HYDROLOGICAL PROCESSESHydrol. Process. 25, 3711–3720 (2011)Published online 15 April 2011 in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/hyp.8096

Performance evaluation of interpolation methodsfor incorporating rain gauge measurements into NEXRADprecipitation data: a case study in the Upper Guadalupe

River Basin

Hongjie Xie,1* Xuesong Zhang,2 Beibei Yu1 and Hatim Sharif3

1 Laboratory for Remote Sensing and Geoinformatics, Department of Geological Sciences, University of Texas at San Antonio, San Antonio, TX78249, USA

2 Joint Global Change Research Institute, Pacific Northwest National Laboratory, College Park, MD 20740, USA3 Department of Civil and Environmental Engineering, University of Texas at San Antonio, San Antonio, TX 78249, USA

Abstract:

High spatial and temporal resolution of precipitation data is critical input for hydrological budget estimation and flashflood modelling. This study evaluated four methods [Bias Adjustment (BA), Simple Kriging with varying Local Means(SKlm), Kriging with External Drift (KED), and Regression Kriging (RK)] for their performances in incorporating gaugerainfall measurements into Next Generation Weather Radar (NEXRAD) multi-sensor precipitation estimator (MPE; hourly and4 ð 4 km2). Measurements from a network of 50 gauges at the Upper Guadalupe River Basin, central Texas and MPE data forthe year 2004 were used in the study. We used three evaluation coefficients percentage bias (PB), coefficient of determination(R2), and Nash–Sutcliffe efficiency (NSE) to examine the performance of the four methods for preserving regional- andlocal-scale characteristics of observed precipitation data. The results show that the two Kriging-based methods (SKlm andRK) are in general better than BA and KED and that the PB and NSE criteria are better than the R2 criterion in assessingthe performance of the four methods. It is also worth noting that the performance of one method at regional scale may bedifferent from its performance at local scale. Critical evaluation of the performance of different methods at local or regionalscale should be conducted according to the different purposes. The results obtained in this study are expected to contributeto the development of more accurate spatial rainfall products for hydrologic budget and flash flood modelling. Copyright 2011 John Wiley & Sons, Ltd.

KEY WORDS NEXRAD; MPE; rain gauge; precipitation; geostatistics

Received 8 December 2009; Accepted 8 March 2011

INTRODUCTION

Precipitation, characterized by high spatial and tempo-ral variability, is one of the primary controlling factorsfor many physical processes such as the hydrologicalcycle, land surface and air interaction, and forest andagriculture crops growth. Previous studies have shownthat accurate estimation of precipitation is critical forsimulating runoff, time shift of hydrographs, sedimentdelivery, and nutrient yield (Arnaud et al., 2002; Hos-sain et al., 2004; Chaplot et al., 2005; Kalinga and Gan,2006; Younger et al., 2009). Traditionally, precipitationmeasurements from rain gauges are usually too sparselydistributed to capture the spatial variability. Weatherradar measurements of precipitation, which provide pre-cipitation data with much higher spatial resolution incomparison to rain gauges, have served meteorology forover 40 years and hydrology for around 20 years (Kra-jewski and Smith, 2002). The U.S. Next Generation

* Correspondence to: Hongjie Xie, Laboratory for Remote Sensing andGeoinformatics, Department of Geological Sciences, University of Texasat San Antonio, San Antonio, TX 78249, USA.E-mail: hongjie.xie@utsa.edu

Weather Radar (NEXRAD), which can provide precip-itation products with high spatial resolution (4 ð 4 km2)at hourly temporal scale, has been used in a wide rangeof hydrological, meteorological, and climatological stud-ies (Bedient et al., 2000; Bradley et al., 2002; Kneblet al., 2005; Kalin and Hantush, 2006). Many studieshave been performed to validate the NEXRDA rain-fall estimates (Young et al., 2000; Jayakrishnan et al.,2004; Xie et al., 2005, 2006; Wang et al., 2008; Habibet al., 2009). Many efforts attempted to incorporate raingauge measurements into NEXRAD precipitation prod-ucts using spatial interpolation techniques (Seo, 1998;Steiner et al., 1999; Seo and Breilenbach, 2002; Haber-landt, 2007; Li et al., 2008). Different methods, rangingfrom simple multiplicative correction methods to com-plex geostatistical methods, have been applied in previousstudies on improving NEXRAD products. For example,Steiner et al. (1999) applied a simple Bias Adjustment(BA) method to correct NEXRAD in Goodwin Creek,a small research watershed in northern Mississippi. Liet al. (2008) developed a linear regression based Krigingmethod to improve daily NEXRAD precipitation usingrain gauge data and applied it in Texas to estimate dailyspatial precipitation in 2003. These results have shown

Copyright 2011 John Wiley & Sons, Ltd.

3712 H. XIE ET AL.

Figure 1. Location of the study area and gauge locations with identification numbers (ID). The three rain gauges used as examples in the PerformanceEvaluation of Different Interpolation Methods at Local Scale Section are gauge IDs 4 and 18 at Kerr County (kr4, kr18) and 1 at Guadalupe County

(gp1)

the potential of further improving NEXRAD data usingrain gauge data to provide more accurate spatial precipi-tation estimation.

The objective of this study is to evaluate four spa-tial interpolation methods [Bias Adjustment (BA), SimpleKriging with varying Local Means (SKlm), Kriging withExternal Drift (KED), and Regression Kriging (RK)] fortheir performances in incorporating gauge measurementsinto NEXRAD precipitation products. We selected theUpper Guadalupe River Basin (UGRB) as the study areabecause of the availability of high quality precipitationrecords from 50 rain gauges across this area. In previousresearch, it was common to evaluate the performanceof different methods to capture the rainfall characteris-tics at regional scale which is important for hydrologicbudget estimation at watershed scale. However, minimalresearch has been devoted to evaluate the accuracy inlocalized precipitation that is critical for accurate flashflood forecasting. Therefore, results from this study willprovide insight into the performances of different meth-ods in terms of characterizing precipitation characteristicsat both regional and local scales, which are valuable fordeveloping accurate precipitation data for ecological andhydrologic modelling.

METHODOLOGY

Study area

The study area lies in the Hill Country of centralTexas, covering the UGRB and partly intersecting the

recharge zone of the Edwards Aquifer (Figure 1). Theregion belongs to a semi-arid climate regime and hasannual mean rainfall of approximately 800 mm. The areais highly vulnerable to hydrologic extremes: intense pre-cipitation events, severe flooding, and droughts (Scanlonet al., 2004).

Data source

The NEXRAD multi-sensor precipitation estimator(MPE), developed by the National Weather Service(NWS) Office of Hydrology since March 2000, is a prod-uct that merges rainfall measurements from rain gauges,and rainfall estimates from NEXRAD and GeostationaryOperational Environmental Satellite (GOES) products.The NWS West Gulf River Forecast Center (WGRFC)switched from Stage III to MPE as the preferred pre-cipitation estimation programme in October 2003, andended Stage III in December 2004 (Wang et al., 2008).The MPE precipitation products are hourly accumulationwith a spatial resolution of about 4 ð 4 km2. There are 50rain gauges covering four counties: Kerr, Kendall, Comal,and Guadalupe in south-central Texas (Figure 1). All raingauge data have a 6-min accumulation time-step. Year2004 data of MPE and 50 rain gauges are used in thestudy.

Spatial interpolation methods

Four methods, applied for incorporating rain gaugedata into the NEXRAD estimation, are BA, SKlm(Goovaerts, 2000), KED (Haberlandt, 2007), and RK

Copyright 2011 John Wiley & Sons, Ltd. Hydrol. Process. 25, 3711–3720 (2011)

INTERPORATION METHODS FOR RAINFALL MAPPING 3713

(Hengl et al., 2004). BA is a simple and widely usedmethod to adjust the system error in the Radar estimates.In BA method, it first calculates the ratio of the meangauge rainfall measurements over the mean radar rainfallestimates and then multiplies this ratio with radar datato estimate spatial rainfall distribution. Kriging methodshave been shown as effective multivariate geostatisti-cal techniques (Lloyd, 2005; Cheng et al., 2007; Haber-landt, 2007; Zhang and Srinivasan, 2009) for rainfalldistribution estimation. In order to efficiently implementthe geostatistical techniques automatically for multipletime-steps, we revised the geographic information sys-tem (GIS)-based precipitation interpolation programmedeveloped by Zhang and Srinivasan (2009) to read inNEXRAD data as auxiliary variable and extended thisGIS programme to include RK and BA methods.

Kriging is a group of advanced geostatistical tech-niques that provides the best linear unbiased estimate.In Kriging methods, rainfall value at location x is esti-mated as Oz�x� D m�x� C ε�x�, where m is the expectedmean rainfall and ε is the residual. In SKlm, KED, andRK methods, we calculate the expected mean rainfall asa linear equation of NEXRAD rainfall value �m�x� Dˇ0 C ˇ1R�x�� and estimate the residual as a weighted sumof residuals that are calculated as the difference betweenrain gauge recorded and expected mean rainfall values atsurrounding rain gauges

(ε�x� D ∑n

iD1 �xi[ε�i�]). R�x� is

the NEXRAD rainfall value at location x. ˇ0 and ˇ1 arelinear coefficients. ε�i� is the residual at rain gauge i. nis the number of rain gauges. �xi is the linear weight ofresidual at rain gauge i. Different Kriging methods usedifferent assumptions and equations to calculate m andε. The algorithms used by the three Kriging methods areintroduced in the following paragraphs. More detailedinformation on SKlm, KED, and RK was provided byGoovaerts (1997) and Hengl et al. (2004).

In RK method, it is assumed that the expected meanrainfall is a known constant. The concurrent pairs ofNEXRAD and rain gauge observed rainfall values areused to estimate the linear coefficient ˇ0 and ˇ1 bygeneralized least squares (GLS). The optimal weights(�xi) are solved using the ‘Ordinary Kriging system’,

n∑

jD1�xj��hij� � ��x� D ��hxi� i D 1, . . . , n

n∑jD1

�xj D 1�1�

where �xi is the weight assigned to the residual at raingauge i, ��x� is the Lagrange parameter accounting forthe constraint on the weights, hij denotes the separationdistance between rain gauges i and j. The ��h� is semi-variagram function.

The general procedures in SKlm method are similar tothose of RK, except that SKlm uses ordinary least squares(OLS) to fit the linear regression between co-locatedrain gauge and NEXRAD rainfall values and employspatial covariance function to interpolate the residuals.The optimal weights in SKlm are obtained by solving

the system of equations below

n∑jD1

�xjC�hij� D C�hxi� i D 1, . . . , n (2)

where C�h� is the spatial covariance between two pointsseparated by distance h.

In SKlm and RK, the expected mean rainfall isassumed to be known, while KED assumes the expectedmean rainfall is unknown. The major difference betweenKED and RK lies in that KED incorporates the estimationof the linear regression coefficients into the OrdinaryKriging equation system, while RK conducts the linearregression and Ordinary Kriging separately. The optimalweights in KED are solved using the following equations

n∑jD1

�xj��hij� � u0 � u1R�i�

D ��hxi� i D 1, 2, . . . , n,n∑

iD1�xi D 1,

n∑iD1

�xiR�i� D R�x�

�3�

Evaluating precipitation estimated by different methods

To be consistent with previous research on spatialrainfall estimation using NEXRAD, we use rain gaugeobserved rainfall as ‘ground truth’ because NEXRADmeasures the atmospheric moisture above ground whilea rain gauge collects precipitation falling on the ground.It is worth noting that measurement of small rainfallevents is challenging for both rain gauges and NEXRAD(http://weather.noaa.gov/radar/radinfo/radinfo.html#clear; Habib et al., 2009), which may lead to significantsampling errors. However, small amount of precipitationhas relatively insignificant effect on hydrologic mod-elling (Westcott et al. 2008; Zhang and Srinivasan, 2009).Therefore, we focussed on those hours with mean spa-tial precipitation rate larger than 0Ð1 mm h�1. A total of737 h was selected. The accumulated areal mean pre-cipitation depth of these 737 h accounts for about 95%of annual mean precipitation (1017Ð4 mm) for the year2004.

Regional-scale evaluation. The performance of differ-ent methods to estimate spatial rainfall at regional scale(the entire UGRB) is evaluated using cross-validation(Isaaks and Srivastava, 1989) for each of the selected737 h. In the procedure, each of the rain gauge measure-ments is temporarily removed at a time and the remainingdata are used to estimate a rainfall value for the locationwhere the temporarily removed rain gauge is located at.The difference between the gauge observed and estimatedvalue is then used to evaluate the accuracy of an interpo-lation method. Let zil, i D 1, . . . n, l D 1 . . . , L, denotesthe i-th station measurement on the l-th hour, where L isthe number of total hours being used in the comparison.Let Ozil denote the predicted value for the same gauge.

Copyright 2011 John Wiley & Sons, Ltd. Hydrol. Process. 25, 3711–3720 (2011)

3714 H. XIE ET AL.

Table I. Evaluation coefficients of precipitation maps produced by different methods for the three hours examined

Date Evaluation coefficients MPE BA SKlm KED RK

Hour 8, 24 April 2004 Property Mean 5Ð97 7Ð74 7Ð87 7Ð67 7Ð86Min 0 0 0 0 0Max 20 25 32 32 33CV 0Ð83 0Ð82 1Ð00 1Ð02 1Ð02

Accuracy PB �21Ð46 0Ð28 0Ð61 1Ð89 0Ð52R2 0Ð86 0Ð85 0Ð85 0Ð85 0Ð85NSE 0Ð732 0Ð83 0Ð85 0Ð85 0Ð85

Hour 8, 22 June 2004 Property Mean 3Ð85 6Ð78 6Ð62 6Ð66 6Ð62Min 0 0 0 0 0Max 36 64 62 55 63CV 1Ð99 1Ð98 2Ð03 1Ð94 2Ð03

Accuracy PB �42Ð43 0Ð18 1Ð24 0Ð21 0Ð71R2 0Ð94 0Ð94 0Ð93 0Ð94 0Ð93NSE 0Ð7 0Ð93 0Ð93 0Ð94 0Ð92

Hour 9, 22 June 2004 Property Mean 7Ð16 9Ð32 9Ð15 9Ð12 9Ð08Min 0 0 0 0 0Max 32 41 42 46 44CV 1Ð33 1Ð33 1Ð36 1Ð38 1Ð37

Accuracy PB �22Ð41 0Ð04 0Ð50 0Ð79 0Ð43R2 0Ð87 0Ð86 0Ð92 0Ð92 0Ð92NSE 0Ð81 0Ð86 0Ð92 0Ð92 0Ð92

Units for mean, min, and max are mm h�1 and for PB is %.

For each hour, the following statistics were computed

Percentage Bias, PB DOZl � Zl

Zlð 100 �4�

Correlation Coefficient �%�, R2

D

n∑iD1

�zil � Zl��Ozil � OZl�

[n∑

iD1

�zil � Zl�2

]0Ð5 [n∑

iD1

�Ozil � OZl�2

]0Ð5

2

�5�

Nash–Sutcliffe efficiency, NSE

D 1Ð0 �

n∑iD1

�Ozil � zil�2

n∑iD1

�zil � zl�2

�6�

where Zl is the mean of gauge measured precipitationof the l-th hour, OZl is the mean of predicted precipi-tation at rain gauge locations of l-th hour. Var�zil� isthe variance of gauge measured precipitation of the l-thhour, Var�Ozil� is the variance of interpolated rainfall val-ues at rain gauges of the l-th hour. PB is calculated torepresent the systematic bias of spatial rainfall distribu-tion estimated by different methods. Negative PB valueindicates underestimation and positive PB value indicatesoverestimation. The smaller the absolute value of PB, thebetter the performance of the predicting method. R2 is thesquare of the Pearson’s product-moment correlation coef-ficient and describes the proportion of the total variance inthe observed data that can be explained by the model. R2

is an indicator of the strength of the relationship betweenthe observed and simulated values. NSE is also called

Nash–Sutcliffe Model efficiency coefficient, which indi-cates how well the plot of the rain gauge observed valueversus the predicted value fits the 1 : 1 line, and rangesfrom �1 to 1 (Nash and Sutcliffe, 1970). Larger R2 andNSE value indicate better agreement between interpola-tions and observations.

Local-scale evaluation. The method that provides bet-ter results at regional scale may not outperform the othermethods for localized rainfall estimation. In addition toregional-scale evaluation, we evaluate the performance ofdifferent rainfall estimation methods at each rain gaugelocation. The same evaluation statistics (i.e. PB, R2, andNSE) were used to evaluate the agreement between theestimated and rain gauge observed rainfall at each raingauge. The form of equations used for local-scale evalu-ation are the same as those listed in the previous section,except that the spatially observed and estimated rain fallvalues are replaced with the observed and estimated rain-fall at a specific rain gauge for a specified time period.The time series of observed and estimated rainfall arethen used to evaluate the performance of different meth-ods at each rain gauge location.

RESULTS

Performance evaluation of different interpolationmethods for regional-scale rainfall estimation

Comparison of spatial precipitation maps interpolatedby different methods. Here, we select three hours withsignificant rainfall accumulation (the 8th hour, 24 April2004; 8th and 9th hours, 22 June 2004) as examplesto show the difference between maps produced bydifferent methods as well as the MPE maps. Table I

Copyright 2011 John Wiley & Sons, Ltd. Hydrol. Process. 25, 3711–3720 (2011)

INTERPORATION METHODS FOR RAINFALL MAPPING 3715

0 20 40 600

20

40

60

Predicted

Obs

erve

d

No Correction

0 20 40 600

20

40

60

Predicted

BA

0 20 40 600

20

40

60

Predicted

SKlm

0 20 40 600

20

40

60

Predicted

Obs

erve

d

KED

0 20 40 600

20

40

60

Predicted

RK

Data Points

Trend line

1:1 line

Figure 2. Scatter plots of rain gauges observed rainfall versus estimated precipitation values from the MPE (no correction) and the four interpolationmethods, at hour 8 on 24 April 2004

lists the four performance evaluation coefficients of fiveprecipitation maps for all the three hours. The coefficientsfor the MPE maps were directly calculated by comparingthe radar cell values with co-located and concurrentgauge measurements. In addition, other properties [mean,maximum, minimum precipitation values, and coefficientof variation (CV)] of the five maps for each hour are alsoincluded in Table I.

The PB values show that the MPE underestimates 21,42, and 22% of areal mean precipitation, respectively,for the 8th hour on 24 April 2004, the 8th hour on22 June 2004, and the 9th hour on 22 June 2004, ascompared with the gauge measurements. These PB valuesare much larger than the 7% underestimation for thesame time period but only using uniform rainfall eventsreported by Wang et al. (2008). This suggests that fornon-uniform rainfall events, the difference between radarestimates and gauge observations should be much largerthan that of the uniform rainfall events. The PB valuesfor four interpolation methods are between 0Ð04% (theBA method) and 1Ð89% (the KED method). The BAmethod shows the lowest PB values among the fourmethods, which suggest that the simple bias correction iseffective in reducing the overall bias. However, in mostcases, NSE of the BA interpolated map is relatively lowerthan those of the three Kriging methods. This indicatesthat, although the simple BA method effectively removedthe overall bias, its performance in terms of reducingdifference between observed and estimated rainfall valuesis not as good as the Kriging methods.

R2 values of rainfall maps derived by the four methodsas well as the MPE product are high and close to eachother, except that MPE and BA obtained lower R2 valuesthan three Kriging methods (0Ð85–0Ð86 vs 0Ð92) for the

9th hour on 22 June 2004. Overall, the high R2 valuesindicate that all methods/maps have similar performancein capturing the precipitation distribution pattern; in otherwords, the R2 criterion does not assess the four methodsfor different performances. The scatter plots in Figure 2show that, although the NEXRAD MPE product obtainedhigh R2 value, its trend line is substantially deviating fromthe 1 : 1 line, as a result of the underestimation of MPE ascompared with gauge data. After incorporating rain gaugeobserved values, the trend lines of the four methods arevery close to the 1 : 1 line. Scatter plots for the two otherhours (not shown) have similar results.

In Figure 3, the general patterns of precipitation distri-bution obtained by different methods are similar, whilethe maximum rainfall rates from the four interpolationmaps are distinguished larger than those from the MPEmap (Table I). This is because that the relatively highrain gauge rainfall rates as compared with the MPE (i.e.negative PB values of the MPE maps) are transferred intothe four interpolated maps. Other properties (mean, min-imum, maximum, CV) of the four interpolated rainfallmaps are similar.

Overall performances of different interpolation meth-ods at regional scale. We used box-and-whisker plotsto show the evaluation coefficients of different methodsfor 737 h. The explanation of the symbols in Figure 4 isdescribed as follows. The lower and upper lines of the‘box’ are the 25th and 75th percentiles of the samples.The line in the middle of the box is the sample median(or 50th percentile). The ‘whiskers’ are lines extendingabove and below the box. The plus signs are values thatare more than 1Ð5 times the interquartile range (differencebetween the 25th and 75th percentiles) away from the top

Copyright 2011 John Wiley & Sons, Ltd. Hydrol. Process. 25, 3711–3720 (2011)

3716 H. XIE ET AL.

(1)

(3)

(2)

Figure 3. Spatial precipitation estimated by different methods at the 8th hour on 24 April 2004 (1), the 8th hour on 22 June 2004 (2), and the 9thhour on 22 June 2004 (3). (a, b, c, d, and e are the original MPE, BA, SKlm, KED, and RK maps, respectively)

or bottom of the box. The notches in the box representa robust estimate of the uncertainty about the mediansfor box-to-box comparison. Boxes whose notches do notoverlap indicate that the medians of the two groups differat a significance level of 0Ð05 (Matlab, 2007).

In the plot of PB values of 737 rainfall hours (upperpanel of Figure 4), we used absolute values, because thepositive and negative may compensate with each otherand lead to a false impression of small median and meanbias values. Similarly as shown in Table I, the MPE of737 h has negative bias while all the other methods havepositive bias. It is evident that median PB values ofthe MPE are much higher than those of the other fourmethods that incorporated with rain gauge data. In termsof PB, the BA method has the smallest median than RKand SKlm, whereas the PB values obtained by SKlm andRK are more compacted compared with those of BA andKED methods. The largest PB value of SKlm is 51Ð4%,which is much less than 509Ð68%, the largest PB value ofBA (not shown). In terms of NSE (Figure 4, lower panel)values, the SKlm and RK methods performed similar toeach other and significantly better than the other twomethods. The MPE has the smallest NSE values. Plotof R2 (Figure 4, middle panel) indicates that the MPE

performed the best for capturing precipitation distributionpattern as compared with the rain gauge observations,followed by SKlm and RK.

Overall, large bias (PB values) of MPE map ascompared with the rain gauge observations indicate thatit is preferred to incorporate high quality rain gaugedata into MPE map to provide more accurate rainfallmap at regional scale. Compared with MPE products, thesimple BA method obtained much smaller PB, but cannotimprove R2 and NSE. Among the four interpolationsapproaches, the overall performance of SKlm and RKare similar to or better than the others.

Performance evaluation of different interpolationmethods at local scale

Comparison of rainfall values estimated by differentmethods at three rain gauges. In addition to accuracyevaluation at regional scale, we also conducted evaluationof the predicted rainfall at each rain gauge. The differencebetween the spatial precipitation maps, as exemplified inFigure 3, indicates that different methods predict variedrainfall values at local scale (e.g. at rain gauge point).For illustration purpose, we plot (Figures 5 and 6) theaccumulated hourly rainfall of areal mean of the UGRB(a) and at three rain gauges (which are randomly chosen)

Copyright 2011 John Wiley & Sons, Ltd. Hydrol. Process. 25, 3711–3720 (2011)

INTERPORATION METHODS FOR RAINFALL MAPPING 3717

Figure 4. Box-and-whisker plots of the PB (PBIAS) (%), R2, and NSEvalues of the selected 737 h in 2004 for the MPE (no correction) and the

four interpolation methods (BA, SKlm, KED, and RK)

(b, c, d) from six different methods (gauges only, nocorrection or MPE only, BA, SKlm, KED, and RK) on2 days (9 June 2004 and 22 June 2004). It is found, on 9June 2004 (Figure 5a), that the accumulated areal meanprecipitation amounts estimated by the four interpolationmethods are very close to the rain gauge observedvalues. The MPE estimates similar rainfall as the fourmethods before the 12th hour and more rainfall thenafter. On 22 June 2004 (Figure 6a), the four methods andrain gauge get similar areal mean rainfall accumulationvalues, whereas MPE shows less accumulated rainfall (by�27%).

Although the four interpolation methods perform sim-ilar to each other for areal mean precipitation estimation,substantial difference between the rainfall values esti-mated at local scale (rain gauge locations: kr4, kr18,and gp1) are shown in parts b–d of Figures 5 and 6.For example, MPE and BA show higher rainfall thanrain gauge observed, whereas SKlm, KED, and RKshow lower rainfall at rain gauge kr4 on 9 June 2004(Figure 5b). On 22 June 2009, at rain gauge gp1, BAestimated much lower rainfall than SKlm, KED, and RK.For the three Kriging methods, there is appreciable dif-ference between rainfall values estimated by the three

methods. For example, at kr18, KED estimated rainfalldepth is about 5 mm lower than that of SKlm and RK on22 June 2004 (Figure 6c).

Table II lists the evaluation coefficients for estimatedrainfall time series at rain gauges kr4, kr18, and gp1by different methods for 737 h in the year 2004. Atsome localized region, there may be substantial differ-ence between the performances of difference interpola-tion methods. For example, at rain gauge gp1, PB valuesof KED and BA are 28Ð51 and 50Ð12%, respectively,which has significant implication for local-scale hydro-logic modelling and analysis. Similar as in Table I, thedifferences of R2 values between four methods are smalland the SKlm and RK methods are in general better thanBA and KED methods, whereas KED and BA performsimilar.

Overall performances of different interpolation meth-ods at local scale. We used box-and-whisker plots toshow the evaluation coefficients of different methods atthe 50 rain gauges. The plot of PB values at 50 raingauges (upper panel of Figure 7) shows that all methodshave similar median values. The largest absolute PB val-ues of BA and MPE are 50Ð12 and 44Ð34%, respectively,which are larger than those of SKlm, KED, and RK (rang-ing between 34Ð84 and 36Ð40). For R2 (Figure 7, middlepanel), MPE and KED obtained slightly higher medianthan the other methods. In terms of NSE (Figure 7, bot-tom panel), the SKlm and RK methods performed similarto each other and significantly better than the other meth-ods. In contrast to regional-scale evaluation, BA does notperform the best for removing the bias at local scale.

DISCUSSION AND CONCLUSIONS

In Sections Performance Evaluation of Different Interpo-lation Methods for Regional-Scale Rainfall Estimationand Performance Evaluation of Different InterpolationMethods at Local Scale, we compared four spatial rain-fall interpolation methods as well as the MPE maps forcapturing the observed rainfall characteristics at regionaland local scales. For regional-scale assessment, the highR2 values indicate that the NEXRAD MPE products areable to capture the spatial precipitation distribution pat-terns well, but with large bias as compared with raingauge observed values, the median and mean absolutePB values of 22 and 42%, respectively.

With respect to selecting methods for regional-scalespatial rainfall estimation, the inconsistent performanceof different methods for each time-step and each evalu-ation coefficient makes it difficult to simply choose oneoptimal method. The number of hours that different meth-ods performed the best among 737 h is listed in Table III.In terms of the number of hours that a method performsthe best, BA, MPE, and SKlm perform the best for PB,R2, and NSE, respectively. It is also worth noting that thenumber of hours that one method performed the best forone evaluation coefficient is less than 62% of 737 h. By

Copyright 2011 John Wiley & Sons, Ltd. Hydrol. Process. 25, 3711–3720 (2011)

3718 H. XIE ET AL.

(a) (b)

(c) (d)

Figure 5. Accumulated hourly precipitation of areal mean (a) and at three rain gauges (b, c, d) estimated by different methods on 9 June 2004. Nocorrection means the original MPE data. (b, c, d denotes rain gauge kr4, kr18, gp1, respectively)

(a) (b)

(c) (d)

Figure 6. Accumulated hourly precipitation of areal mean (a) and at three rain gauges (b, c, d) estimated by different methods on 22 June 2004. Nocorrection means the original MPE data. (b, c, d denotes rain gauge kr4, kr18, gp1, respectively)

selecting one method, we may not obtain optimal resultsfor other portion of the hours (more than 38%).

Local-scale evaluation results indicate that rainfallvalues estimated by different methods at a specific raingauge can be substantially different from each other.This, to some extent, reveals the importance of evaluatingthe performance of different methods at local scale. Thenumber of rain gauges that different methods performedthe best is listed in Table IV. Although, SKlm performedthe best at the all 50 rain gauges in terms of NSE, it only

outperformed the other methods at 5 and 1 rain gaugesin terms of PB and R2, respectively.

Spatial precipitation data are critical for accurate flashflood forecasting and hydrologic budget estimation. In thestudy, we incorporate the rain gauge data into NEXRDAMPE products, using four methods (i.e. BA, SKlm,KED, and RK) and evaluate their performances usingPB, R2, and NSE at regional and local scales. Theresults show that the NEXRAD MPE data can capturethe patterns of spatial precipitation distribution well, but

Copyright 2011 John Wiley & Sons, Ltd. Hydrol. Process. 25, 3711–3720 (2011)

INTERPORATION METHODS FOR RAINFALL MAPPING 3719

Table II. Evaluation parameters of predicted areal mean precipi-tation and precipitation at three rain gauges for the year of 2004

Evaluation coefficients MPE BA SKlm KED RK

kr4 PB 4Ð33 �3Ð92 0Ð21 5Ð55 0Ð25R2 0Ð77 0Ð76 0Ð76 0Ð77 0Ð76NSE 0Ð79 0Ð84 0Ð88 0Ð83 0Ð88

kr18 PB 6Ð54 �0Ð15 1Ð13 0Ð52 0Ð57R2 0Ð65 0Ð65 0Ð65 0Ð64 0Ð65NSE 0Ð65 0Ð74 0Ð80 0Ð73 0Ð79

gp1 PB 36Ð41 50Ð12 31Ð98 28Ð51 32Ð24R2 0Ð80 0Ð81 0Ð80 0Ð81 0Ð80NSE 0Ð69 0Ð73 0Ð79 0Ð71 0Ð79

PB is expressed in %; others have no units.

Figure 7. Box-and-whisker plots of the PB, R2, and NSE values at the50 rain gauges for the MPE (no correction) and the four interpolation

methods (BA, SKlm, KED, and RK)

Table III. The number of hours that different methods performedthe best for different evaluation coefficients

Methods

Evaluation coefficient MPE BA SKlm KED RK

PB 27 450 106 98 121R2 422 5 162 102 108NSE 202 54 320 108 104

The sum of the numbers in each row may be larger than 737 because forsome hours there are several methods performing the same for a specificevaluation coefficient.

Table IV. The numbers of rain gauges (total 50) that differentmethods performed the best for different evaluation coefficients

Methods

Evaluation coefficient MPE BA SKlm KED RK

PB 14 13 5 13 5R2 14 7 1 25 3NSE 0 0 50 0 0

there is substantial discrepancy between the rain gaugeand NEXRAD estimated precipitation. The comparisonbetween different spatial interpolation methods indicatesthat, although no one method can consistently outperformthe other methods in terms of all evaluation coefficientsfor all time-steps and at all rain gauges, the two Kriging-based methods (SKlm and RK) are in general better thanBA and KED, and the PB and NSE criteria are better thanthe R2 criterion. It is worth noting that the performanceof one method for regional-scale evaluation may bedifferent from its performance for local-scale evaluation.This indicates the importance of careful evaluation ofthe performance of different methods at local or regionalscale for different purposes. The results obtained in thisstudy are expected to contribute to the development ofspatial rainfall products for hydrologic budget and flashflood modelling.

ACKNOWLEDGEMENTS

This study was in part supported by the U.S. NASAgrant (#NNX07AL79G). Provisions of NEXRAD datathrough Greg Story at the National Weather ServiceWest Gulf River Forecast Center and rain gauge datafrom Guadalupe Blanco River Authority are sincerelyacknowledged. Critical reviews and constructional com-ments from three anonymous reviewers to improve thequality of this manuscript are greatly appreciated.

REFERENCES

Arnaud P, Bouvier C, Cisneros L, Dominguez R. 2002. Influence ofrainfall spatial variability on flood prediction. Journal of Hydrology260: 216–230.

Bedient PB, Hoblit BC, Gladwell DC, Vieux BE. 2000. NEXRAD radarfor flood prediction in Houston. Journal of Hydrologic Engineering 5:269–277.

Bradley AA, Peters-Lidard C, Nelson BR, Smith JA, Yong CB. 2002.Raingauge network design using NEXRAD precipitation estimate.Journal of the American Water Resources Association 38: 1393–1407.

Chaplot V, Saleh A, Jaynes DB. 2005. Effect of the accuracy of spatialrainfall information on the modeling of water, sediment, and NO3-Nloads at the watershed level. Journal of Hydrology 312: 223–234.

Cheng S, Hsiedh H, Wang Y. 2007. Geostatistical interpolation of space-time rainfall on Tamshui river basin, Taiwan. Hydrological Processes21: 3136–3145.

Goovaerts P. 1997. Geostatistics for Natural Resources Evaluation .Oxford University Press: New York.

Goovaerts P. 2000. Geostatistical approaches for incorporating elevationinto the spatial interpolation of rainfall. Journal of Hydrology 228:113–129.

Haberlandt U. 2007. Geostatistical interpolation of hourly precipitationfrom rain gauges and radar for a large-scale extreme rainfall event.Journal of Hydrology 332: 144–157.

Copyright 2011 John Wiley & Sons, Ltd. Hydrol. Process. 25, 3711–3720 (2011)

3720 H. XIE ET AL.

Habib E, Larson BF, Graschel J. 2009. Validation of NEXRADmultisensory precipitation estimates using an experimental dense raingauge network in South Louisiana. Journal of Hydrology 373(3–4):463–478.

Hengl T, Heuvelink GBM, Stein A. 2004. A generic framework forspatial prediction of soil variables based on regression-kriging.Geoderma 120: 75–93.

Hossain F, Anagnostou EN, Borga M, Dinku T. 2004. Hydrologicalmodel sensitivity to parameter and radar rainfall estimation uncertainty.Hydrological Processes 18(17): 3277–3299.

Isaaks EH, Srivastava RM. 1989. Applied Geostatistics . OxfordUniversity Press: New York.

Jayakrishnan R, Srinivasan R, Arnold JG. 2004. Comparison ofraingauge and WSR-88D stage III precipitation data over the Texas-Gulf River Basin. Journal of Hydrology 292: 135–152.

Kalin L, Hantush MM. 2006. Hydrologic modeling of an EasternPennsylvania watershed in Middle Tennessee. Journal of HydrologicEngineering 9(5): 555–569.

Kalinga AO, Gan TY. 2006. Semi-distributed modelling of basinhydrology with radar and gauged precipitation. Hydrological Processes20: 3725–3746.

Knebl MR, Yang Z, Hutchison K, Maidment DR. 2005. Regional scaleflood modeling using NEXRAD rainfall, GIS, and HEC-HMS/RAS: acase study for the San Antonio River Basin Summer 2002 storm event.Journal of Environmental Management 75(4): 325–336.

Krajewski WF, Smith JA. 2002. Radar hydrology: rainfall estimation.Advances in Water Resources 25: 1387–1394.

Li B, Eriksson M, Srinivasan R, Sherman M. 2008. A geostatisticalmethod for Texas NexRad data calibration. Environmetrics 19(1):1–19.

Lloyd CD. 2005. Assessing the effect of integrating elevation data intothe estimation of monthly precipitation in Great Britain. Journal ofHydrology 308: 128–150.

Matlab. 2007. MATLAB Technical Documentation . The MathWorks Inc.:Natick, Massachusetts.

Nash JE, Sutcliffe JV. 1970. River flow forecasting through conceptualmodels: part I. A discussion of principles. Journal of Hydrology 10(3):282–290.

Scanlon BR, Musgrove M, Sansom A, Xie H, Wilcox B, Sharp J,Alexander C, Vieux B, Jackson R, Archer S, Keese K, Reedy R.

2004. Unique aspects of proposed San Antonio/Guadalupe HydrologicObservatory in Texas . http://adsabs.harvard.edu/abs/2004AGUFM.H31C0393S (accessed on 9 January 2008).

Seo DJ. 1998. Real-time estimation of rainfall fields using radar rainfalland rain gauge data. Journal of Hydrology 208: 37–52.

Seo D-J, Breidenbach JP. 2002. Real-time correction of spatiallynonuniform bias in radar rainfall data using rain gauge measurements.Journal of Hydrometeorology 3: 93–111.

Steiner M, Smith JA, Burges SJ, Alonso CV, Darden RW. 1999. Effectof bias adjustment and rain gauge data quality control on radar rainfallestimation. Water Resources Research 35(8): 2487–2503.

Wang X, Xie H, Sharif H, Zeitler J. 2008. Validating NEXRDA MPEand stage III precipitation products for uniform rainfall on the UpperGuadalupe River Basin of the Texas Hill Country. Journal of Hydrology348(1–2): 73–86.

Westcott NE, Knapp HV, Hilberg SD. 2008. Comparison of gage andmulti-sensor precipitation estimates over a range of spatial andtemporal scales in the Midwestern United States. Journal of Hydrology351(1–2): 1–12.

Xie H, Zhou X, Vivoni E, Hendrickx J, Small E. 2005. GIS basedNEXRAD precipitation database: automated approaches for dataprocessing and visualization. Computational Geosciences 31(1):65–76.

Xie H, Zhou J, Hendrickx E, Vivoni H, Guan H, Tian YQ, Small EE.2006. comparison of NEXRAD stage III and gauge precipitationestimates in central New Mexico. Journal of the American WaterResources Association 42(1): 237–256.

Young CB, Nelson BR, Bradley AA, Krajewski WF, Kruger A. 2000.Evaluating NEXRAD multisensor precipitation estimates for oper-ational hydrologic forecasting. Journal of Hydrometeorology 1(3):241–254.

Younger PM, Freer JE, Beven KJ. 2009. Detecting the effects of spatialvariability of rainfall on hydrological modelling within an uncertaintyanalysis framework. Hydrological Processes 23: 1988–2003.

Zhang X, Srinivasan R. 2009. A comparison of geostatistical approachesfor spatial precipitation estimation. Journal of the American WaterResources Association 45(4): 894–906.

Copyright 2011 John Wiley & Sons, Ltd. Hydrol. Process. 25, 3711–3720 (2011)