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Quantitative Comparison of the Spatial Distribution of Radar and Gauge Rainfall Data SEONG-SIM YOON Sejong University, Seoul, South Korea
ANH TRAN PHUONG University Catholique de Louvain, Louvain-la-Neuve, Belgium
DEG-HYO BAE Sejong University, Seoul, South Korea (Manuscript received 8 June 2011, in final form 10 March 2012) ABSTRACT The common statement that a rain gauge network usually provides better observation at specific points while weather radar provides more accurate observation of the spatial distribution of rain field over a large area has never been subjected to quantitative evaluation. The aim of this paper is to evaluate the statement by using some statistical criteria. The Monte Carlo simulation experiment, inverse distance weighting (IDW) interpolation method, and cross-validation technique are used to investigate the relation between the accuracy of the interpolated rainfall and the rain gauge density. The radar reflectivity–rainfall intensity (Z–R) relationship is constructed by the least squares fitting method from observation data of radar and rain gauges. The variation in this relationship and the accuracy of the radar rainfall with rain gauge density are evaluated by using the Monte Carlo simulation experiment. Three storm events are selected as the case studies. The obtained results show that the accuracy of interpolated and radar rainfall increases nonlinearly with increasing gauge density. The higher correlation coefficient (g) value of radar-rainfall estimation, compared to gauge interpolation, especially in the convective storm, proves that radar observation provides a more accurate spatial structure of the rain field than gauge observation does.
1. Introduction In hydrometeorological applications, more detailed spatial and temporal rainfall data are increasingly required for simulation of the variation of storm structure in both time and space. Traditionally, rainfall is collected by point observations from the rain gauge network. However, because of the nature of the spatial variation of rainfall, it is impossible to investigate the rainfall field by only using the measurement data from individual point observations, especially in convective storms. The situation becomes more serious in a region with complex topography where gauge installation is sometimes not
Corresponding author address: Deg-Hyo Bae, Department of Civil and Environmental Engineering, Sejong University, 98 Kunja-Dong, Kwangjin-Gu, Seoul 143-747, South Korea. E-mail:
[email protected] DOI: 10.1175/JHM-D-11-066.1 Ó 2012 American Meteorological Society
practical and the spatial structure of rainfall is strongly affected by local factors. In addition, in order to simulate the variation of a storm with time, rainfall data must be collected quickly with high temporal resolution. It is difficult to meet this requirement with gauge measurement, except for several types of automatic observation. Consequently, extreme values can sometimes be ignored by gauge observations. Radar, with its ability to observe a large area with high temporal and spatial resolutions, has a long-recognized potential for use as an alternative choice (Calheiros and Zawadzki 1987; Sun et al. 2000; Germann et al. 2006). However, the use of radar-measured rainfall in practice is accompanied by concerns about its accuracy. Because weather radar does not observe the rainfall directly, various uncontrolled errors associated with the radar measurement and the radar–rainfall conversion remain (Wilson and Brandes 1979; Zawadzki 1984; Joss and
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Waldvogel 1990; Fabry et al. 1994; Anagnostou et al. 1998; Chumchean et al. 2003; Rico-Ramirez et al. 2007; Mandapaka et al. 2009). These errors can be classified into mean-field systematic errors [radar system calibration, bright band, and variability of radar reflectivity– rainfall intensity (Z–R) relationship in both time and space], range-dependent systematic errors (vertical reflectivity profile, attenuation, partial beam filling, and time discretization effect), and random errors (subgrid variability of rainfall, vertical variability of reflectivity, radar hardware system noise, anomalous propagation echoes, ground clutter, and other nonmeteorological targets). Gauge measurement also induces errors arising from malfunctions of the tipping-bucket rain gauges, measuring condition errors (wind, wetting, evaporation, and splashing), human interference (Steiner et al. 1999; Habib et al. 1999; Tokay et al. 2003), and errors in gauge sampling (representativeness of the rain gauge, sampling time of the gauge, and frequency of precipitation (Zawadzki 1973; Wilson and Brandes 1979; Kitchen and Blackall 1992; Anagnostou et al. 1998; Habib et al. 2001; Villarini et al. 2008). In brief, both weather radar and rain gauges have their own advantages and disadvantages. Rain gauge observation provides better quality of rainfall at specific locations, while radar observation provides more accurate spatial structure and temporal evolution of rain field over a large area (Zawadzki 1975; Sinclair and Pegram 2004; Goudenhoofdt and Delobble 2008; Villarini et al. 2008). However, the existing literature contains little to guide us in determining when/where gauge or radar observations are superior. Therefore, the aims of this study are to suggest a method to verify this statement by quantitatively comparing the spatial distribution of radar rainfall with the rainfall interpolated from gauge observations with respect to different rain gauge networks and to provide the test results in the southwestern region of the Korean Peninsula. The paper is organized as follows. Section 2 presents the methodology. Study area and data availability are discussed in section 3. The application results and analysis are devoted in this section. Conclusions are presented in section 4.
2. Methodology Figure 1 shows the three-block procedure used to obtain the study objectives. The interpolation block, which is shown in the upper-left panel, applies the Monte Carlo simulation experiment, spatial interpolation technique, and cross validation to investigate the variation of the accuracy of rainfall interpolated from gauge measurement. The radar block in the upper-right panel is used to estimate
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FIG. 1. Flowchart for comparing the spatial distribution of radar and gauge data.
rainfall from radar data based on the Z–R relationship constructed by the least squares fitting method. The relationship between the number of rain gauges per unit area (km2) and the accuracy of the Z–R equations and radar rainfall is also accounted for by using the Monte Carlo experiment simulation. The evaluation block in the lower panel is used to compare the observed rainfall with the rainfall obtained by gauge interpolation and radar estimation according to the criteria of root-mean-square error (RMSE) and correlation coefficient (g). The methodology of these three blocks is described in detail below.
a. Interpolation block This block uses the interpolation technique, Monte Carlo experiment simulation, and cross validation. To estimate rainfall from the surrounding rain gauges, the interpolation technique is used. Several methods have been proposed: Thiessen polygon (Thiessen 1911), inverse distance weighting (IDW), isohyetal method (McCuen 2004), and geostatistics (Royle et al. 1981; Goovaerts 2000). It is a difficult task to select a suitable method for the interpolation because there is not an optimal
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method for all cases. Because of its clear foundation, accuracy, popularity, and convenience, the IDW method was selected as an interpolation technique for this study. IDW is constructed based on the assumption that the weighting factor of a neighboring rain gauge is inversely proportional to the distance from that gauge to the interpolated location, as shown in the formula below:
Wjik 5
1 dajik m
1 å da i51 jik
,
(1)
where Wjik is the weighting factor of the ith gauge in the jth rain gauge network configuration to interpolate rainfall for the kth location, djik is the distance from the ith gauge to the kth interpolated location, m is the number of gauges participating in the interpolation (rain gauge network size), and a is the order of the distance which can be estimated by the optimization technique (Sinclair and Pegram 2004; Chang et al. 2006). For simplicity, the most commonly used value of this parameter is applied in the study: a 5 2 (Jayawardene et al. 2005; Lloyd 2005). Based on the estimated weighting factors, rainfall at the interpolated locations can be computed as
interpolation–training set with a sample size of m and the remainder gauges are defined as the validation set with a sample size of N 2 m. 3) Estimate the rainfall Rmjk(t) at the kth gauge in the validation set by interpolating the measured rainfalls of the gauges in the interpolation set. 4) Evaluate the accuracy of the estimated rainfall of the gauges in the validation set corresponding to the number of rain gauge network m and the jth configuration by criteria RMSEgmj and ggmj . 5) Repeat steps 2–4 to determine the interpolated rainfall for different network configurations. The procedure stops and moves to the next rain gauge network size after 200 iterations.
b. Radar block This block is used to estimate the radar-driven rainfall at the rain gauge locations from radar reflectivity data. To do this, calculations are divided into two main stages: develop the Z–R relationship and convert radar reflectivity to rainfall intensity from the established relationship. A key study in radar-rainfall estimation is to identify the relationship between radar reflectivity Z and rainfall intensity R (Morin et al. 2003). Previous studies have indicated that, on average, Z and R can be related by a power law: Z 5aRb ,
(3)
m
Rmjk (t)5 å Wjik Omji (t) ,
(2)
i51
where Rmjk (t) is the interpolated rainfall corresponding with m rain gauges, the jth rain gauge configuration, at the kth location, time t; and Omji(t) is the observed rainfall at the ith gauge, time t in the jth rain gauge network configuration with m rain gauges. The cross validation technique and Monte Carlo simulation experiment are adopted to evaluate the accuracy of the interpolated rainfall with respect to different rain gauge densities. Several types of cross validation have been mentioned in the literature: repeated random subsampling validation, k-fold, and leave-one-out cross validation (Kohavi 1995). In this study, repeated random subsampling validation is used because of its suitability for our purpose. In this method, the dataset is randomly divided into interpolation–training and validation subsets. And then, the model is fitted to the interpolation set and its accuracy is assessed by using the validation set. As shown in Fig. 1, the detailed method applied to our problem is as follows: 1) Specify the size of the rain gauge network m from the total number of rain gauges N in the radar domain. 2) Corresponding to a given network size, the jth network configuration is randomly selected from all of the rain gauges in the radar domain. The set of rain gauges belonging to this configuration is defined as the
in which the empirical parameters a and b must be determined in order to estimate rainfall intensity from radar reflectivity. Typically, the former parameter ranges from a few tens to several hundreds and the latter from 1 to 3 (Battan 1973; Smith and Krajewski 1993). There have been many studies to estimate these two parameters. They can be generally classified into two main approaches to determine the a and b multipliers: drop size distribution and optimization (Krajewski and Smith 2002). In this study, we use the second approach by applying the least squares fitting method to establish the Z–R relationship from the pairs of observed radar reflectivity and rainfall intensity. It is noted that several authors use a given Z–R relationships (e.g., Marshall–Palmer) to interpret the rainfall from radar data and then optimize only the ‘‘a’’ multiplier by estimating a gauge–radar bias. In addition, the Monte Carlo simulation experiment is used to account for the impact of the number of rain gauges on the Z–R relationship. For a given number of rain gauges, different random configurations in the radar domain are selected. Corresponding with each configuration, pairs of the parameters amj and bmj of the linear relationship between dBZ and log(R) are defined as
amj 510
(1/10m)
m
m
i51
i51
å dBZi210b å log(Ri )
and
(4)
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bmj 5
1 10
m
m
c. Evaluation block
m å log(Ri )dBZi 2 å log(Ri ) å dBZi i51
i51
i51
.
2 m å [log(Ri )]2 2 å log(Ri ) m
i51
m
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(5)
i51
Once amj and bmj have been calculated, the radarrainfall intensities at the grid cells and, therefore, at all rain gauge locations for various numbers of rain gauges and configurations can be computed by using relationship (3). The training dataset for computing Z–R relationship is not used for the validation subset.
This block is used to compare the difference between the interpolated and radar-derived rainfall and the observed rainfall and quantitatively analyze the obtained results. The radar and interpolated rainfall are evaluated at the different rain gauge network sizes. The two criteria used to evaluate the accuracy—RMSE and g—are defined as 1 g RMSEmj 5 T
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 N2m å N 2m å [Rmjk (t)2Omjk (t)]2 t51 k51 T
and
(6)
N2m
g
gmj 5
1 T
å [Rmjk (t) 2 Rmj (t)][Omjk (t) 2 Omj (t)] k51 s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , å T
t51
N2m
å
k51
[Rmjk (t) 2 Rmj (t)]2
where RMSEgmj and ggmj are the RMSE and the g of the interpolated rainfall corresponding to rain gauge density of m and the jth configuration, respectively. The quantities Rmjk(t) and Omjk(t) are the interpolated and observed rainfalls, respectively, corresponding to the m rain gauges and the jth rain gauge configuration, at the kth location, time t. The terms Rmj (t) and Omj (t) are the spatial mean values of the interpolated and observed rainfalls at time t, respectively, corresponding to the number of rain gauges m and the jth configuration. The T is the length of the time series, N is the total number of rain gauges in the radar domain, and N 2 m is the size of the validation set. The average values of statistics RMSEgm and ggm for each rain gauge network density m are then determined by averaging over the sample of 200 sets of configurations through the total number of time series. The statistics RMSErm and g rm for radar estimation are computed in the same way, on which the size of the validation set N 2 m is applied in Eqs. (6) and (7). The above procedure is repeated for different numbers of rain gauges. For each rain gauge density, the accuracy of rainfall estimated from radar and gauge measurement is compared.
3. Data availability and study results a. Study area and data availability 1) STUDY AREA The volume data from Jindo station—an S-band radar, located at 34.478N and 126.32 8E and an altitude of
N2m
å
k51
(7)
[Omjk (t) 2 Omj (t)]2
499 m in the southwestern end of the Korean Peninsula (Fig. 2)—are used for this study. A complete volume is composed of nine plan position indicators (PPI) ranging from 0.18758 to 118. Each PPI, in turn, is composed of 360 bins corresponding with 360 azimuths from 0.58 to 359. 58. The radar data of a complete volume are provided every 10 min. The 3-dB radar beamwidth with 1-km bin length is 18 and the affected radar range is approximately 240 km. However, according to the recent study (Bae et al. 2009), the quality of radar data is relatively high in the range of 120 km. The quality degrades considerably and is not adequately good for radar-rainfall estimation beyond this range. Consequently, only the area within 120 km from the radar site is studied.
2) DATA AVAILABILITY The volume data of radar reflectivity are extracted to obtain the constant altitude PPI (CAPPI) data at the altitude of 1.5 km by using a bilinear interpolation program based on the algorithm suggested by Mohr and Vaughan (1979). The volume data, which are 1 km 3 18 in spherical coordinates, are transformed to the Cartesian coordinates. The spatial and temporal resolutions of the extracted CAPPI data are 1 3 1 km2 and 10 min, respectively. The rainfall data are collected every minute from 81 automatic gauges in the study area. As shown in Fig. 2, the gauges are not uniformly distributed in the study area, but this situation is general in a peninsular and island country such as Korea. The collected rain gauge data are converted to rainfall intensity data with a temporal resolution of 10 min. The automatic rain gauges have a threshold
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FIG. 2. The Jindo radar station, rain gauges, and range rings at 60, 120, 180, and 240 km from the radar.
sensitivity of 0.5 mm of rainfall depth before the rainfall can be measured. Therefore, the minimum value of rainfall data collected is 0.5 mm. Because the study develops the Z–R relationship from the measurement of radar and rain gauges, the rain gauges located in the regions with no or small rainfalls are not used in this study. To compare the quality of radar and rain gauge networks with different rain types, especially their ability in reflecting the spatial structure of rain fields, this study selected three storm events for analysis: a convective rain type that occurred on 9–10 July 2003 (first event), a stratiform type on 3–4 July 2004 (second event), and a jangma front type on 15–16 July 2009 (third event). The jangma front in Korea represents the East Asian monsoon. It is driven by temperature differences between the Asian continent and the Pacific Ocean. This leads to a reliable precipitation spike in July and August in Korea. The characteristics and overviews of these three storms are presented in Table 1 and Fig. 3. Although the maximum (129 mm h21) and mean areal rainfall intensity (1.2 mm h21) of the first event are less than those of the second (141 and 1.76 mm h21, respectively) and the third (207 and 2.73 mm h21, respectively), its coefficient of variation (Cv; 4.42) is greater than that of the second (3.52) and the third (1.57),
No.
Event
1 2 3
9–10 Jul 2003 3–4 Jul 2004 15–16 Jul 2009
Mean Coefficient Minimum Maximum (mm h21) of variation (mm h21) (mm h21) 1.20 1.76 2.73
4.42 3.52 1.57
0 0 0
129 141 207
indicating that the dispersion level of the first event is higher than that of the second and the third, despite the heavier rainfall of the second and third events. Figure 3 represents the accumulated rainfalls calculated from radar observation during the storm event. As expected, the spatial distribution of rainfall from the first event is concentrated at certain locations, while those from the second and the third events are covered to all domains. To avoid bad effects on the interpolation results, we calculated the pairwise correlation coefficients of rainfall intensities of the gauges in the study area. Figure 4 shows a box–whisker plot that depicts these coefficients in relation to the distance between gauges. The correlation coefficient (g) of the rain gauges is reduced nonlinearly with increasing distance between them. Moreover, at short distances, the correlation varies over a large range from just under 0.0 to 0.9, while at far distances, it exhibits a narrow range around the value of 0. It is noted that the mean values of correlation coefficient within 10-km distance range from 0.87 to 0.48 in this study, while those from Gambremichael and Krajewski (2004) vary from 0.95 to 0.20. Compared to the second and third events, g between the rain gauges of the first event seems to be reduced more rapidly, suggesting that the spatial distribution of the second and third events are more uniform than that of the first (refer to Fig. 3). The gauges with a negative correlation on other gauges are not used in this computation. Figure 5 shows the relationships of the agreement between the gauge rainfall intensity and the radar reflectivity with the radar range and 81 rain gauges for the three events. The quality of the radar-rainfall estimation is evaluated by the conditional probability of radarrainfall detection (CPRD) which is determined as the probability that the radar pixels where the gauge is located report rainfall greater than the zero threshold in the condition that the gauge reports measurable rainfall: CPRDi 5
H[Ri (t).0,Gi (t).0] 3100, M[Ri (t)50,Gi (t).0]1H[Ri (t).0,Gi (t).0] (8)
where CPRDi is the CPRD at the ith gauge; Ri(t) and Gi(t) are the radar and observed rainfalls, respectively, at time t and the ith gauge; H[Ri (t) . 0, Gi (t) . 0] is the
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FIG. 3. The accumulated radar-rainfall field for the selected event periods: (a) 9–10 Jul 2003, (b) 3–4 Jul 2004, and (c) 15–16 Jul 2009.
number of values at which both the radar and gauge measurements report rainfall; and M[Ri (t) 5 0, Gi (t) . 0] is the number of values at which radar measurement reports nonrainfall, while gauge measurement reports rainfall. For the consideration of threshold sensitivity of 0.5 mm of rainfall depth, the dBZ less than 2.2 based on the Marshall–Palmer equation is considered as zero
rainfall. On the other hand, the quantity of the radarrainfall estimation is evaluated by correlation coefficient (g) between gauge rainfall intensity and the radar reflectivity (Anagnostou et al. 1998). As can be seen from the figures, most of the CPRD values range from around 50% to approximately 100%, while the g values mainly fluctuate within the range from
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FIG. 4. The correlation of gauge rainfall intensities as a function of the distance between them. (a) Event 9–10 Jul 2003, (b) Event 3–4 Jul 2004, and (c) Event 15–16 Jul 2009.
about 0.3 to 0.9 for the different rain gauges. Therefore, in a subjective decision for this study, the gauges causing a CPRD value lower than or equal to 50% and g lower than or equal to 0.3 are not considered. After all of the above exceptions are excluded, only 52 of the 81 rain gauges within 120 km from the Jindo radar station are used to compare the accuracy of radar and rain gauge measurements for the selected storm events.
b. Study result and analysis To evaluate the accuracy of the radar and rain gauge observations with the density and configuration of rain gauges, for a given number of rain gauges, the number of iterations performed to select the configurations must be set. In this study, the obtained results for both types of measurement are almost invariant after 200
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FIG. 5. (a),(c),(e) Conditional probability of radar-rainfall detection (CPRD) and (b),(d),(f) correlation coefficient (g) values of three rainfall events for all gauge locations in the study area: (a),(b) 9–10 Jul 2003, (c),(d) 3–4 Jul 2004, and (e),(f) 15–16 Jul 2009. The horizontal axis represents the distance from radar to rain gauge.
iterations. Therefore, the number of iterations is set at 200. For radar estimation, the Z–R relationships are constructed by the least squares fitting method based on the pairs of radar reflectivity and gauge rainfall intensity with a time interval of 10 min. Figures 6 and 7 show the change of parameters a and b of the Z–R relationship according to rain gauge density for the three events. For the first event, a varies within the range from 192 to 137 and b from 1.41 to 1.33. For the second and third events, a varies within the range from 141 to 110 and from 103 to 80 and b from 1.20 to 1.18 and from 1.13 to 1.08, respectively. As we expected, the variation of the parameters is much higher at the sparse rain gauge networks than at the dense networks. The rate of variation decreases
nonlinearly with increasing rain gauge density. When the full network is taken into account, there is no variation in the Z–R relationship. Comparing the three events, the variation of the parameters is greater in the first event than in the second and third events, because the former is a convective rain type and the latter a stratiform and a jangma type, respectively. Based on the developed relationships, the radar-derived rainfall intensities at the different rain gauge locations are estimated and compared to the observation data. The accuracy is evaluated by the RMSE and g indicators. Figures 8 and 9 show these values at different temporal resolutions (10, 30, and 60 min). Based on the increase of g and the decrease of RMSE with decreasing temporal resolution from 10 to 60 min, we can conclude that the accuracy of the rainfall
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FIG. 6. Variation of parameter a of the Z–R relationship, which is estimated by least squares fitting method, as a function of rain gauge density for three rainfall events: (a) 9–10 Jul 2003, (b) 3–4 Jul 2004, and (c) 15–16 Jul 2009.
estimated by radar and gauge observations is considerably improved with decreasing temporal resolution. It might be explained by the reduction of the random errors as accumulation time increases. Tables 2 and 3 provide the
values of mean and standard deviation according to temporal resolution and rain gauge density for the selected three events. They suggest the spread in the g and RMSE of the 200 replications. The significance of the
FIG. 7. As in Fig. 6, but for parameter b.
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FIG. 8. Comparison of the g values of the radar and gauge interpolation rainfall with different rain gauge densities and temporal resolutions of (a) 10, (b) 30, and (c) 60 min for three rainfall events (left to right) 9–10 Jul 2003, 3–4 Jul 2004, and 15–16 Jul 2009.
difference between radar and gauge interpolation can be accessed from the statistics. Figure 8 shows the g between radar and interpolation rainfall data and the observation data at different time intervals. The g values of the first, second, and third events are presented in the left, middle, and right panels, respectively. The figure shows that although the g between the radar and interpolation rainfall and the observed rainfall increase with increasing rain gauge density, the correlation between the radar rainfall and the observed rainfall is higher than that of the interpolation. This proves that, in terms of the spatial structure of rainfalls, radar estimation presents better results than gauge interpolation regardless of participating rain
gauge densities. Comparing the g among the events (first event: a convective rain type, second event: a stratiform rain type, and third event: jangma front), the g of the radar estimation shows little difference among three events, whereas that of the interpolation is noticeable. This implies that radar observation can describe well the spatial coverage of the selected storms. It also can be seen that gauge interpolation does not describe well the spatial variation of the rain structure of a convective storm. The superiority of the spatial representativeness of radar rainfall appears more clearly for the convective storm when compared with that of gauge interpolation. The correlation between the interpolated and observed rainfall improves considerably with increasing
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FIG. 9. As in Fig. 9, but for RMSE values.
rain gauge density at numbers less than about 18 (39.8 3 1025 km22) for the first event, 12 (26.5 3 1025 km22) for the second event, and 15 (33.2 3 1025 km22) for the third event. Further increases in the rain gauge densities beyond these numbers do not induce significant improvement in the correlation. For the radar data of the selected events, g does not increase rapidly with increasing rain gauge density, especially for more than four rain gauges with a density of 8.8 3 1025 km22. In brief, gauge interpolation is more sensitive to the variation of the number of rain gauges than radar estimation. Figure 9 shows the RMSE values computed from radar and rain gauge data. The mean-field bias in the radar estimates is also calculated because the RMSE depends on both the spatial distribution of the rain field and
a mean-field bias. The values of mean-field bias for the three events are 1.23, 1.36, and 1.65, respectively. Overall, the difference in RMSE between radar and rain gauge observation is not great. For the first event, because of the fact that radar can better represent the spatial distribution of the convective storm, its RMSE of radar estimation seems to be less than that of gauge interpolation. The difference between the RMSE values of the two measuring devices increases with increasing time interval. On the contrary, on account of the fact that the second event is a stratiform rain type, the RMSE of radar estimation in the second event is likely to be greater than that of gauge interpolation. The trend of the RMSE for the third event is similar to that for the second event. The RMSE values of radar estimation are
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TABLE 2. Mean and standard deviation (SD) of g values obtained from 200 replications according to temporal resolution and rain gauge density. Event 1 is 9–10 Jul 2003, 2 is 3–4 Jul 2004, and 3 is 15–16 Jul 2009. 10-min temporal resolution Event–gauge density
Gauge
Radar
30-min temporal resolution Gauge
Radar
60-min temporal resolution Gauge
Radar
Event
Gauge density
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Event 1
2 9 15 22 29 35 42 49 55 62 69 75 82 88 95 102 108 2 9 15 22 29 35 42 49 55 62 69 75 82 88 95 102 108 2 9 15 22 29 35 42 49 55 62 69 75 82 88 95 102 108
0.204 0.336 0.369 0.391 0.407 0.413 0.418 0.424 0.424 0.429 0.435 0.429 0.435 0.435 0.440 0.440 0.440 0.396 0.479 0.517 0.539 0.545 0.556 0.567 0.567 0.567 0.567 0.572 0.572 0.572 0.578 0.578 0.578 0.578 0.420 0.520 0.560 0.580 0.590 0.600 0.600 0.610 0.610 0.610 0.620 0.620 0.620 0.620 0.620 0.620 0.620
0.164 0.197 0.208 0.213 0.215 0.218 0.220 0.221 0.223 0.224 0.225 0.226 0.227 0.229 0.230 0.231 0.232 0.135 0.132 0.140 0.143 0.146 0.149 0.151 0.153 0.155 0.156 0.156 0.157 0.158 0.159 0.160 0.160 0.161 0.190 0.170 0.164 0.158 0.157 0.156 0.154 0.154 0.153 0.153 0.153 0.153 0.153 0.153 0.153 0.153 0.153
0.506 0.534 0.534 0.539 0.539 0.539 0.545 0.539 0.539 0.539 0.545 0.545 0.539 0.545 0.545 0.545 0.550 0.578 0.600 0.600 0.600 0.600 0.594 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.600 0.594 0.595 0.631 0.636 0.641 0.644 0.647 0.650 0.651 0.653 0.655 0.655 0.655 0.655 0.655 0.655 0.655 0.655
0.254 0.314 0.301 0.293 0.284 0.285 0.286 0.282 0.284 0.281 0.282 0.287 0.281 0.287 0.285 0.286 0.290 0.171 0.163 0.161 0.157 0.160 0.157 0.158 0.160 0.163 0.163 0.162 0.163 0.164 0.164 0.164 0.165 0.164 0.212 0.209 0.188 0.177 0.173 0.170 0.169 0.166 0.166 0.166 0.164 0.163 0.163 0.163 0.163 0.164 0.164
0.473 0.591 0.624 0.640 0.656 0.656 0.667 0.667 0.672 0.672 0.672 0.678 0.678 0.678 0.683 0.683 0.683 0.478 0.591 0.624 0.640 0.656 0.656 0.661 0.667 0.672 0.672 0.672 0.678 0.678 0.678 0.683 0.683 0.683 0.480 0.570 0.620 0.650 0.660 0.670 0.680 0.680 0.690 0.690 0.690 0.700 0.700 0.700 0.700 0.700 0.700
0.194 0.233 0.239 0.244 0.243 0.244 0.244 0.243 0.244 0.244 0.244 0.245 0.246 0.247 0.247 0.248 0.249 0.144 0.140 0.142 0.145 0.149 0.150 0.152 0.155 0.155 0.156 0.157 0.158 0.159 0.159 0.159 0.160 0.160 0.210 0.182 0.171 0.167 0.166 0.164 0.164 0.162 0.162 0.162 0.161 0.161 0.161 0.161 0.160 0.160 0.161
0.726 0.753 0.753 0.753 0.753 0.758 0.753 0.753 0.753 0.753 0.758 0.753 0.753 0.753 0.753 0.753 0.753 0.733 0.761 0.761 0.761 0.761 0.760 0.761 0.755 0.761 0.761 0.760 0.761 0.761 0.761 0.761 0.761 0.761 0.710 0.732 0.756 0.764 0.769 0.776 0.784 0.789 0.792 0.793 0.793 0.793 0.793 0.793 0.793 0.793 0.793
0.144 0.140 0.142 0.145 0.149 0.150 0.152 0.155 0.155 0.156 0.157 0.158 0.159 0.159 0.159 0.160 0.160 0.144 0.140 0.142 0.145 0.149 0.150 0.152 0.155 0.155 0.156 0.157 0.158 0.159 0.159 0.159 0.160 0.160 0.144 0.140 0.142 0.145 0.149 0.150 0.152 0.155 0.155 0.156 0.157 0.158 0.159 0.159 0.159 0.160 0.160
0.305 0.487 0.551 0.578 0.594 0.605 0.615 0.621 0.621 0.621 0.626 0.626 0.626 0.631 0.631 0.631 0.631 0.532 0.661 0.688 0.704 0.721 0.726 0.731 0.737 0.731 0.737 0.742 0.748 0.748 0.748 0.748 0.747 0.748 0.510 0.620 0.670 0.700 0.710 0.720 0.730 0.730 0.740 0.740 0.750 0.750 0.750 0.750 0.750 0.760 0.760
0.235 0.258 0.261 0.261 0.261 0.260 0.259 0.259 0.258 0.259 0.259 0.259 0.260 0.260 0.260 0.261 0.260 0.153 0.139 0.138 0.139 0.141 0.142 0.145 0.146 0.148 0.149 0.150 0.150 0.151 0.151 0.152 0.152 0.152 0.221 0.193 0.179 0.172 0.171 0.168 0.166 0.165 0.164 0.164 0.162 0.162 0.161 0.161 0.160 0.160 0.160
0.712 0.760 0.771 0.771 0.765 0.771 0.771 0.771 0.771 0.771 0.771 0.771 0.771 0.771 0.771 0.771 0.771 0.799 0.826 0.826 0.826 0.826 0.826 0.826 0.826 0.826 0.826 0.826 0.826 0.826 0.826 0.826 0.826 0.826 0.698 0.730 0.744 0.752 0.757 0.764 0.772 0.777 0.781 0.783 0.786 0.789 0.792 0.792 0.792 0.792 0.792
0.153 0.139 0.138 0.139 0.141 0.142 0.145 0.146 0.148 0.149 0.150 0.150 0.151 0.151 0.152 0.152 0.152 0.153 0.139 0.138 0.139 0.141 0.142 0.145 0.146 0.148 0.149 0.150 0.150 0.151 0.151 0.152 0.152 0.152 0.153 0.139 0.138 0.139 0.141 0.142 0.145 0.146 0.148 0.149 0.150 0.150 0.151 0.151 0.152 0.152 0.152
Event 2
Event 3
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TABLE 3. Mean and SD of RMSE values obtained from 200 replications according to temporal resolution and rain gauge density. Event 1 is 9–10 Jul 2003, 2 is 3–4 Jul 2004, and 3 is 15–16 Jul 2009. 10-min temporal resolution Event–gauge density
Gauge
Radar
30-min temporal resolution Gauge
Radar
60-min temporal resolution Gauge
Radar
Event
Gauge density
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Event 1
2 9 15 22 29 35 42 49 55 62 69 75 82 88 95 102 108 2 9 15 22 29 35 42 49 55 62 69 75 82 88 95 102 108 2 9 15 22 29 35 42 49 55 62 69 75 82 88 95 102 108
4.063 3.765 3.670 3.622 3.590 3.573 3.541 3.524 3.508 3.491 3.490 3.489 3.488 3.472 3.470 3.470 3.469 5.294 5.010 4.877 4.821 4.783 4.745 4.726 4.707 4.688 4.688 4.669 4.669 4.650 4.650 4.650 4.650 4.632 8.540 7.870 7.600 7.480 7.410 7.350 7.310 7.280 7.260 7.230 7.210 7.200 7.190 7.180 7.170 7.170 7.170
2.401 2.339 2.314 2.293 2.288 2.275 2.267 2.261 2.251 2.252 2.247 2.244 2.247 2.241 2.241 2.240 2.239 2.008 1.948 1.930 1.910 1.907 1.890 1.882 1.874 1.871 1.866 1.860 1.860 1.852 1.848 1.845 1.847 1.844 2.146 2.082 2.072 2.079 2.081 2.085 2.093 2.110 2.113 2.113 2.118 2.115 2.116 2.118 2.121 2.120 2.116
3.750 3.624 3.545 3.544 3.527 3.526 3.525 3.540 3.539 3.538 3.537 3.536 3.535 3.534 3.534 3.533 3.532 5.118 5.022 4.965 4.946 4.908 4.889 4.850 4.831 4.812 4.812 4.793 4.793 4.774 4.774 4.755 4.755 4.755 7.336 7.201 7.121 7.118 7.118 7.118 7.118 7.118 7.138 7.138 7.138 7.138 7.138 7.138 7.138 7.138 7.138
2.008 1.948 1.930 1.910 1.907 1.890 1.882 1.874 1.871 1.866 1.860 1.860 1.852 1.848 1.845 1.847 1.844 2.008 1.948 1.930 1.910 1.907 1.890 1.882 1.874 1.871 1.866 1.860 1.860 1.852 1.848 1.845 1.847 1.844 2.008 1.948 1.930 1.910 1.907 1.890 1.882 1.874 1.871 1.866 1.860 1.860 1.852 1.848 1.845 1.847 1.844
3.403 3.001 2.877 2.815 2.769 2.738 2.723 2.692 2.692 2.692 2.661 2.661 2.661 2.645 2.645 2.645 2.645 4.301 3.914 3.785 3.693 3.656 3.619 3.600 3.563 3.545 3.545 3.526 3.526 3.490 3.490 3.490 3.490 3.471 7.513 6.827 6.507 6.333 6.263 6.193 6.123 6.083 6.043 6.020 6.000 5.983 5.970 5.957 5.947 5.940 5.937
2.159 2.090 2.061 2.047 2.036 2.024 2.017 2.009 2.004 2.002 1.998 1.997 1.994 1.991 1.988 1.987 1.986 1.624 1.562 1.532 1.512 1.504 1.484 1.472 1.460 1.449 1.447 1.441 1.432 1.433 1.429 1.427 1.428 1.427 1.898 1.849 1.842 1.844 1.852 1.865 1.856 1.858 1.873 1.879 1.881 1.886 1.886 1.887 1.887 1.893 1.888
3.001 2.831 2.769 2.707 2.692 2.692 2.676 2.676 2.676 2.676 2.676 2.676 2.676 2.661 2.663 2.661 2.661 3.916 3.860 3.786 3.766 3.748 3.730 3.693 3.693 3.674 3.655 3.637 3.637 3.618 3.618 3.599 3.599 3.599 6.465 6.370 6.326 6.308 6.300 6.287 6.273 6.263 6.256 6.237 6.237 6.217 6.217 6.217 6.217 6.217 6.217
1.624 1.562 1.532 1.512 1.504 1.484 1.472 1.460 1.449 1.447 1.441 1.432 1.433 1.429 1.427 1.428 1.427 1.624 1.562 1.532 1.512 1.504 1.484 1.472 1.460 1.449 1.447 1.441 1.432 1.433 1.429 1.427 1.428 1.427 1.624 1.562 1.532 1.512 1.504 1.484 1.472 1.460 1.449 1.447 1.441 1.432 1.433 1.429 1.427 1.428 1.427
2.896 2.510 2.350 2.285 2.253 2.205 2.189 2.173 2.173 2.157 2.157 2.141 2.141 2.141 2.125 2.125 2.125 3.620 3.193 3.077 2.999 2.941 2.902 2.883 2.883 2.844 2.844 2.824 2.824 2.805 2.805 2.805 2.786 2.786 6.717 5.957 5.637 5.457 5.370 5.297 5.233 5.167 5.142 5.108 5.078 5.058 5.048 5.035 5.028 5.018 5.012
1.993 1.916 1.887 1.873 1.861 1.845 1.838 1.834 1.826 1.827 1.826 1.826 1.822 1.822 1.817 1.817 1.816 1.368 1.305 1.278 1.263 1.254 1.245 1.232 1.235 1.229 1.223 1.222 1.208 1.206 1.205 1.207 1.203 1.202 1.722 1.671 1.668 1.667 1.669 1.681 1.678 1.678 1.680 1.682 1.685 1.682 1.689 1.688 1.692 1.690 1.701
2.494 2.350 2.269 2.205 2.173 2.141 2.141 2.125 2.125 2.125 2.109 2.109 2.093 2.093 2.093 2.093 2.093 3.265 3.127 3.088 3.049 3.029 2.990 2.990 2.971 2.971 2.951 2.951 2.951 2.931 2.931 2.912 2.912 2.912 5.511 5.385 5.320 5.297 5.283 5.265 5.255 5.247 5.240 5.235 5.229 5.217 5.217 5.217 5.217 5.217 5.217
1.368 1.305 1.278 1.263 1.254 1.245 1.232 1.235 1.229 1.223 1.222 1.208 1.206 1.205 1.207 1.203 1.202 1.368 1.305 1.278 1.263 1.254 1.245 1.232 1.235 1.229 1.223 1.222 1.208 1.206 1.205 1.207 1.203 1.202 1.368 1.305 1.278 1.263 1.254 1.245 1.232 1.235 1.229 1.223 1.222 1.208 1.206 1.205 1.207 1.203 1.202
Event 2
Event 3
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JOURNAL OF HYDROMETEOROLOGY
only less than those gauge interpolation when the number of rain gauges is lower than 4 (8.8 3 1025 km22) at an interval of 10 min and 7 (15.5 3 1025 km22) at an interval of 60 min for the second event, and 27 (59.7 3 1025 km22) at an interval of 10 min and 12 (26.5 3 1025 km22) at an interval of 60 min for the third event. This further supports the idea that gauge interpolation more accurately reflects the stratiform and jangma storm events than the convective event.
4. Summary and conclusions This paper demonstrates the accuracy of rainfall measured by the weather radar and rain gauge network in terms of the spatial distribution in order to quantitatively prove that while rain gauge observation provides more accurate point rainfall, radar better shows the spatial structure of the rain field. The Monte Carlo simulation and cross-validation techniques are used to evaluate the accuracy of the rainfall interpolated by the IDW method from the rain gauge observations. The least squares fitting method is adopted to develop the Z–R relationship from the pairs of gauge and radar observations. The dependence of the accuracy of this relationship (and therefore the radar rainfall) on the number of rain gauges is investigated by using the Monte Carlo simulation. The accuracy of the two approaches is assessed with two criteria: RMSE and g. The study results are based on three storm events that happened on 9–10 July 2003, 3–4 July 2004, and 15–16 July 2009 in the area around the Jindo radar station, with data being taken within 120 km from the radar center. By using the Monte Carlo simulation and the least squares fitting method, a variety of Z–R relationships are developed corresponding to different rain gauge densities and network configurations. The variation of Z–R relationships is relatively high for the sparse rain gauge networks and the convective rain type; however, this variation afterward decreases quickly and is equal to zero for the full network. The accuracy of rainfall estimated by gauge interpolation and radar rises with increasing rain gauge network size. However, in comparison with radar, gauge interpolation is more sensitive to variation in the number of rain gauges. In all cases, the correlation of radar rainfall and observed value is greater than that of gauge interpolation at all rain gauge network sizes. This supports the conclusion that radar rainfall provides a rainfall product with more accurate spatial coverage. This superiority will be greater for the convective rain type. The rain type is also the cause of the lower RMSE values of radar estimation compared to the gauge interpolation in the first event and higher values in the second and
VOLUME 13
third events. It is noted that, with a sufficiently long time and a denser rain gauge network, radar estimation has no advantages over the gauge interpolation. This study has focused on proposing a method to quantitatively evaluate the accuracy of the spatial coverage of the rainfall derived from radar and gauge measurements. The driving hypothesis is that the selected three events are used to provide the suitability of the proposed method in this study and further studies will be necessary to generalize the overall performance for different rain type. In the next stage, more data will be collected for a more precise evaluation of the performance of radar and rain gauge observations regarding the spatial structure. In this study, only the IDW interpolation technique was applied to estimate rainfall from the surrounding gauges, and radar rainfall was estimated by using the least squares fitting method. Other techniques to interpolate rainfall and calculate rainfall from radar, which can improve the accuracy of the estimations, were not considered in this paper. Such techniques and methods should be used in future studies. Acknowledgments. This study was financially supported by the Construction Technology Innovation Program (Grant 08-Tech-Inovation-F01) through the Research Center of Flood Defense Technology for Next Generation in Korea Institute of Construction & Transportation Technology Evaluation and Planning (KICTEP) of Ministry of Land, Transport and Maritime Affairs (MLTM) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (Grant 2011-0030839).
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