Journal of Atmospheric and Solar-Terrestrial Physics 119 (2014) 42–52

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Journal of Atmospheric and Solar-Terrestrial Physics

http://d1364-68

n CorrBristol B

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journal homepage: www.elsevier.com/locate/jastp

The scattering simulation of DSDs and the polarimetric radar rainfallalgorithms at C-band frequency

Tanvir Islam a,b,c,n

a Department of Civil Engineering, University of Bristol, Bristol BS8 1TR, UKb Institute of Industrial Science, The University of Tokyo, Tokyo, Japanc Department of Civil Engineering, Nagasaki University, Nagasaki, Japan

a r t i c l e i n f o

Article history:Received 3 February 2014Received in revised form18 June 2014Accepted 18 June 2014Available online 25 June 2014

Keywords:Dual polarization radarDrop size distribution (DSD)DisdrometerPrecipitation estimationReflectivityPropagation phaseHydrology

x.doi.org/10.1016/j.jastp.2014.06.00826/& 2014 Elsevier Ltd. All rights reserved.

esponding author at: Department of Civil EngS8 1TR, UK. Tel.: þ44 1173315724; fax: þ44ail addresses: tanvir.islam@bristol.ac.uk, tanvi

a b s t r a c t

This study explores polarimetric radar rainfall algorithms at C-band frequency using a total of 162,4151-min raindrop spectra from an extensive disdrometer dataset. Five different raindrop shape modelshave been tested to simulate polarimetric radar variables—the reflectivity factor (Z), differentialreflectivity (Zdr) and specific differential phase (Kdp), through the T-matrix microwave scatteringapproach. The polarimetric radar rainfall algorithms are developed in the form of R(Z), R(Kdp), R(Z, Zdr)and R(Zdr, Kdp) combinations. Based on the best fitted raindrop spectra models rain rate retrievalinformation using disdrometer derived rain rate as a reference, the algorithms are further explored inview of stratiform and convective rain regimes. Finally, an “artificial” algorithm is proposed whichconsiders the developed algorithms for stratiform and convective regimes and uses R(Z), R(Kdp) and R(Z,Zdr) in different scenarios. The artificial algorithm is applied to and evaluated by the Thurnham C-banddual polarized radar data in 6 storm cases perceiving the rationalization in terms of rainfall retrievalaccuracy as compared to the operational Marshall–Palmer algorithm (Z¼200R1.6). A dense network of 73tipping bucket rain gauges is employed for the evaluation, and the result demonstrates that the artificialalgorithm outperforms the Marshall–Palmer algorithm showing R2¼0.84 and MAE¼0.82 mm asopposed to R2¼0.79 and MAE¼0.86 mm respectively.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Since polarimetric radar, also known as dual polarization radar,has the ability of transmitting electromagnetic spectrum on bothhorizontal and vertical planes, it is capable of measuring addi-tional variables like differential reflectivity (Zdr), specific differen-tial phase (Kdp), differential propagation phase (Φdp), cross-corre-lation coefficient (ρ) and linear depolarization ratio (LDR) (Islamand Rico-Ramirez, 2014). In contrast, conventional fixed polariza-tion radars can measure reflectivity factor (Z) only. Use of severalradar variables instead of reflectivity factor (Z) alone brings up theprospects of minimizing uncertainties in rainfall retrievals in manyways, for instance, identification of ground clutter and anomalouspropagation (Islam et al., 2012a; Rico-Ramirez and Cluckie, 2008),attenuation correction (Islam et al., 2014; Kalogiros et al., 2014;Vulpiani et al., 2008), accurate calibration (Gourley et al., 2009),bright band correction (Islam et al., 2013; Matrosov et al., 2007; Qiet al., 2013; Rico-Ramirez et al., 2005; Zhang and Qi, 2010), hail

ineering, University of Bristol,1173315719.r.islam@msn.com

detection (Heinselman and Ryzhkov, 2006), hydrometeor classifi-cation (Cifelli et al., 2011) etc. It is recognized that the rainfallretrievals using Z only rely on the drop size distribution (DSD) to amomentous extent (Steiner et al., 2004). In contrast, the depen-dence on DSDs can be significantly reduced if a combination ofseveral radar variables is used by taking advantage of polarimetricradars. In addition, polarimetric variables can offer better accuracyin estimation of rainfall (R) at the time of increasing rain rateswhereas single polarization radars often misinterpret during thecourse. The advantage of Zdr is that it is a good measure of themedian drop diameter providing raindrop shape information(Ryzhkov et al., 2005b). Kdp is favourable due to its immunity toradar miscalibration, attenuation and partial blockage of radarbeam (Zrnic and Ryzhkov, 1996). Based on validation studies indifferent parts of USA, numerous researchers have confirmed thatthe rainfall estimation is significantly improved with the use ofpolarimetric radar parameters as compared to the conventional Z–R relation only (Brandes et al., 2002; Cao et al., 2008; Matrosovet al., 2005; Ryzhkov and Zrnic, 1996; Ryzhkov et al., 2005a; Zhanget al., 2001). Similar verdicts have been experienced by Gossetet al. (2010) in Africa, May et al. (1999) in Australia, Lee (2006) in

T. Islam / Journal of Atmospheric and Solar-Terrestrial Physics 119 (2014) 42–52 43

Canada, Diss et al. (2009) in France, Silvestro et al. (2009) in Italy,and Bringi et al. (2006) in Japan.

Considering the advantage of additional polarimretric vari-ables, meteorological agencies throughout the world are adaptingthe dual polarization technology. As a result, polarimetric radar isbecoming a standard for operational use. The U.S. NationalWeather Service (NWS) has decided to add polarimetric capabilityto the nationwide network of the Weather Surveillance Radars-1988 Doppler (WSR-88D) (Ryzhkov et al., 2005b). The EuropeanEUMETNET Opera radar network has also undertaken severalprojects to upgrade its radar network to polarimetric capabilities,in particular at C-band frequencies. UK has also added one C-banddual polarization radar to the Met Office radar structure inThurnham, Kent in 2005 (Rico-Ramirez et al., 2009).

A variety of physical and empirical polarimetric radar rainfallalgorithms have been proposed for rainfall estimation during lasttwo decades based on either measured or simulated DSDs. Inparticular, a broad research on S-band radar has been conductedby several researchers in the past suggesting a number of estima-tors using Z, Zdr, and Kdp (Ryzhkov et al., 2005a, 2005b). The radaris not capable of observing raindrop directly, and in fact thesealgorithms are in the form of relationship where the radarvariables are related to rain rate using the information fromobserved DSDs. Another approach has been reported in thepolarimetric radar rainfall community; in this case the DSDs areretrieved first from polarimetric variables and then the rain ratesare estimated from the DSDs. For example, Cao et al. (2010)proposed a Bayesian approach to retrieve rainfall rates using Zand Zdr, and stated that the tested results from an S-band radaragreed well with the in situ measurements. Vulpiani et al. (2009)also validated a procedure for the estimation of rainfall rate froman S-band radar by neural network inversion techniques. Ascompared to the S-band, establishing stable C-band rain rateestimators for operational use are more challenging, emphasizingthe fact that Z and Zdr need to be corrected for attenuation prior tothe estimation of rainfall. The research carried out for the C-bandpolarimetric radar can be found in Meischner et al. (1991) inSouthern Germany, Gorgucci et al. (1996) in Italy, Teschl et al.(2008) in Alpine region, and May et al. (1999), Carey et al. (2000)and Bringi et al. (2001) in Australia. In addition, Silvestro et al.(2009) adopted the R(Kdp), R(Z, Zdr) and R(Zdr, Kdp) formulationsfrom Bringi and Chandrasekar (2001) along with the well-knownMarshall–Palmer Z–R relation (Marshall et al., 1955), and pre-sented a multi-parameter, multi-relationship algorithm named arain intensity multiparameter estimator (RIME) in Italy. Petersen(2009) also reported an operational rain rate algorithm for theprecipitation processing stream of a radar prototype namedARMOR, located in Huntsville, USA. Recently, Bringi et al. (2009)proposed a polarimetric radar retrieval algorithm using oneseasonal disdrometer data from Darwin, Australia.

Unfortunately, the algorithms are dependent on geographicaland atmospheric conditions due to drop size distribution varia-tions, and cannot be suitably used elsewhere (Brandes et al., 1999;Lee and Zawadzki, 2005; Steiner et al., 2004). Given this reasoning,it is imperative to explore the potential of polarimetric algorithmsfor operational use in the UK region. Indeed, Met Office, UK is stillusing the conventional Marshall–Palmar Z–R relationship:Z¼200R1.6 for operational use (Harrison et al., 2000). Thompsonet al. (2008) argued that this conventional Z–R relation is not goodenough if radar data are to be used to their full potential. Theyshowed that on 20 July 2007 flooding in London, the twooperational radars Chenies and Thurnham failed to measure therain accurately. In fact, the rainfall derived from conventional Z–Ralgorithm was only 35% of the value from rain gauges.

A recent attempt has been taken by Bringi et al. (2011) towardsdevelopment of dual polarized radar rainfall algorithms using

three summer months' Joss–Waldvogel disdrometer data fromChilbolton, UK. They showed the potential of polarimetric rainestimators in the summer convective storms. Our work builds onthis prior work to a comprehensive extend, and we have analysedan extensive seven years of disdrometer dataset from the UKregion for the development of polarimetric radar rainfall algo-rithms. The remainder of this paper is structured as follows:Section 2 introduces the dataset used in this study. Section 3summarizes the microwave scattering simulation of DSDs. InSection 4, skills of different estimators derived by the means ofZ, Zdr and Kdp variables in terms of rainfall estimation are discussedand an “artificial” algorithm is proposed. The proposed “artificial”algorithm is applied and tested through Thurnham polarimetricradar scans, and deliberated in Section 5. This is followed by asummary and conclusions section where we conclude the paper.

2. Instrumentation and dataset

This section describes the instrumentation and dataset used inthis study: the disdrometer, wet bulb temperature, rain gauge, andThurnham polarimetric radar dataset.

2.1. Disdrometer

In this study, the disdrometer datasets (April 2003 to March2010 period) have been acquired from a Distromet Joss–WaldvogelImpact Disdrometer RD-69, installed at Chilbolton Facility forAtmospheric and Radio Research and run by the Chilbolton Groupof the Space Science and Technology Department at RutherfordAppleton Laboratory. A detailed procedure for processing thedisdrometer data is given in Section 3.

2.2. Wet bulb temperature

The current work uses wet bulb temperature to distinguish theraindrop spectra from other types of drop characteristics, forinstance, snowfalls (see Section 4). The wet bulb temperature datahave been taken from the nearest Met Office-MIDAS Land SurfaceObservation Station located in Middle Wallop. Any missing valuesare filled in from a nearby station located in the Southamptonoceanography centre within MIDAS.

2.3. Rain gauge network

The rain gauge data for validation of the radar algorithms havebeen collected from the Environment Agency rain gauge network.A total of 73 rain gauges in the Southern Kent area are consideredin the analysis. Fig. 1 shows the spatial distribution of the 73 raingauges covered by the Thurnham radar. The rain gauges are oftipping bucket type with 0.2 mm tip and can record rainfallmeasurement automatically, thus providing high temporal resolu-tion. Note that these rain gauges do not perform well duringfreezing conditions. However, since we have considered our eventsas free from freezing environments, it is assumed that the gaugedata are accurate enough to be considered as the “ground truth”.Moreover, special visual and statistical examinations have beenperformed through cross correlation between the adjacent gaugesto confirm the data quality.

2.4. Radar system

The polarimetric data are taken from the Thurnham radar,located in Kent. Some key technical specifications of the radar isgiven in Table 1 (Rico-Ramirez et al., 2009). The radar transmitshorizontal (H) and vertical (V) polarized pulses using the pulse

Fig. 1. Locations of the 73 tipping bucket rain gauges superimposed in a digitalterrain elevation map with respect to the Thurnham radar. The range ring of theThurnham radar is also shown. The solid contour line shows the upper medwaycatchment.

Table 1Key technical specifications of the Thurnham polarimetric radar. Source: Rico-Ramirez et al. (2009).

Aerial systemAntenna diameter 4.27 mBeam width at half-power 0.95°Polarization Linear H/V: simultaneous transmissionScanning rate Up to 6 RPM (typical 2–3 RPM)Radome type Orange peelTransmitterBand C-bandRadar frequency 5300–5700 MHzWavelength 5.5 cmPeak power 54 dB W (250 kW)Pulse widths 0.4 μsPRF 250–1300 HzRadar dataZh, Zdr,Φdp, ρhv First and second moments of Doppler spectrumLDR Available in bypass modeLocation (Thurnham, Kent)Latitude 51.9242°Longitude 0.6059°Altitude 219 m

T. Islam / Journal of Atmospheric and Solar-Terrestrial Physics 119 (2014) 42–5244

width of 2 μs, PRF of 300 Hz, and gate spacing of 250 m with total1020 gates. The execution of PPI sweeps are made at elevationangles of 0.2°, 0.7°, 1.2°, 2.0°, 2.9°, 4.9° and 90° at a rotation rate of13° s�1 and a beam width of 0.95°. Currently, the radar is operatedat a temporal resolution of around 5 min.

3. Microwave scattering simulation of DSD

The polarimetric radar variables can be derived through micro-wave scattering simulation of DSDs assuming non-sphericalhydrometeors. A detailed explanation regarding the relationbetween scattering simulation and non-spherical hydrometeorsis given in Bringi and Chandrasekar (2001) and Mishchenko et al.(2000).

In this study, the DSDs at the discrete time instant t (inseconds) are calculated from Chilbolton disdrometer data

(Montopoli et al., 2008):

=N D tn t

A dt v dD( , )

( )(1)i

i

i i

where Di is the drop diameter of channel i in mm, N (Di,t) is thenumber of raindrops per unit of volume in the channel i at thediscrete instant t in units per millimetre per cubic meter, ni(t) isthe number of drops counted in the ith channel at the instant t, Ais the sensor area in square meter, dt is the time interval inseconds, vi is the terminal velocities of raindrops in metersper second, and dDi is the ith bin width in millimetres.

The terminal velocity is assumed as a function of the particlediameter (Atlas and Ulbrich, 1977):

=v D3.78 (2)i i0.67

Finally, the rain rate (mm/h) is calculated as follows:

∫π= × −R D v D N D dD0.6 10 ( ) ( ) (3)3 3

At Chilbolton, the drop counts are available at 10 s interval over127 channels with drop diameters ranging from 0.2992 to4.9952 mm. However, since this time series has fluctuations in Di

to t, a 1 min time interval has been used for the DSD calculation.Moreover, a “dead time correction” scheme is applied according toSheppard and Joe (1994) to avoid the miscounting of drops due toresonance of the disdrometer cone. In addition, the rain ratederived lesser than 0.1 mm/h is considered as noise and discardedin the study. Since this study is about radar rainfall retrievalalgorithms only, the rainfall datasets have been further filteredfrom the whole datasets using wet bulb temperature (Tw). Tw isconsidered as a good measure in distinguishing rain and snow.According to rules of thumbs, snow is probable only if Tw is below2 °C and some other atmospheric criteria are fulfilled. We restrictour analyses to time spans with Tw43 °C. Lastly, a total of 162,415data points are used from the entire dataset for exploration.

Following the computation of DSDs, the radar variables Z, Zdr,and Kdp have been derived by the T-matrix scattering approach asdescribed in Mishchenko (2000) for a nonspherical particle. Thescattering amplitudes are calculated for 10 °C. Mathematically, thecopolar radar reflectivity factors Zhh and Zvv (mm6 m�3) at H and Vpolarization states are defined as follows:

∫λπ

σσ=ZK

D N D dD( ) ( )(4)hh vv

D

D

hh vv,

4

5 2 ,min

max

where D is the drop diameter (mm), N(D) is the DSD, λ is the radarwavelength, Dmin and Dmax stand for the minimum and maximumdrop diameter of the actual DSD, respectively, K is the complexdielectric constant of water as a function of λ and temperature, andshh,vv (D) (mm2) are the backscattering scattering cross sectionswhich can be expressed in terms of complex amplitude matrix S:

σ π= S4 (5)hh vv hh vv, ,2

The differential reflectivity (dB) is defined as follows:

=ZZZ

10log(6)dr

hh

vv10

The specific differential phase shift Kdp (°/km), due to theforward propagation phase difference between H and V polariza-tions, is obtained in terms of the forward scattering amplitude f(mm) as follows:

⎡⎣⎢

⎤⎦⎥∫π

λ= ℜ −− { }K f D f D N D dD10180

( ) ( ) ( )(7)dp

D

D

hh vv3

min

max

where ℜ is the real part of the complex number.

T. Islam / Journal of Atmospheric and Solar-Terrestrial Physics 119 (2014) 42–52 45

Note that, for the simulation, the scattering amplitudes arecalculated for 10 °C. Various raindrop spectra models are consid-ered and the simulation results are addressed in the latter section.

4. Polarimetric radar rainfall algorithms

This section summarizes polarimetric radar rainfall algorithmsand the associated sensitivity on different raindrop shape models,radar noise, and stratiform/convective rain regimes. Afterwards, anartificial algorithmwhich uses three polarimetric radar variables Z,Zdr and Kdp in different scenarios is proposed and deliberated.

4.1. Sensitivity of algorithms to raindrop shape size models

Unfortunately there is no consensus currently existing withinthe research community and it is a subject of major arguments onwhich mean drop shape is most adequate in the microwavescattering simulation. It has been stated that underlying differentassumptions influence the performance of scattering simulations(Cao et al., 2010; Matrosov et al., 2002; Teschl et al., 2008). Thedrop-shape dependence relations are essential for studying rain-drop shape, yet it is unconfident that how well they are correlatedin terms of rain rate retrievals. Moreover, three radar parameters Z,Zdr, and Kdp have completely diverse error structures; thus theassumed drop shape model might not be suitable for a particularvariable with respect to regional and atmospheric conditions.Therefore, in this study, we have tested five different raindropshape models for our scattering simulation which are often quotedin the literature—the Beard and Chuang (1987) model (hereinafternamed BC), Goddard et al. (1994) model (hereinafter named GET),Andsager et al. (1999) model (herein after named ABL), Brandeset al. (2002) model (hereinafter named BZV), and Thurai et al.(2007) model (hereinafter named TBHRS). The purpose of usingfive different shape models in our study is to see the raindropshape effect on algorithm coefficients, and ultimately choose thebest model which fits in terms of rain rate retrievals for the UKregion. In general, the drop shapes in these models are exemplifiedby the ratio of the maximum vertical to horizontal axis, termed asaxis ratio (b/a), as a function of its equivolumetric diameter (Deq),given as follows:

Table 2Polarimetric radar rainfall algorithms using five different raindrop spectra models and

Model Algorithm Root mean squared error, RMSE(mm/h)

Mean abs(mm/h)

BC R¼20.1188 Kdp0.7527 0.39 0.09

R¼0.0086 Z0.8725 Zdr�2.7682 0.28 0.07

R¼37.0535 Zdr�1.5762

Kdp0.8950

0.31 0.09

GET R¼21.3306 Kdp0.7120 0.38 0.10

R¼0.0078 Z0.8804 Zdr�2.8052 0.23 0.06

R¼41.4370 Zdr�1.7219

Kdp0.8613

0.31 0.09

ABL R¼22.4643 Kdp0.7190 0.36 0.09

R¼0.0086 Z0.8563 Zdr�2.5561 0.25 0.07

R¼42.3421 Zdr�1.7027

Kdp0.8709

0.27 0.08

BZV R¼21.6894 Kdp0.7335 0.32 0.07

R¼0.0083 Z0.8703 * Zdr�2.7704 0.24 0.06

R¼42.0061 Zdr�1.7749

Kdp0.8871

0.21 0.06

TBHRS R¼20.9399 Kdp0.7445 0.31 0.07

R¼0.0082 Z0.8820 Zdr�3.0053 0.22 0.06

R¼40.5411 Zdr�1.7677

Kdp0.8919

0.22 0.06

= + × − ×

+ × − ×

≤

≤

− −

− −( ) ( )( )( )

(

)

ba

D D

D D

BC 1.0048 5.7 10 2.628 10

3.682 10 1.677 10 1

D

7 mm (8)

eq eq

eq eq

eq

4 2 2

3 3 4 4

= − × − ×

+ ×

≤

≤

− −

− ( )( )( )

(

)

ba

D D

D

GET 1.075 6.5 10 3.6 10

4.0 10 1. 1

D

5 mm (9)

eq eq

eq

eq

2 3 2

3 3

= − − ×

≤

≤

− ( )( ) (

)

ba

D DABL 1.012 0.01445 1.028 10 1. 1

D

4. 4 mm (10)

eq eq

eq

2 2

= + × − ×

+ × − ×

>

− −

− −( ) ( )( )( )

()

ba

D D

D D

BZV 0.9951 2.51 10 3.644 10

5.303 10 2.492 10 D

1. 5 mm (11)

eq eq

eq eq eq

2 2 2

3 3 4 4

= − × − ×

+ × − ×

>

= − + −

− ×

<

<

− −

− −

−

( ) ( )

( )( )

( )

( )

( )

(

)

( )(

)

ba

D D

D D D

ba

D D D

D

D

TBHRS 1.065 6.25 10 3.99 10

7.66 10 4.095 10

1. 5 mm

1.173 0.5165 0.4698 0.1317

8.5 10 0. 7

1. 5 mm (12)

eq eq

eq eq eq

eq eq eq

eq

eq

2 3 2

4 3 5 4

2 3

3 4

Using the aforementioned raindrop spectra models, the polari-metric radar rainfall algorithms R(Kdp), R(Z, Zdr), and R(Zdr, Kdp)have been developed by performing nonlinear regression between

their statistical relations taking disdrometer derived rain rate as reference.

olute error, MAE Pearson correlationcoefficient, r

Explained variance, R2

0.96 0.920.98 0.960.98 0.96

0.96 0.920.99 0.970.97 0.95

0.96 0.930.98 0.960.98 0.96

0.97 0.940.98 0.970.99 0.97

0.97 0.940.99 0.970.99 0.97

T. Islam / Journal of Atmospheric and Solar-Terrestrial Physics 119 (2014) 42–5246

rainfall rate and different combinations of the simulated polari-metric variables, considering a total of 162,415 1-min filteredevents (Tw43 °C). The algorithms obtained using the five differentraindrop shape models are enumerated in Table 2, includingreflectivity factor Z in mm6 m�3, differential reflectivity Zdrexpressed in linear units [Zdr¼100.1(Zdr)(dB)], and specific differen-tial phase Kdp in °/km. The three estimators R(Kdp), R(Z, Zdr), and R(Zdr, Kdp) are given herein in the power law forms, which arewidely accepted and used within the research community. How-ever, Bringi et al. (2009) proposed a 4th order polynomial form ofR(Kdp) estimator, R(Kdp)¼�aKdp

4þbKdp3 – cKdp

2þdKdp. Illingworthand Blackman (2002) also expressed a third-order polynomial fitof Z/R as a function of ZDR, Z/R¼ f(ZDR)¼aþbZDR–cZDR

2þdZDR3,

where ZDR in dB. Nevertheless, in our case, the conventionalpower-law form has produced a satisfactory fit in least squaresense. The statistical relations of rain rate estimated from thesealgorithms are also listed in Table 2 taking disdrometer derivedrain rate as a reference. The coefficients of the estimators slightlyvary from one model to another, but the variations are not sosignificant. If we take statistical measures listed in Table 2 as aperformance indicator, the best fitted R(Kdp) and R(Z, Zdr) estima-tors are based on the TBHRS model, and R(Zdr, Kdp) is from the BZVmodel. In addition to these three estimators, we also obtain the R(Z) estimator considering all 162,415 raindrop spectra and list asfollows:

=Z R218.4134 (13)1.5549

=R K20.9399 (14)dp0.7445

= −R Z Z0.0082 (15)dr0.8820 3.0053

= −R Z K42.0061 (16)dr dp1.7749 0.8871

The scattergrams of the simulated R from the four estimatorsversus the derived R from the disdrometer dataset are shown inFig. 2. Taking explained variance (R2) as a reference, the R(Z, Zdr)

Fig. 2. Scatterplots of simulated R from four radar rainfall algorithms R

and R(Zdr, Kdp) estimators show the best goodness of fit amongfour estimators with R2¼0.97, whereas the R(Z) estimator demon-strates the lowest skill with R2¼0.90. The explained variance for R(Kdp) estimators is given as 0.94.

4.2. Effects of noise and measurement errors

The fitness of the four estimators in the aforementioned sectionlooks quite satisfactory, yet in reality the radar measurements areseverely affected by noise and measurement errors. Fig. 3 showsthe scatterplots of the same estimators assuming the whiteGaussian noise of s(Z)¼1.0 dBZ, s(Zdr)¼0.2 dB, and s(Kdp) 0.35°/km. The white Gaussian noise herein is assumed by observing theaverage noise of signals in the Thurnham radar system. Interest-ingly, by adding noise to the radar variables, the case is actuallyaltered. The R(Kdp) and R(Zdr, Kdp) estimators, which have pre-viously shown excellent correlations, however, this time demon-strate significant residuals with R2¼0.11 and R2¼0.04 respectively.The R(Z, Zdr) and R(Z) appear less affected to variation, yet thecorrelations go down to R2¼0.92 and R2¼0.86 respectively. For adetailed investigation, we calculate the theoretical error (e) withand without the Gaussian noise for 10 different rain classes(Table 3) between the disdrometer derived rainfall and estimatedrainfall from the four estimators by:

=∑ −

∑

=

=e

n R R

n R

1/ ( )

1/ (17)

ni

d r

ni

d

1 2

1

where Rd is the disdrometer derived rain rates, Rr is the estimatedrain rates by any of the four estimators and n is the number ofsamples in a particular rain class. The theoretical error plot for fourradar rainfall algorithms with and without considering the Gaus-sian noise is shown in Fig. 6. From the figure, it is quite apparentthat the error is more on low rain rate regimes, and the errorreduces towards high rain rate regimes. This is true for all fouralgorithms, either considering or not considering the white Gaus-sian noise. Similar to the previous scatter plots, without

(Z), R(Kdp), R(Z, Zdr), and R(Zdr, Kdp) against disdrometer derived R.

Fig. 3. Same as Fig. 4, but considering white Gaussian noise of s(Z)¼1.0 dBZ, s(Zdr)¼0.2 dB, and s(Kdp) 0.35°/km.

Table 3Divisions of the 10 rain classes and their thresholds.

Class Threshold (mm/h)

1 0.1oRr0.22 0.2oRr0.53 0.5oRr14 1oRr55 5oRr106 10oRr207 20oRr308 30oRr509 50oRr80

10 80oRr120

T. Islam / Journal of Atmospheric and Solar-Terrestrial Physics 119 (2014) 42–52 47

considering the white Gaussian noise, the best skill in terms of lesserror can be seen by the R(Z, Zdr) and R(Zdr, Kdp) estimators, while R(Z) estimator is the most error prone among the four estimators. Ifwe add the white Gaussian noise to the radar variables, thetheoretical error gets increased to a momentous extent. In lowrain classes, among the four estimators, the R(Kdp) and R(Zdr, Kdp)estimators are significantly affected by the radar noise, whereas R(Z, Zdr) and R(Z) are less affected. However, the R(Kdp) and R(Zdr,Kdp) algorithms seem to perform better than the R(Z, Zdr) and R(Z)algorithms in higher rain classes. Hence, the R(Z, Zdr) and R(Z)estimators should be favoured in case of weak rain intensities andR(Kdp) and R(Zdr, Kdp) should be favoured in case of strong rainintensities (Fig. 4).

4.3. Stratiform and convective rain regimes

It is well documented that drop size distributions vary withrespect to rain intensity, type and season (Rosenfeld and Ulbrich,2003). The complex microstructures of clouds are responsible forDSD variations deciding the establishment of different precipita-tion types, for example stratiform and convective. Harrison et al.(2000) state that fixed radar rainfall estimators for all precipitation

types can lead to uncertainties in the retrieved precipitation. Inour previous study, by classifying DSDs into stratiform and con-vective clusters from the similar Chilbolton disdrometer data, wehave shown that DSD structures are significantly different instratiform and convective rain complexes (Islam et al., 2012b;Islam et al., 2012c; Islam et al., 2012d). In a similar spirit to ourprevious study, we separate our entire 162,415 DSDs into strati-form and convective clusters and perform the T-matrix scatteringsimulation to obtain the polarimetric radar variables. Scatterplotsof Zdr (in dB) and Kdp (°/km) against Z (dBZ) variables for stratiformand convective DSD clusters are shown in Figs. 5 and 6. The figuresindicate an apparent variation of the data points in stratiform andconvective regimes. The Z–Zdr can give a brief overview of DSDcharacteristics, and in our case the scatter plots are well separatedin stratiform and convective rain regimes. This implies that weakconvection has smaller mean drop diameters than stratiform rain.As reflectivity increases and convection becomes vigorous, themean diameters increase and become larger than in the stratiformregion. This is due to the melting graupel or small melting hailwhich ends up as larger drops. Or these ice particles might act ascores to liquid water around them which increase the size. Similarseparation can be noticed from the Z–Kdp scatterplot. In fact, wecan clearly say that most of the stratiform spectra fall belowZ¼35 dBZ and convective spectra fall over Z¼40 dBZ, while thereis an overlap of stratiform and convective spectra within Z¼35 to40 dBZ. Similar to the whole DSD datasets, as mentioned inSection 4.1, we obtain the polarimetric radar rainfall algorithmsfor stratiform and convective DSD clusters provided in Table 4. Ofcourse, based on the best fitted information for different raindropspectra models, the R(Kdp), R(Z, Zdr) estimators are derived basedon the TBHRS model, and R(Zdr, Kdp) estimator is derived using theBZV model.

4.4. The artificial algorithm

It is accepted in the research community that there are meritsand demerits of different algorithms in different rain intensities

Fig. 4. Theoretical error plots for different radar rainfall estimators in 10 rain classes (see Table 3). Rain intensity increases from class 1 to class 10. Top panel is noise free,while bottom panel is considering white Gaussian noise of s(Z)¼1.0 dBZ, s(Zdr)¼0.2 dB, and s(Kdp) 0.35°/km.

Fig. 5. Scatterplots between simulated Z and Zdr from the disdrometer DSD forstratiform (top) and convective (bottom) clusters.

Fig. 6. Scatterplot between simulated Z and Kdp from disdrometer DSD for strati-form (blue dotted points) and convective (green crossed points) clusters. (Forinterpretation of the references to colour in this figure legend, the reader is referredto the web version of this article.)

T. Islam / Journal of Atmospheric and Solar-Terrestrial Physics 119 (2014) 42–5248

and conditions. Thus, we propose an artificial algorithm, a mod-ified version of composite estimator based on a variant of theapproach described by Ryzhkov et al. (2005a), latter adapted byBringi et al. (2009) for C-band. A descriptive chart of the artificialalgorithm is given in Fig. 7. The concept of this decision tree basedartificial algorithm is to use different algorithms in stratiform andconvective regimes, which uses different combination of the radarvariables to form R(Z, Zdr, Kdp). One of the approaches to distin-guish stratiform and convective raindrop spectra from radar datais a DSD based indexing technique as stated in Thurai et al. (2010).

We also refer the article of Bringi et al. (2009) where theyexplained the classification procedure. However, in our case wehave used a simple scheme, and considered Zr35 dBZ as strati-form, while Z440 dBZ as convective according to the UK clima-tology. A mixed regime is also included in the artificial algorithm,where both stratiform and convective raindrop spectra are pre-sent. In the stratiform spectrum (Zr35 dBZ), when Zdr is equal toor over 0.1 dB, the algorithm uses R(Z, Zdr) estimator from EquationT3, whereas for Zdro0.1 dB, the R(Z) estimator from Equation T1 is

T. Islam / Journal of Atmospheric and Solar-Terrestrial Physics 119 (2014) 42–52 49

used. In the mixed spectrum (35oZr40 dBZ), the algorithm usesR(Z, Zdr) estimator for ZdrZ0.1 dB (Eq. (16)) and R(Z) estimator forZdro0.1 dB (Eq. (13)), which are obtained considering our wholeDSD datasets. The differential phase is severely affected by back-scatter differential phase complications and becomes too noisyalong the radar beam. The noise effect is substantially more atC-band frequency and in the low rain rate regimes as we haveshown in Fig. 4. Hence, the use of Kdp in the low rain rate regimesis not suitable and skipped in our artificial algorithm. However, Kdp

is excellent in the convective rain, in particular with the presenceof hail as stated in Ryzhkov et al. (2005b). In fact, in the convectiveregime of our artificial algorithm (Z440 dBZ), our first choice is touse of R(Kdp) from Equation T6, if KdpZ0.15°/km. If Kdpo0.15°/kmand ZdrZ0.1 dB, then the R(Z, Zdr) estimator acquired from con-vective DSDs can be used, that is Equation T8. Otherwise, we haverelied upon the R(Z) estimator attained for convective raindropspectra (Equation T5). It is to be noted that the R(Zdr, Kdp)algorithm is not included in the artificial algorithm since use ofZdr and Kdp together is quite unreliable at C-band frequency.

5. Application of the artificial algorithm to polarimetric radar

5.1. Polarimetric radar data processing

The radar used in the study, the Thurnham radar, is wellcalibrated as the UK Met Office regularly checks the system gainbased on solar standardizations, and there is no need to adjust theradar constants. However, radar signals are affected by otherdifferent sources of errors and radar data need to be processedprior to use. One of the most common problems is misconstrue offalse echoes, known as non-precipitation echoes, in particularwhen the radar scans at low elevation angles. Another ambiguityis that C-band radar suffers considerable attenuation of the radarsignal due to absorption and scattering of electromagnetic waveswith precipitation media. Therefore, measured Z and Zdr need to be

Table 4Polarimetric radar rainfall algorithms for stratiform and convective DSD clusters.

DSD cluster Algorithm Equation no

Stratiform Z¼227.3552 R1.5759 T1R¼14.3366 Kdp

0.6355 T2R¼0.0147 Z0.8486 Zdr

�4.9994 T3R¼51.0910 Zdr

�3.6124 Kdp0.8592 T4

Convective Z¼123.0353 R1.6966 T5R¼21.9232 Kdp

0.6647 T6R¼0.0073 Z0.8819 Zdr

�2.6874 T7R¼37.1842 Zdr

�1.5298 Kdp0.9010 T8

Fig. 7. Descriptive block chart illustrating the artificial algorithm

treated with a reliable correction procedure. Though Kdp is free ofsignal attenuation, however, it is too noisy and it also needsadjustment through a filtering approach.

Considering the above points, all pre-processing has beenperformed prior to the use of the Thurnham radar data. Particu-larly, the Z has been corrected for attenuation through the iterativeZPHI algorithm as suggested in Bringi et al. (2001). In fact, thisalgorithm is the modified version of the original ZPHI methodproposed by Testud et al. (2000). The algorithm uses totaldifferential propagation phase (ΔΦDP) to estimate the path inte-grated attenuation:

⎡⎣ ⎤⎦ ⎡⎣ ⎤⎦⎡⎣ ⎤⎦

=−

+ −

−

−A r

Z r A

I r r A I r r( )

( ) 1

( : ) 1 ( : ) (18)h

hh mb

fb

m fb

m

( )

0

where

αΔΦ= −A r rlog 0.1 ( : ) (19)f DP m0

⎡⎣ ⎤⎦∫=I r r b Z s ds( : ) 0.46 ( )(20)m

r

r

hh mb

0 ( )m

0

⎡⎣ ⎤⎦∫=I r r b Z s ds( : ) 0.46 ( ) (21)mr

r

hh mb

( )m

Here, the coefficient b is taken from the scattering simulationsresults. The α value is optimized by minimizing the error betweenthe measured and computed ΦDP. The computed ΦDP profile can beobtained by:

∫Φα

=rA s ds

( ) 2( )

(22)DP cr

rh

( )0

The Zdr profile has been corrected for attenuation utilizing thecorrection method offered by Tan et al. (1995). The offset of Zdr hasbeen determined by scrutinizing the corrected Z and corrected Zdrscatter relation with respect to the mean value of Zdr and Zperceived from scattering simulations of measured DSD. The Kdp

has been derived using the iterative finite impulse response (FIR)range filter based on 300 m gate spacing, forced to each rangeprofile of Φdp. Once the filter is applied, Kdp has been computedfrom the Φdp profile.

5.2. Evaluation through a dense gauge network

For evaluation of the proposed artificial algorithm, we haveconsidered 6 significant storm cases, which have occurred in theyear of 2007. Fig. 8 shows the average daily accumulations ofrainfall, computed from 73 rain gauge data, for the selected 6 storm

for rain rate retrievals with Z, Zdr and Kdp as input variables.

Fig. 8. Averaged daily gauge accumulations from the 73 tipping bucket rain gauges for the six significant events in the year of 2007.

T. Islam / Journal of Atmospheric and Solar-Terrestrial Physics 119 (2014) 42–5250

cases. The storm events are selected in such a way that the eventsrepresent a wide range of atmospheric conditions, for examplecold and warm seasons, as well stratiform and convective rainregimes to facilitate the algorithm evaluation more realisticallyand robustly.

We evaluate hourly rain accumulations in terms of pointestimates calculated from the conventional Marshall–Palmer algo-rithm (RMP) and the artificial algorithm (RArtificial) to those esti-mated by the rain gauges in Fig. 9. The scattergrams are plottedcombining all the radar scans from the selected events containingrainy cells over the rain gauges. The statistical measures aretabulated in Table 5. Note that individual radar bins exactly overthe corresponding rain gauges are considered for comparison.Only those data points are taken when the gauge measures hourlyaccumulations 40.2 mm and the radar estimates hourly accumu-lations 40 mm. In both cases, RMP and RArtificial, Z have beencorrected for attenuation using polarimetric information. Usingthe RMP algorithm, the statistical measures are obtained asR2¼0.79 and MAE¼0.86 mm, r¼0.88, and RMSE¼1.33 mm. How-ever, if we use the RArtificial algorithm, the correlation improves toR2¼0.84, while the error factor is reduced to MAE¼0.82 mm(r¼0.92 and RMSE¼1.23 mm). It is to be remembered that radargage comparisons might be affected due to variations of DSD(Rico-Ramirez et al., 2007). Moreover, when comparing radarrainfall with point gauge data, representativeness errors arisebecause of the differences between the two very different samplevolumes. In a recent study, Bringi et al. (2011) showed that whencomparing point to area rainfall measurements on a 4 km2 pixel,the point to area difference (i.e. the variance reduction factor) wasaround 20% for rainfall accumulations larger than 1 mm/h andaround 40% for rainfall accumulations larger than 6 mm/h. Takinginto account of those uncertainties, our results imply that the MPrelation is very well suited for the region. There is an improvementif using the polarimetric-based artificial algorithm, but the relativeperformance between the artificial and Marshall Palmer

algorithms is marginal. This might be due to the fact that thepolarimetric data quality of the Thurnham radar, particularly in Zdrand Φdp, is quite erratic. Bringi et al. (2011) state that the copolarcorrelation coefficient between the horizontal and vertical polar-ized signals for the Thurnham radar is fairly lower (�0.94) thanthat should have been in rain (�0.99). This has led to high errorsin polarization parameters. Thompson et al. (2008) have alsoexperienced the similar data quality issues.

6. Conclusions

An extensive seven years of disdrometer data from the Chil-bolton observatory, UK have been analysed for the development ofpolarimetric radar rainfall algorithms at C-band frequency. Aftervarious filtering approaches, a total of 162,415 1 min raindropspectra are obtained from the disdrometer dataset simulatingpolarimetric radar variables Z, Zdr, and Kdp according to the UKclimatology. For the simulation, five different raindrop spectramodels have been tested to understand the sensitivity of algo-rithms coefficients to raindrop shape assumptions. The developedalgorithms have shown slight variations in coefficients for differ-ent raindrop spectra models. The best fitted rain rate retrievalsfrom these estimators to those derived from the disdrometer areconsidered as the performance measure, and based on thisinformation, the algorithms are further explored in light of strati-form and convective rain regimes using a simple classificationscheme. Finally, an artificial algorithm is proposed which takesaccount of stratiform and convective estimators and uses differentpolarimetric estimators in different contexts. The artificial algo-rithm is applied and tested to a C-band operational polarimetricradar, located in Thurnham, UK by employing 73 tipping bucketrain gauges. Six significant rainy events are used for the evalua-tion. The evaluation is compared against the conventional Mar-shall–Palmer algorithm, which is currently in use operationally by

Table 5Performance of the RMP and RArtificial algorithms.

Algorithm R2 MAE (mm) r RMSE (mm)

RMP 0.79 0.86 0.88 1.33RArtificial 0.84 0.82 0.92 1.23

Fig. 9. Radar hourly rain accumulations versus gage hourly rain accumulations for a total of 1728 radar scans. Top panel is from the Marshall–Palmer algorithm (RMP) andbottom panel is from the artificial algorithm (RArtificial).

T. Islam / Journal of Atmospheric and Solar-Terrestrial Physics 119 (2014) 42–52 51

the UK Met Office. It has been shown that the artificial algorithmperforms slightly better than the operational Marshall–Palmeralgorithm in terms of rainfall retrievals accuracy. The explainedvariance and mean absolute error using the Marshall–Palmeralgorithm have been revealed as R2¼0.79 and MAE¼0.86 mmrespectively. The statistical measures are improved by the use ofartificial algorithm representing R2¼0.84 and MAE¼0.82 mm.

It is worth mentioning that the previous established algorithmsproposed in the literature so far have been developed using a smallnumber of DSD datasets as compared to this study. For instance, inthe past studies, a total of 2160 1 min averaged N(D) by Bringi et al.(2009), 25,920 1 min events by Ryzhkov et al. (2005a), and around30,000 min of 2DVD data by Cao et al. (2010) were used in theiranalysis. On the other hand, a large dataset consisting of 162,4151 min DSD events is used in our study, and due to such a largedataset, it is expected that the DSDs are more representative of thegiven region. Moreover, the Thurnham polarimetric radar iscurrently on a test phase and not fully functional. During thestudy, we have found that radar data quality, more specifically, thepolarization variables Zdr and Φdp, are too noisy. We expect theperformance of our artificial algorithm can be significantlyimproved if fully functional standard radar data are used. Webelieve such an improvement will be truly beneficial to theoperational community when the UK Met Office upgrades itsradar network to polarimetric capabilities in the upcoming years.

Acknowledgements

The author would like to thank the British Atmospheric DataCentre and the Radio Communications Research Unit at the STFCRutherford Appleton Laboratory for providing the disdrometerdataset. The support from the UK Met Office is also acknowledgedfor providing the Thurnham radar data and the EnvironmentAgency for the rain gauge data. The author also extend theacknowledgements to Dr. Miguel A. Rico-Ramirez and Prof. DaweiHan of University of Bristol for their encouragements and supportfor this study.

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