatrosov KAClark B EMartner andA Tokay ldquoX-bandpolarimetric radar measurements of rainfallrdquo Journal of AppliedMeteorology vol 41 no 9 pp 941ndash952 2002

[33] G-J Huang V N Bringi and M Thurai ldquoOrientation angledistributions of drops after an 80-m fall using a 2D videodisdrometerrdquo Journal of Atmospheric and Oceanic Technologyvol 25 no 9 pp 1717ndash1723 2008

[34] R Meneghini and K Nakamura ldquoRange profiling of the rainrate by an airborne weather radarrdquo Remote Sensing of Environ-ment vol 31 no 3 pp 193ndash209 1990

[35] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onpolarimetric variables at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[36] J Testud E L Bouar E Obligis and M Ali-Mehenni ldquoTherain profiling algorithm applied to polarimetric weather radarrdquoJournal of Atmospheric andOceanic Technology vol 17 no 3 pp332ndash356 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Geological ResearchJournal of

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Geology Advances in

Advances in Meteorology 7

Table 2 The rainfall relations of 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) with different raindrop shape assumptions

DS 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) 119877(119870DP 119885DR)

DS1 R = 00273119885060 R = 029119885DR527 R = 445119870DP

0942 R = 00161198850889119885DRminus494 R = 537119870DP

0857119885DRminus148

DS2 R = 00277119885059 R = 038119885DR487 R = 533119870DP

0913 R = 00141198850852119885DRminus408 R = 752119870DP

0855119885DRminus198

DS3 R = 00277119885060 R = 042119885DR498 R = 615119870DP

0908 R = 00151198850818119885DRminus372 R = 822119870DP

0855119885DRminus198

DS4 R = 00277119885060 R = 041119885DR498 R = 599119870DP

0896 R = 00141198850844119885DRminus406 R = 674119870DP

0785119885DRminus213

DS5 R = 00277119885060 R = 040119885DR503 R = 562119870DP

0897 R = 00131198850861119885DRminus43 R = 847119870DP

0840119885DRminus238

DS6 R = 00280119885059 R = 043119885DR469 R = 563119870DP

0857 R = 00131198850857119885DRminus40 R = 150119870DP

0483119885DRminus077

R(Z

ZD

R)

(mm

h)

R = 001589085Z08927

ZDRminus49936

NB = 1300

RMSE = 2776

CC = 0965

R (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

(a)

R = 13428687294KDP08991

ZDRminus26757

NB = 188

RMSE = 2593

CC = 0967

R (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(K

DPZ

DR)

(mm

h)

(b)

Figure 6 The scatter plots of rainfall obtained by DSDs and (a) 119877(119885 119885DR) and (b) 119877(119870DP 119885DR) using 119885 for DS3 119885DR for DS1 and 119870DP forDS3

high modes of 119885DR with DS1 DS3 and DS6 were 02sim03 dBand 17sim18 dB 02sim03 dB and 16sim17 dB and 00sim01 dB and17sim18 dB respectively The occurrence frequencies of lowmode for each raindrop axis ratio were significantly differentfrom each other (Figures 5(d)sim5(f)) The averages and stan-dard deviation of119870DPwith different raindrop shapeswere 011and 004 009 and 003 and 01 and 003 respectively Themodes of all drop shapes were the same but the occurrencefrequencies were different (Figures 5(g)sim5(i))

312 The Statistics of Rainfall Relations with Different Rain-drop Axis Ratios Because the occurrence frequencies of119885DRand 119870DP with different raindrop axis ratios were differentfrom each other the rainfall relations using those variablesshould be different with drop shape assumptions Table 2shows the rainfall relations obtained by using different rain-drop shape assumptions The coefficients of 119877(119885) were notsignificantly different with drop shape assumptions howeverthose of other relations were different with each drop shape

Table 3 shows the cross correlations (hereinafter CC) andRMSEs (root mean square errors) of rainfall relations 119877(119885)119877(119885DR) 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) obtained bycalculations using DSDs data with different raindrop shapes

The statistics of 119877(119885) and 119877(119885DR) were not significantlydifferent with raindrop shapesThe CC and RMSE of 119877(119885DR)and 119877(119885 119885DR) were the worst and the best among theother rainfall relations The statistics of 119877(119870DR) 119877(119885 119885DR)and 119877(119870DP 119885DR) were much more variable with differentraindrop axis ratios than the ones of 119877(119885) and 119877(119885DR) TheRMSEs of 119877(119870DP) 119877(119885 119885DR) and 119877(119870DP 119885DR) with rain-drop shapes were distributed from 3030 to 3828mm 2965to 3523mm and 3151 to 5412mm respectivelyThe best per-formance of each relation occurred at DS3 for 119877(119885) DS1 for119877(119885DR) DS1 for 119877(119870DP) DS1 for 119877(119885 119885DR) and DS3 for119877(119870DP 119885DR)

In order to calculate more accurate 119877(119885 119885DR) and119877(119870DP 119885DR) the 119885 and 119885DR with the best performance werechosen Figure 6 shows the scatter plots of rainfall obtainedby DSDs and 119877(119885 119885DR) and 119877(119870DP 119885DR) using the beststatistics among raindrop axis ratio 119885 119885DR and 119870DP werechosen from DS3 DS1 and DS1 respectively Comparingwith 119877(119885 119885DR) and 119877(119870DP 119885DR) of single raindrop axisratio relations having the best performance new combinedrelations had better RMSE and CC The RMSEs of new rela-tions 119877(119885 119885DR) and 119877(119870DP 119885DR) had better score as muchas around 02mm and 06mm respectively Even though

8 Advances in Meteorology

Table 3 The correlation coefficients and RMSEs (mm) of rainfall obtained by rainfall relations and DSDs CC means cross correlation

DS 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) 119877(119870DP 119885DR)

CC RMSE CC RMSE CC RMSE CC RMSE CC RMSEDS1 0913 4705 0572 6241 0875 3030 0964 2965 0951 3313DS2 0913 4709 0569 6248 0861 3198 0956 3272 0956 3222DS3 0914 4704 0562 6261 0861 3178 0949 3523 0960 3151DS4 0913 4706 0569 6249 0828 3549 0954 3334 0931 3882DS5 0913 4706 0572 6243 0849 3326 0957 3210 0950 3348DS6 0913 4713 0572 6244 0795 3828 0956 3239 0814 5412

Table 4The rainfall relations NE RMSE and CC of each raindropaxis ratio relation

DropShape Relation NE RMSE CC

DS1119877(119870DP) = 445119870DP

0942 052 4996 082119877(119885 119885DR) = 001571198850889119885DR

minus494 031 4802 097119877(119870DP 119885DR) = 537119870DP

0857119885DRminus148 056 5262 088

DS2119877(119870DP) = 530119870DP

0913 052 4645 078119877(119885 119885DR) = 001411198850853119885DR

minus408 036 3793 073119877(119870DP 119885DR) = 752119870DP

0855119885DRminus198 060 5146 073

DS3119877(119870DP) = 615119870DP

0908 055 4698 078119877(119885 119885DR) = 001481198850818119885DR

minus372 043 4479 089119877(119870DP 119885DR) = 822119870DP

0855119885DRminus198 063 5247 073

DS4119877(119870DP) = 599119870DP

0896 054 4673 078119877(119885 119885DR) = 001361198850840119885DR

minus406 040 4134 089119877(119870DP 119885DR) = 674119870DP

0785119885DRminus213 060 5249 073

DS5119877(119870DP) = 562119870DP

0897 053 4625 078119877(119885 119885DR) = 001331198850861119885DR

minus431 037 3900 088119877(119870DP 119885DR) = 847119870DP

0840119885DRminus238 065 5390 071

DS6119877(119870DP) = 563119870DP

0857 054 4647 078119877(119885 119885DR) = 001251198850857119885DR

minus399 038 3967 089119877(119870DP 119885DR) = 150119870DP

0483119885DRminus077 065 7141 076

the CC and RMSE of 119877(119885) and 119877(119885DR) with different dropshapes were not significant the combined relations had betterperformance

32 Validations of Rainfall Relations with Different RaindropAxis Ratio Relations To investigate the performance ofrainfall relationsNE (normalized error) RMSE andCCwerecalculated using rainfall from each relation with six raindropshapes and that of gage rainfall

Table 4 summarizes the relations and the statistics suchas NE RMSE and CC The NEs and RMSEs of 119877(119870DR)calculated by each raindrop axis were distributed from 052 to055 and from 4625 to 4996 respectively The 119877(119870DR) withassumption of DS5 was the best score of RMSE in other rain-drop shapes In case of119877(119885 119885DR) the distribution ofNEs andRMSEs was from 031 to 043 and from 3793 to 4602 respec-tively The best RMSE score of 119877(119885 119885DR) was from DS2The NEs and RMSEs of 119877(119870DP 119885DR) occurred from 055 to065 and from 5146 to 7141 respectively The performance of

119877(119870DP 119885DR) was the worst score and 119877(119885 119885DR) had the bestscore in all raindrop axis ratio relations The performancesof validation were different from that of rainfall relationcalculation It would be caused by the variations of DSDs inthis study

To compare the performance between new combined119877(119870DP 119885DR) and 119877(119885 119885DR) the statistics were also calcu-lated Figure 7 shows the scatter plots rainfall from rainfallrelation and gage rainfall with some statistics The NEand RMSE of two relations from single raindrop shapeassumption showed better results However it seems that the119877(119885 119885DR)with two-raindrop axis ratio was more close to thegage rainfall in the range of weaker than 20mmh and the119877(119870DP 119885DR) with two drop shapes was more accurate in therainfall of higher than 20mmh

33 Rainfall Estimation Using Specific Attenuation331 Calculation of Specific Attenuation The 119860

119867can be

calculated from the radial profile of the attenuated reflectivity119885119886and the two-way PIA (Path Integrated Attenuation) along

the propagation path (1199031 1199032) proposed by Meneghini and

Nakamura [34]

119860 (119903) =119886 (119903) [119885119886]

119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(8)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

119886 (119904) [119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

119886 (119904) [119885119886 (119904)]119887119889119904

(9)

If 119886 is not dependent on range then (8) becomes

119860 (119903) =[119885119886]119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(10)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

[119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

[119885119886 (119904)]119887119889119904

(11)

119862 (119887PIA) = exp (023119887PIA) minus 1 (12)

Advances in Meteorology 9

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 036

RMSE = 3793

CC = 0888

Rada

r tot

alR

(ZZ

DR)

BC

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 060

RMSE = 5146

CC = 0732

Rada

r tot

alR

(KD

PZ

DR)

BC

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 032

RMSE = 5194

CC = 0818

Rada

r tot

alR

(ZZ

DR)

best

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 092

RMSE = 7302

CC = 0695

Rada

r tot

alR

(KD

PZ

DR)

best

(d)

Figure 7The scatter plot of rainfall from gage and (a) 119877(119885 119885DR) (b) 119877(119870DP 119885DR)with single raindrop axis ratio relation (c) 119877(119885 119885DR) and(d) 119877(119870DP 119885DR) with two-raindrop axis ratio relation

Bringi et al [35] recommended estimating PIA usingΦDPby

PIA (1199031 1199032) = 120572 [ΦDP (1199032) minusΦDP (1199031)] = 120572ΔΦDP (13)

and Testud et al [36] used (10) and (12) to obtain radialprofiles of 119860

119867at C-band In this study 119860

119867was calculated

by the method proposed by Ryzhkov et al [23] The constant

119887 was set by 06 and 120572 was by 0027 calculated by the ratio of119860119867to 119870DP obtained from DSDsFigure 8 shows the scatter plot of rainfall from 119877(119885)

119877(119870DP) and 119877(119860119867) and rainfall from DSDs and an PPIs

(Plan Position Indicators) at 05 degree elevation angle of gagerainfall and rainfall from 119877(119870DP) and 119877(119860

119867) at 0251 KST on

the 8th of August in 2011The 119877(119860

119867) relation had much better fit to the rainfall of

DSDs than that of119877(119870DP) and119877(119885) relation Comparingwith

10 Advances in Meteorology

Beard and Chuang 1987

Rain rate DSD (mmh)

R(Z

) (m

mh

)

10minus1

100

101

102

103

10minus1

100

101

102

103

R = 00277Z05994

NB = minus2122

RMSE = 4709

CC = 0913

(a)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

NB = minus1295136

RMSE = 3198

CC = 0861

R = 533039KDP091341

R(K

DP)

(mm

h)

(b)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(A

H)

(mm

h)

R = 337359AH10194

NB = 327

RMSE = 3667

CC = 0984

(c)

150100705040302015107310500

R(KDP) (mmh)

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(d)

R(AH) (mmh)

150100705040302015107310500

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(e)

Figure 8 The scatter plot of (a) 119877(119885) (b) 119877(119870DP) and (c) 119877(119860119867) with statistics and the rainfall distribution of 119877(119870DP) and 119877(119860

119867) at 0251

KST on the 8th of August in 2001

Advances in Meteorology 11

Table 5 The rainfall relations of 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assumptions

DS 119877(119885119870DP 119860119867) 119877(119885 119885DR 119870DP 119860119867)

DS1 119877 = 1527119885minus004119870DP0327

119860119867

0713119877 = 310Z012

119885DRminus083

119870DP0304

119860119867

0677

DS2 119877 = 12012119885minus024119870DP0551

119860119867

0685119877 = 4947Zminus015119885DR

minus026119870DP

0468119860119867

0681

DS3 119877 = 17211119885minus027119870DP0619

119860119867

0650119877 = 4502Z014

119885DRminus039

119870DP0486

119860119867

0653

DS4 119877 = 10798119885minus019119870DP0403

119860119867

0778119877 = 193Z018

119885DRminus111

119870DP0114

119860119867

0702

DS5 119877 = 20275119885minus027119870DP0543

119860119867

0720119877 = 24Z037

119885DRminus147

119870DPminus0025

119860119867

0656

DS6 119877 = 397119885minus011119870DP0044

119860119867

0808119877 = 571Z007

119885DRminus092

119870DP0238

119860119867

0687

the distribution of rainfall obtained by 119877(119870DP) and 119877(119860119867)

119877(119860119867) has better spatial resolution and more homogeneous

pattern than those of 119877(119870DP)

332 Validations of 119877(119860119867) 119877(119885119870

119863119875 119860119867) and 119877(119885 119885

119863119877

119870119863119875

119860119867) Relations As mentioned in the previous section

119877(119860119867) has the potential to be the best choice for estimating

rainfall using polarimetric variables To verify the accuracy119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) relations

were obtained and the accuracy of 119877(119860119867) 119877(119885119870DP 119860119867)

and 119877(119885 119885DR 119870DP 119860119867) which had the best performance inthe relations calculated by the six raindrop axis ratio relationswere examined by comparing with 119877(119870DP)

Figure 9 shows the scatter plot of rainfall from gagerainfall and 119877(119870DP) 119877(119860

119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR

119870DP 119860119867) for 84 hours The accuracy of 119877(119885 119885DR 119870DP 119860119867)was the best and119877(119885119870DP 119860119867)was the second in 4 relations119877(119860119867)was not better than 119877(119870DP) in whole range of rainfall

However in the range of higher rainfall it seems that 119877(119860119867)

was closer to the gage rainfall The error of 119877(119860119867) would be

caused by the missing radial profile ofΦDP along the rayThemissing has occurred if the difference of ΦDP between thestarting and end gate is negative According to the results119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) would compensatefor this region

34 Optimum Rainfall Algorithm To find out the optimumrainfall algorithm for Korean S-band polarimetric radar thegage rainfall amount was categorized by three steps 0 to5mmh assigned as light rain 5 to 30mmh as medium rainand higher than 30mmh as high rain In previous sectionthe relations have different accuracy not only for the raindropaxis ratio relation but also for rainfall amount The samplenumbers for each category were 3322 samples 1980 samplesand 92 samples respectively

Figure 10 shows the RMSEs of 119877(119870DP) 119877(119885 119885DR)119877(119870DP 119885DR) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) withdifferent rainfall categories defined in three steps All rela-tions have different RMSEs with respect to the raindrop axisratio relations 119877(119870DP) with DS3 119877(119885 119885DR) with DS2 and119877(119870DP 119885DR) with DS3 have the best score at the high rainfallregime at the low rainfall regime and at the medium rainfallregime respectively Even though 119877(119885 119885DR) has the bestperformance among other relations in total rainfall eventsusing different rainfall relations with different rainfall regimewould be an optimum rainfall algorithm for Korean S-band

polarimetric radar A possible optimum polarimetric rainfallalgorithm can be expressed by

119877 = 00141198850852119885DRminus408 0 lt Rainfall lt 5mmhminus1

119877 = 822119870DP0855

119885DRminus198

5 lt Rainfall lt 30mmhminus1

119877 = 615119870DP0908 30mmhminus1 lt Rainfall

(14)

Table 5 shows the rainfall relations of 119877(119885119870DP 119860119867) and119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assump-tions The coefficients of each relation with respect to thedrop shapes were much different comparing with relationsobtained by combining two polarimetric variables

In case of rainfall relations combined with119860119867 119877(119885 119885DR

119870DP 119860119867) has better score than 119877(119885119870DP 119860119867) Both119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with DS3 showedbetter result than other raindrop shape assumptions119877(119885 119885DR 119870DP 119860119867) at the low medium and high rainfallregimes has similar RMSE to 119877(119885 119885DR) 119877(119870DP 119885DR) and119877(119870DP) respectively

Equations (14) would be an optimum rainfall algorithmbut there is still a problem to solve how the rainfall categoriesare defined using radar and gage Gage does not have goodspatial resolution to cover radar resolution like 125m or 1 kmand each rainfall relation has its own error at certain rainfallregime Therefore 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867)withDS3 can be used regardless rainfall intensity And in case119885DR bias calibration is not available or does not have enoughquality for quantitative use 119877(119885119870DP 119860119867) with DS3 can beused as a representative rainfall estimation

4 Summary and Conclusions

Polarimetric radars will be main tools to monitor andforecast severe weather and flash flooding within severalyears in Korea To get an optimum rainfall algorithm usingpolarimetric variables observed from Bislsan radar which isthe first polarimetric radar in Korea rainfall cases for 84hours caused by different conditions which are Changmafront and typhoon Changma front only and typhoon onlythat occurred in 2011 were analyzed And rainfall relationswere obtained by using long period DSDs with six differentraindrop axis ratio relations

In the analysis of 119885 119885DR and119870DP occurrence frequencythere were two modes of 119885DR occurrence frequency and

12 Advances in Meteorology

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100Ra

dar t

otal

R(K

DP)

BC

NE = 052

RMSE = 4645

CC = 0778

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 051

RMSE = 5005

CC = 0797

Rada

r tot

al R

(AH

) AS

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100NE = 046

RMSE = 4374

CC = 0820

Rada

r tot

al R

(ZK

DPA

H) A

S

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 045

RMSE = 4368

CC = 0852

Rada

r tot

al R

(ZZ

DRK

DPA

H) A

S

(d)

Figure 9 The scatter plot of gage rainfall and 119877(119870DP) 119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DP 119870DP 119860119867) rainfall for 84 hours

the variations of 119870DP and 119885DR histograms were higherthan that of 119885 with raindrop ratio relations According tothese variations the combined relations of 119877(119885 119885DR) and119877(119870DP 119885DR) using 119885 with DS3 119885DR with DS1 and 119870DP withDS1 were closer to the rainfall of DSDs

To examine the performance of each rainfall relationNE RMSE CC were calculated using rainfall recorded at121 gages within radar coverage for 84 hours The statisticsof each rainfall relation were different with raindrop shape

assumptions and rainfall intensity119877(119870DP 119885DR)had theworstperformance and119877(119885 119885DR) had the best score in all raindropshapes 119860

119867was calculated by observed ΦDP and 119885 using the

method by Ryzhkov et al [23] and the rainfall relations using119860119867were also calculated and analyzedThe performance of rainfall relations were comparedwith

three different rainfall categories to findout an optimumrain-fall relation for the S-band polarimetric in Korea 119877(119885 119885DR)119877(119870DP 119885DR) and 119877(119870DP) had the best RMSE at the light

Advances in Meteorology 13

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP) with drop shape

(a)

0

5

10

15

20

Drop shape

25

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(Z ZDR) with drop shape

(b)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP ZDR) with drop shape

(c)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(ZKDP AH) with drop shape

(d)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

0ndash5mm5ndash30mmOver 30mm

RMSE of R(Z ZDR KDP AH) with drop shape

(e)

Figure 10The RMSEs of (a) 119877(119870DP) (b) 119877(119885 119885DP) (c) 119877(119870DP 119885DP) (d) 119877(119885119870DP 119860119867) and (e) 119877(119885 119885DP 119870DP 119860119867)with raindrop axis ratiorelations in the three rainfall categories

14 Advances in Meteorology

rain medium rain and high rainfall regimes respectively119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) showed relativelygood performance in all rainfall regimesThe combination of119877(119885 119885DR) 119877(119870DP 119885DR) and 119877(119870DP) with rainfall intensitywould be an optimum rainfall algorithm if the referenceof rainfall would be defined correctly Regardless of rainfallintensity 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) obtainedby assuming DS3 can be used as a representative rainfall rela-tion without consideration of rainfall intensity regime Par-ticularly if the qualified 119885DR is not available 119877(119885119870DP 119860119867)with DS3 drop shape assumption can be used as an optimumrainfall relation in Korea

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge providing radar data weatherchart and AWS data for this work from the Ministry ofLand Infrastructure Transport and Korea MeteorologicalAdministration The authors also acknowledge providingcodes for scattering simulation from Professor V N Bringi atColorado StateUniversityThisworkwas funded by theKoreaMeteorological Industry Promotion Agency under GrantKMIPA 2015-1050

References

[1] E Campos and I Zawadzki ldquoInstrumental uncertainties in Z-R relationsrdquo Journal of Applied Meteorology vol 39 no 7 pp1088ndash1102 2000

[2] C-H You D-I Lee S-M Jang et al ldquoCharacteristics ofrainfall systems accompanied with Changma front at Chujadoin Koreardquo Asia-Pacific Journal of Atmospheric Sciences vol 46no 1 pp 41ndash51 2010

[3] P CWaterman ldquoSymmetry unitarity and geometry in electro-magnetic scatteringrdquo Physical Review D vol 3 no 4 pp 825ndash839 1971

[4] M IMishchenko LD Travis andDWMackowski ldquoT-matrixcomputations of light scattering by nonspherical particles areviewrdquo Journal of Quantitative Spectroscopy and RadiativeTransfer vol 55 no 5 pp 535ndash575 1996

[5] H R Pruppacher and K V Beard ldquoA wind tunnel investigationof the internal circulation and shape of water drops fallingat terminal velocity in airrdquo Quarterly Journal of the RoyalMeteorological Society vol 96 no 408 pp 247ndash256 1970

[6] D C Blanchard ldquoThe behavior of water drops at terminalvelocity in airrdquo EOS vol 31 no 6 pp 836ndash842 1950

[7] G-J Huang V N Bringi M Schonhuber et al ldquoDrop shapeand canting angle distributions in rain from2-Dvideo disdrom-eterrdquo in Proceedings of the 33rd Conference on Radar Meteorol-ogy Extended Abstract P8A8 Cairns Australia August 2007

[8] M Thurai V N Bringi and W A Petersen ldquoRain microstruc-ture retrievals using 2-D video disdrometer and C-band polari-metric radarrdquo Advances in Geosciences vol 20 pp 13ndash18 2009

[9] K V Beard and C Chuang ldquoA new model for the equilibriumshape of raindropsrdquo Journal of the Atmospheric Sciences vol 44pp 1509ndash1524 1987

[10] K Andsager K V Beard and N S Laird ldquoA laboratory studyof oscillations and axis ratios for large raindropsrdquo Journal of theAtmospheric Sciences vol 55 pp 208ndash226 1999

[11] J W Wilson and E A Brandes ldquoRadar measurement of rain-fallmdasha summaryrdquo Bulletin AmericanMeteorological Society vol60 no 9 pp 1048ndash1058 1979

[12] P M Austin ldquoRelation betweenmeasured radar reflectivity andsurface rainfallrdquo Monthly Weather Review vol 115 no 5 pp1053ndash1070 1987

[13] J Vivekanandan D S Zrnic S M Ellis R Oye A V Ryzhkovand J Straka ldquoCloud microphysics retrieval using S-band dual-polarization radar measurementsrdquo Bulletin of the AmericanMeteorological Society vol 80 no 3 pp 381ndash388 1999

[14] A V Ryzhkov and D S Zrnic ldquoDiscrimination between rainand snow with a polarimetric radarrdquo Journal of Applied Meteo-rology vol 37 no 10 pp 1228ndash1240 1998

[15] S E Giangrande and A V Ryzhkov ldquoEstimation of rainfallbased on the results of polarimetric echo classificationrdquo Journalof AppliedMeteorology and Climatology vol 47 no 9 pp 2445ndash2462 2008

[16] A V Ryzhkov and D S Zrnic ldquoAssessment of rainfall measure-ment that uses specific differential phaserdquo Journal of AppliedMeteorology vol 35 no 11 pp 2080ndash2090 1996

[17] P T May T D Keenan D S Zrnic L D Carey and S ARutledge ldquoPolarimetric radar measurements of tropical rain ata 5-cm wavelengthrdquo Journal of Applied Meteorology vol 38 no6 pp 750ndash765 1999

[18] V N Bringi and V Chandrasekar ldquoThe polarimetric basis forcharacterizing precipitationrdquo in Polarimetric Doppler WeatherRadar Principles and Applications pp 378ndash533 CambridgeUniversity Press Cambridge UK 2001

[19] E A Brandes G Zhang and J Vivekanandan ldquoExperiments inrainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[20] A V Ryzhkov T J Schuur D W Burgess P L Heinselman SE Giangrande and D S Zrnic ldquoThe joint polarization exper-iment polarimetric rainfall measurements and hydrometeorclassificationrdquo Bulletin of the American Meteorological Societyvol 86 no 6 pp 809ndash824 2005

[21] A V Ryzhkov S E Giangrande and T J Schuur ldquoRainfall esti-mation with a polarimetric prototype of WSR-88Drdquo Journal ofApplied Meteorology vol 44 no 4 pp 502ndash515 2005

[22] R Cifelli V Chandrasekar S Lim P C Kennedy Y Wang andS A Rutledge ldquoA new dual-polarization radar rainfall algo-rithm application in Colorado precipitation eventsrdquo Journal ofAtmospheric andOceanic Technology vol 28 no 3 pp 352ndash3642011

[23] A Ryzhkov M Diederich P Zhang and C Simmer ldquoPotentialutilization of specific attenuation for rainfall estimationmitiga-tion of partial beam blockage and radar networkingrdquo Journal ofAtmospheric and Oceanic Technology vol 31 no 3 pp 599ndash6192014

[24] C-H You M-Y Kang D-I Lee and H Uyeda ldquoRainfallestimation by S-band polarimetric radar in Korea Part Ipreprocessing and preliminary resultsrdquoMeteorological Applica-tions vol 21 no 4 pp 975ndash983 2014

[25] C-H You D-I Lee andM-Y Kang ldquoRainfall estimation usingspecific differential phase for the first operational polarimetricradar in Koreardquo Advances in Meteorology vol 2014 Article ID413717 10 pages 2014

Advances in Meteorology 15

[26] V N Bringi V Chandrasekar J Hubbert E Gorgucci W LRandeu and M Schoenhuber ldquoRaindrop size distribution indifferent climatic regimes from disdrometer and dual-polarizedradar analysisrdquo Journal of the Atmospheric Sciences vol 60 no2 pp 354ndash365 2003

[27] E A Brandes G Zhang and J Vivekanandan ldquoExperimentsin rainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[28] K V Beard and R J Kubesh ldquoLaboratory measurements ofsmall raindrop distortion Part 2 oscillation frequencies andmodesrdquo Journal of the Atmospheric Sciences vol 48 no 20 pp2245ndash2264 1991

[29] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[30] J W F Goddard K L Morgan A Illingworth and HSauvageot ldquoDual-wavelength polarization measurements inprecipitation using the CAMRA and Rabelias radarsrdquo in Pro-ceedings of the 27th Conference on Radar Meteorology pp 196ndash198 American Meteorology Society Vail Colo USA 1995

[31] A V Ryzhkov D S Zrnic J C Hubbert V N Bringi JVivekanandan and E A Brandes ldquoPolarimetric radar obser-vations and interpretation of co-cross-polar correlation coeffi-cientsrdquo Journal of Atmospheric and Oceanic Technology vol 19no 3 pp 340ndash354 2002

[32] S YMatrosov KAClark B EMartner andA Tokay ldquoX-bandpolarimetric radar measurements of rainfallrdquo Journal of AppliedMeteorology vol 41 no 9 pp 941ndash952 2002

[33] G-J Huang V N Bringi and M Thurai ldquoOrientation angledistributions of drops after an 80-m fall using a 2D videodisdrometerrdquo Journal of Atmospheric and Oceanic Technologyvol 25 no 9 pp 1717ndash1723 2008

[34] R Meneghini and K Nakamura ldquoRange profiling of the rainrate by an airborne weather radarrdquo Remote Sensing of Environ-ment vol 31 no 3 pp 193ndash209 1990

[35] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onpolarimetric variables at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[36] J Testud E L Bouar E Obligis and M Ali-Mehenni ldquoTherain profiling algorithm applied to polarimetric weather radarrdquoJournal of Atmospheric andOceanic Technology vol 17 no 3 pp332ndash356 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

8 Advances in Meteorology

Table 3 The correlation coefficients and RMSEs (mm) of rainfall obtained by rainfall relations and DSDs CC means cross correlation

DS 119877(119885) 119877(119885DR) 119877(119870DP) 119877(119885 119885DR) 119877(119870DP 119885DR)

CC RMSE CC RMSE CC RMSE CC RMSE CC RMSEDS1 0913 4705 0572 6241 0875 3030 0964 2965 0951 3313DS2 0913 4709 0569 6248 0861 3198 0956 3272 0956 3222DS3 0914 4704 0562 6261 0861 3178 0949 3523 0960 3151DS4 0913 4706 0569 6249 0828 3549 0954 3334 0931 3882DS5 0913 4706 0572 6243 0849 3326 0957 3210 0950 3348DS6 0913 4713 0572 6244 0795 3828 0956 3239 0814 5412

Table 4The rainfall relations NE RMSE and CC of each raindropaxis ratio relation

DropShape Relation NE RMSE CC

DS1119877(119870DP) = 445119870DP

0942 052 4996 082119877(119885 119885DR) = 001571198850889119885DR

minus494 031 4802 097119877(119870DP 119885DR) = 537119870DP

0857119885DRminus148 056 5262 088

DS2119877(119870DP) = 530119870DP

0913 052 4645 078119877(119885 119885DR) = 001411198850853119885DR

minus408 036 3793 073119877(119870DP 119885DR) = 752119870DP

0855119885DRminus198 060 5146 073

DS3119877(119870DP) = 615119870DP

0908 055 4698 078119877(119885 119885DR) = 001481198850818119885DR

minus372 043 4479 089119877(119870DP 119885DR) = 822119870DP

0855119885DRminus198 063 5247 073

DS4119877(119870DP) = 599119870DP

0896 054 4673 078119877(119885 119885DR) = 001361198850840119885DR

minus406 040 4134 089119877(119870DP 119885DR) = 674119870DP

0785119885DRminus213 060 5249 073

DS5119877(119870DP) = 562119870DP

0897 053 4625 078119877(119885 119885DR) = 001331198850861119885DR

minus431 037 3900 088119877(119870DP 119885DR) = 847119870DP

0840119885DRminus238 065 5390 071

DS6119877(119870DP) = 563119870DP

0857 054 4647 078119877(119885 119885DR) = 001251198850857119885DR

minus399 038 3967 089119877(119870DP 119885DR) = 150119870DP

0483119885DRminus077 065 7141 076

the CC and RMSE of 119877(119885) and 119877(119885DR) with different dropshapes were not significant the combined relations had betterperformance

32 Validations of Rainfall Relations with Different RaindropAxis Ratio Relations To investigate the performance ofrainfall relationsNE (normalized error) RMSE andCCwerecalculated using rainfall from each relation with six raindropshapes and that of gage rainfall

Table 4 summarizes the relations and the statistics suchas NE RMSE and CC The NEs and RMSEs of 119877(119870DR)calculated by each raindrop axis were distributed from 052 to055 and from 4625 to 4996 respectively The 119877(119870DR) withassumption of DS5 was the best score of RMSE in other rain-drop shapes In case of119877(119885 119885DR) the distribution ofNEs andRMSEs was from 031 to 043 and from 3793 to 4602 respec-tively The best RMSE score of 119877(119885 119885DR) was from DS2The NEs and RMSEs of 119877(119870DP 119885DR) occurred from 055 to065 and from 5146 to 7141 respectively The performance of

119877(119870DP 119885DR) was the worst score and 119877(119885 119885DR) had the bestscore in all raindrop axis ratio relations The performancesof validation were different from that of rainfall relationcalculation It would be caused by the variations of DSDs inthis study

To compare the performance between new combined119877(119870DP 119885DR) and 119877(119885 119885DR) the statistics were also calcu-lated Figure 7 shows the scatter plots rainfall from rainfallrelation and gage rainfall with some statistics The NEand RMSE of two relations from single raindrop shapeassumption showed better results However it seems that the119877(119885 119885DR)with two-raindrop axis ratio was more close to thegage rainfall in the range of weaker than 20mmh and the119877(119870DP 119885DR) with two drop shapes was more accurate in therainfall of higher than 20mmh

33 Rainfall Estimation Using Specific Attenuation331 Calculation of Specific Attenuation The 119860

119867can be

calculated from the radial profile of the attenuated reflectivity119885119886and the two-way PIA (Path Integrated Attenuation) along

the propagation path (1199031 1199032) proposed by Meneghini and

Nakamura [34]

119860 (119903) =119886 (119903) [119885119886]

119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(8)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

119886 (119904) [119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

119886 (119904) [119885119886 (119904)]119887119889119904

(9)

If 119886 is not dependent on range then (8) becomes

119860 (119903) =[119885119886]119887119862 (119887PIA)

119868119886(1199031 1199032) + 119862 (119887PIA) 119868119886 (119903 1199032)

(10)

where

119868119886(1199031 1199032) = 046119887int

1199032

1199031

[119885119886 (119904)]119887119889119904

119868119886(119903 1199032) = 046119887int

1199032

119903

[119885119886 (119904)]119887119889119904

(11)

119862 (119887PIA) = exp (023119887PIA) minus 1 (12)

Advances in Meteorology 9

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 036

RMSE = 3793

CC = 0888

Rada

r tot

alR

(ZZ

DR)

BC

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 060

RMSE = 5146

CC = 0732

Rada

r tot

alR

(KD

PZ

DR)

BC

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 032

RMSE = 5194

CC = 0818

Rada

r tot

alR

(ZZ

DR)

best

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 092

RMSE = 7302

CC = 0695

Rada

r tot

alR

(KD

PZ

DR)

best

(d)

Figure 7The scatter plot of rainfall from gage and (a) 119877(119885 119885DR) (b) 119877(119870DP 119885DR)with single raindrop axis ratio relation (c) 119877(119885 119885DR) and(d) 119877(119870DP 119885DR) with two-raindrop axis ratio relation

Bringi et al [35] recommended estimating PIA usingΦDPby

PIA (1199031 1199032) = 120572 [ΦDP (1199032) minusΦDP (1199031)] = 120572ΔΦDP (13)

and Testud et al [36] used (10) and (12) to obtain radialprofiles of 119860

119867at C-band In this study 119860

119867was calculated

by the method proposed by Ryzhkov et al [23] The constant

119887 was set by 06 and 120572 was by 0027 calculated by the ratio of119860119867to 119870DP obtained from DSDsFigure 8 shows the scatter plot of rainfall from 119877(119885)

119877(119870DP) and 119877(119860119867) and rainfall from DSDs and an PPIs

(Plan Position Indicators) at 05 degree elevation angle of gagerainfall and rainfall from 119877(119870DP) and 119877(119860

119867) at 0251 KST on

the 8th of August in 2011The 119877(119860

119867) relation had much better fit to the rainfall of

DSDs than that of119877(119870DP) and119877(119885) relation Comparingwith

10 Advances in Meteorology

Beard and Chuang 1987

Rain rate DSD (mmh)

R(Z

) (m

mh

)

10minus1

100

101

102

103

10minus1

100

101

102

103

R = 00277Z05994

NB = minus2122

RMSE = 4709

CC = 0913

(a)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

NB = minus1295136

RMSE = 3198

CC = 0861

R = 533039KDP091341

R(K

DP)

(mm

h)

(b)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(A

H)

(mm

h)

R = 337359AH10194

NB = 327

RMSE = 3667

CC = 0984

(c)

150100705040302015107310500

R(KDP) (mmh)

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(d)

R(AH) (mmh)

150100705040302015107310500

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(e)

Figure 8 The scatter plot of (a) 119877(119885) (b) 119877(119870DP) and (c) 119877(119860119867) with statistics and the rainfall distribution of 119877(119870DP) and 119877(119860

119867) at 0251

KST on the 8th of August in 2001

Advances in Meteorology 11

Table 5 The rainfall relations of 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assumptions

DS 119877(119885119870DP 119860119867) 119877(119885 119885DR 119870DP 119860119867)

DS1 119877 = 1527119885minus004119870DP0327

119860119867

0713119877 = 310Z012

119885DRminus083

119870DP0304

119860119867

0677

DS2 119877 = 12012119885minus024119870DP0551

119860119867

0685119877 = 4947Zminus015119885DR

minus026119870DP

0468119860119867

0681

DS3 119877 = 17211119885minus027119870DP0619

119860119867

0650119877 = 4502Z014

119885DRminus039

119870DP0486

119860119867

0653

DS4 119877 = 10798119885minus019119870DP0403

119860119867

0778119877 = 193Z018

119885DRminus111

119870DP0114

119860119867

0702

DS5 119877 = 20275119885minus027119870DP0543

119860119867

0720119877 = 24Z037

119885DRminus147

119870DPminus0025

119860119867

0656

DS6 119877 = 397119885minus011119870DP0044

119860119867

0808119877 = 571Z007

119885DRminus092

119870DP0238

119860119867

0687

the distribution of rainfall obtained by 119877(119870DP) and 119877(119860119867)

119877(119860119867) has better spatial resolution and more homogeneous

pattern than those of 119877(119870DP)

332 Validations of 119877(119860119867) 119877(119885119870

119863119875 119860119867) and 119877(119885 119885

119863119877

119870119863119875

119860119867) Relations As mentioned in the previous section

119877(119860119867) has the potential to be the best choice for estimating

rainfall using polarimetric variables To verify the accuracy119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) relations

were obtained and the accuracy of 119877(119860119867) 119877(119885119870DP 119860119867)

and 119877(119885 119885DR 119870DP 119860119867) which had the best performance inthe relations calculated by the six raindrop axis ratio relationswere examined by comparing with 119877(119870DP)

Figure 9 shows the scatter plot of rainfall from gagerainfall and 119877(119870DP) 119877(119860

119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR

119870DP 119860119867) for 84 hours The accuracy of 119877(119885 119885DR 119870DP 119860119867)was the best and119877(119885119870DP 119860119867)was the second in 4 relations119877(119860119867)was not better than 119877(119870DP) in whole range of rainfall

However in the range of higher rainfall it seems that 119877(119860119867)

was closer to the gage rainfall The error of 119877(119860119867) would be

caused by the missing radial profile ofΦDP along the rayThemissing has occurred if the difference of ΦDP between thestarting and end gate is negative According to the results119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) would compensatefor this region

34 Optimum Rainfall Algorithm To find out the optimumrainfall algorithm for Korean S-band polarimetric radar thegage rainfall amount was categorized by three steps 0 to5mmh assigned as light rain 5 to 30mmh as medium rainand higher than 30mmh as high rain In previous sectionthe relations have different accuracy not only for the raindropaxis ratio relation but also for rainfall amount The samplenumbers for each category were 3322 samples 1980 samplesand 92 samples respectively

Figure 10 shows the RMSEs of 119877(119870DP) 119877(119885 119885DR)119877(119870DP 119885DR) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) withdifferent rainfall categories defined in three steps All rela-tions have different RMSEs with respect to the raindrop axisratio relations 119877(119870DP) with DS3 119877(119885 119885DR) with DS2 and119877(119870DP 119885DR) with DS3 have the best score at the high rainfallregime at the low rainfall regime and at the medium rainfallregime respectively Even though 119877(119885 119885DR) has the bestperformance among other relations in total rainfall eventsusing different rainfall relations with different rainfall regimewould be an optimum rainfall algorithm for Korean S-band

polarimetric radar A possible optimum polarimetric rainfallalgorithm can be expressed by

119877 = 00141198850852119885DRminus408 0 lt Rainfall lt 5mmhminus1

119877 = 822119870DP0855

119885DRminus198

5 lt Rainfall lt 30mmhminus1

119877 = 615119870DP0908 30mmhminus1 lt Rainfall

(14)

Table 5 shows the rainfall relations of 119877(119885119870DP 119860119867) and119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assump-tions The coefficients of each relation with respect to thedrop shapes were much different comparing with relationsobtained by combining two polarimetric variables

In case of rainfall relations combined with119860119867 119877(119885 119885DR

119870DP 119860119867) has better score than 119877(119885119870DP 119860119867) Both119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with DS3 showedbetter result than other raindrop shape assumptions119877(119885 119885DR 119870DP 119860119867) at the low medium and high rainfallregimes has similar RMSE to 119877(119885 119885DR) 119877(119870DP 119885DR) and119877(119870DP) respectively

Equations (14) would be an optimum rainfall algorithmbut there is still a problem to solve how the rainfall categoriesare defined using radar and gage Gage does not have goodspatial resolution to cover radar resolution like 125m or 1 kmand each rainfall relation has its own error at certain rainfallregime Therefore 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867)withDS3 can be used regardless rainfall intensity And in case119885DR bias calibration is not available or does not have enoughquality for quantitative use 119877(119885119870DP 119860119867) with DS3 can beused as a representative rainfall estimation

4 Summary and Conclusions

Polarimetric radars will be main tools to monitor andforecast severe weather and flash flooding within severalyears in Korea To get an optimum rainfall algorithm usingpolarimetric variables observed from Bislsan radar which isthe first polarimetric radar in Korea rainfall cases for 84hours caused by different conditions which are Changmafront and typhoon Changma front only and typhoon onlythat occurred in 2011 were analyzed And rainfall relationswere obtained by using long period DSDs with six differentraindrop axis ratio relations

In the analysis of 119885 119885DR and119870DP occurrence frequencythere were two modes of 119885DR occurrence frequency and

12 Advances in Meteorology

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100Ra

dar t

otal

R(K

DP)

BC

NE = 052

RMSE = 4645

CC = 0778

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 051

RMSE = 5005

CC = 0797

Rada

r tot

al R

(AH

) AS

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100NE = 046

RMSE = 4374

CC = 0820

Rada

r tot

al R

(ZK

DPA

H) A

S

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 045

RMSE = 4368

CC = 0852

Rada

r tot

al R

(ZZ

DRK

DPA

H) A

S

(d)

Figure 9 The scatter plot of gage rainfall and 119877(119870DP) 119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DP 119870DP 119860119867) rainfall for 84 hours

the variations of 119870DP and 119885DR histograms were higherthan that of 119885 with raindrop ratio relations According tothese variations the combined relations of 119877(119885 119885DR) and119877(119870DP 119885DR) using 119885 with DS3 119885DR with DS1 and 119870DP withDS1 were closer to the rainfall of DSDs

To examine the performance of each rainfall relationNE RMSE CC were calculated using rainfall recorded at121 gages within radar coverage for 84 hours The statisticsof each rainfall relation were different with raindrop shape

assumptions and rainfall intensity119877(119870DP 119885DR)had theworstperformance and119877(119885 119885DR) had the best score in all raindropshapes 119860

119867was calculated by observed ΦDP and 119885 using the

method by Ryzhkov et al [23] and the rainfall relations using119860119867were also calculated and analyzedThe performance of rainfall relations were comparedwith

three different rainfall categories to findout an optimumrain-fall relation for the S-band polarimetric in Korea 119877(119885 119885DR)119877(119870DP 119885DR) and 119877(119870DP) had the best RMSE at the light

Advances in Meteorology 13

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP) with drop shape

(a)

0

5

10

15

20

Drop shape

25

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(Z ZDR) with drop shape

(b)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP ZDR) with drop shape

(c)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(ZKDP AH) with drop shape

(d)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

0ndash5mm5ndash30mmOver 30mm

RMSE of R(Z ZDR KDP AH) with drop shape

(e)

Figure 10The RMSEs of (a) 119877(119870DP) (b) 119877(119885 119885DP) (c) 119877(119870DP 119885DP) (d) 119877(119885119870DP 119860119867) and (e) 119877(119885 119885DP 119870DP 119860119867)with raindrop axis ratiorelations in the three rainfall categories

14 Advances in Meteorology

rain medium rain and high rainfall regimes respectively119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) showed relativelygood performance in all rainfall regimesThe combination of119877(119885 119885DR) 119877(119870DP 119885DR) and 119877(119870DP) with rainfall intensitywould be an optimum rainfall algorithm if the referenceof rainfall would be defined correctly Regardless of rainfallintensity 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) obtainedby assuming DS3 can be used as a representative rainfall rela-tion without consideration of rainfall intensity regime Par-ticularly if the qualified 119885DR is not available 119877(119885119870DP 119860119867)with DS3 drop shape assumption can be used as an optimumrainfall relation in Korea

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge providing radar data weatherchart and AWS data for this work from the Ministry ofLand Infrastructure Transport and Korea MeteorologicalAdministration The authors also acknowledge providingcodes for scattering simulation from Professor V N Bringi atColorado StateUniversityThisworkwas funded by theKoreaMeteorological Industry Promotion Agency under GrantKMIPA 2015-1050

References

[1] E Campos and I Zawadzki ldquoInstrumental uncertainties in Z-R relationsrdquo Journal of Applied Meteorology vol 39 no 7 pp1088ndash1102 2000

[2] C-H You D-I Lee S-M Jang et al ldquoCharacteristics ofrainfall systems accompanied with Changma front at Chujadoin Koreardquo Asia-Pacific Journal of Atmospheric Sciences vol 46no 1 pp 41ndash51 2010

[3] P CWaterman ldquoSymmetry unitarity and geometry in electro-magnetic scatteringrdquo Physical Review D vol 3 no 4 pp 825ndash839 1971

[4] M IMishchenko LD Travis andDWMackowski ldquoT-matrixcomputations of light scattering by nonspherical particles areviewrdquo Journal of Quantitative Spectroscopy and RadiativeTransfer vol 55 no 5 pp 535ndash575 1996

[5] H R Pruppacher and K V Beard ldquoA wind tunnel investigationof the internal circulation and shape of water drops fallingat terminal velocity in airrdquo Quarterly Journal of the RoyalMeteorological Society vol 96 no 408 pp 247ndash256 1970

[6] D C Blanchard ldquoThe behavior of water drops at terminalvelocity in airrdquo EOS vol 31 no 6 pp 836ndash842 1950

[7] G-J Huang V N Bringi M Schonhuber et al ldquoDrop shapeand canting angle distributions in rain from2-Dvideo disdrom-eterrdquo in Proceedings of the 33rd Conference on Radar Meteorol-ogy Extended Abstract P8A8 Cairns Australia August 2007

[8] M Thurai V N Bringi and W A Petersen ldquoRain microstruc-ture retrievals using 2-D video disdrometer and C-band polari-metric radarrdquo Advances in Geosciences vol 20 pp 13ndash18 2009

[9] K V Beard and C Chuang ldquoA new model for the equilibriumshape of raindropsrdquo Journal of the Atmospheric Sciences vol 44pp 1509ndash1524 1987

[10] K Andsager K V Beard and N S Laird ldquoA laboratory studyof oscillations and axis ratios for large raindropsrdquo Journal of theAtmospheric Sciences vol 55 pp 208ndash226 1999

[11] J W Wilson and E A Brandes ldquoRadar measurement of rain-fallmdasha summaryrdquo Bulletin AmericanMeteorological Society vol60 no 9 pp 1048ndash1058 1979

[12] P M Austin ldquoRelation betweenmeasured radar reflectivity andsurface rainfallrdquo Monthly Weather Review vol 115 no 5 pp1053ndash1070 1987

[13] J Vivekanandan D S Zrnic S M Ellis R Oye A V Ryzhkovand J Straka ldquoCloud microphysics retrieval using S-band dual-polarization radar measurementsrdquo Bulletin of the AmericanMeteorological Society vol 80 no 3 pp 381ndash388 1999

[14] A V Ryzhkov and D S Zrnic ldquoDiscrimination between rainand snow with a polarimetric radarrdquo Journal of Applied Meteo-rology vol 37 no 10 pp 1228ndash1240 1998

[15] S E Giangrande and A V Ryzhkov ldquoEstimation of rainfallbased on the results of polarimetric echo classificationrdquo Journalof AppliedMeteorology and Climatology vol 47 no 9 pp 2445ndash2462 2008

[16] A V Ryzhkov and D S Zrnic ldquoAssessment of rainfall measure-ment that uses specific differential phaserdquo Journal of AppliedMeteorology vol 35 no 11 pp 2080ndash2090 1996

[17] P T May T D Keenan D S Zrnic L D Carey and S ARutledge ldquoPolarimetric radar measurements of tropical rain ata 5-cm wavelengthrdquo Journal of Applied Meteorology vol 38 no6 pp 750ndash765 1999

[18] V N Bringi and V Chandrasekar ldquoThe polarimetric basis forcharacterizing precipitationrdquo in Polarimetric Doppler WeatherRadar Principles and Applications pp 378ndash533 CambridgeUniversity Press Cambridge UK 2001

[19] E A Brandes G Zhang and J Vivekanandan ldquoExperiments inrainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[20] A V Ryzhkov T J Schuur D W Burgess P L Heinselman SE Giangrande and D S Zrnic ldquoThe joint polarization exper-iment polarimetric rainfall measurements and hydrometeorclassificationrdquo Bulletin of the American Meteorological Societyvol 86 no 6 pp 809ndash824 2005

[21] A V Ryzhkov S E Giangrande and T J Schuur ldquoRainfall esti-mation with a polarimetric prototype of WSR-88Drdquo Journal ofApplied Meteorology vol 44 no 4 pp 502ndash515 2005

[22] R Cifelli V Chandrasekar S Lim P C Kennedy Y Wang andS A Rutledge ldquoA new dual-polarization radar rainfall algo-rithm application in Colorado precipitation eventsrdquo Journal ofAtmospheric andOceanic Technology vol 28 no 3 pp 352ndash3642011

[23] A Ryzhkov M Diederich P Zhang and C Simmer ldquoPotentialutilization of specific attenuation for rainfall estimationmitiga-tion of partial beam blockage and radar networkingrdquo Journal ofAtmospheric and Oceanic Technology vol 31 no 3 pp 599ndash6192014

[24] C-H You M-Y Kang D-I Lee and H Uyeda ldquoRainfallestimation by S-band polarimetric radar in Korea Part Ipreprocessing and preliminary resultsrdquoMeteorological Applica-tions vol 21 no 4 pp 975ndash983 2014

[25] C-H You D-I Lee andM-Y Kang ldquoRainfall estimation usingspecific differential phase for the first operational polarimetricradar in Koreardquo Advances in Meteorology vol 2014 Article ID413717 10 pages 2014

Advances in Meteorology 15

[26] V N Bringi V Chandrasekar J Hubbert E Gorgucci W LRandeu and M Schoenhuber ldquoRaindrop size distribution indifferent climatic regimes from disdrometer and dual-polarizedradar analysisrdquo Journal of the Atmospheric Sciences vol 60 no2 pp 354ndash365 2003

[27] E A Brandes G Zhang and J Vivekanandan ldquoExperimentsin rainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[28] K V Beard and R J Kubesh ldquoLaboratory measurements ofsmall raindrop distortion Part 2 oscillation frequencies andmodesrdquo Journal of the Atmospheric Sciences vol 48 no 20 pp2245ndash2264 1991

[29] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[30] J W F Goddard K L Morgan A Illingworth and HSauvageot ldquoDual-wavelength polarization measurements inprecipitation using the CAMRA and Rabelias radarsrdquo in Pro-ceedings of the 27th Conference on Radar Meteorology pp 196ndash198 American Meteorology Society Vail Colo USA 1995

[31] A V Ryzhkov D S Zrnic J C Hubbert V N Bringi JVivekanandan and E A Brandes ldquoPolarimetric radar obser-vations and interpretation of co-cross-polar correlation coeffi-cientsrdquo Journal of Atmospheric and Oceanic Technology vol 19no 3 pp 340ndash354 2002

[32] S YMatrosov KAClark B EMartner andA Tokay ldquoX-bandpolarimetric radar measurements of rainfallrdquo Journal of AppliedMeteorology vol 41 no 9 pp 941ndash952 2002

[33] G-J Huang V N Bringi and M Thurai ldquoOrientation angledistributions of drops after an 80-m fall using a 2D videodisdrometerrdquo Journal of Atmospheric and Oceanic Technologyvol 25 no 9 pp 1717ndash1723 2008

[34] R Meneghini and K Nakamura ldquoRange profiling of the rainrate by an airborne weather radarrdquo Remote Sensing of Environ-ment vol 31 no 3 pp 193ndash209 1990

[35] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onpolarimetric variables at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[36] J Testud E L Bouar E Obligis and M Ali-Mehenni ldquoTherain profiling algorithm applied to polarimetric weather radarrdquoJournal of Atmospheric andOceanic Technology vol 17 no 3 pp332ndash356 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Advances in Meteorology 9

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 036

RMSE = 3793

CC = 0888

Rada

r tot

alR

(ZZ

DR)

BC

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 060

RMSE = 5146

CC = 0732

Rada

r tot

alR

(KD

PZ

DR)

BC

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 032

RMSE = 5194

CC = 0818

Rada

r tot

alR

(ZZ

DR)

best

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 092

RMSE = 7302

CC = 0695

Rada

r tot

alR

(KD

PZ

DR)

best

(d)

Figure 7The scatter plot of rainfall from gage and (a) 119877(119885 119885DR) (b) 119877(119870DP 119885DR)with single raindrop axis ratio relation (c) 119877(119885 119885DR) and(d) 119877(119870DP 119885DR) with two-raindrop axis ratio relation

Bringi et al [35] recommended estimating PIA usingΦDPby

PIA (1199031 1199032) = 120572 [ΦDP (1199032) minusΦDP (1199031)] = 120572ΔΦDP (13)

and Testud et al [36] used (10) and (12) to obtain radialprofiles of 119860

119867at C-band In this study 119860

119867was calculated

by the method proposed by Ryzhkov et al [23] The constant

119887 was set by 06 and 120572 was by 0027 calculated by the ratio of119860119867to 119870DP obtained from DSDsFigure 8 shows the scatter plot of rainfall from 119877(119885)

119877(119870DP) and 119877(119860119867) and rainfall from DSDs and an PPIs

(Plan Position Indicators) at 05 degree elevation angle of gagerainfall and rainfall from 119877(119870DP) and 119877(119860

119867) at 0251 KST on

the 8th of August in 2011The 119877(119860

119867) relation had much better fit to the rainfall of

DSDs than that of119877(119870DP) and119877(119885) relation Comparingwith

10 Advances in Meteorology

Beard and Chuang 1987

Rain rate DSD (mmh)

R(Z

) (m

mh

)

10minus1

100

101

102

103

10minus1

100

101

102

103

R = 00277Z05994

NB = minus2122

RMSE = 4709

CC = 0913

(a)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

NB = minus1295136

RMSE = 3198

CC = 0861

R = 533039KDP091341

R(K

DP)

(mm

h)

(b)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(A

H)

(mm

h)

R = 337359AH10194

NB = 327

RMSE = 3667

CC = 0984

(c)

150100705040302015107310500

R(KDP) (mmh)

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(d)

R(AH) (mmh)

150100705040302015107310500

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(e)

Figure 8 The scatter plot of (a) 119877(119885) (b) 119877(119870DP) and (c) 119877(119860119867) with statistics and the rainfall distribution of 119877(119870DP) and 119877(119860

119867) at 0251

KST on the 8th of August in 2001

Advances in Meteorology 11

Table 5 The rainfall relations of 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assumptions

DS 119877(119885119870DP 119860119867) 119877(119885 119885DR 119870DP 119860119867)

DS1 119877 = 1527119885minus004119870DP0327

119860119867

0713119877 = 310Z012

119885DRminus083

119870DP0304

119860119867

0677

DS2 119877 = 12012119885minus024119870DP0551

119860119867

0685119877 = 4947Zminus015119885DR

minus026119870DP

0468119860119867

0681

DS3 119877 = 17211119885minus027119870DP0619

119860119867

0650119877 = 4502Z014

119885DRminus039

119870DP0486

119860119867

0653

DS4 119877 = 10798119885minus019119870DP0403

119860119867

0778119877 = 193Z018

119885DRminus111

119870DP0114

119860119867

0702

DS5 119877 = 20275119885minus027119870DP0543

119860119867

0720119877 = 24Z037

119885DRminus147

119870DPminus0025

119860119867

0656

DS6 119877 = 397119885minus011119870DP0044

119860119867

0808119877 = 571Z007

119885DRminus092

119870DP0238

119860119867

0687

the distribution of rainfall obtained by 119877(119870DP) and 119877(119860119867)

119877(119860119867) has better spatial resolution and more homogeneous

pattern than those of 119877(119870DP)

332 Validations of 119877(119860119867) 119877(119885119870

119863119875 119860119867) and 119877(119885 119885

119863119877

119870119863119875

119860119867) Relations As mentioned in the previous section

119877(119860119867) has the potential to be the best choice for estimating

rainfall using polarimetric variables To verify the accuracy119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) relations

were obtained and the accuracy of 119877(119860119867) 119877(119885119870DP 119860119867)

and 119877(119885 119885DR 119870DP 119860119867) which had the best performance inthe relations calculated by the six raindrop axis ratio relationswere examined by comparing with 119877(119870DP)

Figure 9 shows the scatter plot of rainfall from gagerainfall and 119877(119870DP) 119877(119860

119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR

119870DP 119860119867) for 84 hours The accuracy of 119877(119885 119885DR 119870DP 119860119867)was the best and119877(119885119870DP 119860119867)was the second in 4 relations119877(119860119867)was not better than 119877(119870DP) in whole range of rainfall

However in the range of higher rainfall it seems that 119877(119860119867)

was closer to the gage rainfall The error of 119877(119860119867) would be

caused by the missing radial profile ofΦDP along the rayThemissing has occurred if the difference of ΦDP between thestarting and end gate is negative According to the results119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) would compensatefor this region

34 Optimum Rainfall Algorithm To find out the optimumrainfall algorithm for Korean S-band polarimetric radar thegage rainfall amount was categorized by three steps 0 to5mmh assigned as light rain 5 to 30mmh as medium rainand higher than 30mmh as high rain In previous sectionthe relations have different accuracy not only for the raindropaxis ratio relation but also for rainfall amount The samplenumbers for each category were 3322 samples 1980 samplesand 92 samples respectively

Figure 10 shows the RMSEs of 119877(119870DP) 119877(119885 119885DR)119877(119870DP 119885DR) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) withdifferent rainfall categories defined in three steps All rela-tions have different RMSEs with respect to the raindrop axisratio relations 119877(119870DP) with DS3 119877(119885 119885DR) with DS2 and119877(119870DP 119885DR) with DS3 have the best score at the high rainfallregime at the low rainfall regime and at the medium rainfallregime respectively Even though 119877(119885 119885DR) has the bestperformance among other relations in total rainfall eventsusing different rainfall relations with different rainfall regimewould be an optimum rainfall algorithm for Korean S-band

polarimetric radar A possible optimum polarimetric rainfallalgorithm can be expressed by

119877 = 00141198850852119885DRminus408 0 lt Rainfall lt 5mmhminus1

119877 = 822119870DP0855

119885DRminus198

5 lt Rainfall lt 30mmhminus1

119877 = 615119870DP0908 30mmhminus1 lt Rainfall

(14)

Table 5 shows the rainfall relations of 119877(119885119870DP 119860119867) and119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assump-tions The coefficients of each relation with respect to thedrop shapes were much different comparing with relationsobtained by combining two polarimetric variables

In case of rainfall relations combined with119860119867 119877(119885 119885DR

119870DP 119860119867) has better score than 119877(119885119870DP 119860119867) Both119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with DS3 showedbetter result than other raindrop shape assumptions119877(119885 119885DR 119870DP 119860119867) at the low medium and high rainfallregimes has similar RMSE to 119877(119885 119885DR) 119877(119870DP 119885DR) and119877(119870DP) respectively

Equations (14) would be an optimum rainfall algorithmbut there is still a problem to solve how the rainfall categoriesare defined using radar and gage Gage does not have goodspatial resolution to cover radar resolution like 125m or 1 kmand each rainfall relation has its own error at certain rainfallregime Therefore 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867)withDS3 can be used regardless rainfall intensity And in case119885DR bias calibration is not available or does not have enoughquality for quantitative use 119877(119885119870DP 119860119867) with DS3 can beused as a representative rainfall estimation

4 Summary and Conclusions

Polarimetric radars will be main tools to monitor andforecast severe weather and flash flooding within severalyears in Korea To get an optimum rainfall algorithm usingpolarimetric variables observed from Bislsan radar which isthe first polarimetric radar in Korea rainfall cases for 84hours caused by different conditions which are Changmafront and typhoon Changma front only and typhoon onlythat occurred in 2011 were analyzed And rainfall relationswere obtained by using long period DSDs with six differentraindrop axis ratio relations

In the analysis of 119885 119885DR and119870DP occurrence frequencythere were two modes of 119885DR occurrence frequency and

12 Advances in Meteorology

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100Ra

dar t

otal

R(K

DP)

BC

NE = 052

RMSE = 4645

CC = 0778

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 051

RMSE = 5005

CC = 0797

Rada

r tot

al R

(AH

) AS

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100NE = 046

RMSE = 4374

CC = 0820

Rada

r tot

al R

(ZK

DPA

H) A

S

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 045

RMSE = 4368

CC = 0852

Rada

r tot

al R

(ZZ

DRK

DPA

H) A

S

(d)

Figure 9 The scatter plot of gage rainfall and 119877(119870DP) 119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DP 119870DP 119860119867) rainfall for 84 hours

the variations of 119870DP and 119885DR histograms were higherthan that of 119885 with raindrop ratio relations According tothese variations the combined relations of 119877(119885 119885DR) and119877(119870DP 119885DR) using 119885 with DS3 119885DR with DS1 and 119870DP withDS1 were closer to the rainfall of DSDs

To examine the performance of each rainfall relationNE RMSE CC were calculated using rainfall recorded at121 gages within radar coverage for 84 hours The statisticsof each rainfall relation were different with raindrop shape

assumptions and rainfall intensity119877(119870DP 119885DR)had theworstperformance and119877(119885 119885DR) had the best score in all raindropshapes 119860

119867was calculated by observed ΦDP and 119885 using the

method by Ryzhkov et al [23] and the rainfall relations using119860119867were also calculated and analyzedThe performance of rainfall relations were comparedwith

three different rainfall categories to findout an optimumrain-fall relation for the S-band polarimetric in Korea 119877(119885 119885DR)119877(119870DP 119885DR) and 119877(119870DP) had the best RMSE at the light

Advances in Meteorology 13

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP) with drop shape

(a)

0

5

10

15

20

Drop shape

25

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(Z ZDR) with drop shape

(b)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP ZDR) with drop shape

(c)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(ZKDP AH) with drop shape

(d)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

0ndash5mm5ndash30mmOver 30mm

RMSE of R(Z ZDR KDP AH) with drop shape

(e)

Figure 10The RMSEs of (a) 119877(119870DP) (b) 119877(119885 119885DP) (c) 119877(119870DP 119885DP) (d) 119877(119885119870DP 119860119867) and (e) 119877(119885 119885DP 119870DP 119860119867)with raindrop axis ratiorelations in the three rainfall categories

14 Advances in Meteorology

rain medium rain and high rainfall regimes respectively119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) showed relativelygood performance in all rainfall regimesThe combination of119877(119885 119885DR) 119877(119870DP 119885DR) and 119877(119870DP) with rainfall intensitywould be an optimum rainfall algorithm if the referenceof rainfall would be defined correctly Regardless of rainfallintensity 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) obtainedby assuming DS3 can be used as a representative rainfall rela-tion without consideration of rainfall intensity regime Par-ticularly if the qualified 119885DR is not available 119877(119885119870DP 119860119867)with DS3 drop shape assumption can be used as an optimumrainfall relation in Korea

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge providing radar data weatherchart and AWS data for this work from the Ministry ofLand Infrastructure Transport and Korea MeteorologicalAdministration The authors also acknowledge providingcodes for scattering simulation from Professor V N Bringi atColorado StateUniversityThisworkwas funded by theKoreaMeteorological Industry Promotion Agency under GrantKMIPA 2015-1050

References

[1] E Campos and I Zawadzki ldquoInstrumental uncertainties in Z-R relationsrdquo Journal of Applied Meteorology vol 39 no 7 pp1088ndash1102 2000

[2] C-H You D-I Lee S-M Jang et al ldquoCharacteristics ofrainfall systems accompanied with Changma front at Chujadoin Koreardquo Asia-Pacific Journal of Atmospheric Sciences vol 46no 1 pp 41ndash51 2010

[3] P CWaterman ldquoSymmetry unitarity and geometry in electro-magnetic scatteringrdquo Physical Review D vol 3 no 4 pp 825ndash839 1971

[4] M IMishchenko LD Travis andDWMackowski ldquoT-matrixcomputations of light scattering by nonspherical particles areviewrdquo Journal of Quantitative Spectroscopy and RadiativeTransfer vol 55 no 5 pp 535ndash575 1996

[5] H R Pruppacher and K V Beard ldquoA wind tunnel investigationof the internal circulation and shape of water drops fallingat terminal velocity in airrdquo Quarterly Journal of the RoyalMeteorological Society vol 96 no 408 pp 247ndash256 1970

[6] D C Blanchard ldquoThe behavior of water drops at terminalvelocity in airrdquo EOS vol 31 no 6 pp 836ndash842 1950

[7] G-J Huang V N Bringi M Schonhuber et al ldquoDrop shapeand canting angle distributions in rain from2-Dvideo disdrom-eterrdquo in Proceedings of the 33rd Conference on Radar Meteorol-ogy Extended Abstract P8A8 Cairns Australia August 2007

[8] M Thurai V N Bringi and W A Petersen ldquoRain microstruc-ture retrievals using 2-D video disdrometer and C-band polari-metric radarrdquo Advances in Geosciences vol 20 pp 13ndash18 2009

[9] K V Beard and C Chuang ldquoA new model for the equilibriumshape of raindropsrdquo Journal of the Atmospheric Sciences vol 44pp 1509ndash1524 1987

[10] K Andsager K V Beard and N S Laird ldquoA laboratory studyof oscillations and axis ratios for large raindropsrdquo Journal of theAtmospheric Sciences vol 55 pp 208ndash226 1999

[11] J W Wilson and E A Brandes ldquoRadar measurement of rain-fallmdasha summaryrdquo Bulletin AmericanMeteorological Society vol60 no 9 pp 1048ndash1058 1979

[12] P M Austin ldquoRelation betweenmeasured radar reflectivity andsurface rainfallrdquo Monthly Weather Review vol 115 no 5 pp1053ndash1070 1987

[13] J Vivekanandan D S Zrnic S M Ellis R Oye A V Ryzhkovand J Straka ldquoCloud microphysics retrieval using S-band dual-polarization radar measurementsrdquo Bulletin of the AmericanMeteorological Society vol 80 no 3 pp 381ndash388 1999

[14] A V Ryzhkov and D S Zrnic ldquoDiscrimination between rainand snow with a polarimetric radarrdquo Journal of Applied Meteo-rology vol 37 no 10 pp 1228ndash1240 1998

[15] S E Giangrande and A V Ryzhkov ldquoEstimation of rainfallbased on the results of polarimetric echo classificationrdquo Journalof AppliedMeteorology and Climatology vol 47 no 9 pp 2445ndash2462 2008

[16] A V Ryzhkov and D S Zrnic ldquoAssessment of rainfall measure-ment that uses specific differential phaserdquo Journal of AppliedMeteorology vol 35 no 11 pp 2080ndash2090 1996

[17] P T May T D Keenan D S Zrnic L D Carey and S ARutledge ldquoPolarimetric radar measurements of tropical rain ata 5-cm wavelengthrdquo Journal of Applied Meteorology vol 38 no6 pp 750ndash765 1999

[18] V N Bringi and V Chandrasekar ldquoThe polarimetric basis forcharacterizing precipitationrdquo in Polarimetric Doppler WeatherRadar Principles and Applications pp 378ndash533 CambridgeUniversity Press Cambridge UK 2001

[19] E A Brandes G Zhang and J Vivekanandan ldquoExperiments inrainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[20] A V Ryzhkov T J Schuur D W Burgess P L Heinselman SE Giangrande and D S Zrnic ldquoThe joint polarization exper-iment polarimetric rainfall measurements and hydrometeorclassificationrdquo Bulletin of the American Meteorological Societyvol 86 no 6 pp 809ndash824 2005

[21] A V Ryzhkov S E Giangrande and T J Schuur ldquoRainfall esti-mation with a polarimetric prototype of WSR-88Drdquo Journal ofApplied Meteorology vol 44 no 4 pp 502ndash515 2005

[22] R Cifelli V Chandrasekar S Lim P C Kennedy Y Wang andS A Rutledge ldquoA new dual-polarization radar rainfall algo-rithm application in Colorado precipitation eventsrdquo Journal ofAtmospheric andOceanic Technology vol 28 no 3 pp 352ndash3642011

[23] A Ryzhkov M Diederich P Zhang and C Simmer ldquoPotentialutilization of specific attenuation for rainfall estimationmitiga-tion of partial beam blockage and radar networkingrdquo Journal ofAtmospheric and Oceanic Technology vol 31 no 3 pp 599ndash6192014

[24] C-H You M-Y Kang D-I Lee and H Uyeda ldquoRainfallestimation by S-band polarimetric radar in Korea Part Ipreprocessing and preliminary resultsrdquoMeteorological Applica-tions vol 21 no 4 pp 975ndash983 2014

[25] C-H You D-I Lee andM-Y Kang ldquoRainfall estimation usingspecific differential phase for the first operational polarimetricradar in Koreardquo Advances in Meteorology vol 2014 Article ID413717 10 pages 2014

Advances in Meteorology 15

[26] V N Bringi V Chandrasekar J Hubbert E Gorgucci W LRandeu and M Schoenhuber ldquoRaindrop size distribution indifferent climatic regimes from disdrometer and dual-polarizedradar analysisrdquo Journal of the Atmospheric Sciences vol 60 no2 pp 354ndash365 2003

[27] E A Brandes G Zhang and J Vivekanandan ldquoExperimentsin rainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[28] K V Beard and R J Kubesh ldquoLaboratory measurements ofsmall raindrop distortion Part 2 oscillation frequencies andmodesrdquo Journal of the Atmospheric Sciences vol 48 no 20 pp2245ndash2264 1991

[29] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[30] J W F Goddard K L Morgan A Illingworth and HSauvageot ldquoDual-wavelength polarization measurements inprecipitation using the CAMRA and Rabelias radarsrdquo in Pro-ceedings of the 27th Conference on Radar Meteorology pp 196ndash198 American Meteorology Society Vail Colo USA 1995

[31] A V Ryzhkov D S Zrnic J C Hubbert V N Bringi JVivekanandan and E A Brandes ldquoPolarimetric radar obser-vations and interpretation of co-cross-polar correlation coeffi-cientsrdquo Journal of Atmospheric and Oceanic Technology vol 19no 3 pp 340ndash354 2002

[32] S YMatrosov KAClark B EMartner andA Tokay ldquoX-bandpolarimetric radar measurements of rainfallrdquo Journal of AppliedMeteorology vol 41 no 9 pp 941ndash952 2002

[33] G-J Huang V N Bringi and M Thurai ldquoOrientation angledistributions of drops after an 80-m fall using a 2D videodisdrometerrdquo Journal of Atmospheric and Oceanic Technologyvol 25 no 9 pp 1717ndash1723 2008

[34] R Meneghini and K Nakamura ldquoRange profiling of the rainrate by an airborne weather radarrdquo Remote Sensing of Environ-ment vol 31 no 3 pp 193ndash209 1990

[35] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onpolarimetric variables at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[36] J Testud E L Bouar E Obligis and M Ali-Mehenni ldquoTherain profiling algorithm applied to polarimetric weather radarrdquoJournal of Atmospheric andOceanic Technology vol 17 no 3 pp332ndash356 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

10 Advances in Meteorology

Beard and Chuang 1987

Rain rate DSD (mmh)

R(Z

) (m

mh

)

10minus1

100

101

102

103

10minus1

100

101

102

103

R = 00277Z05994

NB = minus2122

RMSE = 4709

CC = 0913

(a)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

NB = minus1295136

RMSE = 3198

CC = 0861

R = 533039KDP091341

R(K

DP)

(mm

h)

(b)

Beard and Chuang 1987

Rain rate DSD (mmh)

10minus1

100

101

102

103

10minus1

100

101

102

103

R(A

H)

(mm

h)

R = 337359AH10194

NB = 327

RMSE = 3667

CC = 0984

(c)

150100705040302015107310500

R(KDP) (mmh)

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(d)

R(AH) (mmh)

150100705040302015107310500

BSL range 101 km Bin size 0125 km 8Bins 13

20110808 251 4 KST EL 050

(e)

Figure 8 The scatter plot of (a) 119877(119885) (b) 119877(119870DP) and (c) 119877(119860119867) with statistics and the rainfall distribution of 119877(119870DP) and 119877(119860

119867) at 0251

KST on the 8th of August in 2001

Advances in Meteorology 11

Table 5 The rainfall relations of 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assumptions

DS 119877(119885119870DP 119860119867) 119877(119885 119885DR 119870DP 119860119867)

DS1 119877 = 1527119885minus004119870DP0327

119860119867

0713119877 = 310Z012

119885DRminus083

119870DP0304

119860119867

0677

DS2 119877 = 12012119885minus024119870DP0551

119860119867

0685119877 = 4947Zminus015119885DR

minus026119870DP

0468119860119867

0681

DS3 119877 = 17211119885minus027119870DP0619

119860119867

0650119877 = 4502Z014

119885DRminus039

119870DP0486

119860119867

0653

DS4 119877 = 10798119885minus019119870DP0403

119860119867

0778119877 = 193Z018

119885DRminus111

119870DP0114

119860119867

0702

DS5 119877 = 20275119885minus027119870DP0543

119860119867

0720119877 = 24Z037

119885DRminus147

119870DPminus0025

119860119867

0656

DS6 119877 = 397119885minus011119870DP0044

119860119867

0808119877 = 571Z007

119885DRminus092

119870DP0238

119860119867

0687

the distribution of rainfall obtained by 119877(119870DP) and 119877(119860119867)

119877(119860119867) has better spatial resolution and more homogeneous

pattern than those of 119877(119870DP)

332 Validations of 119877(119860119867) 119877(119885119870

119863119875 119860119867) and 119877(119885 119885

119863119877

119870119863119875

119860119867) Relations As mentioned in the previous section

119877(119860119867) has the potential to be the best choice for estimating

rainfall using polarimetric variables To verify the accuracy119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) relations

were obtained and the accuracy of 119877(119860119867) 119877(119885119870DP 119860119867)

and 119877(119885 119885DR 119870DP 119860119867) which had the best performance inthe relations calculated by the six raindrop axis ratio relationswere examined by comparing with 119877(119870DP)

Figure 9 shows the scatter plot of rainfall from gagerainfall and 119877(119870DP) 119877(119860

119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR

119870DP 119860119867) for 84 hours The accuracy of 119877(119885 119885DR 119870DP 119860119867)was the best and119877(119885119870DP 119860119867)was the second in 4 relations119877(119860119867)was not better than 119877(119870DP) in whole range of rainfall

However in the range of higher rainfall it seems that 119877(119860119867)

was closer to the gage rainfall The error of 119877(119860119867) would be

caused by the missing radial profile ofΦDP along the rayThemissing has occurred if the difference of ΦDP between thestarting and end gate is negative According to the results119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) would compensatefor this region

34 Optimum Rainfall Algorithm To find out the optimumrainfall algorithm for Korean S-band polarimetric radar thegage rainfall amount was categorized by three steps 0 to5mmh assigned as light rain 5 to 30mmh as medium rainand higher than 30mmh as high rain In previous sectionthe relations have different accuracy not only for the raindropaxis ratio relation but also for rainfall amount The samplenumbers for each category were 3322 samples 1980 samplesand 92 samples respectively

Figure 10 shows the RMSEs of 119877(119870DP) 119877(119885 119885DR)119877(119870DP 119885DR) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) withdifferent rainfall categories defined in three steps All rela-tions have different RMSEs with respect to the raindrop axisratio relations 119877(119870DP) with DS3 119877(119885 119885DR) with DS2 and119877(119870DP 119885DR) with DS3 have the best score at the high rainfallregime at the low rainfall regime and at the medium rainfallregime respectively Even though 119877(119885 119885DR) has the bestperformance among other relations in total rainfall eventsusing different rainfall relations with different rainfall regimewould be an optimum rainfall algorithm for Korean S-band

polarimetric radar A possible optimum polarimetric rainfallalgorithm can be expressed by

119877 = 00141198850852119885DRminus408 0 lt Rainfall lt 5mmhminus1

119877 = 822119870DP0855

119885DRminus198

5 lt Rainfall lt 30mmhminus1

119877 = 615119870DP0908 30mmhminus1 lt Rainfall

(14)

Table 5 shows the rainfall relations of 119877(119885119870DP 119860119867) and119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assump-tions The coefficients of each relation with respect to thedrop shapes were much different comparing with relationsobtained by combining two polarimetric variables

In case of rainfall relations combined with119860119867 119877(119885 119885DR

119870DP 119860119867) has better score than 119877(119885119870DP 119860119867) Both119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with DS3 showedbetter result than other raindrop shape assumptions119877(119885 119885DR 119870DP 119860119867) at the low medium and high rainfallregimes has similar RMSE to 119877(119885 119885DR) 119877(119870DP 119885DR) and119877(119870DP) respectively

Equations (14) would be an optimum rainfall algorithmbut there is still a problem to solve how the rainfall categoriesare defined using radar and gage Gage does not have goodspatial resolution to cover radar resolution like 125m or 1 kmand each rainfall relation has its own error at certain rainfallregime Therefore 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867)withDS3 can be used regardless rainfall intensity And in case119885DR bias calibration is not available or does not have enoughquality for quantitative use 119877(119885119870DP 119860119867) with DS3 can beused as a representative rainfall estimation

4 Summary and Conclusions

Polarimetric radars will be main tools to monitor andforecast severe weather and flash flooding within severalyears in Korea To get an optimum rainfall algorithm usingpolarimetric variables observed from Bislsan radar which isthe first polarimetric radar in Korea rainfall cases for 84hours caused by different conditions which are Changmafront and typhoon Changma front only and typhoon onlythat occurred in 2011 were analyzed And rainfall relationswere obtained by using long period DSDs with six differentraindrop axis ratio relations

In the analysis of 119885 119885DR and119870DP occurrence frequencythere were two modes of 119885DR occurrence frequency and

12 Advances in Meteorology

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100Ra

dar t

otal

R(K

DP)

BC

NE = 052

RMSE = 4645

CC = 0778

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 051

RMSE = 5005

CC = 0797

Rada

r tot

al R

(AH

) AS

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100NE = 046

RMSE = 4374

CC = 0820

Rada

r tot

al R

(ZK

DPA

H) A

S

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 045

RMSE = 4368

CC = 0852

Rada

r tot

al R

(ZZ

DRK

DPA

H) A

S

(d)

Figure 9 The scatter plot of gage rainfall and 119877(119870DP) 119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DP 119870DP 119860119867) rainfall for 84 hours

the variations of 119870DP and 119885DR histograms were higherthan that of 119885 with raindrop ratio relations According tothese variations the combined relations of 119877(119885 119885DR) and119877(119870DP 119885DR) using 119885 with DS3 119885DR with DS1 and 119870DP withDS1 were closer to the rainfall of DSDs

To examine the performance of each rainfall relationNE RMSE CC were calculated using rainfall recorded at121 gages within radar coverage for 84 hours The statisticsof each rainfall relation were different with raindrop shape

assumptions and rainfall intensity119877(119870DP 119885DR)had theworstperformance and119877(119885 119885DR) had the best score in all raindropshapes 119860

119867was calculated by observed ΦDP and 119885 using the

method by Ryzhkov et al [23] and the rainfall relations using119860119867were also calculated and analyzedThe performance of rainfall relations were comparedwith

three different rainfall categories to findout an optimumrain-fall relation for the S-band polarimetric in Korea 119877(119885 119885DR)119877(119870DP 119885DR) and 119877(119870DP) had the best RMSE at the light

Advances in Meteorology 13

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP) with drop shape

(a)

0

5

10

15

20

Drop shape

25

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(Z ZDR) with drop shape

(b)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP ZDR) with drop shape

(c)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(ZKDP AH) with drop shape

(d)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

0ndash5mm5ndash30mmOver 30mm

RMSE of R(Z ZDR KDP AH) with drop shape

(e)

Figure 10The RMSEs of (a) 119877(119870DP) (b) 119877(119885 119885DP) (c) 119877(119870DP 119885DP) (d) 119877(119885119870DP 119860119867) and (e) 119877(119885 119885DP 119870DP 119860119867)with raindrop axis ratiorelations in the three rainfall categories

14 Advances in Meteorology

rain medium rain and high rainfall regimes respectively119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) showed relativelygood performance in all rainfall regimesThe combination of119877(119885 119885DR) 119877(119870DP 119885DR) and 119877(119870DP) with rainfall intensitywould be an optimum rainfall algorithm if the referenceof rainfall would be defined correctly Regardless of rainfallintensity 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) obtainedby assuming DS3 can be used as a representative rainfall rela-tion without consideration of rainfall intensity regime Par-ticularly if the qualified 119885DR is not available 119877(119885119870DP 119860119867)with DS3 drop shape assumption can be used as an optimumrainfall relation in Korea

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge providing radar data weatherchart and AWS data for this work from the Ministry ofLand Infrastructure Transport and Korea MeteorologicalAdministration The authors also acknowledge providingcodes for scattering simulation from Professor V N Bringi atColorado StateUniversityThisworkwas funded by theKoreaMeteorological Industry Promotion Agency under GrantKMIPA 2015-1050

References

[1] E Campos and I Zawadzki ldquoInstrumental uncertainties in Z-R relationsrdquo Journal of Applied Meteorology vol 39 no 7 pp1088ndash1102 2000

[2] C-H You D-I Lee S-M Jang et al ldquoCharacteristics ofrainfall systems accompanied with Changma front at Chujadoin Koreardquo Asia-Pacific Journal of Atmospheric Sciences vol 46no 1 pp 41ndash51 2010

[3] P CWaterman ldquoSymmetry unitarity and geometry in electro-magnetic scatteringrdquo Physical Review D vol 3 no 4 pp 825ndash839 1971

[4] M IMishchenko LD Travis andDWMackowski ldquoT-matrixcomputations of light scattering by nonspherical particles areviewrdquo Journal of Quantitative Spectroscopy and RadiativeTransfer vol 55 no 5 pp 535ndash575 1996

[5] H R Pruppacher and K V Beard ldquoA wind tunnel investigationof the internal circulation and shape of water drops fallingat terminal velocity in airrdquo Quarterly Journal of the RoyalMeteorological Society vol 96 no 408 pp 247ndash256 1970

[6] D C Blanchard ldquoThe behavior of water drops at terminalvelocity in airrdquo EOS vol 31 no 6 pp 836ndash842 1950

[7] G-J Huang V N Bringi M Schonhuber et al ldquoDrop shapeand canting angle distributions in rain from2-Dvideo disdrom-eterrdquo in Proceedings of the 33rd Conference on Radar Meteorol-ogy Extended Abstract P8A8 Cairns Australia August 2007

[8] M Thurai V N Bringi and W A Petersen ldquoRain microstruc-ture retrievals using 2-D video disdrometer and C-band polari-metric radarrdquo Advances in Geosciences vol 20 pp 13ndash18 2009

[9] K V Beard and C Chuang ldquoA new model for the equilibriumshape of raindropsrdquo Journal of the Atmospheric Sciences vol 44pp 1509ndash1524 1987

[10] K Andsager K V Beard and N S Laird ldquoA laboratory studyof oscillations and axis ratios for large raindropsrdquo Journal of theAtmospheric Sciences vol 55 pp 208ndash226 1999

[11] J W Wilson and E A Brandes ldquoRadar measurement of rain-fallmdasha summaryrdquo Bulletin AmericanMeteorological Society vol60 no 9 pp 1048ndash1058 1979

[12] P M Austin ldquoRelation betweenmeasured radar reflectivity andsurface rainfallrdquo Monthly Weather Review vol 115 no 5 pp1053ndash1070 1987

[13] J Vivekanandan D S Zrnic S M Ellis R Oye A V Ryzhkovand J Straka ldquoCloud microphysics retrieval using S-band dual-polarization radar measurementsrdquo Bulletin of the AmericanMeteorological Society vol 80 no 3 pp 381ndash388 1999

[14] A V Ryzhkov and D S Zrnic ldquoDiscrimination between rainand snow with a polarimetric radarrdquo Journal of Applied Meteo-rology vol 37 no 10 pp 1228ndash1240 1998

[15] S E Giangrande and A V Ryzhkov ldquoEstimation of rainfallbased on the results of polarimetric echo classificationrdquo Journalof AppliedMeteorology and Climatology vol 47 no 9 pp 2445ndash2462 2008

[16] A V Ryzhkov and D S Zrnic ldquoAssessment of rainfall measure-ment that uses specific differential phaserdquo Journal of AppliedMeteorology vol 35 no 11 pp 2080ndash2090 1996

[17] P T May T D Keenan D S Zrnic L D Carey and S ARutledge ldquoPolarimetric radar measurements of tropical rain ata 5-cm wavelengthrdquo Journal of Applied Meteorology vol 38 no6 pp 750ndash765 1999

[18] V N Bringi and V Chandrasekar ldquoThe polarimetric basis forcharacterizing precipitationrdquo in Polarimetric Doppler WeatherRadar Principles and Applications pp 378ndash533 CambridgeUniversity Press Cambridge UK 2001

[19] E A Brandes G Zhang and J Vivekanandan ldquoExperiments inrainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[20] A V Ryzhkov T J Schuur D W Burgess P L Heinselman SE Giangrande and D S Zrnic ldquoThe joint polarization exper-iment polarimetric rainfall measurements and hydrometeorclassificationrdquo Bulletin of the American Meteorological Societyvol 86 no 6 pp 809ndash824 2005

[21] A V Ryzhkov S E Giangrande and T J Schuur ldquoRainfall esti-mation with a polarimetric prototype of WSR-88Drdquo Journal ofApplied Meteorology vol 44 no 4 pp 502ndash515 2005

[22] R Cifelli V Chandrasekar S Lim P C Kennedy Y Wang andS A Rutledge ldquoA new dual-polarization radar rainfall algo-rithm application in Colorado precipitation eventsrdquo Journal ofAtmospheric andOceanic Technology vol 28 no 3 pp 352ndash3642011

[23] A Ryzhkov M Diederich P Zhang and C Simmer ldquoPotentialutilization of specific attenuation for rainfall estimationmitiga-tion of partial beam blockage and radar networkingrdquo Journal ofAtmospheric and Oceanic Technology vol 31 no 3 pp 599ndash6192014

[24] C-H You M-Y Kang D-I Lee and H Uyeda ldquoRainfallestimation by S-band polarimetric radar in Korea Part Ipreprocessing and preliminary resultsrdquoMeteorological Applica-tions vol 21 no 4 pp 975ndash983 2014

[25] C-H You D-I Lee andM-Y Kang ldquoRainfall estimation usingspecific differential phase for the first operational polarimetricradar in Koreardquo Advances in Meteorology vol 2014 Article ID413717 10 pages 2014

Advances in Meteorology 15

[26] V N Bringi V Chandrasekar J Hubbert E Gorgucci W LRandeu and M Schoenhuber ldquoRaindrop size distribution indifferent climatic regimes from disdrometer and dual-polarizedradar analysisrdquo Journal of the Atmospheric Sciences vol 60 no2 pp 354ndash365 2003

[27] E A Brandes G Zhang and J Vivekanandan ldquoExperimentsin rainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[28] K V Beard and R J Kubesh ldquoLaboratory measurements ofsmall raindrop distortion Part 2 oscillation frequencies andmodesrdquo Journal of the Atmospheric Sciences vol 48 no 20 pp2245ndash2264 1991

[29] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[30] J W F Goddard K L Morgan A Illingworth and HSauvageot ldquoDual-wavelength polarization measurements inprecipitation using the CAMRA and Rabelias radarsrdquo in Pro-ceedings of the 27th Conference on Radar Meteorology pp 196ndash198 American Meteorology Society Vail Colo USA 1995

[31] A V Ryzhkov D S Zrnic J C Hubbert V N Bringi JVivekanandan and E A Brandes ldquoPolarimetric radar obser-vations and interpretation of co-cross-polar correlation coeffi-cientsrdquo Journal of Atmospheric and Oceanic Technology vol 19no 3 pp 340ndash354 2002

[32] S YMatrosov KAClark B EMartner andA Tokay ldquoX-bandpolarimetric radar measurements of rainfallrdquo Journal of AppliedMeteorology vol 41 no 9 pp 941ndash952 2002

[33] G-J Huang V N Bringi and M Thurai ldquoOrientation angledistributions of drops after an 80-m fall using a 2D videodisdrometerrdquo Journal of Atmospheric and Oceanic Technologyvol 25 no 9 pp 1717ndash1723 2008

[34] R Meneghini and K Nakamura ldquoRange profiling of the rainrate by an airborne weather radarrdquo Remote Sensing of Environ-ment vol 31 no 3 pp 193ndash209 1990

[35] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onpolarimetric variables at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[36] J Testud E L Bouar E Obligis and M Ali-Mehenni ldquoTherain profiling algorithm applied to polarimetric weather radarrdquoJournal of Atmospheric andOceanic Technology vol 17 no 3 pp332ndash356 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Advances in Meteorology 11

Table 5 The rainfall relations of 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assumptions

DS 119877(119885119870DP 119860119867) 119877(119885 119885DR 119870DP 119860119867)

DS1 119877 = 1527119885minus004119870DP0327

119860119867

0713119877 = 310Z012

119885DRminus083

119870DP0304

119860119867

0677

DS2 119877 = 12012119885minus024119870DP0551

119860119867

0685119877 = 4947Zminus015119885DR

minus026119870DP

0468119860119867

0681

DS3 119877 = 17211119885minus027119870DP0619

119860119867

0650119877 = 4502Z014

119885DRminus039

119870DP0486

119860119867

0653

DS4 119877 = 10798119885minus019119870DP0403

119860119867

0778119877 = 193Z018

119885DRminus111

119870DP0114

119860119867

0702

DS5 119877 = 20275119885minus027119870DP0543

119860119867

0720119877 = 24Z037

119885DRminus147

119870DPminus0025

119860119867

0656

DS6 119877 = 397119885minus011119870DP0044

119860119867

0808119877 = 571Z007

119885DRminus092

119870DP0238

119860119867

0687

the distribution of rainfall obtained by 119877(119870DP) and 119877(119860119867)

119877(119860119867) has better spatial resolution and more homogeneous

pattern than those of 119877(119870DP)

332 Validations of 119877(119860119867) 119877(119885119870

119863119875 119860119867) and 119877(119885 119885

119863119877

119870119863119875

119860119867) Relations As mentioned in the previous section

119877(119860119867) has the potential to be the best choice for estimating

rainfall using polarimetric variables To verify the accuracy119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) relations

were obtained and the accuracy of 119877(119860119867) 119877(119885119870DP 119860119867)

and 119877(119885 119885DR 119870DP 119860119867) which had the best performance inthe relations calculated by the six raindrop axis ratio relationswere examined by comparing with 119877(119870DP)

Figure 9 shows the scatter plot of rainfall from gagerainfall and 119877(119870DP) 119877(119860

119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DR

119870DP 119860119867) for 84 hours The accuracy of 119877(119885 119885DR 119870DP 119860119867)was the best and119877(119885119870DP 119860119867)was the second in 4 relations119877(119860119867)was not better than 119877(119870DP) in whole range of rainfall

However in the range of higher rainfall it seems that 119877(119860119867)

was closer to the gage rainfall The error of 119877(119860119867) would be

caused by the missing radial profile ofΦDP along the rayThemissing has occurred if the difference of ΦDP between thestarting and end gate is negative According to the results119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) would compensatefor this region

34 Optimum Rainfall Algorithm To find out the optimumrainfall algorithm for Korean S-band polarimetric radar thegage rainfall amount was categorized by three steps 0 to5mmh assigned as light rain 5 to 30mmh as medium rainand higher than 30mmh as high rain In previous sectionthe relations have different accuracy not only for the raindropaxis ratio relation but also for rainfall amount The samplenumbers for each category were 3322 samples 1980 samplesand 92 samples respectively

Figure 10 shows the RMSEs of 119877(119870DP) 119877(119885 119885DR)119877(119870DP 119885DR) 119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) withdifferent rainfall categories defined in three steps All rela-tions have different RMSEs with respect to the raindrop axisratio relations 119877(119870DP) with DS3 119877(119885 119885DR) with DS2 and119877(119870DP 119885DR) with DS3 have the best score at the high rainfallregime at the low rainfall regime and at the medium rainfallregime respectively Even though 119877(119885 119885DR) has the bestperformance among other relations in total rainfall eventsusing different rainfall relations with different rainfall regimewould be an optimum rainfall algorithm for Korean S-band

polarimetric radar A possible optimum polarimetric rainfallalgorithm can be expressed by

119877 = 00141198850852119885DRminus408 0 lt Rainfall lt 5mmhminus1

119877 = 822119870DP0855

119885DRminus198

5 lt Rainfall lt 30mmhminus1

119877 = 615119870DP0908 30mmhminus1 lt Rainfall

(14)

Table 5 shows the rainfall relations of 119877(119885119870DP 119860119867) and119877(119885 119885DR 119870DP 119860119867) with different raindrop shape assump-tions The coefficients of each relation with respect to thedrop shapes were much different comparing with relationsobtained by combining two polarimetric variables

In case of rainfall relations combined with119860119867 119877(119885 119885DR

119870DP 119860119867) has better score than 119877(119885119870DP 119860119867) Both119877(119885119870DP 119860119867) and 119877(119885 119885DR 119870DP 119860119867) with DS3 showedbetter result than other raindrop shape assumptions119877(119885 119885DR 119870DP 119860119867) at the low medium and high rainfallregimes has similar RMSE to 119877(119885 119885DR) 119877(119870DP 119885DR) and119877(119870DP) respectively

Equations (14) would be an optimum rainfall algorithmbut there is still a problem to solve how the rainfall categoriesare defined using radar and gage Gage does not have goodspatial resolution to cover radar resolution like 125m or 1 kmand each rainfall relation has its own error at certain rainfallregime Therefore 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867)withDS3 can be used regardless rainfall intensity And in case119885DR bias calibration is not available or does not have enoughquality for quantitative use 119877(119885119870DP 119860119867) with DS3 can beused as a representative rainfall estimation

4 Summary and Conclusions

Polarimetric radars will be main tools to monitor andforecast severe weather and flash flooding within severalyears in Korea To get an optimum rainfall algorithm usingpolarimetric variables observed from Bislsan radar which isthe first polarimetric radar in Korea rainfall cases for 84hours caused by different conditions which are Changmafront and typhoon Changma front only and typhoon onlythat occurred in 2011 were analyzed And rainfall relationswere obtained by using long period DSDs with six differentraindrop axis ratio relations

In the analysis of 119885 119885DR and119870DP occurrence frequencythere were two modes of 119885DR occurrence frequency and

12 Advances in Meteorology

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100Ra

dar t

otal

R(K

DP)

BC

NE = 052

RMSE = 4645

CC = 0778

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 051

RMSE = 5005

CC = 0797

Rada

r tot

al R

(AH

) AS

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100NE = 046

RMSE = 4374

CC = 0820

Rada

r tot

al R

(ZK

DPA

H) A

S

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 045

RMSE = 4368

CC = 0852

Rada

r tot

al R

(ZZ

DRK

DPA

H) A

S

(d)

Figure 9 The scatter plot of gage rainfall and 119877(119870DP) 119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DP 119870DP 119860119867) rainfall for 84 hours

the variations of 119870DP and 119885DR histograms were higherthan that of 119885 with raindrop ratio relations According tothese variations the combined relations of 119877(119885 119885DR) and119877(119870DP 119885DR) using 119885 with DS3 119885DR with DS1 and 119870DP withDS1 were closer to the rainfall of DSDs

To examine the performance of each rainfall relationNE RMSE CC were calculated using rainfall recorded at121 gages within radar coverage for 84 hours The statisticsof each rainfall relation were different with raindrop shape

assumptions and rainfall intensity119877(119870DP 119885DR)had theworstperformance and119877(119885 119885DR) had the best score in all raindropshapes 119860

119867was calculated by observed ΦDP and 119885 using the

method by Ryzhkov et al [23] and the rainfall relations using119860119867were also calculated and analyzedThe performance of rainfall relations were comparedwith

three different rainfall categories to findout an optimumrain-fall relation for the S-band polarimetric in Korea 119877(119885 119885DR)119877(119870DP 119885DR) and 119877(119870DP) had the best RMSE at the light

Advances in Meteorology 13

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP) with drop shape

(a)

0

5

10

15

20

Drop shape

25

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(Z ZDR) with drop shape

(b)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP ZDR) with drop shape

(c)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(ZKDP AH) with drop shape

(d)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

0ndash5mm5ndash30mmOver 30mm

RMSE of R(Z ZDR KDP AH) with drop shape

(e)

Figure 10The RMSEs of (a) 119877(119870DP) (b) 119877(119885 119885DP) (c) 119877(119870DP 119885DP) (d) 119877(119885119870DP 119860119867) and (e) 119877(119885 119885DP 119870DP 119860119867)with raindrop axis ratiorelations in the three rainfall categories

14 Advances in Meteorology

rain medium rain and high rainfall regimes respectively119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) showed relativelygood performance in all rainfall regimesThe combination of119877(119885 119885DR) 119877(119870DP 119885DR) and 119877(119870DP) with rainfall intensitywould be an optimum rainfall algorithm if the referenceof rainfall would be defined correctly Regardless of rainfallintensity 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) obtainedby assuming DS3 can be used as a representative rainfall rela-tion without consideration of rainfall intensity regime Par-ticularly if the qualified 119885DR is not available 119877(119885119870DP 119860119867)with DS3 drop shape assumption can be used as an optimumrainfall relation in Korea

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge providing radar data weatherchart and AWS data for this work from the Ministry ofLand Infrastructure Transport and Korea MeteorologicalAdministration The authors also acknowledge providingcodes for scattering simulation from Professor V N Bringi atColorado StateUniversityThisworkwas funded by theKoreaMeteorological Industry Promotion Agency under GrantKMIPA 2015-1050

References

[1] E Campos and I Zawadzki ldquoInstrumental uncertainties in Z-R relationsrdquo Journal of Applied Meteorology vol 39 no 7 pp1088ndash1102 2000

[2] C-H You D-I Lee S-M Jang et al ldquoCharacteristics ofrainfall systems accompanied with Changma front at Chujadoin Koreardquo Asia-Pacific Journal of Atmospheric Sciences vol 46no 1 pp 41ndash51 2010

[3] P CWaterman ldquoSymmetry unitarity and geometry in electro-magnetic scatteringrdquo Physical Review D vol 3 no 4 pp 825ndash839 1971

[4] M IMishchenko LD Travis andDWMackowski ldquoT-matrixcomputations of light scattering by nonspherical particles areviewrdquo Journal of Quantitative Spectroscopy and RadiativeTransfer vol 55 no 5 pp 535ndash575 1996

[5] H R Pruppacher and K V Beard ldquoA wind tunnel investigationof the internal circulation and shape of water drops fallingat terminal velocity in airrdquo Quarterly Journal of the RoyalMeteorological Society vol 96 no 408 pp 247ndash256 1970

[6] D C Blanchard ldquoThe behavior of water drops at terminalvelocity in airrdquo EOS vol 31 no 6 pp 836ndash842 1950

[7] G-J Huang V N Bringi M Schonhuber et al ldquoDrop shapeand canting angle distributions in rain from2-Dvideo disdrom-eterrdquo in Proceedings of the 33rd Conference on Radar Meteorol-ogy Extended Abstract P8A8 Cairns Australia August 2007

[8] M Thurai V N Bringi and W A Petersen ldquoRain microstruc-ture retrievals using 2-D video disdrometer and C-band polari-metric radarrdquo Advances in Geosciences vol 20 pp 13ndash18 2009

[9] K V Beard and C Chuang ldquoA new model for the equilibriumshape of raindropsrdquo Journal of the Atmospheric Sciences vol 44pp 1509ndash1524 1987

[10] K Andsager K V Beard and N S Laird ldquoA laboratory studyof oscillations and axis ratios for large raindropsrdquo Journal of theAtmospheric Sciences vol 55 pp 208ndash226 1999

[11] J W Wilson and E A Brandes ldquoRadar measurement of rain-fallmdasha summaryrdquo Bulletin AmericanMeteorological Society vol60 no 9 pp 1048ndash1058 1979

[12] P M Austin ldquoRelation betweenmeasured radar reflectivity andsurface rainfallrdquo Monthly Weather Review vol 115 no 5 pp1053ndash1070 1987

[13] J Vivekanandan D S Zrnic S M Ellis R Oye A V Ryzhkovand J Straka ldquoCloud microphysics retrieval using S-band dual-polarization radar measurementsrdquo Bulletin of the AmericanMeteorological Society vol 80 no 3 pp 381ndash388 1999

[14] A V Ryzhkov and D S Zrnic ldquoDiscrimination between rainand snow with a polarimetric radarrdquo Journal of Applied Meteo-rology vol 37 no 10 pp 1228ndash1240 1998

[15] S E Giangrande and A V Ryzhkov ldquoEstimation of rainfallbased on the results of polarimetric echo classificationrdquo Journalof AppliedMeteorology and Climatology vol 47 no 9 pp 2445ndash2462 2008

[16] A V Ryzhkov and D S Zrnic ldquoAssessment of rainfall measure-ment that uses specific differential phaserdquo Journal of AppliedMeteorology vol 35 no 11 pp 2080ndash2090 1996

[17] P T May T D Keenan D S Zrnic L D Carey and S ARutledge ldquoPolarimetric radar measurements of tropical rain ata 5-cm wavelengthrdquo Journal of Applied Meteorology vol 38 no6 pp 750ndash765 1999

[18] V N Bringi and V Chandrasekar ldquoThe polarimetric basis forcharacterizing precipitationrdquo in Polarimetric Doppler WeatherRadar Principles and Applications pp 378ndash533 CambridgeUniversity Press Cambridge UK 2001

[19] E A Brandes G Zhang and J Vivekanandan ldquoExperiments inrainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[20] A V Ryzhkov T J Schuur D W Burgess P L Heinselman SE Giangrande and D S Zrnic ldquoThe joint polarization exper-iment polarimetric rainfall measurements and hydrometeorclassificationrdquo Bulletin of the American Meteorological Societyvol 86 no 6 pp 809ndash824 2005

[21] A V Ryzhkov S E Giangrande and T J Schuur ldquoRainfall esti-mation with a polarimetric prototype of WSR-88Drdquo Journal ofApplied Meteorology vol 44 no 4 pp 502ndash515 2005

[22] R Cifelli V Chandrasekar S Lim P C Kennedy Y Wang andS A Rutledge ldquoA new dual-polarization radar rainfall algo-rithm application in Colorado precipitation eventsrdquo Journal ofAtmospheric andOceanic Technology vol 28 no 3 pp 352ndash3642011

[23] A Ryzhkov M Diederich P Zhang and C Simmer ldquoPotentialutilization of specific attenuation for rainfall estimationmitiga-tion of partial beam blockage and radar networkingrdquo Journal ofAtmospheric and Oceanic Technology vol 31 no 3 pp 599ndash6192014

[24] C-H You M-Y Kang D-I Lee and H Uyeda ldquoRainfallestimation by S-band polarimetric radar in Korea Part Ipreprocessing and preliminary resultsrdquoMeteorological Applica-tions vol 21 no 4 pp 975ndash983 2014

[25] C-H You D-I Lee andM-Y Kang ldquoRainfall estimation usingspecific differential phase for the first operational polarimetricradar in Koreardquo Advances in Meteorology vol 2014 Article ID413717 10 pages 2014

Advances in Meteorology 15

[26] V N Bringi V Chandrasekar J Hubbert E Gorgucci W LRandeu and M Schoenhuber ldquoRaindrop size distribution indifferent climatic regimes from disdrometer and dual-polarizedradar analysisrdquo Journal of the Atmospheric Sciences vol 60 no2 pp 354ndash365 2003

[27] E A Brandes G Zhang and J Vivekanandan ldquoExperimentsin rainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[28] K V Beard and R J Kubesh ldquoLaboratory measurements ofsmall raindrop distortion Part 2 oscillation frequencies andmodesrdquo Journal of the Atmospheric Sciences vol 48 no 20 pp2245ndash2264 1991

[29] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[30] J W F Goddard K L Morgan A Illingworth and HSauvageot ldquoDual-wavelength polarization measurements inprecipitation using the CAMRA and Rabelias radarsrdquo in Pro-ceedings of the 27th Conference on Radar Meteorology pp 196ndash198 American Meteorology Society Vail Colo USA 1995

[31] A V Ryzhkov D S Zrnic J C Hubbert V N Bringi JVivekanandan and E A Brandes ldquoPolarimetric radar obser-vations and interpretation of co-cross-polar correlation coeffi-cientsrdquo Journal of Atmospheric and Oceanic Technology vol 19no 3 pp 340ndash354 2002

[32] S YMatrosov KAClark B EMartner andA Tokay ldquoX-bandpolarimetric radar measurements of rainfallrdquo Journal of AppliedMeteorology vol 41 no 9 pp 941ndash952 2002

[33] G-J Huang V N Bringi and M Thurai ldquoOrientation angledistributions of drops after an 80-m fall using a 2D videodisdrometerrdquo Journal of Atmospheric and Oceanic Technologyvol 25 no 9 pp 1717ndash1723 2008

[34] R Meneghini and K Nakamura ldquoRange profiling of the rainrate by an airborne weather radarrdquo Remote Sensing of Environ-ment vol 31 no 3 pp 193ndash209 1990

[35] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onpolarimetric variables at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[36] J Testud E L Bouar E Obligis and M Ali-Mehenni ldquoTherain profiling algorithm applied to polarimetric weather radarrdquoJournal of Atmospheric andOceanic Technology vol 17 no 3 pp332ndash356 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

12 Advances in Meteorology

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100Ra

dar t

otal

R(K

DP)

BC

NE = 052

RMSE = 4645

CC = 0778

(a)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 051

RMSE = 5005

CC = 0797

Rada

r tot

al R

(AH

) AS

(b)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100NE = 046

RMSE = 4374

CC = 0820

Rada

r tot

al R

(ZK

DPA

H) A

S

(c)

0 20 40 60 80 100Gage total AWS (mm)

0

20

40

60

80

100

NE = 045

RMSE = 4368

CC = 0852

Rada

r tot

al R

(ZZ

DRK

DPA

H) A

S

(d)

Figure 9 The scatter plot of gage rainfall and 119877(119870DP) 119877(119860119867) 119877(119885119870DP 119860119867) and 119877(119885 119885DP 119870DP 119860119867) rainfall for 84 hours

the variations of 119870DP and 119885DR histograms were higherthan that of 119885 with raindrop ratio relations According tothese variations the combined relations of 119877(119885 119885DR) and119877(119870DP 119885DR) using 119885 with DS3 119885DR with DS1 and 119870DP withDS1 were closer to the rainfall of DSDs

To examine the performance of each rainfall relationNE RMSE CC were calculated using rainfall recorded at121 gages within radar coverage for 84 hours The statisticsof each rainfall relation were different with raindrop shape

assumptions and rainfall intensity119877(119870DP 119885DR)had theworstperformance and119877(119885 119885DR) had the best score in all raindropshapes 119860

119867was calculated by observed ΦDP and 119885 using the

method by Ryzhkov et al [23] and the rainfall relations using119860119867were also calculated and analyzedThe performance of rainfall relations were comparedwith

three different rainfall categories to findout an optimumrain-fall relation for the S-band polarimetric in Korea 119877(119885 119885DR)119877(119870DP 119885DR) and 119877(119870DP) had the best RMSE at the light

Advances in Meteorology 13

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP) with drop shape

(a)

0

5

10

15

20

Drop shape

25

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(Z ZDR) with drop shape

(b)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP ZDR) with drop shape

(c)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(ZKDP AH) with drop shape

(d)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

0ndash5mm5ndash30mmOver 30mm

RMSE of R(Z ZDR KDP AH) with drop shape

(e)

Figure 10The RMSEs of (a) 119877(119870DP) (b) 119877(119885 119885DP) (c) 119877(119870DP 119885DP) (d) 119877(119885119870DP 119860119867) and (e) 119877(119885 119885DP 119870DP 119860119867)with raindrop axis ratiorelations in the three rainfall categories

14 Advances in Meteorology

rain medium rain and high rainfall regimes respectively119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) showed relativelygood performance in all rainfall regimesThe combination of119877(119885 119885DR) 119877(119870DP 119885DR) and 119877(119870DP) with rainfall intensitywould be an optimum rainfall algorithm if the referenceof rainfall would be defined correctly Regardless of rainfallintensity 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) obtainedby assuming DS3 can be used as a representative rainfall rela-tion without consideration of rainfall intensity regime Par-ticularly if the qualified 119885DR is not available 119877(119885119870DP 119860119867)with DS3 drop shape assumption can be used as an optimumrainfall relation in Korea

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge providing radar data weatherchart and AWS data for this work from the Ministry ofLand Infrastructure Transport and Korea MeteorologicalAdministration The authors also acknowledge providingcodes for scattering simulation from Professor V N Bringi atColorado StateUniversityThisworkwas funded by theKoreaMeteorological Industry Promotion Agency under GrantKMIPA 2015-1050

References

[1] E Campos and I Zawadzki ldquoInstrumental uncertainties in Z-R relationsrdquo Journal of Applied Meteorology vol 39 no 7 pp1088ndash1102 2000

[2] C-H You D-I Lee S-M Jang et al ldquoCharacteristics ofrainfall systems accompanied with Changma front at Chujadoin Koreardquo Asia-Pacific Journal of Atmospheric Sciences vol 46no 1 pp 41ndash51 2010

[3] P CWaterman ldquoSymmetry unitarity and geometry in electro-magnetic scatteringrdquo Physical Review D vol 3 no 4 pp 825ndash839 1971

[4] M IMishchenko LD Travis andDWMackowski ldquoT-matrixcomputations of light scattering by nonspherical particles areviewrdquo Journal of Quantitative Spectroscopy and RadiativeTransfer vol 55 no 5 pp 535ndash575 1996

[5] H R Pruppacher and K V Beard ldquoA wind tunnel investigationof the internal circulation and shape of water drops fallingat terminal velocity in airrdquo Quarterly Journal of the RoyalMeteorological Society vol 96 no 408 pp 247ndash256 1970

[6] D C Blanchard ldquoThe behavior of water drops at terminalvelocity in airrdquo EOS vol 31 no 6 pp 836ndash842 1950

[7] G-J Huang V N Bringi M Schonhuber et al ldquoDrop shapeand canting angle distributions in rain from2-Dvideo disdrom-eterrdquo in Proceedings of the 33rd Conference on Radar Meteorol-ogy Extended Abstract P8A8 Cairns Australia August 2007

[8] M Thurai V N Bringi and W A Petersen ldquoRain microstruc-ture retrievals using 2-D video disdrometer and C-band polari-metric radarrdquo Advances in Geosciences vol 20 pp 13ndash18 2009

[9] K V Beard and C Chuang ldquoA new model for the equilibriumshape of raindropsrdquo Journal of the Atmospheric Sciences vol 44pp 1509ndash1524 1987

[10] K Andsager K V Beard and N S Laird ldquoA laboratory studyof oscillations and axis ratios for large raindropsrdquo Journal of theAtmospheric Sciences vol 55 pp 208ndash226 1999

[11] J W Wilson and E A Brandes ldquoRadar measurement of rain-fallmdasha summaryrdquo Bulletin AmericanMeteorological Society vol60 no 9 pp 1048ndash1058 1979

[12] P M Austin ldquoRelation betweenmeasured radar reflectivity andsurface rainfallrdquo Monthly Weather Review vol 115 no 5 pp1053ndash1070 1987

[13] J Vivekanandan D S Zrnic S M Ellis R Oye A V Ryzhkovand J Straka ldquoCloud microphysics retrieval using S-band dual-polarization radar measurementsrdquo Bulletin of the AmericanMeteorological Society vol 80 no 3 pp 381ndash388 1999

[14] A V Ryzhkov and D S Zrnic ldquoDiscrimination between rainand snow with a polarimetric radarrdquo Journal of Applied Meteo-rology vol 37 no 10 pp 1228ndash1240 1998

[15] S E Giangrande and A V Ryzhkov ldquoEstimation of rainfallbased on the results of polarimetric echo classificationrdquo Journalof AppliedMeteorology and Climatology vol 47 no 9 pp 2445ndash2462 2008

[16] A V Ryzhkov and D S Zrnic ldquoAssessment of rainfall measure-ment that uses specific differential phaserdquo Journal of AppliedMeteorology vol 35 no 11 pp 2080ndash2090 1996

[17] P T May T D Keenan D S Zrnic L D Carey and S ARutledge ldquoPolarimetric radar measurements of tropical rain ata 5-cm wavelengthrdquo Journal of Applied Meteorology vol 38 no6 pp 750ndash765 1999

[18] V N Bringi and V Chandrasekar ldquoThe polarimetric basis forcharacterizing precipitationrdquo in Polarimetric Doppler WeatherRadar Principles and Applications pp 378ndash533 CambridgeUniversity Press Cambridge UK 2001

[19] E A Brandes G Zhang and J Vivekanandan ldquoExperiments inrainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[20] A V Ryzhkov T J Schuur D W Burgess P L Heinselman SE Giangrande and D S Zrnic ldquoThe joint polarization exper-iment polarimetric rainfall measurements and hydrometeorclassificationrdquo Bulletin of the American Meteorological Societyvol 86 no 6 pp 809ndash824 2005

[21] A V Ryzhkov S E Giangrande and T J Schuur ldquoRainfall esti-mation with a polarimetric prototype of WSR-88Drdquo Journal ofApplied Meteorology vol 44 no 4 pp 502ndash515 2005

[22] R Cifelli V Chandrasekar S Lim P C Kennedy Y Wang andS A Rutledge ldquoA new dual-polarization radar rainfall algo-rithm application in Colorado precipitation eventsrdquo Journal ofAtmospheric andOceanic Technology vol 28 no 3 pp 352ndash3642011

[23] A Ryzhkov M Diederich P Zhang and C Simmer ldquoPotentialutilization of specific attenuation for rainfall estimationmitiga-tion of partial beam blockage and radar networkingrdquo Journal ofAtmospheric and Oceanic Technology vol 31 no 3 pp 599ndash6192014

[24] C-H You M-Y Kang D-I Lee and H Uyeda ldquoRainfallestimation by S-band polarimetric radar in Korea Part Ipreprocessing and preliminary resultsrdquoMeteorological Applica-tions vol 21 no 4 pp 975ndash983 2014

[25] C-H You D-I Lee andM-Y Kang ldquoRainfall estimation usingspecific differential phase for the first operational polarimetricradar in Koreardquo Advances in Meteorology vol 2014 Article ID413717 10 pages 2014

Advances in Meteorology 15

[26] V N Bringi V Chandrasekar J Hubbert E Gorgucci W LRandeu and M Schoenhuber ldquoRaindrop size distribution indifferent climatic regimes from disdrometer and dual-polarizedradar analysisrdquo Journal of the Atmospheric Sciences vol 60 no2 pp 354ndash365 2003

[27] E A Brandes G Zhang and J Vivekanandan ldquoExperimentsin rainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[28] K V Beard and R J Kubesh ldquoLaboratory measurements ofsmall raindrop distortion Part 2 oscillation frequencies andmodesrdquo Journal of the Atmospheric Sciences vol 48 no 20 pp2245ndash2264 1991

[29] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[30] J W F Goddard K L Morgan A Illingworth and HSauvageot ldquoDual-wavelength polarization measurements inprecipitation using the CAMRA and Rabelias radarsrdquo in Pro-ceedings of the 27th Conference on Radar Meteorology pp 196ndash198 American Meteorology Society Vail Colo USA 1995

[31] A V Ryzhkov D S Zrnic J C Hubbert V N Bringi JVivekanandan and E A Brandes ldquoPolarimetric radar obser-vations and interpretation of co-cross-polar correlation coeffi-cientsrdquo Journal of Atmospheric and Oceanic Technology vol 19no 3 pp 340ndash354 2002

[32] S YMatrosov KAClark B EMartner andA Tokay ldquoX-bandpolarimetric radar measurements of rainfallrdquo Journal of AppliedMeteorology vol 41 no 9 pp 941ndash952 2002

[33] G-J Huang V N Bringi and M Thurai ldquoOrientation angledistributions of drops after an 80-m fall using a 2D videodisdrometerrdquo Journal of Atmospheric and Oceanic Technologyvol 25 no 9 pp 1717ndash1723 2008

[34] R Meneghini and K Nakamura ldquoRange profiling of the rainrate by an airborne weather radarrdquo Remote Sensing of Environ-ment vol 31 no 3 pp 193ndash209 1990

[35] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onpolarimetric variables at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[36] J Testud E L Bouar E Obligis and M Ali-Mehenni ldquoTherain profiling algorithm applied to polarimetric weather radarrdquoJournal of Atmospheric andOceanic Technology vol 17 no 3 pp332ndash356 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Advances in Meteorology 13

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP) with drop shape

(a)

0

5

10

15

20

Drop shape

25

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(Z ZDR) with drop shape

(b)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(KDP ZDR) with drop shape

(c)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

RMSE of R(ZKDP AH) with drop shape

(d)

0

5

10

15

20

25

Drop shape

RMSE

of r

adar

rain

fall

(mm

)

1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6

0ndash5mm5ndash30mmOver 30mm

RMSE of R(Z ZDR KDP AH) with drop shape

(e)

Figure 10The RMSEs of (a) 119877(119870DP) (b) 119877(119885 119885DP) (c) 119877(119870DP 119885DP) (d) 119877(119885119870DP 119860119867) and (e) 119877(119885 119885DP 119870DP 119860119867)with raindrop axis ratiorelations in the three rainfall categories

14 Advances in Meteorology

rain medium rain and high rainfall regimes respectively119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) showed relativelygood performance in all rainfall regimesThe combination of119877(119885 119885DR) 119877(119870DP 119885DR) and 119877(119870DP) with rainfall intensitywould be an optimum rainfall algorithm if the referenceof rainfall would be defined correctly Regardless of rainfallintensity 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) obtainedby assuming DS3 can be used as a representative rainfall rela-tion without consideration of rainfall intensity regime Par-ticularly if the qualified 119885DR is not available 119877(119885119870DP 119860119867)with DS3 drop shape assumption can be used as an optimumrainfall relation in Korea

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge providing radar data weatherchart and AWS data for this work from the Ministry ofLand Infrastructure Transport and Korea MeteorologicalAdministration The authors also acknowledge providingcodes for scattering simulation from Professor V N Bringi atColorado StateUniversityThisworkwas funded by theKoreaMeteorological Industry Promotion Agency under GrantKMIPA 2015-1050

References

[1] E Campos and I Zawadzki ldquoInstrumental uncertainties in Z-R relationsrdquo Journal of Applied Meteorology vol 39 no 7 pp1088ndash1102 2000

[2] C-H You D-I Lee S-M Jang et al ldquoCharacteristics ofrainfall systems accompanied with Changma front at Chujadoin Koreardquo Asia-Pacific Journal of Atmospheric Sciences vol 46no 1 pp 41ndash51 2010

[3] P CWaterman ldquoSymmetry unitarity and geometry in electro-magnetic scatteringrdquo Physical Review D vol 3 no 4 pp 825ndash839 1971

[4] M IMishchenko LD Travis andDWMackowski ldquoT-matrixcomputations of light scattering by nonspherical particles areviewrdquo Journal of Quantitative Spectroscopy and RadiativeTransfer vol 55 no 5 pp 535ndash575 1996

[5] H R Pruppacher and K V Beard ldquoA wind tunnel investigationof the internal circulation and shape of water drops fallingat terminal velocity in airrdquo Quarterly Journal of the RoyalMeteorological Society vol 96 no 408 pp 247ndash256 1970

[6] D C Blanchard ldquoThe behavior of water drops at terminalvelocity in airrdquo EOS vol 31 no 6 pp 836ndash842 1950

[7] G-J Huang V N Bringi M Schonhuber et al ldquoDrop shapeand canting angle distributions in rain from2-Dvideo disdrom-eterrdquo in Proceedings of the 33rd Conference on Radar Meteorol-ogy Extended Abstract P8A8 Cairns Australia August 2007

[8] M Thurai V N Bringi and W A Petersen ldquoRain microstruc-ture retrievals using 2-D video disdrometer and C-band polari-metric radarrdquo Advances in Geosciences vol 20 pp 13ndash18 2009

[9] K V Beard and C Chuang ldquoA new model for the equilibriumshape of raindropsrdquo Journal of the Atmospheric Sciences vol 44pp 1509ndash1524 1987

[10] K Andsager K V Beard and N S Laird ldquoA laboratory studyof oscillations and axis ratios for large raindropsrdquo Journal of theAtmospheric Sciences vol 55 pp 208ndash226 1999

[11] J W Wilson and E A Brandes ldquoRadar measurement of rain-fallmdasha summaryrdquo Bulletin AmericanMeteorological Society vol60 no 9 pp 1048ndash1058 1979

[12] P M Austin ldquoRelation betweenmeasured radar reflectivity andsurface rainfallrdquo Monthly Weather Review vol 115 no 5 pp1053ndash1070 1987

[13] J Vivekanandan D S Zrnic S M Ellis R Oye A V Ryzhkovand J Straka ldquoCloud microphysics retrieval using S-band dual-polarization radar measurementsrdquo Bulletin of the AmericanMeteorological Society vol 80 no 3 pp 381ndash388 1999

[14] A V Ryzhkov and D S Zrnic ldquoDiscrimination between rainand snow with a polarimetric radarrdquo Journal of Applied Meteo-rology vol 37 no 10 pp 1228ndash1240 1998

[15] S E Giangrande and A V Ryzhkov ldquoEstimation of rainfallbased on the results of polarimetric echo classificationrdquo Journalof AppliedMeteorology and Climatology vol 47 no 9 pp 2445ndash2462 2008

[16] A V Ryzhkov and D S Zrnic ldquoAssessment of rainfall measure-ment that uses specific differential phaserdquo Journal of AppliedMeteorology vol 35 no 11 pp 2080ndash2090 1996

[17] P T May T D Keenan D S Zrnic L D Carey and S ARutledge ldquoPolarimetric radar measurements of tropical rain ata 5-cm wavelengthrdquo Journal of Applied Meteorology vol 38 no6 pp 750ndash765 1999

[18] V N Bringi and V Chandrasekar ldquoThe polarimetric basis forcharacterizing precipitationrdquo in Polarimetric Doppler WeatherRadar Principles and Applications pp 378ndash533 CambridgeUniversity Press Cambridge UK 2001

[19] E A Brandes G Zhang and J Vivekanandan ldquoExperiments inrainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[20] A V Ryzhkov T J Schuur D W Burgess P L Heinselman SE Giangrande and D S Zrnic ldquoThe joint polarization exper-iment polarimetric rainfall measurements and hydrometeorclassificationrdquo Bulletin of the American Meteorological Societyvol 86 no 6 pp 809ndash824 2005

[21] A V Ryzhkov S E Giangrande and T J Schuur ldquoRainfall esti-mation with a polarimetric prototype of WSR-88Drdquo Journal ofApplied Meteorology vol 44 no 4 pp 502ndash515 2005

[22] R Cifelli V Chandrasekar S Lim P C Kennedy Y Wang andS A Rutledge ldquoA new dual-polarization radar rainfall algo-rithm application in Colorado precipitation eventsrdquo Journal ofAtmospheric andOceanic Technology vol 28 no 3 pp 352ndash3642011

[23] A Ryzhkov M Diederich P Zhang and C Simmer ldquoPotentialutilization of specific attenuation for rainfall estimationmitiga-tion of partial beam blockage and radar networkingrdquo Journal ofAtmospheric and Oceanic Technology vol 31 no 3 pp 599ndash6192014

[24] C-H You M-Y Kang D-I Lee and H Uyeda ldquoRainfallestimation by S-band polarimetric radar in Korea Part Ipreprocessing and preliminary resultsrdquoMeteorological Applica-tions vol 21 no 4 pp 975ndash983 2014

[25] C-H You D-I Lee andM-Y Kang ldquoRainfall estimation usingspecific differential phase for the first operational polarimetricradar in Koreardquo Advances in Meteorology vol 2014 Article ID413717 10 pages 2014

Advances in Meteorology 15

[26] V N Bringi V Chandrasekar J Hubbert E Gorgucci W LRandeu and M Schoenhuber ldquoRaindrop size distribution indifferent climatic regimes from disdrometer and dual-polarizedradar analysisrdquo Journal of the Atmospheric Sciences vol 60 no2 pp 354ndash365 2003

[27] E A Brandes G Zhang and J Vivekanandan ldquoExperimentsin rainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[28] K V Beard and R J Kubesh ldquoLaboratory measurements ofsmall raindrop distortion Part 2 oscillation frequencies andmodesrdquo Journal of the Atmospheric Sciences vol 48 no 20 pp2245ndash2264 1991

[29] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[30] J W F Goddard K L Morgan A Illingworth and HSauvageot ldquoDual-wavelength polarization measurements inprecipitation using the CAMRA and Rabelias radarsrdquo in Pro-ceedings of the 27th Conference on Radar Meteorology pp 196ndash198 American Meteorology Society Vail Colo USA 1995

[31] A V Ryzhkov D S Zrnic J C Hubbert V N Bringi JVivekanandan and E A Brandes ldquoPolarimetric radar obser-vations and interpretation of co-cross-polar correlation coeffi-cientsrdquo Journal of Atmospheric and Oceanic Technology vol 19no 3 pp 340ndash354 2002

[32] S YMatrosov KAClark B EMartner andA Tokay ldquoX-bandpolarimetric radar measurements of rainfallrdquo Journal of AppliedMeteorology vol 41 no 9 pp 941ndash952 2002

[33] G-J Huang V N Bringi and M Thurai ldquoOrientation angledistributions of drops after an 80-m fall using a 2D videodisdrometerrdquo Journal of Atmospheric and Oceanic Technologyvol 25 no 9 pp 1717ndash1723 2008

[34] R Meneghini and K Nakamura ldquoRange profiling of the rainrate by an airborne weather radarrdquo Remote Sensing of Environ-ment vol 31 no 3 pp 193ndash209 1990

[35] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onpolarimetric variables at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[36] J Testud E L Bouar E Obligis and M Ali-Mehenni ldquoTherain profiling algorithm applied to polarimetric weather radarrdquoJournal of Atmospheric andOceanic Technology vol 17 no 3 pp332ndash356 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

14 Advances in Meteorology

rain medium rain and high rainfall regimes respectively119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) showed relativelygood performance in all rainfall regimesThe combination of119877(119885 119885DR) 119877(119870DP 119885DR) and 119877(119870DP) with rainfall intensitywould be an optimum rainfall algorithm if the referenceof rainfall would be defined correctly Regardless of rainfallintensity 119877(119885 119885DR 119870DP 119860119867) and 119877(119885119870DP 119860119867) obtainedby assuming DS3 can be used as a representative rainfall rela-tion without consideration of rainfall intensity regime Par-ticularly if the qualified 119885DR is not available 119877(119885119870DP 119860119867)with DS3 drop shape assumption can be used as an optimumrainfall relation in Korea

Conflict of Interests

The authors declare that they have no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors acknowledge providing radar data weatherchart and AWS data for this work from the Ministry ofLand Infrastructure Transport and Korea MeteorologicalAdministration The authors also acknowledge providingcodes for scattering simulation from Professor V N Bringi atColorado StateUniversityThisworkwas funded by theKoreaMeteorological Industry Promotion Agency under GrantKMIPA 2015-1050

References

[1] E Campos and I Zawadzki ldquoInstrumental uncertainties in Z-R relationsrdquo Journal of Applied Meteorology vol 39 no 7 pp1088ndash1102 2000

[2] C-H You D-I Lee S-M Jang et al ldquoCharacteristics ofrainfall systems accompanied with Changma front at Chujadoin Koreardquo Asia-Pacific Journal of Atmospheric Sciences vol 46no 1 pp 41ndash51 2010

[3] P CWaterman ldquoSymmetry unitarity and geometry in electro-magnetic scatteringrdquo Physical Review D vol 3 no 4 pp 825ndash839 1971

[4] M IMishchenko LD Travis andDWMackowski ldquoT-matrixcomputations of light scattering by nonspherical particles areviewrdquo Journal of Quantitative Spectroscopy and RadiativeTransfer vol 55 no 5 pp 535ndash575 1996

[5] H R Pruppacher and K V Beard ldquoA wind tunnel investigationof the internal circulation and shape of water drops fallingat terminal velocity in airrdquo Quarterly Journal of the RoyalMeteorological Society vol 96 no 408 pp 247ndash256 1970

[6] D C Blanchard ldquoThe behavior of water drops at terminalvelocity in airrdquo EOS vol 31 no 6 pp 836ndash842 1950

[7] G-J Huang V N Bringi M Schonhuber et al ldquoDrop shapeand canting angle distributions in rain from2-Dvideo disdrom-eterrdquo in Proceedings of the 33rd Conference on Radar Meteorol-ogy Extended Abstract P8A8 Cairns Australia August 2007

[8] M Thurai V N Bringi and W A Petersen ldquoRain microstruc-ture retrievals using 2-D video disdrometer and C-band polari-metric radarrdquo Advances in Geosciences vol 20 pp 13ndash18 2009

[9] K V Beard and C Chuang ldquoA new model for the equilibriumshape of raindropsrdquo Journal of the Atmospheric Sciences vol 44pp 1509ndash1524 1987

[10] K Andsager K V Beard and N S Laird ldquoA laboratory studyof oscillations and axis ratios for large raindropsrdquo Journal of theAtmospheric Sciences vol 55 pp 208ndash226 1999

[11] J W Wilson and E A Brandes ldquoRadar measurement of rain-fallmdasha summaryrdquo Bulletin AmericanMeteorological Society vol60 no 9 pp 1048ndash1058 1979

[12] P M Austin ldquoRelation betweenmeasured radar reflectivity andsurface rainfallrdquo Monthly Weather Review vol 115 no 5 pp1053ndash1070 1987

[13] J Vivekanandan D S Zrnic S M Ellis R Oye A V Ryzhkovand J Straka ldquoCloud microphysics retrieval using S-band dual-polarization radar measurementsrdquo Bulletin of the AmericanMeteorological Society vol 80 no 3 pp 381ndash388 1999

[14] A V Ryzhkov and D S Zrnic ldquoDiscrimination between rainand snow with a polarimetric radarrdquo Journal of Applied Meteo-rology vol 37 no 10 pp 1228ndash1240 1998

[15] S E Giangrande and A V Ryzhkov ldquoEstimation of rainfallbased on the results of polarimetric echo classificationrdquo Journalof AppliedMeteorology and Climatology vol 47 no 9 pp 2445ndash2462 2008

[16] A V Ryzhkov and D S Zrnic ldquoAssessment of rainfall measure-ment that uses specific differential phaserdquo Journal of AppliedMeteorology vol 35 no 11 pp 2080ndash2090 1996

[17] P T May T D Keenan D S Zrnic L D Carey and S ARutledge ldquoPolarimetric radar measurements of tropical rain ata 5-cm wavelengthrdquo Journal of Applied Meteorology vol 38 no6 pp 750ndash765 1999

[18] V N Bringi and V Chandrasekar ldquoThe polarimetric basis forcharacterizing precipitationrdquo in Polarimetric Doppler WeatherRadar Principles and Applications pp 378ndash533 CambridgeUniversity Press Cambridge UK 2001

[19] E A Brandes G Zhang and J Vivekanandan ldquoExperiments inrainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[20] A V Ryzhkov T J Schuur D W Burgess P L Heinselman SE Giangrande and D S Zrnic ldquoThe joint polarization exper-iment polarimetric rainfall measurements and hydrometeorclassificationrdquo Bulletin of the American Meteorological Societyvol 86 no 6 pp 809ndash824 2005

[21] A V Ryzhkov S E Giangrande and T J Schuur ldquoRainfall esti-mation with a polarimetric prototype of WSR-88Drdquo Journal ofApplied Meteorology vol 44 no 4 pp 502ndash515 2005

[22] R Cifelli V Chandrasekar S Lim P C Kennedy Y Wang andS A Rutledge ldquoA new dual-polarization radar rainfall algo-rithm application in Colorado precipitation eventsrdquo Journal ofAtmospheric andOceanic Technology vol 28 no 3 pp 352ndash3642011

[23] A Ryzhkov M Diederich P Zhang and C Simmer ldquoPotentialutilization of specific attenuation for rainfall estimationmitiga-tion of partial beam blockage and radar networkingrdquo Journal ofAtmospheric and Oceanic Technology vol 31 no 3 pp 599ndash6192014

[24] C-H You M-Y Kang D-I Lee and H Uyeda ldquoRainfallestimation by S-band polarimetric radar in Korea Part Ipreprocessing and preliminary resultsrdquoMeteorological Applica-tions vol 21 no 4 pp 975ndash983 2014

[25] C-H You D-I Lee andM-Y Kang ldquoRainfall estimation usingspecific differential phase for the first operational polarimetricradar in Koreardquo Advances in Meteorology vol 2014 Article ID413717 10 pages 2014

Advances in Meteorology 15

[26] V N Bringi V Chandrasekar J Hubbert E Gorgucci W LRandeu and M Schoenhuber ldquoRaindrop size distribution indifferent climatic regimes from disdrometer and dual-polarizedradar analysisrdquo Journal of the Atmospheric Sciences vol 60 no2 pp 354ndash365 2003

[27] E A Brandes G Zhang and J Vivekanandan ldquoExperimentsin rainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[28] K V Beard and R J Kubesh ldquoLaboratory measurements ofsmall raindrop distortion Part 2 oscillation frequencies andmodesrdquo Journal of the Atmospheric Sciences vol 48 no 20 pp2245ndash2264 1991

[29] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[30] J W F Goddard K L Morgan A Illingworth and HSauvageot ldquoDual-wavelength polarization measurements inprecipitation using the CAMRA and Rabelias radarsrdquo in Pro-ceedings of the 27th Conference on Radar Meteorology pp 196ndash198 American Meteorology Society Vail Colo USA 1995

[31] A V Ryzhkov D S Zrnic J C Hubbert V N Bringi JVivekanandan and E A Brandes ldquoPolarimetric radar obser-vations and interpretation of co-cross-polar correlation coeffi-cientsrdquo Journal of Atmospheric and Oceanic Technology vol 19no 3 pp 340ndash354 2002

[32] S YMatrosov KAClark B EMartner andA Tokay ldquoX-bandpolarimetric radar measurements of rainfallrdquo Journal of AppliedMeteorology vol 41 no 9 pp 941ndash952 2002

[33] G-J Huang V N Bringi and M Thurai ldquoOrientation angledistributions of drops after an 80-m fall using a 2D videodisdrometerrdquo Journal of Atmospheric and Oceanic Technologyvol 25 no 9 pp 1717ndash1723 2008

[34] R Meneghini and K Nakamura ldquoRange profiling of the rainrate by an airborne weather radarrdquo Remote Sensing of Environ-ment vol 31 no 3 pp 193ndash209 1990

[35] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onpolarimetric variables at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[36] J Testud E L Bouar E Obligis and M Ali-Mehenni ldquoTherain profiling algorithm applied to polarimetric weather radarrdquoJournal of Atmospheric andOceanic Technology vol 17 no 3 pp332ndash356 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Advances in Meteorology 15

[26] V N Bringi V Chandrasekar J Hubbert E Gorgucci W LRandeu and M Schoenhuber ldquoRaindrop size distribution indifferent climatic regimes from disdrometer and dual-polarizedradar analysisrdquo Journal of the Atmospheric Sciences vol 60 no2 pp 354ndash365 2003

[27] E A Brandes G Zhang and J Vivekanandan ldquoExperimentsin rainfall estimation with a polarimetric radar in a subtropicalenvironmentrdquo Journal of Applied Meteorology vol 41 no 6 pp674ndash685 2002

[28] K V Beard and R J Kubesh ldquoLaboratory measurements ofsmall raindrop distortion Part 2 oscillation frequencies andmodesrdquo Journal of the Atmospheric Sciences vol 48 no 20 pp2245ndash2264 1991

[29] M Thurai G J Huang V N Bringi W L Randeu and MSchonhuber ldquoDrop shapes model comparisons and calcu-lations of polarimetric radar parameters in rainrdquo Journal ofAtmospheric and Oceanic Technology vol 24 no 6 pp 1019ndash1032 2007

[30] J W F Goddard K L Morgan A Illingworth and HSauvageot ldquoDual-wavelength polarization measurements inprecipitation using the CAMRA and Rabelias radarsrdquo in Pro-ceedings of the 27th Conference on Radar Meteorology pp 196ndash198 American Meteorology Society Vail Colo USA 1995

[31] A V Ryzhkov D S Zrnic J C Hubbert V N Bringi JVivekanandan and E A Brandes ldquoPolarimetric radar obser-vations and interpretation of co-cross-polar correlation coeffi-cientsrdquo Journal of Atmospheric and Oceanic Technology vol 19no 3 pp 340ndash354 2002

[32] S YMatrosov KAClark B EMartner andA Tokay ldquoX-bandpolarimetric radar measurements of rainfallrdquo Journal of AppliedMeteorology vol 41 no 9 pp 941ndash952 2002

[33] G-J Huang V N Bringi and M Thurai ldquoOrientation angledistributions of drops after an 80-m fall using a 2D videodisdrometerrdquo Journal of Atmospheric and Oceanic Technologyvol 25 no 9 pp 1717ndash1723 2008

[34] R Meneghini and K Nakamura ldquoRange profiling of the rainrate by an airborne weather radarrdquo Remote Sensing of Environ-ment vol 31 no 3 pp 193ndash209 1990

[35] V N Bringi V Chandrasekar N Balakrishnan and D SZrnic ldquoAn examination of propagation effects in rainfall onpolarimetric variables at microwave frequenciesrdquo Journal ofAtmospheric and Oceanic Technology vol 7 no 6 pp 829ndash8401990

[36] J Testud E L Bouar E Obligis and M Ali-Mehenni ldquoTherain profiling algorithm applied to polarimetric weather radarrdquoJournal of Atmospheric andOceanic Technology vol 17 no 3 pp332ndash356 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ClimatologyJournal of

EcologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EarthquakesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom

Applied ampEnvironmentalSoil Science

Volume 2014

Mining

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal of

Geophysics

OceanographyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of Computational Environmental SciencesHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

GeochemistryHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Atmospheric SciencesInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OceanographyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MineralogyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MeteorologyAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Paleontology JournalHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geological ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Geology Advances in