Algorithm Development for the Optimum Rainfall Estimation Using Polarimetric Variables in Korea

In this study, to get an optimum rainfall estimation using polarimetric variables observed from Bislsan radar which is the first polarimetric radar in Korea, rainfall cases for 84 hours caused by different conditions, which are Changma front and typhoon, Changma front only, and typhoon only, occurred in 2011, were analyzed. And rainfall algorithms were developed by using long period drop size distributions with six different raindrop axis ratio relations. The combination of the relations between R and Z, ZDR, R and KDP, ZDR, and R and KDP with different rainfall intensity would be an optimum rainfall algorithm if the reference of rainfall would be defined correctly. In the case the reference is not defined adequately, the relation between R and Z, ZDR,KDP,AH and R and Z,KDP, AH can be used as a representative rainfall relation. Particularly if the qualified ZDR is not available, the relation between R and Z, KDP, AH can be used as an optimum rainfall relation in Korea.


Introduction
Measurement of drop size distributions (DSDs) have been extensively used to calculate both radar reflectivity and rain rate for conventional radar and there is no unique relation between horizontal reflectivity () and rain rate () (hereinafter ()) in the world because DSDs could vary from storm to storm and within the storm itself [1,2].Calculations of polarimetric parameters such as , differential reflectivity ( DR ), differential phase shift (Φ DP ), cross correlation coefficients ( ℎ ), specific differential phase ( DP ), and specific attenuation (  ) could be obtained using T-matrix scattering techniques derived by Waterman [3] and later developed further by Mishchenko et al. [4].The raindrop axis is one of the parameters for calculating polarimetric variables of T-matrix simulation.The variations of raindrop axis ratio in nature are intensively related to the oscillating of raindrop and hence are also connected to the polarimetric variables.There are many researches on the investigation of raindrop shape by laboratory study [5,6], field measurements [7,8], and modeling [9,10].
Many researchers noticed that radar rainfall estimation is contaminated by a number of uncertainties such as hardware calibration, partial beam filling, rain attenuation, and nonweather echoes [11,12].To mitigate these problems, the particle identification algorithm using polarimetric parameters for improving data quality control and rainfall estimates by the discrimination of nonmeteorological artifacts such as anomalous propagation, birds, insects, and second trip echo was developed [13][14][15].And improvement of quantitative precipitation estimation (QPE) accuracy is one of the major points of polarization radar [16][17][18][19][20]. Ryzhkov et al. [21] compared the rainfall relations with different drop shape assumptions and developed rainfall algorithm using polarimetric radar for the prototype WSR-88D.Cifelli et al. [22] compared the two rainfall algorithms, CSU-HIDRO (Colorado State University-Hydrometeor IDentification of Rainfall) and JPOLE-(Joint Polarization Experiment-) like, in the high plains environment.Recently, Ryzhkov et al. [23] investigated the potential utilization of   for rainfall estimation using X-band and S-band radar.They found that () method yields robust estimates of rain rates and rain totals even at S band which has very small attenuation.
There have been also many researches on polarimetric radar to implement it into operational uses.Based on these theoretical and other experimental researches, many countries are replacing or modifying their radars into polarimetric radar for operational use.There are three major agencies, Ministry of National Defense (MND), Ministry of Land, Infrastructure and Transportation (MOLIT), and Korea Meteorological Administration (KMA), which operate radars to monitor and forecast severe weather and flash flood operationally in Korea.Among these agencies, MOLIT installed polarimetric radars in 2009 and 2012 for the first time in Korea.KMA has installed the S-band polarimetric radar at the most northwestern part of Korea in 2014.For successful implementation of their radars for the purpose of operational uses, many researches on rainfall estimation, hydrometeor classification, and DSDs retrieval are required.However, there are few studies on these polarimetric related issues except for getting relationships using long period disdrometer data and assessment of each relation after applying a very simple quality control for differential phase shift [24].They found that the accuracy of rainfall estimation using (,  DR ) obtained by DSDs of Busan area in Korea was the best one comparing with relations calculated by ones of Oklahoma in US.And the quality control and unfolding of Φ DP for calculating  DP were applied to the rainfall estimation [25].The above two studies used only 84,574 samples of DSDs excluding winter rainfall events, two and four raindrop shapes for calculation of rainfall relations.
This paper discussed how to improve the accuracy of the rainfall estimation using all polarimetric variables with different raindrop shapes and get optimum rainfall algorithm for Korean S-band polarimetric radar.In Section 2, rain gage, DSDs and radar dataset, calculation of rainfall relations, raindrop axis ratio relations, and the method of validation are described.Section 3 provides the optimum rainfall algorithms with and without rainfall category followed by the calculation of   using observed Φ DP and  and the validations of rainfall estimation.Finally, we provide some conclusions and derived results are summarized in Section 4.

Data and Methodology
2.1.Rain Gage and Radar Dataset.The rainfall data from rain gages operated by the KMA were used to evaluate the accuracy of radar rainfall.Rain gages located from 5 km to 95 km within radar coverage are included in the analysis.Figure 1 shows the location of all instruments used in this study.The circle means the radar coverage, solid rectangle is the center of Bislsan radar, plus sign shows the distributed rain gages within radar coverage, and open rectangle is the location of a POSS (Precipitation Occurrence Sensor System) disdrometer that was installed around 82 km away from radar.
Radar data were collected by Bislsan polarimetric radar that was installed and operated by MOLIT in Korea since 2009.The specifications of Bislsan polarimetric radar and the quality control algorithm of B DP were shown by You et al. [24,25].

Calculations of Polarimetric Variables and Validation.
The relations for converting radar variables into rain rate are required to get rainfall because radar could not observe the rainfall directly.In order to calculate these relations, disdrometer data which can measure the DSDs are needed.Oneminute DSDs obtained by POSS (Precipitation Occurrence Sensor System) from 2001 to 2004 were used and processed to remove the unreliable data as shown by You et al. [25].DSDs data for calculations of relationships were 114,105 samples after quality control and removal of negative  DP .The total number concentration with respect to the drop size and the averaged parameters of gamma distributions was shown in Figure 2(a).The slope, shape, and intercept for gamma model were 8.2, 5.5, and 10 5.4 , respectively, and median diameter was 1.3 mm.Most of the data are distributed in a wide range with a maximum rain rate of about 199.3 mm h −1 and the average was 2.47 mm h −1 (Figure 2(b)).
Polarimetric variables were calculated using T-matrix scattering techniques derived by Waterman [3] and later developed further by Mishchenko et al. [4].To get the variables using DSDs, six raindrop shape assumptions are used.
The first raindrop axis ratio used in this study has slightly modified the relation proposed by Pruppacher and Beard [5] and will be called DS1: where , , and  are the major axis, minor axis, and equivolume diameter of raindrop in mm, respectively: Equation ( 2) is for equilibrium axis ratio derived from the numerical model of Beard and Chuang [9], which is in good agreement with the results from wind tunnel measurements (hereinafter DS2).The practical shapes of raindrops in turbulent flow are expected to be different shapes from the equilibrium shapes due to the drop oscillations.Oscillating drops appear to be more spherical on average than the drops with equilibrium shapes as shown by Andsager et al. [10] in laboratory studies.They figured out that the raindrops' shape between 1.1 and 4.4 mm is better explained by the following formula: Bringi et al. [26] suggested using (3) for drops with sizes smaller than 4.4 mm and (2) for larger sizes (hereinafter DS3).The shape-diameter relation that combines the observations of different authors was recently proposed by Brandes et al. [27,hereinafter DS4]: The relations of raindrop axis ratio (DS5) proposed by Beard and Kubesh [28] and Thurai et al. [29] were combined, given by

Advances in Meteorology
Korea Meteorological Administration (KMA) 15 UTC June 24, 2011 (00 KST June 25, 2011) Korea Meteorological Administration (KMA) Korea Meteorological Administration (KMA) 03 UTC July 9, 2011 (12 KST July 9, 2011) Korea Meteorological Administration (KMA) The relation of raindrop axis ratio that slightly modified the relation proposed by Goddard et al. [30] was used (hereinafter DS6): Another parameter in the T-matrix calculations is the temperature, which is assumed to be 20 ∘ C in this study.It is also necessary to take the canting angle into consideration of the T-matrix simulation because it can account for a 6% reduction in the coefficient of the ( DP ) relation [31] and may cause small negative biases of the estimators [32].The distribution of canting angles of raindrops is Gaussian with a mean of 0 ∘ and a standard deviation of 7 ∘ , which have been recently determined by Huang et al. [33].

Validations.
Because the rainfall in Korea is mostly accompanied with Changma front and Typhoon, three rainfall cases, which are caused by Changma front and typhoon, Changma front only, and typhoon only, were used for validations (Table 1).
Figure 3 shows the surface weather chart of each case.The typhoon MAERI was located at the eastern ocean of Taiwan and the Changma front was elongated from eastern China continent to the central Japan through the southern part of   Figure 4 shows the time series of averaged rainfall amount observed on the ground rain gages within radar coverage from 5 km to 95 km.Averaged rainfall amount refers to that obtained by averaging the amount of rainfall observed by rain gages within the radius of the radar.There are three peaks of rainfall in case of Changma front and typhoon; the first two peaks were due to Changma front and the third one was due to the influence of the typhoon.There are three peaks of rainfall accompanied with Changma front in the second rainfall event.The third event was also caused by typhoon but was relatively short.The period of the selected rainfall was 84 hours, 29 hours for Changma front and typhoon, 46 hours for Changma front only, and 9 hours for typhoon only.
The normalized error (NE), fractional root mean square error (RMSE), and correlation coefficients (CC) of rainfall relations and 121 gages were used to investigate the performance of each rainfall relation: where  is the number of the RR and RG pairs and   and   are the averaged rain rate of radar and gage for an hour, respectively.The above statistical variables are calculated using 1-hour rainfall amount of radar and gage at the point.The point rainfall of radar was obtained by averaging rainfall over a small area (1 km × 1 ∘ ) centered on each rain gage.

The Statistics of Rainfall Relations with Different Raindrop Axis Ratios.
Because the occurrence frequencies of  DR and  DP with different raindrop axis ratios were different from each other, the rainfall relations using those variables should be different with drop shape assumptions.Table 2 shows the rainfall relations obtained by using different raindrop shape assumptions.The coefficients of () were not significantly different with drop shape assumptions; however those of other relations were different with each drop shape.Table 3 shows the cross correlations (hereinafter CC) and RMSEs (root mean square errors) of rainfall relations, (), ( DR ), ( DP ), (,  DR ), and ( DP ,  DR ), obtained by calculations using DSDs data with different raindrop shapes.In order to calculate more accurate (,  DR ) and ( DP ,  DR ), the  and  DR with the best performance were chosen.Figure 6 shows the scatter plots of rainfall obtained by DSDs and (,  DR ) and ( DP ,  DR ) using the best statistics among raindrop axis ratio.,  DR , and  DP were chosen from DS3, DS1, and DS1, respectively.Comparing with (,  DR ) and ( DP ,  DR ) of single raindrop axis ratio relations having the best performance, new combined relations had better RMSE and CC.The RMSEs of new relations, (,  DR ) and ( DP ,  DR ), had better score as much as around 0.2 mm and 0.6 mm, respectively.Even though To compare the performance between new combined ( DP ,  DR ) and (,  DR ), the statistics were also calculated. Figure 7 shows the scatter plots rainfall from rainfall relation and gage rainfall with some statistics.The NE and RMSE of two relations from single raindrop shape assumption showed better results.However, it seems that the (,  DR ) with two-raindrop axis ratio was more close to the gage rainfall in the range of weaker than 20 mm/h and the ( DP ,  DR ) with two drop shapes was more accurate in the rainfall of higher than 20 mm/h.

Calculation of Specific Attenuation.
The   can be calculated from the radial profile of the attenuated reflectivity   and the two-way PIA (Path Integrated Attenuation) along the propagation path ( 1 ,  2 ) proposed by Meneghini and Nakamura [34]: where If  is not dependent on range, then (8) becomes where and Testud et al. [36] used (10) and ( 12) to obtain radial profiles of   at C-band.In this study,   was calculated by the method proposed by Ryzhkov et al. [23].The constant  was set by 0.6 and  was by 0.027 calculated by the ratio of   to  DP obtained from DSDs. Figure 8 shows the scatter plot of rainfall from (), ( DP ), and (  ) and rainfall from DSDs and an PPIs (Plan Position Indicators) at 0.5 degree elevation angle of gage rainfall and rainfall from ( DP ) and (  ) at 0251 KST on the 8th of August in 2011.
The (  ) relation had much better fit to the rainfall of DSDs than that of ( DP ) and () relation.Comparing with

Figure 2 :
Figure 2: Histogram of (a) total number concentration with respect to the drop size and gamma parameters and (b) rain rate calculated using 114,105 samples of 1-minute DSD after quality control.

Figure 4 :
Figure 4: Time series of averaged rainfall amount, which was accompanied with (a) Changma front and typhoon, (b) Changma front only, and (c) typhoon only, averaged rainfall from all rain gages within radar coverage.

Korea on 0000 LST June 25 (
Figure 3(a)).The MAERI moved to the north, located at the southern west sea of Korea, and made rainfall in the Korean peninsula on 0900 LST June 26 in 2011 (Figure 3(b)).Changma front was located at the southern part of Korea and brought rainfall at the analyzed area on 1200 LST July 9 in 2011 (Figure 3(c)).The rainfall was affected by Changma front all the time during case 2. The typhoon MUIFA was located at the southwestern sea of Korea on 0000 LST August 8 in 2011 and caused rainfall at the target area (Figure 3(d)).
The statistics of () and ( DR ) were not significantly different with raindrop shapes.The CC and RMSE of ( DR ) and (,  DR ) were the worst and the best among the other rainfall relations.The statistics of ( DR ), (,  DR ), and ( DP ,  DR ) were much more variable with different raindrop axis ratios than the ones of () and ( DR ).The RMSEs of ( DP ), (,  DR ), and ( DP ,  DR ) with raindrop shapes were distributed from 3.030 to 3.828 mm, 2.965 to 3.523 mm, and 3.151 to 5.412 mm, respectively.The best performance of each relation occurred at DS3 for (), DS1 for ( DR ), DS1 for ( DP ), DS1 for (,  DR ), and DS3 for ( DP ,  DR ).

Table 1 :
Rainfall cases with different sources for the study.

Table 3 :
The correlation coefficients and RMSEs (mm) of rainfall obtained by rainfall relations and DSDs.CC means cross correlation.

Table 4 :
The rainfall relations, NE, RMSE, and CC of each raindrop axis ratio relation.Table4summarizes the relations and the statistics such as NE, RMSE, and CC.The NEs and RMSEs of ( DR ) calculated by each raindrop axis were distributed from 0.52 to 0.55 and from 4.625 to 4.996, respectively.The ( DR ) with assumption of DS5 was the best score of RMSE in other raindrop shapes.In case of (,  DR ), the distribution of NEs and RMSEs was from 0.31 to 0.43 and from 3.793 to 4.602, respectively.The best RMSE score of (,  DR ) was from DS2.The NEs and RMSEs of ( DP ,  DR ) occurred from 0.55 to 0.65 and from 5.146 to 7.141, respectively.The performance of ( DP ,  DR ) was the worst score and (,  DR ) had the best score in all raindrop axis ratio relations.The performances of validation were different from that of rainfall relation calculation.It would be caused by the variations of DSDs in this study.