Before calculating reflectivity bias for PSN using BSL, ZH and ZDR must be corrected for bias. ZDR bias correction is important for the absolute calibration of the radar using a self-consistency method. Gorgucci et al. (1999) proposed using a vertical pointing scan of light rain to take advantage of the nearly spherical shape of the raindrops as seen from below. Ryzhkov et al. (2005) used the elevation angle dependency of ZDR as an alternative technique and concluded that the high variability of ZDR in rainfall prohibited the method from achieving the required absolute calibration accuracy of 0.2 dB. They instead proposed a method that utilizes the structural characteristics of the melting layer in stratiform clouds and the dry aggregated snow present above the melting layer. ZDR measurements from dry aggregated snow above the melting layer resulted in a mean S-band value of 0.2 dB and an accuracy of 0.1–0.2 dB. Trabal et al. (2009) evaluated two methods using the intrinsic properties of dry aggregated snow present above the melting layer and light rain measurements close to the ground and found that a ZDR calibration accuracy of 0.2 dB or better was achieved using either method.

Vertical pointing data were not available in the present case, and the scan strategy, with six elevation angles, was unable to detect the melting layer. Therefore, in this study, light rain measurements close to the ground were used to calibrate ZDR. Light rain was defined using a threshold of 20 dBZ ≤Z≤ 28 dBZ, as proposed by Marks et al. (2011). The assumption of ZDR is close to 0 in the case of the small raindrop-like drizzle chosen for this study. The ZDR values observed from BSL with reflectivity in the range of 20 to 28 dBZ for a given time period were averaged. Then the averaged ZDR was taken as a ZDR bias.

The ZH bias was calculated by a self-consistency method using a nine-gate moving average of bias-corrected ZDR in the range of 0.2 to 3.0 dB to improve the accuracy. This method depends on the notion that ZH, ZDR, and KDP are independent in rain and that ZH can be estimated from ZDR and KDP. The difference between the computed and observed values of ZH is referred to as the Z bias. Following the method of Ryzhkov et al. (2005), the entire spatial and temporal domain was divided into 1 dB intervals of ZH between Zmin (30 dBZ) and Zmax (50 dBZ), and the KDP (ZH) and ZDR (ZH) within each interval were calculated. The ZH bias is then determined by matching the integrals as follows: I1=∑Zmin⁡Zmax⁡KDP(Z)n(Z)ΔZ, I2=∑Zmin⁡Zmax⁡100.1Zmf(ZDR)n(Z)ΔZ, The function of f(ZDR) in Eq. () can be well approximated by a fourth-order polynomial fit for certain range of ZDR (Gourley et al., 2009) like Eq. (). f(ZDR)=10-5(a0+a1ZDR+a2ZDR2+a3ZDR3). The estimated ZH bias is determined from Vivekanandan et al. (2003) by ZHbias(dB)=10log⁡(I2I1), If the radar is well calibrated, ZH bias should be equal to 0. The coefficients of f(ZDR) were calculated by T-matrix scattering method using long period DSD data and are 4.26, -4.67, 2.67, and -0.54, respectively.

To calculate the reflectivity bias of PSN, which is a single polarization radar, three approaches were used: the equidistance line method, the overlapping area method, and the disdrometer method. The first approach is to compare the reflectivities along the line that is equidistant between the two radars. To determine this line for the two radars, the effective radius was set to 100 km, and the distance between the two radars and the azimuthal angle pointing from BSL to PSN were calculated using their latitude and longitude values. The start and end azimuthal angles for comparison of reflectivity were then calculated as follows: AZst=β-acos⁡(0.5×dr/rc),AZend=β-acos⁡(0.5×dr/rc)+2×acos⁡(0.5×dr/rc), where AZst and AZend are the start and end azimuthal angles for the comparison, respectively; β is an azimuthal angle, which is the angle between north and the bearing from BSL points to PSN and rc and dr are the effective radius and distance from BSL to PSN, respectively. The distance between the two radars is 76.9 km, and the start and end azimuthal angles of BSL (PSN) are 79 (35) and 213 (261)∘, respectively (Fig. 4).

To compare the reflectivity observed of targets at the almost same height from both radars, the beam height was calculated assuming a standard atmospheric beam propagation (Rinehart, 2010), as follows: H=r2+(R′+H0)2+2r(R′+H0)sin⁡φ-R′, where r is the slant range from the radar, φ is the elevation angle of the radar beam, H0 is the height of the radar antenna above sea level, and R′= (4/3) R, where R is the Earth's radius (6371 km). The radar antenna heights of PSN and BSL are 547 and 1085 m, respectively. Figure 5 shows the beam height of PSN with blue solid line and BSL at the equidistance line (blue dashed line as shown in Fig. 4). EL1 to EL6 show the elevation angles from smallest to largest. The smallest difference in beam height between the two radars is 149 m, which was obtained using the fourth elevation angle of PSN and the third elevation angle of BSL. Therefore, the reflectivity bias of PSN was calculated by averaging the difference of reflectivity along with the equidistance line observed from the fourth elevation angle of PSN and the third one of BSL.

In the second approach, the overlapping area for the two radars was calculated by matching the coordinates. The polar coordinate of two radars was converted to a Cartesian coordinate with a spatial resolution of 1 km. The overlapping area was then determined by considering the distances between the two radars in the east–west and north–south directions. Figure 6 shows a schematic diagram of the overlapping area for the two radars. The distance between the two radars in east–west and north–south direction is 42 and 64 km, respectively. The reflectivity observed from both radars at the pixels designated at the overlapping area as shown by a blue rectangle in the right panel of Fig. 6, was compared to calculate the ZH bias of PSN. The extracted domain of PSN and BSL for the comparison is 158 × 136 km.

The third and final approach is to use DSD observations from the PARSIVEL disdrometer. The reflectivity was calculated from the DSD at 1 min resolution and averaged over 10 min to match the radar time resolution. Figure 7 shows a schematic of the procedure used to match the radar and PARSIVEL data. The PARSIVEL disdrometer is located ∼ 9 km from the radar, at an azimuthal angle of 87∘. The radar reflectivity was averaged over a domain of 13 gates × 3∘ in azimuth, centered at the PARSIVEL location. The reflectivity observed by BSL or PARSIVEL subtracted from that observed by PSN was taken as a ZH bias and it will be applied to all pixels of PSN coverage.

The normalized error (NE), root-mean-square error (RMSE), and correlation coefficient (CC) between rainfall estimates and measurements from 121 gages were calculated to measure the performance of each bias correction method. The rain gages were 0.5 mm tipping-bucket type. Time resolution of gages is 1 min and data quality control was done by KMA. These quantities are defined as follows: NE=1N∑i=1NRR,i-RG,iRG‾, RMSE=1N∑i=1N(RR,i-RG,i)21/2, CC=∑i=1N(RR,i-RR‾)(RG,i-RG‾)∑i=1N(RR,i-RR‾)21/2∑i=1N(RG,i-RG‾)21/2, where N is the number of radar rainfall (RR) and gage rainfall (RG) pairs, and RR‾ and RG‾ are the average hourly rain rates from radar and gages, respectively. These quantities were calculated using total accumulated rainfall amounts for analyzed time period from radar and gage measurements at each point. The radar rainfall value at each point was obtained by averaging rainfall over a small area (1 km × 1∘) centered on the corresponding rain gage. The radar rainfall was calculated using the relation Z= 200 R1.6 and Z= 300 R1.4.

Before estimating radar rainfall rates, reflectivity biases were calculated using each of the three methods. Figure 8 shows time series of the average reflectivity difference between PSN and BSL at the equidistance line and the number of samples used in each calculation, on 25 August 2014. The average difference over the entire time period was -7.85 dB, and the largest difference was -12.46 dB. It means that the reflectivity observed by PSN was underestimated comparing with BSL. The number of samples used for each calculation was determined using a beam height difference threshold of 0.1 km. The number of samples was generally above 60, but it was smaller than 60 after 14:50 LST. The dominant peak of the averaged reflectivity difference occurred from 15:00 LST and would be caused by the decreased sample number for the comparison of reflectivity observed from both radars. Figure 9 shows the same information for 8 September 2012. The average reflectivity difference over the entire time period was -2.56 dB, and the largest difference was -6.77 dB. The number of samples was less than 50 until 03:10 LST, after which it increased to more than 50. This result suggests that the rainfall observed from both BSL and PSN radar was not located enough over the equidistance line to get a reliable comparison until 03:10 LST.

Figure 10 shows the scatter plot of total accumulated radar rainfall amount for the analyzed time period, calculated using Z= 200 R1.6 and Z= 300 R1.4, and gage rainfall, for 25 August 2014 and 8 September 2012. The RMSE, NE, and CC of rainfall pairs for Z= 200 R1.6 (Z= 300 R1.4) on 25 August 2014 were improved from 65.7 (66.1) to 32.6 (27.0) mm, from 0.79 (0.81) to 0.36 (0.31), and from 0.88 (0.87) to 0.89 (0.88), respectively. On 8 September 2012, the RMSE, NE, and CC for Z = 200 R1.6 (Z= 300 R1.4) changed from 30.0 (28.5) to 22.5 (20.0) mm, from 0.58 (0.56) to 0.41 (0.36), and from 0.81 (0.8) to 0.78 (0.76), respectively, by the use of bias correction. In both cases, the use of corrected reflectivity for rainfall estimation resulted in much better accuracy than using raw reflectivity did.

Figure 11 shows time series of the mean reflectivity differences between PSN and BSL in the overlapping area and the number of samples used for calculation of ZH bias on 25 August 2014. Bias values ranged from -11.7 to -8.3 dB over the period analyzed. The bias was stable until 14:40 LST, after which it fluctuated as the number of samples decreased. Figure 12 shows the same information for 8 September 2012. Bias values ranged from -4.66 to 0.22 dB, and lower bias values occurred from 03:00 to 04:00 LST. The fluctuation also would be caused by the sudden change of microphysical characteristics of rainfall pass through the overlapping area for both radars. It would reduce the accuracy of ZH of BSL corrected by self-consistency. The radar rainfall estimation was done by using observed and corrected ZH as an input of Z-R relations.

Figure 13 shows a scatter plot of total accumulated radar rainfall amount for the entire analyzed time period, calculated using Z= 200 R1.6 and Z= 300 R1.4, and gage rainfall, for 25 August 2014 and 8 September 2012. The RMSE and NE of rainfall pairs for Z= 200 R1.6 (Z= 300 R1.4) on 25 August 2014 were improved from 65.7 (66.1) to 29.7 (25.8) mm and from 0.79 (0.81) to 0.31 (0.28), respectively. On 8 September 2012, RMSE and NE for Z= 200 R1.6 (Z= 300 R1.4) were improved from 30.0 (28.5) to 21.8 (19.1) mm and from 0.58 (0.56) to 0.40 (0.34), respectively, by the use of bias correction, while CC for Z= 200 R1.6 was unchanged at 0.81 and that of Z= 300 R1.4 changed from 0.8 to 0.79. Again, in both cases the use of corrected reflectivity for rainfall estimation was found to improve the accuracy compared with raw reflectivity.

Before using the disdrometer bias correction method to estimate rainfall rates, 10 min rain rates obtained directly from DSDs and from collocated gages were compared. Figure 14 shows the time series of rain rate obtained by PARSIVEL and collocated gages on 25 August 2014. Daily total rainfall amounts for PARSIVEL and the gages were 129.4 and 116.0 mm, respectively. The difference in the totals is only 13.4 mm, and the RMSE and CC between the 10 min time series were 0.52 mm h-1 and 0.99, respectively. On 8 September 2012 (not shown), daily total rainfall amounts for PARSIVEL and the gage were 54.4 and 55.0 mm, respectively. The difference between the total daily rainfall amounts was 0.7 mm and the RMSE and CC between the two 10 min series were 0.62 mm h-1 and 0.96, respectively. It is concluded that DSDs were sufficiently reliable to use as a reference with which to calculate the radar bias.

Figure 15 shows time series of reflectivity obtained by radar and by PARSIVEL, and the radar bias, on 25 August 2014. The bias was more stable before 12:00 LST than after 15:00 LST. PARSIVEL reflectivity fell to 0 from 12:30 to 13:40 LST because the precipitation system moved away from the PARSIVEL site. The sudden change of rainfall would cause the unstable reflectivity difference from 13:40 to 15:00 LST. The threshold of reflectivity value observed from both PSN and PARSIVEL should be considered for the comparison to get more reliable ZH bias. The bias would be obtained more accurately when the reflectivity values observed from both instruments were higher than 15 dBZ in this event. Because of this discontinuity, the bias can be considered reliable only until 12:00 LST. The bias values ranged from -13.4 to -3.1 dB until 12:00 LST. Figure 16 shows time series of reflectivity obtained by radar and by PARSIVEL and the radar bias on 8 September 2012. On this occasion there were no reflectivity data from either PARSIVEL or radar until 03:30 LST. The bias values were distributed from -14.3 to 12.7 dB.

Figure 17 shows a scatter plot of total accumulated radar rainfall amount for the entire time period, calculated using Z= 200 R1.6 and Z= 300 R1.4, and gage rainfall on 25 August 2014 and 8 September 2012. The RMSE and NE of rainfall pairs for Z= 200 R1.6 (Z= 300 R1.4) on 25 August 2014 were improved from 65.7 (66.1) mm to 42.0 (61.4) mm and from 0.79 (0.81) to 0.40 (0.53), respectively. On 8 September 2012, RMSE and NE for Z= 200 R1.6 (Z= 300 R1.4) decreased from 30.1 (28.6) to 24.6 (23.9) mm, and from 0.58 (0.56) to 0.46 (0.44), respectively, while CC for Z= 200 R1.6 (Z= 300 R1.4) decreased from 0.81 (0.8) to 0.65 (0.59). In both cases, using corrected rather than raw reflectivity for rainfall estimation improved accuracy as measured by RMSE and NE but reduced accuracy as measured by CC.

Figure 18 shows RMSE of total rainfall amount for entire time period obtained by gage and Z= 200 R1.6 from each of the different bias correction methods on 25 August 2014 and 8 September 2012. Red, black, green, and blue bars show the RMSE obtained using the uncorrected, equidistance line, overlapping area, and disdrometer methods, respectively. The disdrometer method produced the lowest RMSE before 12:00 LST and the highest RMSE after 12:00 LST (Fig. 18a). This behavior can be attributed to the varying stability of the reflectivity calculated by PARSIVEL (Fig. 15). The overlapping method is more accurate than the equidistance line method for the entire time period, except at 14:00 LST. All the bias correction methods performed better than the uncorrected method, except for the period during which DSDs were unavailable. On 8 September 2012, the RMSE of the overlapping area method was lower than that of the other methods for the entire period, except at 05:00 and 06:00 LST (Fig. 18b). The disdrometer method produced lower RMSE at 06:00 LST, when DSDs were available, and the equidistance line method was more accurate at 05:00 LST, when the sample number was high (Fig. 15). Comparing the RMSE between two events, the large fluctuation was occurred. It would be caused by the difference of total rainfall amount between two rainfall systems. The maximum total rainfall amount for both cases were around 250 mm for 25 August and 150 mm for 8 September 2012. Another reason of the fluctuation would be the difference of radar hardware calibration error for PSN between two events.

Considering the entire period covering both events, the overlapping area method showed the best performance, as measured by RMSE. The accuracy of radar rainfall estimates could be improved by combining the three approaches, using metrics such as DSD temporal stability and the number of samples available for the equidistance line method to select the best method for a particular situation. It is worth noting that the result would be changed when the drop size distributions was fluctuated with height, especially at the layer between radar beam and ground in the disdrometer method.

Three methods for determining the reflectivity bias of single polarization radar using dual polarization radar reflectivity and disdrometer data were proposed and examined for two rainfall events caused by low pressure over the Korean Peninsula on 25 August 2014 and 8 September 2012. Single polarization radar reflectivity was underestimated by more than 12 and 7 dB during the August and September events, respectively. All three methods improved the accuracy of estimated rainfall, except during a period when DSDs were not observed (as the precipitation system did not pass over the disdrometer location).

The rainfall estimation using Z= 200 R1.6 and Z= 300 R1.4 and gage rainfall were examined for 25 August 2014 and 8 September 2012 to investigate the accuracy of each method. The RMSE, NE, and CC of rainfall pairs for Z= 200 R1.6 (Z= 300 R1.4) on 25 August 2014 with the equidistance method were improved from 65.7 (66.1) to 32.6 (27.0) mm, from 0.79 (0.81) to 0.36 (0.31), and from 0.88 (0.87) to 0.89 (0.88), respectively. On 8 September 2012, the RMSE, NE, and CC for Z = 200 R1.6 (Z= 300 R1.4) changed from 30.0 (28.5) to 22.5 (20.0) mm, from 0.58 (0.56) to 0.41 (0.36), and from 0.81 (0.8) to 0.78 (0.76), respectively.

The RMSE and NE of rainfall pairs for Z= 200 R1.6 (Z= 300 R1.4) on 25 August 2014 with the overlapping method were improved from 65.7 (66.1) to 29.7 (25.8) mm and from 0.79 (0.81) to 0.31 (0.28), respectively. On 8 September 2012, RMSE and NE for Z= 200 R1.6 (Z= 300 R1.4) were improved from 30.0 (28.5) to 21.8 (19.1) mm and from 0.58 (0.56) to 0.40 (0.34), respectively, by the use of bias correction, while CC for Z= 200 R1.6 was unchanged at 0.81 and that of Z= 300 R1.4 changed from 0.8 to 0.79.

The RMSE and NE of rainfall pairs for Z= 200 R1.6 (Z= 300 R1.4) on 25 August 2014 with the disdrometer method were improved from 65.7 (66.1) mm to 42.0 (61.4) mm and from 0.79 (0.81) to 0.40 (0.53), respectively. On 8 September 2012, RMSE and NE for Z= 200 R1.6 (Z= 300 R1.4) decreased from 30.1 (28.6) to 24.6 (23.9) mm, and from 0.58 (0.56) to 0.46 (0.44), respectively, while CC for Z= 200 R1.6 (Z= 300 R1.4) decreased from 0.81 (0.8) to 0.65 (0.59).

The use of these bias correction methods reduced rainfall RMSE by up to 50 %. Overall, the accuracy of rainfall estimation was highest when the overlapping area method was used to correct radar reflectivity.

The reflectivity biases obtained using the disdrometer and equidistance line methods were more temporally variable than those obtained using the overlapping area method. There were several hours during which the disdrometer method was more accurate than the overlapping area method. We suggest that combining the overlapping area method with the disdrometer method, using threshold criteria such as the temporal stability of reflectivity and the number of samples available would allow more accurate estimates of rainfall. However, optimum values for the domain size for the overlapping area method, the sample number threshold for the equidistance line method, and the reflectivity threshold for the disdrometer method should be determined in order to combine the three methods most effectively.