Raindrop Size Distribution Characteristics of the Extreme Rainstorm Event in Zhengzhou 20 July, 2021 and Its Impacts on Radar Quantitative Precipitation Estimation
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摘要: 利用雨滴谱仪观测的雨滴谱数据，分析了2021年7月20日郑州极端暴雨的雨滴谱特征，并结合双偏振雷达观测，分析了不同定量降水估测（QPE）方法在此次极端暴雨过程中的性能。结果表明，在此次极端暴雨过程的最强降水时段，雨滴谱表现为很高的粒子数浓度和很大的粒子平均直径；而整个降水过程雨滴谱的截距参数与我国其它地区雨滴谱特征差异不明显，但质量加权平均直径大于其他地区的雨滴谱；在降水最强的2021年7月20日08:00～09:00（协调世界时，下同）前后，雨滴谱的特征发生了显著变化，首先是质量加权平均直径迅速增长，随后粒子数浓度也陡增，从而导致降水率的迅速增强。使用郑州双偏振雷达数据，基于各种QPE方法和参数计算得到了08:00～09:00的雷达反演降水量，并与雨量计观测结果比较。结果表明对于基于反射率的QPE关系（R(ZH)），如果不提高或者去除反射率上限进行QPE，会导致降水严重低估，且该方法对参数的准确性较为依赖；基于差传播相移率的QPE关系（R(Kdp)）对雨滴谱差异性敏感度相对较低，其性能主要依赖于差传播相移率的准确性；最优的R(Kdp)关系反演效果比R(ZH)更好，能达到实际降水量的70%以上。Abstract: In this study, we investigated the raindrop size distribution (DSD) characteristics of an extreme rainstorm event on July 20, 2021, in Zhengzhou using disdrometer observation data. The performance of many radar quantitative precipitation estimation (QPE) approaches was then examined using polarimetric radar data. The results show that during the peak rain rate period, the DSD indicated a high number concentration and large mean particle size. During this event, the normalized intercept parameter was similar to those observed in other regions of China, but the mass-weighted diameter was significantly higher. The DSD experienced significant changes before the peak rain rate period. The number concentration increased as the mass-weighted diameter increased, resulting in a quick increase in the rain rate. Polarimetric radar data were used to calculate the hourly QPE rainfall during 0800 UTC–0900 UTC, July 20, 2021, based on several QPE approaches and parameters, and then the performances of each approach were examined against the gauge observation. The result showed that the cap of reflectivity-based estimator (R(ZH) )should be removed or raised; otherwise, the rainfall would be significantly underestimated. The estimator was sensitive to the QPE parameters; however, the specific differential phase-based estimator (R(Kdp)) was relatively insensitive to the QPE parameters, and the accuracy of the specific differential phase was responsible for its performance. The best R(Kdp) estimator reached over 70% of the observational hourly rainfall and outperformed the best R(ZH) estimator during this extreme rainstorm event.
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图 1 2021年7月20日（a）质控前与（b）质控后的雨滴谱仪与雨量计观测的1分钟降水量比较
Figure 1. Scatter plots of 1-min rainfall observed by disdrometer versus rain gauge (a) before quality control and (b) after quality control on July 20, 2021
图 2 2021年7月20日08:00～09:00（协调世界时，下同）雨滴谱仪观测的降水粒子速度和等效直径的频数散点，颜色表示雨滴的个数。粗实线为雨滴理论下落末速度，两条细实线分别为下落速度的1.5倍和0.5倍
Figure 2. Frequency scatterplot of raindrop size and velocity at 0800 UTC–0900 UTC July 20, 2021, with colors indicating the drop numbers. The bold solid line represents the theoretical terminal velocity of raindrops, and the thin solid lines represent 1.5 and 0.5 times the theoretical line
图 3 2021年7月20日08:00～09:00雨滴谱仪观测的雨滴谱特征量的频率分布：（a）质量加权平均直径Dm（单位：mm）；（b）降水率R（单位：mm h−1）；（c）粒子数浓度Nt（单位：m−3）；（d）归一化的截距参数Nw（单位：mm−1 m−3）。图中还表示了该特征量的均值（Mean）和标准差（SD）
Figure 3. Frequency of different raindrop size distribution (DSD) parameters observed by disdrometer at 0800 UTC–0900 UTC, July 20, 2021. (a) mass-weighted mean diameter (Dm), (b) rain rate R, (c) total number concentration (Nt), and (d) normalized intercept parameter (Nw), superimposed with mean values (Mean) and standard deviations (SD)
图 4 2021年7月20日雨滴谱仪观测的（a）R–Dm的频数分布和（b）Dm–Nw的散点分布。（a）中黑线和实线分别是使用全部样本和降水率大于100 mm h−1的样本利用最小二乘法拟合得到的拟合曲线，填色表示样本数。（b）中红色叉、蓝色圆点和红色圆点分别是全天的1分钟对流性降水样本、全天的1分钟层状云降水样本和08:00～09:00的1分钟降水样本；黑色方框分别是Bringi et al.（2003）中的海洋性和大陆性对流性降水的Dm–lg(Nw)的分布区域；黑色实线为Bringi et al.（2003）中层状云降水的Dm–Nw关系
Figure 4. (a) Scatter density for R versus Dm, (b) scatter plot for Dm versus Nw superimposed with a power-law relationship using the least-squares fit method on July 20, 2021. The black line and red line in (a) indicate the fitting result for all samples and for samples with rain rates greater than 100 mm h−1, the color indicate samples number.. In (b), red crosses and blue hollow dots represent 1-minute convection and stratiform samples on July 20, 2021; red dots represent 1-minute samples at 0800 UTC–0900 UTC July 20, 2021; mean values for convection (purple) and stratiform (gray) of different studies are also superimposed; the black line is the lg(Nw)–Dm relationship for stratiform in Bringi et al. (2003); two rectangles are maritime and continental convective clusters in Bringi et al. (2003)
图 5 2021年7月20日06:30～09:59雨滴谱特征量的时间变化（红线、蓝线和黑线分别表示Nt、Dm和R）。其中灰色矩形区域是07:43～09:08时段，即降水率超过100 mm h−1的时段
Figure 5. Time series of DSD parameters at 0630 UTC–0959 UTC July 20, 2021. Red, blue, and black lines represent Nt, Dm, and R, respectively. The gray box is the period with a rain rate larger than 100 mm h−1, namely, 0743 UTC–0908 UTC
图 6 使用表1中不同关系参数的反演得到的降水率与雷达观测量的关系：（a）基于R(ZH)关系R随Zh的变化；（b）基于R(Kdp)关系R随Kdp的变化。图中的绿色、红色和黑色线分别代表使用表1中业务、08:00～09:00和全天关系得到的降水率。（a）中的垂直于Y轴的实线和虚线分别表示反射率为53 dBZ和55 dBZ时降水率的值
Figure 6. Retrieved rain rate versus radar parameters using different QPE parameters in Table 1. (a) Reflectivity (Zh)versus rain rate based on R(ZH) method and (b) Kdp versus rain rate based on R(Kdp) method. The green, red, and black curve lines represent the retrieved rain rate using parameters of “Operational”, “0800UTC–0900 UTC”, and “Whole day” in Table 1. The solid and dashed lines perpendicular to the Y axis in (a) represent the rain rates with reflectivity of 53 and 55 dBZ, respectively
图 7 2021年7月20日08:00～09:00雨滴谱仪观测的降水率与基于（a、b）R(ZH)和（c、d）R(Kdp)反演关系计算得到的降水率比较：（a、c）使用全天参数；（b、d）使用08:00～09:00参数
Figure 7. Scatter plots of rain rate observed by disdrometer verus that retrieved using (a, b) R(ZH) and (c, d) R(Kdp) with parameters obtained based on samples of (a, c) the whole day and (b, d) 0800 UTC–0900 UTC at 0800 UTC–0900 UTC July 20, 2021
图 8 2021年7月21日08:00～08:54时刻郑州雷达第二仰角在雨滴谱仪位置的Zh及Kdp，实线、长虚线和短虚线分别表示Zh、原始观测的Kdp及使用线性规划（LP）方法获得的Kdp
Figure 8. Zh and Kdp of the second tilt of Zhengzhou Doppler radar at the disdrometer’ s location at 0800 UTC–0854 UTC. The solid, long dashed, and short dashed lines respectively represent Zh, observed Kdp, and Kdp retrieved with linear programming (LP) method
图 9 使用不同方法计算得到的08:00～09:00的雷达估计降水量。左、中、右的各五个柱状分别表示使用表1中的业务关系、全天关系和08:00～09:00关系得到的结果。点、横线、左斜线、分别表示使用R(ZH)关系且反射率上限设为53 dBZ、设为55 dBZ以及不设反射率上限；右斜线和格子纹柱状表示使用R(Kdp)关系且Kdp值来自基数据以及来自线性规划方法百分数表示雷达估测降水量与雨量计观测降水量的比值。
Figure 9. Hourly rainfall at 0800 UTC–0900 UTC estimated using different QPE methods. The groups with 5 bars located at the left, middle, and right portion of the plot represent the result using the parameters of “Operational,” “Whole day,” and “0800 UTC–0900 UTC” in Table 1. The dotted, transverse line, left slash, right slash, and cross pattern bars in each group represent the result using R(ZH) with Zh capped at 53 dBZ, at 55 dBZ, and without Zh cap, R(Kdp) with Kdp obtained from radar volume data and using linear programming method. The percentage indicates the ratio of radar estimated rainfall to gauge observational rainfall.
表 1 S波段雷达降水反演关系参数
Table 1. S-band radar quantitative precipitation estimation parameters
反演关系 来源 关系参数 a b $ R({Z_H}) = aZ_H^b $ 业务 0.0170 0.714 全天 0.0170 0.706 08:00～09:00 0.2148 0.521 $ R({K_{dp}}) = aK_{dp}^b $ 业务 44.0 0.822 全天 45.2 0.820 08:00～09:00 57.7 0.711 
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