Rainfall estimation by S-band polarimetric radar in Korea. Part I: preprocessing and preliminary results

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1 METEOROLOGICAL APPLICATIONS Meteorol. Appl. 21: (2014) Published online 2 June 2014 in Wiley Online Library (wileyonlinelibrary.com) DOI: /met.1454 Rainfall estimation by S-band polarimetric radar in Korea. Part I: preprocessing and preliminary results Cheol-Hwan You, a Mi-Young Kang, a Dong-In Lee b * and Hiroshi Uyeda a a Hydrospheric Atmospheric Research Center, Nagoya University, Nagoya, Japan b Department of Environmental Atmospheric Sciences, Pukyong National University, Busan, Republic of Korea ABSTRACT: The empirical relationships used to estimate rainfall amounts from polarimetric radar observations were developed and tested by using long-period drop size distribution (DSD) data and monitoring of rainfall events prior to operational use in Korea. Rainfall associated with Typhoon Meari in 2011 was selected to assess the performance of these relationships for point and areal rainfall amounts. Data quality was checked in regions of light rain to enable the quantitative use of polarimetric variables. The distributions of the cross-correlation co-efficient and standard deviation of the differential phase shift agreed with those established in a previous study, but the absolute average deviation of differential reflectivity (Z DR ) was a little distorted. Biases in reflectivity (Z ) and differential reflectivity were calculated following established methods and found to be 0.18 and 0.47 db, respectively. The accuracy of rainfall amounts calculated from R(K DP ) and R(K DP,Z DR ) was poor. The best estimates of rainfall were obtained using R(Z, Z DR ) based on DSDs from Oklahoma (OKC) in the USA and Busan (BSC) for both the point and areal mean cases. Correlation co-efficients of R(Z, Z DR ) using the BSC DSDs were better than those using the OKC DSDs for areal mean rainfall amounts. Rainfall amounts in this particular case in Korea were estimated more accurately using the Brandes drop shape for R(Z, Z DR ) than the equilibrium drop shape. KEY WORDS rainfall estimation; polarimetric variables; raindrop size distributions; calibration Received 24 April 2013; Revised 20 December 2013; Accepted 6 January Introduction Weather radar is a very useful remote sensing tool for estimating rainfall amounts because of its fine spatial and temporal sampling compared with other observational methods. However, many researchers have pointed out that radar rainfall estimation is subject to uncertainties, including those caused by calibration of the radar hardware, partial beam filling, attenuation by rain, the brightband signature associated with melting ice or snow, and non-weather echoes (e.g., Wilson and Brandes, 1979; Austin, 1987). Measurements of rainfall by radar are based on the relationship between the reflectivity factor (Z ) and the rain rate (R), which is known as the Z R relationship (hereafter R(Z )). Experimentally measured drop size distributions (DSDs) have been used extensively to calculate both radar reflectivity and rain rates (Campos and Zawadzki, 2000). It can be shown theoretically that this R(Z ) relationship is not unique and depends on the DSD, which can vary both from storm to storm and within the storm itself (Battan, 1973; You et al., 2010). Theoretical research on the possibility of DSD retrieval and more accurate rainfall estimation using dual-polarization radar was carried out in the late 1970s (Seliga and Bringi, 1976, 1978). Dual-polarization radar has played an important role in improving forecast accuracy, and has also contributed to an improved understanding of the genesis of severe weather phenomena (Doviak and Zrnic, 1993; Zrnic and Ryzhkov, * Correspondence: D.-I. Lee, Department of Environmental Atmospheric Sciences, Pukyong National University, Daeyeon 3- Dong, Nam-Gu, Busan, Republic of Korea. leedi@pknu.ac.kr 1999; Bringi and Chandrasekar, 2001). Based on this theoretical research, many countries are replacing or modifying their radars to provide a dual-polarization radar network. In the United States, WSR-88D (Weather Surveillance Radar Doppler) radars with dual-polarization capability were deployed after extensive test-bed trials (Doviak et al., 2002; Ryzhkov et al., 2005c). In France, 24 weather radars, including 6 dual-polarization radars, were installed in 2007 within the context of the Meteo-France PANTHERE project (Programme Aramis Nouvelles Technologies en Hydrometeorologie Extension et Renouvellement; Parent-du Chatelet et al., 2003). The National Research Institute for Earth Science and Disaster Prevention (NIED), Japan, deployed an X-band polarimetric radar network (X-NET) in the Tokyo metropolitan area with the aim of improving the understanding of the processes driving the development of severe storms and developing a prediction system for meteorological disasters in urban areas (Maki et al., 2008). Three major agencies in Korea, the Ministry of National Defense (MND), the Ministry of Land, Transportation and Maritime Affairs (MLTM), and the Korea Meteorological Administration (KMA), use radars for operational monitoring and forecasting of severe weather and flash floods. The NMD and KMA plan to install their own dual-polarization radar networks. The MLTM already has two S-band dual-polarization radars for operational use and will be installing four more. There have been many studies on the operational use of dual-polarization radar. A particle identification algorithm for improving data quality control and rainfall estimates by separating out non-meteorological effects has been developed (Ryzhkov and Zrnic, 1998; Vivekanandan et al., 1999; Giangrande and Ryzhkov, 2008). The improvement of quantitative precipitation estimation (QPE) accuracy is one of the 2014 The Authors. Meteorological Applications published by John Wiley & Sons Ltd This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

2 976 C.-H. You et al. Figure 1. The location of the Bislsan radar (solid square), the POSS disdrometer (open square), and gauges ( + ) distributed within the radar coverage. A total of 104 rain gauges within km of the radar coverage area were selected. An asterisk shows the position of the rain gauge with the longest time series of observed rainfall during Typhoon Meari. main advantages of using dual-polarization radar (Ryzhkov and Zrnic, 1996; May et al., 1999; Bringi and Chandrasekar, 2001; Brandes et al., 2002; Ryzhkov et al., 2005c). Recently, Cifelli et al. (2011) compared two rainfall algorithms, the CSU-HIDRO (Colorado State University-Hydrometeor identification) and one based on the JPOLE (Joint Polarization Experiment), in a high plains environment. They concluded that further studies are necessary to evaluate their relative performance in different environments. In Korea, the R(Z ) relationship has been calculated for different rainfall types using a disdrometer (Jang et al., 2004; You et al., 2004). The improvement of rainfall estimation accuracy using operational Doppler weather radars installed in Korea has also been investigated (Suk et al., 2005). However, studies of the rainfall estimation algorithm using dual-polarization radar for operational use in Korea are rare. A new relationship for more accurate rainfall estimation is needed for successful operational use of polarimetric radar. This study discusses the development of empirical relationships for rainfall estimation from polarimetric radar observations using long-period disdrometer data. Comparisons of the performance of these relationships for different drop shape assumptions will also be discussed. Section 2 describes the disdrometer used to develop the relationships, the radar dataset used to estimate rainfall amounts, and the statistical evaluation methods employed. Section 3 compares the performance of each relationship followed by the results obtained using the spatio-temporally integrated reflectivity calibration by Ryzhkov et al. (2005a). Finally, Section 4 summarizes the results. 2. Data and methods Long-period disdrometer data collected in the southern part of Korea since 2001 were used to determine the relationships required to estimate rainfall amounts from polarimetric radar data. The disdrometer site is located very close to the first operational dual-polarization radar installed at Bislsan in To assess the performance of these relationships, rainfall events occurring over 22 h associated with Typhoon Meari and lying within the radar coverage were selected. The Korean peninsula was affected by 327 typhoons from 1904 to 2010, and Typhoon Rusa in 2002 produced the largest total rainfall (870 mm). On average, three typhoons pass over Korea every year (KMA, 2011) Disdrometer data The POSS (Precipitation Occurrence Sensor System) disdrometer used for this study was installed at Pukyong National University about 82 km from the Bislsan radar site (Figure 1). The disdrometer is a low power, continuous wave, X-band bistatic system. The transmitter and receiver are housed separately, and mounted 45 cm apart on a frame (Sheppard, 1990) to determine the 1 min DSDs for drop diameters ranging from approximately 0.34 to 5.34 mm. One minute DSDs for the period March 2001 September 2004, excluding wintertime, were used. Unreliable data defined as belonging to the following categories were removed: 1 min rain rate less than 0.1 mm h 1 or higher than 200 mm h 1 ; total number concentration of all channels less than 10; drop numbers counted only in the 10 th channel and higher; and drop numbers counted only in the 5 th channel and lower. After quality control, there were samples of DSD data available to develop the relationships. To match the T- matrix, the DSDs were interpolated from 0.35 to 5.35 mm at an increment of 0.1 mm. The dataset covers a wide range of rain rates, with a maximum rain rate of about 199 mm h 1 (Figure 2).

3 Preliminary results of radar rainfall estimates in Korea 977 Figure 2. Histogram of rain rate calculated from the quality-controlled disdrometer dataset. The vertical axis (log scale) gives the total time over which rain fell at rates within each bin. Precise total times are given as numbers above each bar. Table 1. Bislsan radar specifications. Polarization Simultaneous H /V Beam width 0.95 Antenna height 1085 m Transmitter Klystron Frequency 2795 MHz Latitude/longitude N/ E Range 100 km Number of elevation angles 6 ( 0.5,0.0,0.5,0.8,1.2,1.6 ) Updated interval 2.5 min Production variables Z, V r, SW, Z DR, ρ hv, DP, K DP Jang et al. (2004) compared POSS and rain-gauge rainfall amounts. They used POSS and rain-gauge data covering a period of 44 days in 2001 and found a bias of around The total rainfall amounts over the 44 days for the POSS and the rain gauge were 488 and 510 mm, respectively. Polarimetric variables, including reflectivity (Z ), differential reflectivity (Z DR ), cross-correlation co-efficient (ρ hv ), and specific differential phase shift (K DP ), were calculated using the T-matrix scattering techniques derived by Waterman (1971), and later developed further by Mishchenko et al. (1996). The Brandes and equilibrium drop shapes were assumed for S-band (wavelength 11 cm) at a temperature of 20 C Radar dataset Data from the S-band Bislsan radar operated by the MLTM in Korea since 2009 were used for the study. The transmitted peak power is 750 kw, the beam width is 0.95, and the maximum range is around 100 km. Values of Z, Z DR, DP, and ρ hv were estimated with a gate size of km and updated every 2.5 min with six elevation angles (Table 1). K DP was calculated from DP using 17 gates and 25 gates for strong and weak rainfall, respectively. To assess the performance of each relationship, 0.5 elevation angle data were used for the rainfall caused by Typhoon Meari in The quality of moment data such as Z DR, ρ hv, and DP was checked before the data were used for rainfall estimation. Indicators of data quality were obtained for light rain, which has no variability in drop shape, canting angle, or scattering properties (Doviak and Zrnic, 1993). Light rain was defined as 20 dbz Z 28 dbz, and the average absolute deviation (AAD) of Z DR and standard deviation of the differential phase shift were used (Marks et al. 2011). Additional thresholds (positive ρ hv and DP, Z DR and K DP higher than 10 km 1 ) were used for a stricter definition of light rain. After quality checking, the polarimetric radar variables, Z, Z DR,andρ hv, were smoothed using a running mean over three, five, and five gates in the radial direction, respectively (Ryzhkov et al., 2005a). A very simple quality control was also applied: pixels with cross-correlation co-efficients <0.8 (Marks et al., 2011), or where the standard deviation of the differential phase shift was >20, were considered to be non-meteorological targets, and removed. The evolution of Typhoon Meari can be seen from the radar mosaic images at 1600 LST (UTC +9 h) on 25 June, 2300 LST on 25 June, 0900 LST on 26 June, and 1400 LST on 26 June (Figure 3). The rainfall system caused by Meari passed through the Bislsan radar coverage (Figures 3(a)(c)) and moved into northeastern Korea (Figure 3(d)) Rain-gauge dataset The radar rainfall data were compared with rain-gauge data. Tipping-bucket rain gauges were used; minimum amount was 0.5 mm with a sampling interval of 1 min, to calculate the hourly rainfall amounts. Both manual and automatic quality control algorithms were applied by the KMA. Data from 104 rain gauges within km of the radar coverage were used. Figure 4 shows the time series of rain rates and rainfall accumulation obtained from the rain gauge with the longest observation period of the 104 gauges (1600 LST on 25 June to 1400 LST on 26 June 2011). The maximum rain rate was 15.5 mm h 1, and the total rainfall amount over 22 h was mm Methodology for statistical evaluation of rainfall estimation New polarimetric rainfall relationships were obtained using long-period DSDs from a POSS disdrometer in Korea. To evaluate the performance of these relationships, some of the relationships published by Ryzhkov et al. (2005b) were used. Table 2 shows all of the relationships calculated from DSDs, with different raindrop axis ratios at different locations. The s are described by Beard and Chuang (1987) as: r = D D D D 4 (1) where r is the axis ratio of raindrops and D is their equi-volume diameter in mm. Brandes et al. (2002) proposed a combined shape diameter relationship using observations from different authors: r = D D D D 4 (2) Each relationship was evaluated using the fractional bias (FB), fractional root mean square error (FRMSE), and fractional

4 978 C.-H. You et al. (a) (b) (c) (d) Figure 3. Time series of mosaic images of precipitation rate from the KMA weather radar network: (a) 1600 LST, 25 June; (b) 2300 LST, 25 June; (c) 0900 LST, 26 June; and (d) 1400 LST, 26 June. standard deviation (FSD) of rainfall estimates (Ryzhkov et al., 2005a), together with correlation co-efficients: FB = 1 N N i=1 R R,i R G,i R G,i (3) [ 1 N ( ) ] 1/2 RR,i R 2 G,i FRMSE = (4) N i=1 R G,i FSD = ( FRMSE 2 FB 2) 1/2 where N is the number of samples, and R R,i and R G,i are the radar and gauge hourly rain rates for the radar gauge pair, respectively. These statistical variables are calculated from hourly point and areal rainfall amounts. Point rainfall was calculated by averaging rainfall over a small area (500 m 1 ) (5) centred on each rain gauge. Areal mean rain rate is the mean of the hourly rainfall amounts from all of the rain gauges that recorded rain within the analysis region. 3. Results 3.1. Quality check and absolute calibration of Z and Z DR Before the rainfall estimation relationships were applied, data quality was checked for the polarimetric variables in light rain (defined as 20 dbz Z 28 dbz) using the cross-correlation co-efficient, the AAD of Z DR, and the standard deviation of the differential phase shift. The AAD of Z DR is defined by: AAD [Z DR ] = N [ ] Z DR (i) Z DR /N (6) i=1

5 Preliminary results of radar rainfall estimates in Korea 979 Figure 4. Time series of rain rate (left axis) and rainfall accumulation (right axis) obtained from the rain gauge with the longest observation period. Table 2. List of different relationships used for validation. OKC = Oklahoma City (USA). No. Relationships Axis ratio assumptions 1 R = Z R = 44.0K DP Measured DSD (OKC), 3 R = 47.3K DP Measured DSD (OKC), 4 R = 47.8K DP Measured DSD (Busan), 5 R = 54.0K DP Measured DSD (Busan), 6 R = 136.0K DP Z 2.86 DR Measured DSD (OKC), 7 R = 108.3K DP Z 2.05 DR Measured DSD (Busan), 8 R = 189.5K DP Z 3.29 DR Measured DSD (Busan), 9 R = Z 0.77 Z 1.67 DR Measured DSD (OKC), 10 R = Z Z 1.51 DR Measured DSD (OKC), 11 R = Z Z 5.38 DR Measured DSD (Busan), 12 R = Z Z 5.38 DR Measured DSD (Busan), Figure 5. Time series of cross-correlation co-efficients (right axis, dashed line), standard deviation of differential phase shift (left axis, dotted line), and AAD [Z DR ] (left axis, solid line). Table 3. Co-efficients of the fourth-order polynomial fit (a 0 to a 3 of Equation 3 in text) used in this study. Z DR range (db) a 0 a 1 a 2 a Figure 6. Scatter plot of K DP /Z versus Z DR in S-band at a temperature of 20 C using observed DSD data. The white line is the line of best fit for the relationship between K DP /Z and Z DR used in this study. where N is the Z DR sample size, and Z DR is the average of Z DR values; AAD was found to be <0.3 db for normal applications (Marks et al., 2011). The standard deviation of DP was computed using a 25 gate sample in the radial direction. The acceptable value for K DP computation should be around 2 or 3, or lower (Doviak and Zrnic, 1993; Bringi and Chandrasekar, 2001). Figure 5 shows time series plots of the above parameters from 1600 LST on 25 June to 1400 LST on 26 June. The crosscorrelation co-efficient (dashed line, right axis) is >0.99, the standard deviation of DP (dotted line, left axis) is <3,and the AAD of Z DR (solid line, left axis) is <0.4 db. These results are in good agreement with those of Marks et al., 2011, except for AAD [Z DR ] in a few of the time periods. Polarimetric diversity provides a new method for the absolute calibration of reflectivity, which has long been a problem with single-polarization radar data. This method depends on the notion that Z, Z DR,andK DP are interdependent in rain, and that Z can be estimated from Z DR and K DP, which are immune to radar miscalibration (Gorgucci et al., 1992, 1999; Goddard et al., 1994; Scarchilli et al., 1996; Vivekanandan et al., 2003). The difference between the computed and measured values of Z is referred to as the Z bias. Following the method of Ryzhkov et al. (2005a), the entire spatial and temporal domain was divided into 1 db intervals of Z between Z min (30 dbz) and Z max (50 dbz), and the K DP (Z ) and Z DR (Z ) within each interval were calculated. The Z bias is then determined by matching the integrals: and I 1 = Z max Z max Z min K DP (Z ) n (Z ) Z (7) I 2 = Zm f (Z DR ) n (Z ) Z (8) Z min

6 980 C.-H. You et al. (a) (b) (c) (d) Figure 7. Scatter plots of hourly gauge rainfall against rainfall amounts obtained from the radar rainfall relationships R(Z, Z DR ). R(Z, Z DR ) obtained from measured DSDs at Oklahoma City assuming (a) an equilibrium drop shape (OKC1), and (b) a Brandes drop shape (OKC2). R(Z, Z DR ) obtained from measured DSDs at Busan assuming (c) an equilibrium drop shape (BSC1), and (d) a Brandes drop shape (BSC2). where Z m is the measured reflectivity and n(z ) is the number of gates for a given 1 db interval of reflectivity between Z min and Z max.herez is in dbz and Z DR is in db. Over a certain range of Z DR, the function f (Z DR ) can be approximated closely by a fourth-order polynomial (Gourley et al., 2009): f (Z DR ) = 10 5 ( a 0 + a 1 Z DR + a 2 ZDR 2 + a 3ZDR 3 ) (9) The estimated Z BIAS is then determined from Vivekanandan et al. (2003) using: ( ) I2 Z BIAS (db) = 10 log (10) A well-calibrated radar will have Z BIAS = 0. I 1 The co-efficients of f (Z DR ) and the scatter plots of computed against measured values of Z are shown in Table 3 and Figure 6, respectively. The absolute reflectivity bias (Z BIAS ) was 0.18 db in the rain regions, which were defined as the regions where ρ hv > 0.99 and 0.2 db < Z DR < 3.0 db. The calibration of Z DR was performed three times with upward pointing observations; this is discussed by Kwon (2012). The Z DR bias for this study is 0.47 db, and this was obtained from data acquired on 11 May Rainfall estimation and its validation Rainfall estimation relationships, R(K DP ), R(K DP, Z DR ), and R(Z, Z DR ), were calculated using long-period (4 years) disdrometer data from the Busan area. The relationships based on

7 Preliminary results of radar rainfall estimates in Korea 981 (a) (b) (c) (d) Figure 8. As Figure 7, but for areal mean rainfall. the assumption of an equilibrium-drop axis-ratio are as follows: R = 47.8K DP (11) R = 0.008Z Z 5.38 DR (12) R = 108.3K DP Z 2.05 DR (13) The correlation co-efficients for each relationship are 0.88, 0.89 and 0.91, respectively. The relationships obtained using the Brandes drop shape assumption are as follows: R = 54.0K DP (14) R = Z Z 5.38 DR (15) R = 189.5K DP Z 3.29 DR (16) The correlation co-efficients for each of the relationships are 0.86, 0.89 and 0.90, respectively. Rainfall caused by Typhoon Meari that lay within the Bisl radar coverage for 22 h from 1600 LST on 25 June to 1400 LST on 26 June 2011 was used in this analysis. To ensure a rigorous assessment, no threshold was set for either rain gauge or radar rainfall. Figure 7 shows the scatter plots of rainfall amounts from the rain gauge and each R(Z, Z DR ) relationship at the raingauge site. The radar rainfall amount obtained from measured DSDs at Oklahoma City using R(Z, Z DR ) with the equilibrium drop shape (OKC1) and (OKC2) assumptions underestimates the measured point rainfall (Figures 7(a) and (b)). The radar rainfall amount obtained from measured DSDs at Busan using the equilibrium drop axis ratio (BSC1) and Brandes drop shape (BSC2) assumptions is closer to, or even overestimates, the rain-gauge rainfall (Figures 7(c) and (d)). The difference shown in Figure 7 is significant in the case of areal mean rainfall (Figure 8). A comparison with results from R(K DP )andr(k DP, Z DR ) shows that R(Z, Z DR ) performs much better (not shown here). The results of the statistical evaluation of each relationship are summarized in Table 4. The rainfall amounts obtained

8 982 C.-H. You et al. Table 4. The statistics of rainfall estimates from each relationship. OKC indicates drop size distributions (DSDs) observed at Oklahoma City and BSC those observed at Busan. CC = correlation co-efficient. Relationship Drop shape Point Areal FB (%) FRMSE (%) FSD (%) CC FB (%) FRMSE (%) FSD (%) CC R = Z R = 44.0K DP OKC, equilibrium R = 47.3K DP OKC, Brandes R = 47.8K DP BSC, equilibrium R = 54.0K DP BSC, Brandes R = 136.0K DP Z DR OKC, equilibrium R = 108.3K DP Z DR BSC, equilibrium R = 189.5K DP Z DR BSC, Brandes R = Z Z DR OKC, equilibrium R = Z Z DR OKC, Brandes R = Z Z DR BSC, equilibrium R = Z Z DR BSC, Brandes from all R(K DP ) and R(K DP, Z DR ) relationships were less accurate than from the conventional R(Z ) rainfall relationship for both point and area. This may be because the rainfall intensity of Typhoon Meari was too low to produce a specific differential phase shift. The results of R(Z, Z DR ) for point rainfall show that the FBs for each of the OKC1, OKC2, BSC1 and BSC2 relationships were 38.2%, 40.4%, 10.8% and 24.6%, respectively. The results for the R(Z, Z DR ) obtained using DSDs measured at Oklahoma in the United States and Busan in Korea were better than the other relationships for both point and areal mean rainfall estimation. The correlation co-efficients for point rainfall estimation using R(Z, Z DR ) were 0.8 at both locations (BSC, OKC), for both drop shape assumptions. However, the correlation co-efficients for areal mean rainfall estimation were 0.97 at Busan and 0.95 at Oklahoma City. The results using R(Z, Z DR ) calculated from DSDs observed at Busan show that, in this study area, the FB, FRMSE and FSD for the Brandes drop shape assumption (BSC2) are better than those for the equilibrium drop shape (BSC1). 4. Summary and conclusions Within a few years, polarimetric radars will be the main tools used in the monitoring and forecasting of severe weather and flash flooding in Korea. To assess the performance of empirical rainfall relationships for point and areal rainfall, the rainfall associated with Typhoon Meari in 2011 was studied. To allow the quantitative use of polarimetric variables, a data quality check was performed under light rain conditions. The distributions of the cross-correlation co-efficient and the standard deviation of the differential phase shift compared well with previous results, but the absolute average deviation of the differential reflectivity was a little distorted. Calibration of Z and Z DR was carried out following Ryzhkov et al. (2005a) and the upward pointing scan of Kwon (2012), respectively. The values of the biases were 0.18 and 0.47 db, respectively. The rainfall relationships R(K DP ), R(K DP, Z DR )andr(z, Z DR ) were obtained from DSDs at Oklahoma and Busan. The accuracy of the rainfall amounts calculated from R(K DP ) and R(K DP, Z DR ) were not good, as was also the case in previous studies. Results from R(Z, Z DR ) obtained using DSD data measured at Oklahoma (OKC) and Busan (BSC) gave better estimates of both point and areal mean rainfall. The results for R(Z, Z DR ) obtained at different locations had the same correlation co-efficients for point rainfall. However, the BSC relationships gave better estimates of areal mean rainfall amounts than those for OKC. A comparison of rainfall estimates in the study area using R(Z, Z DR ) calculated from the BSC DSDs, but with different drop axis assumptions, showed that the Brandes drop shape (BSC2) performs better than the equilibrium drop shape (BSC1). For the rainfall events that occurred over the rather short period studied here, R(Z, Z DR ) using DSDs observed in the Busan area was found to perform better than using DSDs from Oklahoma City. In addition, the Brandes drop shape assumption performed better than the equilibrium ratio axis assumption. This study provides a starting point for further research into the development of the optimum rainfall algorithm for the estimation of rainfall using polarimetric radar in Korea. Acknowledgements Radar data and AWS data for this work were provided by the Ministry of Land, Transportation and Maritime Affairs, and the Korea Meteorological Administration. The authors thank Dr Alexander Ryzhkov for providing the code for calculating relationships, and for valuable discussions. This research was supported by the National Research Foundation of Korea (NRF) through a grant provided by the Korean Ministry of Education, Science & Technology (MEST) in 2014 (No. K ). 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