GIS-based spatial precipitation estimation using next generation radar ...

Environmental Modelling & Software xxx (2010) 1e8

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GIS-based spatial precipitation estimation using next generation radar and raingauge data Xuesong Zhang a, *, Raghavan Srinivasan b a b

Joint Global Change Research Institute, Pacific Northwest National Laboratory, 5825 University Research Court, Suite 3500, College Park, MD 20740, USA Spatial Sciences Laboratory, Department of Ecosystem Sciences and Management, Texas A&M University, 1500 Research Pkwy, Suite B223, College Station, TX 77845, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 1 July 2009 Received in revised form 10 May 2010 Accepted 21 May 2010 Available online xxx

Precipitation is one important input variable for land surface hydrologic and ecological models. Next Generation Radar (NEXRAD) can provide precipitation products that cover most of the conterminous United States at high resolution (approximately 4 km
4 km). There are two major issues concerning the application of NEXRAD data: 1) the lack of a NEXRAD geo-processing and geo-referring program and 2) bias correction of NEXRAD estimates. However, in public domain, there is no Geographic Information System (GIS) software that can use geostatistical approaches to calibrate NEXRAD data using raingauge data, and automatically process NEXRAD data for hydrologic and ecological models. In this study, we developed new GIS software for NEXRAD validation and calibration (NEXRAD-VC) using raingauge data. NEXRAD-VC can automatically read in NEXRAD data in NetCDF or XMRG format, transform projection of NEXRAD data to match with raingauge data, apply different geostatistical approaches to calibrate NEXRAD data using raingauge data, evaluate performance of different calibration methods using leaveone-out cross-validation scheme, output spatial precipitation maps in ArcGIS grid format, calculate spatial average precipitation for each spatial modeling unit used by hydrologic and ecological models. The major functions of NEXRAD-VC are illustrated in the Little River Experimental Watershed (LREW) in Georgia using daily precipitation records of fifteen raingauges and NEXRAD products of five years. The validation results show that NEXRAD has a high success rate for detecting rain and no-rain events: 82.8% and 95.6%, respectively. NEXRAD estimates have high correlation with raingauge observations (correlation coefficient of 0.91), but relatively larger relative mean absolute error value of 36%. It is also worth noting that the performance of NEXRAD increases with the decreasing of rainfall variability. Three methods (Bias Adjustment method (BA), Regressing Kriging (RK), and Simple Kriging with varying local means (SKlm)) were employed to calibrate NEXRAD using raingauge data. Overall, SKlm performed the best among these methods. Compared with NEXRAD, SKlm improved the correlation coefficient to 0.96 and the relative mean absolute error to 22.8%, respectively. SKlm also increased the success rate of detection of rain and no-rain events to 87.47% and 96.05%, respectively. Further analysis of the performance of the three calibration methods and NEXRAD for daily spatial precipitation estimation shows that no one method can consistently provide better results than the other methods for each evaluation coefficient for each day. It is suggested that multiple methods be implemented to predict spatial precipitation. The NEXRAD-VC developed in this study can serve as an effective and efficient tool to batch process large amounts of NEXRAD data for hydrologic and ecological modeling. Ó 2010 Elsevier Ltd. All rights reserved.

Keywords: Geographic Information System Geostatistics Next Generation Radar Precipitation

Software availability Software name: NEXRAD-VC Year first available: 2008 Software required: ArcGIS 9.x Programming languages: Visual Basic and ArcObject

Training workshop: relevant information is available at http://ssl. tamu.edu Availability: Contact the first author to obtain this software and user manual for free

1. Introduction * Corresponding author. Tel.: þ1 301 314 6706; fax: þ1 301 314 6719. E-mail address: [email protected] (X. Zhang).

As one important input variable for land surface hydrologic and ecological models, precipitation is characterized by high spatial and

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temporal variability. Accurate estimation of precipitation is critical for hydrologic and ecological modeling (e.g. Arnold et al., 1998; Fodor and Kovács, 2005). Traditionally, precipitation measurements are available at raingauges, which are usually too sparsely distributed to capture the spatial variability. Development and comparison of methods to estimate spatial precipitation distribution from sparse networks of stations has been a focus of research for some time (e.g. Goovaerts, 2000; Jeffrey et al., 2001; Jolly et al., 2005; Hancock and Hutchinson, 2006; Bannayan and Hoogenboom, 2008; Zhang and Srinivasan, 2008). In recent years, the National Weather Service (NWS) has installed a network of (approximately 160) WSR-88Ds (Weather Surveillance Radar-1988 Doppler) radar stations as part of a Next Generation Radar (NEXRAD) program that began implementation in 1991 (Young et al., 2000; Hardegree et al., 2008). NEXRAD data, at approximately 4
4 km2 resolution, provide nominal coverage of 96 percent of the conterminous United States (Crum et al., 1998). The ability of NEXRAD to provide spatially distributed precipitation estimates makes it one interesting source of precipitation data for hydrologists and natural resource managers. The NEXRAD rainfall products have been used for multiple purposes in hydrologic and ecological modeling (George et al., 1998; Krajewski and Smith, 2002; Zhang et al., 2004; Hardegree et al., 2008). Although ideas for the practical application of NEXRAD precipitation data in agricultural and natural resources management have been derived, their implementation has been relatively slow (Hardegree et al., 2008). There are two main issues concerning the application of NEXRAD data in hydrological and ecological modeling. The first issue is the lack of geo-processing and geo-referencing tool for the NEXRAD data (Hardegree et al., 2008). Digital, distributed NEXRAD precipitation products in binary coded format can be obtained from the NWS, but software to facilitate the storage and accessibility of radar precipitation products are still lacking (Hardegree et al., 2008). Some efforts have been exerted to develop automated approaches to facilitate the application of NEXRAD data, though. For example, Xie et al. (2005) developed a geographical information system (GIS)-based approach for the automated processing of (NEXRAD) Stage III precipitation data. Also, Hardegree et al. (2008) modified NWS source code to provide decoding and geo-referencing tools. Another central question for the application of NEXRAD precipitation data in hydrologic and ecological modeling is how good the estimates are (Krajewski and Smith, 2002). In general, a traditional raingauge is able to provide accurate measurement of precipitation because it physically measures the depth of precipitation. Several studies have been conducted to evaluate the accuracy of the NEXRAD data relative to raingauge data. For example, Young et al. (2000) evaluated NEXRAD multisensory precipitation in Oklahoma, and found the bias of the NEXRAD data to be about 20 percent. Jayakrishnan et al. (2004) compared raingauge and WSR88D Stage III precipitation data over the Texas-Gulf basin, and found large differences (about 42 percent of the raingauge measurements) between the observed and estimated data. Xie et al. (2006) evaluated NEXRAD stage III precipitation data over central New Mexico, a semiarid area, and their results indicated that NEXRAD pronouncedly overestimated or underestimated precipitation compared with raingauge observed data. Wang et al. (2008) validated NEXRAD rainfall products using raingauges at the upper Guadalupe River Basin, and found discrepancies between NEXRAD and raingauge data reaching 20 percent. The large differences between NEXRAD and raingauge data have significant implications for the use of NEXRAD data in natural system modeling. Evaluating the quality of NEXRAD rainfall products and making necessary corrections are important before their application to hydrological studies (Jayakrishnan et al., 2004). In contrast to raingauges, NEXRAD provides precipitation data with improved

spatial sampling frequencies. Several efforts have attempted to improve the accuracy of NEXRAD precipitation data using raingauge measurements (e.g. Seo et al., 1990; Seo, 1998; Steiner et al., 1999; Haberlandt, 2007; Li et al., 2008). Different methods, ranging from simple multiplicative calibration methods to complex geostatistical methods, have been applied in previous studies on improving NEXRAD products. For example, Steiner et al. (1999) applied a simple bias adjustment method to calibrate NEXRAD in Goodwin Creek, a small research watershed in northern Mississippi. Li et al. (2008) developed a linear regression based Kriging method to calibrate daily NEXRAD precipitation data using raingauge data, and applied it in Texas to estimate daily spatial precipitation in 2003. These results have shown the potential of calibrating NEXRAD data using the raingauge data to provide more accurate spatial precipitation. To the best of the authors’ knowledge, minimal research has been conducted to develop user-friendly GIS programs that can process, validate and calibrate NEXRAD data using raingauge observations with different methods. Therefore, the major objectives of this study are to develop GIS software that can automatically process NEXRAD data and to illustrate the major functions of this software for validating and calibrating NEXRAD precipitation data using raingauge records. The results of this study are expected to provide natural resource managers with a powerful tool to analyze and improve the accuracy of NEXRAD data for hydrologic and ecological modeling. The following sections of this paper are organized as follows. Section 2 introduces the NEXRAD precipitation products and the GIS-based NEXRAD processing program. Section 3 describes the study area, the methods that are used to validate and calibrate NEXRAD estimates using raingauge data, and the metrics used to evaluate the precipitation estimated using different methods. Section 4 presents and discusses the results of evaluating the accuracy of NEXRAD and comparing the performances of the different calibration methods. Finally, conclusions are provided in Section 5. 2. GIS-based NEXRAD processing program The production of NEXRAD precipitation products involves several major procedures and various “stages” of processing by the US National Weather Service (Anagnostou and Krajewski, 1998; Fulton, 1998). First, a radar system measures the reflectivity of a volume of air by scanning over a fixed polar grid with a radial resolution of 1-degree in azimuth by 1 km in range. The relationship between these reflectivities and precipitation is expressed in the so-called ZeR relationship. Often it is not possible to derive a single equation that is accurate for every storm type and storm intensity, leading to different relationships (e.g. convective ZeR relationship or Rosenfeld tropical ZeR relationship) for converting the reflectivities into rainfall rates contingent on the rainfall type. These first precipitation estimates are referred to as Stage I data. Next, Stage II data are produced through correcting Stage I data using bias adjustment. Finally, Stage III mosaics the data from multiple radar systems for the areas under the umbrella of more than one radar unit. Based on several years of operational experience with Stage II/III, much of the software was overhauled in 2000 and redeveloped into the Multisensor Precipitation Estimator (MPE) (http://www.nws.noaa.gov/oh/hrl/dmip/stageiii_info.htm). The MPE incorporates the rainfall measurements from gauges, rainfall estimates from NEXRAD and Geostationary Operational Environmental Satellites (GOES) (Wang et al., 2008). Most of the NWS’ cooperative observers’ data have been used as a quality control on the MPE NEXRAD results (http://water.weather.gov/ precip/about.php). Further information about MPE NEXRAD is provided by Seo and Breidenbach (2002). The MPE products are

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precipitation approximations over a grid of about 4
4 km2 that is usually referred to as an HRAP (Hydrologic Rainfall Analysis Project) grid (Reed and Maidment, 1999). Daily NEXRAD data from 2006 and later across the conterminous United States can be obtained in shapefile and netCDF formats from http://water. weather.gov. These daily NEXRAD data are derived from hourly NEXRAD precipitation data (in compressed binary format) provided by the River Forecast Centers (RFC) (http://water.weather. gov/precip/download.php) in the U.S. There is still a lack of userfriendly software to process and calibrate the NEXRAD data for hydrologic and ecological modeling. GIS is a powerful tool for facilitating geospatially-related research including spatial interpolation of climate data and analysis of storm kinematics (Tsanis and Gad, 2001; Zhang and Srinivasan, 2008). In this study, we developed the NEXRAD Validation and Calibration software (NEXRAD-VC) as an extension of ArcGIS 9.x to facilitate spatial precipitation estimations. The workflow chart of NEXRAD-VC is shown in Fig. 1. The major advantage of NEXRAD-VC is the provision of a user-friendly means to derive precipitation data from the original format of NEXRAD and incorporate raingauge data to improve the accuracy of the NEXRAD data. The major functions of NEXRAD-VC are described as follows: 1) Few requirements on input data preparation: Users of NEXRAD-VC only need to prepare raingauge shapefiles, precipitation records for each raingauge in text format, and hydrologic unit (e.g. subbasin) shapefiles. In addition, the users need to download NEXRAD data in NetCDF or compressed binary file format, which will be sequentially read by NEXRAD-VC and transformed into ArcGIS grid format. 2) Automatic projection transformation: NEXRAD-VC provides an automatic projection transformation function to spatially match the raingauge and hydrologic unit shapefiles with

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NEXRAD data. NEXRAD data in NetCDF and compressed binary formats are in HRAP grid coordinate system with a polar stereographic projection true at 60 N/105 W. In most cases, raingauge and hydrologic unit maps are in some projected coordinate systems. The automatic projection transformation function of NEXRAD-VC can save the users a large amount of time by transforming the NEXRAD data to the projection of the raingauge and hydrologic unit maps. 3) Validation and calibration of NEXRAD data using raingauge observations: NEXRAD-VC can identify the concurrent paired precipitation records where both raingauge observations and NEXRAD data are available. Using these pairs of records, different statistical evaluation coefficients are calculated to evaluate the accuracy of NEXRAD data and the cross-validation performance of different NEXRAD data calibration methods. 4) Multiple output files: The NEXRAD data calibrated by different methods are output in raster format, which can be easily visualized using ArcGIS or other GIS software. The spatial average precipitation is derived for each hydrologic unit and output in text format for distributed hydrologic and ecological modeling. In addition, for each raingauge, raingauge observations, NEXRAD estimates, and calibrated NEXRAD values using the specified cross-validation method, are outputs in one text file. These output files allow users to validate the accuracy of NEXRAD data and evaluate the performance of different calibration methods. Overall, NEXRAD-VC provides a user-friendly GIS tool useful for batch processing large amounts of NEXRAD data. This software is available for free and training workshop information is available from http://ssl.tamu.edu. NEXRAD-VC has been used by Sexton et al. (submitted for publication) and Srinivasan et al. (submitted for publication) for precipitation estimation in German Branch (GB)

Fig. 1. Work flowchart of GIS-based NEXRAD evaluation and calibration program.

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watershed (w50 km2), MD, and Upper Mississippi River Basin (w491,665 km2). In this study, we use accumulated daily MPE operational precipitation records obtained from the National Weather Service (NWS) South East River Forecast Center (SERFC) to illustrate the major functions of NEXRAD-VC. 3. NEXRAD data validation and calibration methods 3.1. Little River Experimental Watershed As most of the NWS’ cooperative observers have been used as a quality control on the MPE NEXRAD data (http://water.weather. gov/about.php), another set of independent raingauge observations are required to validate the performance of NEXRAD data. We selected the Little River Experimental Watershed (LREW) in Georgia (Fig. 2) as the study area to evaluate the accuracy of the NEXRAD data, and to test different methods for calibrating the NEXRAD data using raingauge observations. The LREW in southwest Georgia is the upper 334 km2 of the Little River and is the subject of long-term hydrologic and water quality research by USDA-ARS and cooperators (Sheridan, 1997). Land use within the watershed is approximately 50 percent woodland, 31 percent row crops (primarily peanuts and cotton), 10 percent pasture, and 2 percent water. The LREW is currently selected as an experimental watershed for the USDA’s Conservation Effect Assessment Project (CEAP) to evaluate the economic and environmental effect of agricultural land management practices. The development of accurate spatial precipitation is important for the accurate modeling of agricultural crops growth in this area. Precipitation occurs almost exclusively as rainfall with an annual mean at Tifton, Georgia of 1000 mm. Daily precipitation records of five years were collected from fifteen raingauges in this study area. The annual areal mean precipitation amounts are 1045.4 mm, 1132.23 mm,

1203.57 mm, 871.24 mm, and 891.92 mm for 2002, 2003, 2004, 2006, and 2007, respectively. Both a wet year (2004) and dry years (2006 and 2007) were included in the analysis. 3.2. Radar calibration techniques The simple bias adjustment (BA) method, which aims to calibrate the NEXRAD estimated mean to match the raingauge observed mean precipitation, has been widely used to calibrate NEXRAD data for distributed hydrologic modeling (e.g. Steiner et al., 1999; Zhang et al., 2004). Relatively complex geostatistical procedures have been shown as promising methods for incorporating auxiliary variables (e.g. elevation) into spatial precipitation interpolation of precipitation (Goovaerts, 2000). Li et al. (2008) exhibited the combination of a linear regression and a geostatistical procedure (Ordinary Kriging) for effective calibration of NEXRAD data. In this study, Simple Kriging with varying local means (SKlm) (Goovaerts, 2000) and Regression Kriging (RK) (Hengl et al., 2004), that have been shown as effective multivariate geostatistical techniques (Zhang and Srinivasan, 2008), were used to calibrate NEXRAD data. The basic forms of the three calibration techniques (i.e. BA, SKlm and RK) applied in this study are introduced as follows. 3.2.1. Bias adjustment method Operational radar rainfall estimates rarely match the amounts recorded by raingauges, because of spatial mismatches (approximately 4
4 km2 for NEXRAD data vs. 100 cm2 for the tipping bucket raingauge) and differences between direct and indirect measurement (NEXRAD estimates precipitation in the air, whereas raingauges observe precipitation falling on the ground). Adjusting NEXRAD results using information provided by raingauges is common in hydrologic modeling (Steiner et al., 1999). A simple bias adjustment method is to remove the average difference between the radar estimates at the raingauge locations and the corresponding raingauge rainfall amounts. That is,

Radj ¼ B$R

(1)

Pn Zðxi Þ=n B ¼ Pni¼1 i¼1 Rðx i Þ=n

(2)

where Radj is the bias adjusted NEXRAD data, R is the NEXRAD data value, B is the bias adjustment factor, Z(xi) and R(xi) are, respectively, the raingauge observed and NEXRAD estimated precipitation, respectively, at a location xi, i ¼ 1,2,.n and n is the number of data points sampled using raingauges. Steiner et al. (1999) applied this bias adjustment method in Goodwin Creek, a small research watershed in northern Mississippi, and they achieved radar rainfall estimates with root-mean-square errors (RMSE) of approximately 10 percent for storm total rainfall accumulations of 30 mm or more.

Fig. 2. The locations of raingauges, NEXRAD grids and boundary of LREW.

3.2.2. Regression Kriging Kriging is a group of advanced geostatistical techniques that provides the best linear unbiased estimate. The aim of these spatial prediction techniques is to estimate the value of a random variable (precipitation amount), Z, at one or more unsampled points from a set of sample data (Z(x1),Z(x2),.Z(xn)) at points (x1,x2,.,xn) within a spatial domain. In Kriging methods, the random variable Z is decomposed into a trend (m) and a residual (3), where Z(x) ¼ m (x) þ 3(x). The Kriging estimator is given by a linear combination of the surrounding observations (Goovaerts, 1997). The weights of the points that surround the predicted points are calculated based on the spatial dependence (i.e. semivariogram or covariance) of the random field. Previous studies (e.g. Goovaerts, 2000; Hengl et al., 2004; Haberlandt, 2007; Li et al., 2008) showed that the

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performance of Kriging methods can be improved by using external information (e.g. elevation) to estimate m(x). Regression Kriging (RK) is one of these techniques that combine the theory of generalized linear models (GLM) with Kriging (Hengl et al., 2004). In RK, the trend m(x) is commonly fitted using linear P regression analysis. The general form of m(u) is Kk¼0 bk yk ðuÞ where y1(u),y2(u),.,yK(u) are known external explanatory variables, the coefficients bk are unknown trend model coefficients to be determined, and K is the number of predictors. In this study, the trend surface is obtained by m(x) ¼ b1 þ b2R(x). Using the pairs of R(xi) and Z(xi) values at the points with both NEXRAD estimates and raingauge observations, the coefficients b1 and b2 are estimated by least square regression. The continuous gridded NEXRAD data allow a continuous trend surface m(x) be obtained. The residual 3(x) can be calculated at a series of raingauge locations (x1,x2,.,xn). The unknown residual 3(u) at the unsampled location u is a linear P combination of neighboring observed residuals ð ni¼1 lui ½3ðxi ÞÞ. Thus we can obtain continuous surfaces of both m(x) and 3(x), leading to the predicted precipitation field (Z(x)). Following Hengl et al. (2004), the optimal weights of neighboring residuals are estimated by solving a series of linear functions known as the “Ordinary Kriging system” (Goovaerts, 2000),

8 > > > < Pn l gh   mðuÞ ¼ gðh Þ ij ui Pjn¼ 1 uj > > j ¼ 1 luj ¼ 1 > :

i ¼ 1; .; n

1 X ð3ðxi Þ  3ðxi þ hÞÞ2 2NðhÞ

method to re-estimate the trend. These procedures are repeated until the estimates stabilize. The convergence of this iterative GLS process may take much time and computational resources. Practically, a single iteration can be used as a satisfactory solution (Kitanidis, 1994). In this study, three iterations were adopted to estimate the GLS residuals. 3.2.3. Simple Kriging with varying local means Goovaerts (2000) presented Simple Kriging with varying local means (SKlm) to incorporate secondary information for improving spatial prediction of precipitation. Similar to RK, SKlm also uses linear regression to estimate the varying means. That is, m (x) ¼ b1 þ b2R(x). The major differences between RK and SKlm are 1) SKlm uses Ordinary Least Squares (OLS) to estimate the varying means, and 2) SKlm uses a different set of equations to estimate the weights in equation (3). The optimal weights are obtained by solving the equation system below n X





luj C hij ¼ Cðhui Þ i ¼ 1; .; n

(7)

j¼1

where C(h) is the spatial covariance between two points separated by distance h. For more detailed information on SKlm, please refer to Goovaerts (1997).

(3) 3.3. Evaluation coefficients

where lui is the weight assigned to the residual at location xi(3(xi)), n is the number of surrounding observations, m(u) is the Lagrange parameter accounting for the constraint on the weights, hij denotes the separation distance between sampled location xi and xj. The semi-variance g(h) is computed using the equation below

gðhÞ ¼

5

3.3.1. Validating NEXRAD data using raingauge data Following previous studies (e.g. Jayakrishnan et al., 2004; Xie et al., 2006; Wang et al., 2008; Young and Brunsell, 2008), we assume the raingauge observation as the ground truth for validating NEXRAD data in this study. Several evaluation coefficients were selected to compare the raingauge and NEXRAD data.

NðhÞ

(4)

i

where h is the distance between two point locations, N(h) is the number of pairs of points separated by h, 3(xi)  3(xi þ h) is the residual difference between point xi and another point separated by distance h. In this study, one type of semivariogram model (i.e. Spherical model) was applied. Following Cressie (1985), the semivariogram model was fitted using regression with the objective to achieve minimum weighted sum of squares (WSS). A global optimization algorithm, Particle Swarm Optimization (PSO), was used to calibrate the nonlinear semivariogram models. For further information about PSO, please refer to Kennedy and Eberhart (2001). The trend model coefficients are preferably solved using the generalized least squares (GLS) estimation to account for spatial correlation of residuals (Cressie, 1993):





T 1 b b $y $yT $C 1 $z GLS ¼ y $C

(5)

where y is a matrix of predictors at all observed location with dimension of (n
K þ 1), z is the vector of observed data, and C is the n
n covariance matrix of the residuals:

Cðx1 ; x2 Þ C ¼ « Cðxn ; x1 Þ

/ 1 /

Cðx1 ; xn Þ « Cðxn ; xn Þ

(6)

where C(xi,xj) is the covariance between point pairs (xi,xj). The generalized least squares method was suggested to estimate the trend through an iterative means. The ordinary least squares estimates are obtained, and a variogram is fitted to the residuals. This variogram is then used in the generalized least squares regression

1) NEXRAD detection conditioned on gauge observations exceeding a given threshold (Young and Brunsell, 2008):

  Drain ¼ P b z  threshjz  thresh   PL b i¼1 4 z i  thresh and zi  thresh
100 ¼ PL i¼1 4ðzi  threshÞ

(8)

where Drain is the success rate that NEXRAD detects rainfall events, zi denote raingauge observed rainfall, i ¼ 1,2,.L, where L is the available number of pairs of raingauges and NEXRAD values, b zl denote the NEXRAD estimation of rainfall. 4(t) ¼ 1 if t is true, otherwise 4(t) ¼ 0. The threshold that must be exceeded is denoted by thresh. In this study, thresh was set to 0.254 mm, which is the minimum resolution of the tipping bucket raingauge in the study area. Similarly, the success rate that NEXRAD detects no-rain events is defined as

  Dnorain ¼ P b z < threshjz < thresh   PL b i¼1 4 z i < thresh and zi < thresh
100 ¼ PL i¼1 4ðzi < threshÞ

(9)

2) Pearson correlation coefficient (r) between radar and raingauge rainfall: According to Xie et al. (2006), only the pairs of concurrent non-zero rainfall values from both raingauges and NEXRAD were used for comparison. 3) Mean absolute error (MAE):

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MAE ¼

 PN  b i¼1 z i  zi N

(10)

where N is the number of the concurrent non-zero rainfall values from both raingauges and NEXRAD. 4) Relative mean absolute error (RMAE) is the ratio of MAE to the mean of raingauges observations.

MAE
100 RMAE ¼ PN i¼1 zi =N

(11)

The above four coefficients are applied to evaluate the NEXRAD data using observed raingauge data. Drain and Dno-rain are indicators of the capability of NEXRAD to successfully identify the presence and absence of rainfall events, respectively. Higher values of Drain and Dno-rain mean better performance. r measures the correlation between raingauge observations and NEXRAD estimates. Larger r means stronger correlation. MAE is used to measure how close NEXRAD estimates are to the observed values. Smaller values of MAE indicate better performance. RMAE is scaled MAE, which is used for comparison of MAE at different scales. It is worth noting the spatial mismatch between the scale of precipitation estimates by NEXRAD and raingauges. Therefore, it is important to evaluate whether the precipitation events are uniform and employ those events with uniform distribution. Wang et al. (2008) proposed to use the coefficient of variation (CV) of the 3 by 3 radar cells around a raingauge to evaluate whether one precipitation event is uniform or not. In this study, the rainfall events were classified into uniform (CV < 0.2), medially variable (0.2  CV < 0.5), and highly variable (0.5  CV). The evaluation coefficients were calculated to illustrate the performance of NEXRAD data under different rainfall variability conditions. 3.3.2. Comparing performance of different calibration methods Cross-validation is applied to compare the performance of various methods (i.e. BA, RK, and SKlm) for calibrating NEXRAD data using raingauge data. Cross-validation is a common method that has been used to evaluate the prediction performance of spatial interpolation methods (Isaaks and Srivastava, 1989). In the procedure, each of the raingauge data is temporarily removed one at a time and the remaining data is used to estimate the value of the deleted datum. For each time step, we estimate precipitation at each of the 15 raingauges using the observed precipitation of the surrounding raingauges and compare the estimates with raingauge observations. This method is the so-called leave-one-out crossvalidation, which is computationally intensive but can provide more accurate information on model evaluation than other splitsample cross-validation schemes (Kohavi, 1995; Zhang et al., 2009). In order to evaluate the overall performance of different calibration methods, the evaluation coefficients described in Section 3.3.1 were calculated. In addition to calculating the overall performance indicator, the performances of different calibration methods were compared for spatial precipitation estimation. For each day with a real mean precipitation reading larger than 0 mm, the evaluation coefficients, including r, MAE, and RMAE, were calculated using the interpolated and observed rainfall values at each raingauge.

The five years worth of daily data at 15 gauging stations resulted in 27 390 pairs of gauge-radar observations available for analysis. Of these pairs, 27 105 were used after excluding those pairs with missing values. The calculated Drain and Dno-rain were 82.8% and 95.6%, respectively. These values show that NEXRAD data perform better for detecting no-rain events than for rain events. Using all the raingauge-NEXRAD data pairs with non-zero rainfall values, three evaluation coefficients (i.e. r, MAE, and RMAE) were calculated (Table 1). NEXRAD estimates have high correlation with Raingauge observations (r ¼ 0.91), but a relatively larger RMAE value of 36%. To show the effect of rainfall variability on NEXRAD data performance, the evaluation coefficients were calculated for rain events with different spatial variability (Table 1). It is shown that NEXRAD data perform better for rainfall events with small variability. For example, r increases from 0.71 for highly variable condition to 0.94 for uniform condition, while RMAE decreases from 68.47% for highly variable condition to 26% for uniform condition. The possible reasons for the elevated performance of NEXRAD data for uniform rainfall events are: 1) one raingauge cannot represent well the mean precipitation over one NEXRAD data pixel under high rainfall variability condition; 2) measurement of small rainfall events is challenging for both raingauges and NEXRAD (http://weather.noaa. gov/radar/radinfo/radinfo.html#clear; Habib et al., 2001), which may lead to significant sampling errors for highly variable rain events whose rainfall amount is much lower than that of uniform and medially variable rain events (Table 1); 3) NEXRAD measures the atmospheric moisture above ground, while raingauge collects precipitation falling on the ground. This difference between the measurements by NEXRAD and raingauges may play an important role in comparing NEXRAD data and raingauge observations for small rate rainfall events. In reality, sampling errors of raingauge and the spatial mismatch between raingauge observations and NEXRAD data may affect the reported results. It is important to realize the limitations of using raingauge records to validate NEXRAD data. In this study, due to the difficulty of obtaining true rainfall values, raingauge observations were assumed to be the “ground truth” and used to validate and calibrate NEXRAD data. 4.2. Comparing the performance of different calibration methods 4.2.1. Overall performance comparison The BA, RK, and SKlm methods were applied to calibrate NEXRAD data using the observed raingauge data. The overall evaluation coefficients for the three methods were calculated and listed in Table 2. In the calculation of these coefficients, the same pairs of data that have been applied to validate NEXRAD data were used by replacing the NEXRAD estimates with the calibrated NEXRAD

Table 1 Validation of NEXRAD data using raingauge data for rain events with different spatial variability. Evaluation coefficient Rainfall variability

Mean rainfall (mm)

Number of pairs

r

MAE (mm)

RMAE (%)

Uniform

raingauge 14.31 NEXRAD 13.62

3395

0.94 3.72

26

4. Results and discussion

Medially variable

raingauge NEXRAD

9.47 9.31

3088

0.85 3.55

37.53

4.1. Validating NEXRAD data with raingauge data

Highly variable

raingauge NEXRAD

3.17 3.21

4273

0.71 2.17

68.47

Drain and Dno-rain were calculated using the entire test data set to assess the ability of NEXRAD to detect rain presence and absence.

All

raingauge NEXRAD

8.5 8.25

10 756

0.91 3.06

36

Please cite this article in press as: Zhang, X., Srinivasan, R., GIS-based spatial precipitation estimation using next generation radar and raingauge data, Environ. Model. Softw. (2010), doi:10.1016/j.envsoft.2010.05.012

X. Zhang, R. Srinivasan / Environmental Modelling & Software xxx (2010) 1e8

Table 4 Percentage of days that different prediction methods perform the best in terms of r and MAE, respectively.

Table 2 Evaluation coefficients of different calibration methods. Evaluation coefficients Methods Drain (%) Dno-rain (%) Drain þ Dno-rain (%) r BA RK SKlm

82.66 86.87 87.47

97.27 96.01 96.05

179.94 182.88 183.52

7

Prediction techniques

MAE (mm) RMAE (%)

0.93 2.61 0.95 2.12 0.96 1.94

30.6 25.05 22.8

values by BA, RK, and SKlm using the leave-one-out cross-validation method. After calibrating NEXRAD data using raingauge data, performance measures of r, Drain, and Dno-rain are slightly improved, with larger improvement in MAE and RMAE (Table 2). For detection capability assessment, SKlm and RK performed much better than BA for detecting rain presence, while BA slightly outperformed the other two methods for detecting no-rain events. The highest success rate for detecting both rain presence and absence (Drain þ Dno-rain) obtained by SKlm indicates its superior detection capability to the other methods. Compared with NEXRAD data, SKlm can improve success detection rate for both rain presence and non-presence, and the overall success rate (Drain þ Dno-rain) was improved from 178.4% to 183.52% by SKlm. In terms of the other three evaluation coefficients (i.e. r, MAE and RMAE), SKlm obtained the largest correlation coefficient and smallest MAE and RMAE values among the three calibration methods. In comparison to NEXRAD data, SKlm improved the correlation coefficient from 0.91 to 0.96, and decreased the RMAE from 36% to 22.8%. The overall assessment results show that SKlm performed the best for calibrating NEXRAD data using raingauge data in this study area. 4.2.2. Performance comparison for daily spatial precipitation prediction Spatial rainfall maps are critical inputs into distributed hydrologic and ecological models. The capability of different calibration methods for spatial precipitation prediction was evaluated using 693 days of raingauge and NEXRAD areal mean rainfall values larger than 0, because r is not meaningful for zero areal mean rainfall. For each day, three evaluation coefficients (i.e. r, MAE, and RMAE) were calculated. Table 3 lists the mean values of the evaluation coefficients for different calibration techniques. In comparison to NEXRAD data, all three calibration techniques substantially reduced the MAE and RMAE values. It is worth noting that the correlation coefficient obtained by BA and RK is less than or equal to that of NEXRAD data, respectively, while SKlm obtained much larger r value than NEXRAD data. On average, SKlm outperforms the other two methods for calibrating NEXRAD data using raingauge observations. Further analysis shows that no one method can consistently outperform the others in terms of all evaluation coefficients and for all days. Table 4 lists the percentage of number of days that different methods performed the best for r and MAE, respectively. Although SKlm can provide better results on most of the days, it is still worth noting that the NEXRAD data, BA, and RK collectively can outperform or perform equally to SKlm on 430 and 288 days in terms of r and MAE, respectively. Implementing multiple methods to estimate spatial precipitation maps is a practical way to provide more accurate spatial precipitation map.

Evaluation coefficients

NEXRAD %

BA %

RK %

SKlm %

r

43.00 15.87

3.17 8.08

13.71 17.60

45.17 62.91

MAE

5. Conclusions In public domain, there is no Geographic Information System (GIS) software available to calibrate NEXRAD data with raingauge data using geostatistical approaches, and automatically process NEXRAD data for hydrologic and ecological models. The NEXRADVC developed in this study can automatically read in NEXRAD data in NetCDF or XMRG format, transform projection of NEXRAD data to match with raingauge data, apply different geostatistical approaches to calibrate NEXRAD data using raingauge data, evaluate performance of different calibration methods using leaveone-out cross-validation scheme, output spatial precipitation maps in ArcGIS grid format, calculate spatial average precipitation for each spatial modeling unit used by hydrologic and ecological models. The NEXRAD-VC was applied to validate NEXRAD data using five years observed precipitation data from fifteen raingauges in the LREW. The results show that NEXRAD data has high success rate of detecting rain and no-rain events with Drain and Dno-rain of 82.8% and 95.6%, respectively. NEXRAD estimates have high correlation with Raingauge observations (r ¼ 0.91), but relatively larger RMAE value of 36%. The performance of NEXRAD data increases with the decreasing of rainfall variability. In comparison to medially variable and highly variable rainfall events, uniform rainfall events have much lower RMAE and higher correlation coefficients. Three methods that use both raingauge and NEXRAD data for precipitation estimation were compared in the study area. Comparison of overall performance of the three calibration techniques indicates that SKlm performs better than the other two methods (i.e. BA and RK). In comparison to NEXRAD data, SKlm improved the success rate of detecting rain presence and absence from 178.43% to 183.52% and reduced MAE from 3.06 mm to 1.94 mm. Further analysis used 693 days with areal mean precipitation larger than 0 to evaluate the three calibration techniques for spatial rainfall estimation. On average, SKlm performed the best, but it is worth noting that no one method can perform better than the other methods in terms of all evaluation coefficients and for all days. SKlm outperformed the NEXRAD data, BA, and RK for 45.17% and 62.91% of the 693 days in terms of r and MAE, respectively. For practical estimation of precipitation distribution, it is suggested to implement multiple methods to predict spatial precipitation. The NEXRAD-VC developed in this study can serve as an effective and efficient tool to validate and calibrate large amount of NEXRAD data using raingauge data, and provide spatial precipitation for hydrologic and ecological models.

Table 3 Mean evaluation coefficients of different methods for the 693 days.

Acknowledgements

Methods Evaluation coefficients

NEXRAD

BA

RK

SKlm

r

0.6 2.67 122

0.51 2.22 76.2

0.6 1.79 56.3

0.66 1.66 52.1

MAE (mm) RMAE (%)

The authors thank the editor and four anonymous reviewers for their precious suggestions on revising this paper, which greatly improved the quality of this manuscript. The authors also would like to thank the USGS and Texas Water Resources Institute for

Please cite this article in press as: Zhang, X., Srinivasan, R., GIS-based spatial precipitation estimation using next generation radar and raingauge data, Environ. Model. Softw. (2010), doi:10.1016/j.envsoft.2010.05.012

8

X. Zhang, R. Srinivasan / Environmental Modelling & Software xxx (2010) 1e8

providing partial funding for this research under Agreement No. 503181. The first author (Xuesong Zhang) is also supported by the US DOE Great Lakes Bioenergy Research Center (DOE BER Office of Science DE-FC02-07ER64494). In addition, the authors acknowledge Dr. Michael Van Liew at Montana Department of Environmental Quality and Dr. David Bosch at Southeast Watershed Research Laboratory, Agricultural Research Service, USDA, for providing part of the data used in this study. Dr. Dong-Jun Seo at National Weather Service provided valuable information on MPE NEXRAD. Drs. Judi Bradberry, David Kitzmiller, James Paul, and Ron Jones at National Weather Service provided the MPE NEXRAD data used in this study and valuable discussion on the quality control and availability of NEXRAD. We thank David Manowitz at Joint Global Change Research Institute, Pacific Northwest National Laboratory for correcting grammar of this manuscript.

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Please cite this article in press as: Zhang, X., Srinivasan, R., GIS-based spatial precipitation estimation using next generation radar and raingauge data, Environ. Model. Softw. (2010), doi:10.1016/j.envsoft.2010.05.012