*3.3. Discussion on C*−*S Classification Schemes*

The classification of precipitation into convective and stratiform is important in this study. Previous studies have proved that BR09 and TH15 schemes in log10 *Nw*–*D*<sup>0</sup> domain are applicable based on the measurements not only from disdrometers but also from polarimetric radars [46,50,53,55,56]. As such, these classification approaches are adopted. However, there are also a few other C−S classification schemes. In order to reveal the impacts of the classification approach on the analysis results, this study also applied the C−S classification schemes described in Testud et al. [52] (hereafter referred as to TE01) and Bringi et al. [51] (hereafter referred as to BR03) for comparison purpose. Both schemes are

popularly used as well, and both are based on the variation of *R* with time and utilize 10 (5) adjacent DSD measurements at a 1-min (2-min) interval. The major difference between them is that TE01 assesses the values of *R* with an upper limit of 10 mm h−<sup>1</sup> for stratiform rain, whereas BR03 evaluates the standard deviation of *R* (σ*R*) with a lower threshold of 5 mm h−<sup>1</sup> for convective rain. It should be mentioned that some DSDs may satisfy the conditions *<sup>R</sup>* <sup>&</sup>lt; 5 mm h−<sup>1</sup> and <sup>σ</sup>*<sup>R</sup>* <sup>≤</sup> 1.5 mm h−<sup>1</sup> according to BR03, and, thus, fail to be classified as either stratiform or convective rain.

TH15 scheme is not suitable for Beijing, because no obvious peak of sample occurrences above Equation (14) can be found in Figure 5. Therefore, only integral rainfall parameters derived from BR09, BR03, and TE01 are listed in Table 2. Compared with BR09, both TE01 and BR03 schemes classify more convective (less stratiform) DSDs, which result in more (less) rainfall amount and a higher proportion of convective (stratiform) rain. However, almost all DSD parameter values for both rain types derived by TE01 and BR03 are not higher than those derived based on BR09, except the log10 *Nw* value for convective rain. Compared with Figure 4, convective rain classified by TE01 (Figure A1) and BR03 (Figure A2) in log10 *Nw*–*D*<sup>0</sup> domain contain much more samples under BR09 line but above TH15 line, corresponding to the DSDs with higher number concentration but smaller size. As a result, the smallest log10 *Nw* but highest *D*<sup>0</sup> for convective rain are obtained by BR09.

For stratiform rain, the DSD parameters from S\_TE01 are higher than those from S\_BR03. For convective rain, however, it is the opposite (Table 2). Further study shows that the percentage of samples with *R* > 5 mm h−<sup>1</sup> in C\_BR03 is higher than that in C\_TE01. In other words, the lower threshold of 5 mm h−<sup>1</sup> for convective rain set in BR03 scheme plays a key role in the different results between TE01 and BR03.

In summary, for stratiform rain, the impacts of different C−S classification schemes are not distinct relative to convective rain, due to the higher number of samples for the former than the latter. Although DSDs classified by the aforementioned three schemes in log10 *Nw*–*D*<sup>0</sup> domain can be separated by BR09 line in general (Figures 4, A1 and A2), the specific properties of DSDs could be different. The BR09 scheme is recommended, since it has been proved with radar observations [55,56].

#### **4. Radar-Based Quantitative Precipitation Estimation**

This study first computed *Zh* and *R* using Equations (5) and (10), based on the DSD measurements, to support weather radar applications in Beijing. The power-law relation *Zh*= a*Rb* was then derived using nonlinear regression approach. It is well known that the *Zh*–*R* relationship is dependent on local DSD variability, which can be influenced by many factors, such as rainfall type, climate regime, and orographic effect [17,35,57]. Finding a suitable *Zh*–*R* relation for Beijing is also critical to RMAPS model for QPE forecast [36].

Figure 8 shows a scatterplot of *Zh*–*R* pairs for both rain types classified by BR09 scheme along with the corresponding fitted power-law curves and equations. The fitted curve for the entire dataset is highlighted in black dots. For comparison, other four commonly used *Zh*–*R* relationships are also indicated in Figure 8, including those for the continental stratiform rain (*Zh* = 200*R*1.6) [58], tropical systems (*Zh* = 250*R*1.2) [59], operational WSR-88D radars (*Zh* = 300*R*1.4) [60], and Meiyu convective rain in China (*Zh* = 368*R*1.21) [11]. Obviously, *Zh* is proportional to *R* in the double logarithmic domain. Based on the fitted relations for the two rain types, for a given *Zh*, higher *R* can be obtained using the stratiform relation than a convective algorithm. The relationship for the entire dataset (i.e., *Zh* = 265.14*R*1.399) is closer to the relationship for stratiform rain.

**Figure 8.** Scatterplot of *Zh* (mm6 m<sup>−</sup>3) vs. *R* (mm h<sup>−</sup>1) computed from PARSIVEL2 DSD measurements for stratiform (red dots) and convective (blue dots) rain classified using BR09 scheme. The fitted power-law curves for stratiform and convective rain, as well as the entire dataset, are indicated by thick solid dark-red, solid dark-blue, and black dotted lines, respectively. The relationships for continental stratiform rain, *Zh* = 200*R*1.6 [58], tropical systems, *Zh* = 250*R*1.2 [59], the operational WSR-88D, *Zh* = 300*R*1.4 [60], and Meiyu convective rain, *Zh* = 368*R*1.21 [11] are also indicated in thin dashed yellow, purple, lime and green lines, respectively. Equations are overlaid using the same color with the corresponding curves.

It is worth noting that the relationship for the operational WSR-88D (thin dashed lime line) [60] is very similar to our result based on the entire dataset, which implies that the relationship *Zh* = 300*R*1.4 could potentially be employed for QPE in Beijing. For convective rain, both *Zh* = 250*R*1.2 and *Zh* = 368*R*1.21 will underestimate the rainfall intensities, likely due to the smaller diameter and higher number concentration of raindrops in these two climate regions than in Beijing (as detailed in Section 3.2). Compared with *Zh* = 300*R*1.4, *Zh* = 200*R*1.6 has relatively larger discrepancy compared to our result.

Although a suitable *Zh*–*R* relationship can be helpful to retrieve rain rate from radar reflectivity, the dispersion of samples in *Zh*–*R* domain is still large. For example, for a given *Zh* = 103 mm6 m−3, *R* can range from 0.5–10 mm h−<sup>1</sup> (Figure 8). To further investigate the essence of *Zh*–*R* relationships from a microphysical point of view, the scatter distribution of *Zh*–*R* pairs are color coded by *D*<sup>0</sup> and log10 *Nw* in Figure 9a,b. It is concluded that DSDs can be further grouped in size or number concentration in *Zh*–*R* domain, which means the QPE could be further improved when considering more physical observables.

**Figure 9.** Scatterplots of *Zh* (mm<sup>6</sup> <sup>m</sup><sup>−</sup>3) vs. *<sup>R</sup>* (mm h<sup>−</sup>1) color coded by (**a**) *<sup>D</sup>*0, (**b**) log10 *Nw*, (**c**) *<sup>K</sup>*DP, and (**d**) *Z*DR. The *Zh* = 300*R*1.4 dashed line is superimposed for reference.

In addition, dual-polarization radar variables are computed using the *T*-matrix method. The polarimetric measurements are proven to be capable of improving the performance of QPE. Figure 9c,d show the distribution of *Zh* versus *R*, color coded by *K*DP and *Z*DR, respectively. Overall, similar variation patterns can be seen compared with Figure 9a,b. This is not surprising, since *D*<sup>0</sup> and log10 *Nw* can essentially be derived from the combination of *Zh*, *Z*DR, and *K*DP [34,45,61].

The distributions of *ZH*, *Z*DR, and *K*DP are illustrated in Figure 10. It should be noted again that *ZH* in dBZ is used in Figure 10a, while QPE estimators are fitted using *Zh* in linear scale. The details of boxplot in the center of each panel are listed in Table 3. The median value of *ZH* is about 20 dBZ, and the number of *ZH* higher than 40 dBZ is less than 5%. A large amount of *K*DP are smaller than 0.1 ◦ km−1. The distribution of each parameter has two peaks: The first peak of *ZH* and *K*DP is close to their median values, while the second peaks are at about 27.5 dBZ and 0.07 ◦ km−1, respectively. The two peaks of *Z*DR are about 0.13 and 0.45 dB, and the median value lies between the two peaks.

**Figure 10.** The distributions of (**a**) *ZH*, (**b**) *Z*DR, and (**c**) *K*DP derived from DSD measurements using the *T*-matrix scattering approach.


**Table 3.** The quantiles of polarization radar variables derived from DSDs using the *T*-matrix scattering method.

This study also derived the polarimetric radar rainfall relations *R*dpr(*Zh*,*Z*DR), *R*dpr(*K*DP,*Z*DR), and *R*dpr(*K*DP) using the least-squares method and compared with the *Zh*–*R* relationships. Here, the subscript "dpr" represents Dual-Polarization Radar for short. The obtained estimators based on the total DSD dataset are listed as follows:

$$R\_{\rm dpr}(Z\_h, Z\_{\rm DR}) = a Z\_h^{\beta} 10^{\gamma Z\_{\rm DR}},\tag{15}$$

$$R\_{\rm dpr}(K\_{\rm DP}, Z\_{\rm D\mathcal{R}}) = aK\_{\rm DP}^{\beta} 10^{\chi Z\_{\rm D\mathcal{R}}},\tag{16}$$

$$R\_{\rm dpr}(K\_{\rm DP}) = \alpha K\_{\rm DP'}^{\beta} \tag{17}$$

$$R\_{\rm dpr}(Z\_h) = \alpha Z\_{h'}^{\beta} \tag{18}$$

where α, β, and γ are generic coefficients and exponents in each relation. The specific values are listed in Table 4.

**Table 4.** The fitted parameters of radar QPE estimators (Equations (15)–(18)) derived using the total DSD dataset.


In order to evaluate the application performance of various QPE estimators, the hourly rainfall amount (mm) derived using each radar rainfall relation is compared with collocated rain gauge observations (distance between disdrometer and gauge is less than 10 m). Figure 11a–d shows the scatter plots of rainfall estimated using radar relations versus gauge measurements. In addition, a set of evaluation metrics, including the Pearson correlation coefficient (PCC), standard deviation (STD), normalized mean absolute error (NMAE), and root-mean-square error (RMSE) are computed and indicated in Figure 11.

Obviously, *R*dpr(*Zh*,*Z*DR) performs the best in terms of all evaluation metrics, followed by *R*dpr(*K*DP,*Z*DR), *R*dpr(*K*DP), and then *R*dpr(*Zh*). The estimated hourly rainfall amount from *R*dpr(*Zh*,*Z*DR) (Figure 11a) is the closest to rain gauge measurements at low intensities. However, *R*dpr(*K*DP,*Z*DR) provides the best estimation at higher rainfall intensities, especially during severe precipitation hours.

Recent studies [5,6] demonstrated that the combination of different estimators may improve the accuracy of QPE. However, their achievements were mainly based on S-band radar measurements. In this study, we attempted to extend this strategy to X-band applications. Similar thresholds to the Dual-Polarization Radar Operational Processing System version 2 (DROPS2) [5] are used at X-band: *ZH* = 37 dBZ, *Z*DR = 0.185 dB, and *K*DP = 0.03 ◦ km−1. For clarification, this paper referred to the implemented DROPS2.0 architecture as *R*dpr(DROPS2–X). As expected, *R*dpr(DROPS2–X) (Figure 11e) provides the best results among various rainfall relations, which demonstrates the feasibility of the thresholds applied on X-band dual-polarization radar variables. Compared with Figure 11b, *R*dpr(DROPS2–X) inherits the advantage of *R*dpr(*K*DP,*Z*DR) for all severe precipitation hours. Nevertheless, it should be noted that except *R*dpr(*Zh*), the differences among all other QPE estimators are not distinct: All have PCC higher than 0.98, STD and RMSE smaller than 1.0, and NMAE smaller than 0.2.

**Figure 11.** Scattergram (based on the total rainfall observations) of hourly rainfall estimates (mm) from various radar rainfall relations vs. rain gauge measurements: (**a**) *R*dpr(*Zh*,*Z*DR), (**b**) *R*dpr(*K*DP,*Z*DR), (**c**) *R*dpr(*K*DP), (**d**) *R*dpr(*Zh*), and (**e**) *R*dpr(DROPS2–X). The grey diagonal straight line in each panel represents the 1–1 relationship. The quantitative evaluation results are also indicated in each panel, including the Pearson correlation coefficient (PCC), standard deviation (STD—mm), normalized mean absolute error (NMAE), and root-mean-square error (RMSE—mm).
