*3.2. Statistical Properties of Nw–D*<sup>0</sup>

*Nw* and *D*<sup>0</sup> are two main parameters defining the DSD [46,47], which also play an important role in retrieving precipitation microphysics on a global scale as part of the GPM mission [48,49]. In fact, major microphysical processes that dominate the DSD properties can partially be recognized in the log10 *Nw*–*D*<sup>0</sup> domain [46]. The distribution of log10 *Nw* vs *D*<sup>0</sup> is also an indicator to separate convective

and stratiform rain types (C−S). In this study, the separation scheme described in Bringi et al. [50] (hereafter referred to as BR09) is adopted, as shown in Equation (13). Briefly, *Nw*–*D*<sup>0</sup> pairs above (below) Equation (13) are recognized as convective (stratiform) rain,

$$
\log\_{10} N\_w^{\text{BRO9}} = -1.6 D\_0 + 6.3. \tag{13}
$$

By using C\_BR09 and S\_BR09 to, respectively, denote the convective and stratiform rain, classified by Equation (13), Table 2 summaries a series of DSD parameters for different rainfall types. There are 1488 (24011) minutes of DSDs classified as convective (stratiform) rain, which account for 5.8% (94.2%) of the entire dataset of occurance and correspond to 54.8% (45.2%) of total rainfall amount. Generally, the means of all DSD parameters for C\_BR09 are higher than those for S\_BR09.


**Table 2.** Properties of DSDs for different rain-type classification schemes.

Note: Rain types and classification schemes are listed in the first row. 'C'/'S' indicates convective/stratiform rain, whereas 'BR09', 'BR03' and 'TE01' represent the classification schemes developed by Bringi et al. [50], Bringi et al. [51], and Testud et al. [52], respectively. For example, C\_BR09 and S\_BR09 correspond to convective and stratiform rain classified by BR09 scheme. The number of spectra (occurrence), as well as their proportion of the entire dataset are given before and after the '/' in row 2. Row 3 is same as row 2, but for the rainfall amount. The 1th and 99th quantiles of rain rate for each dataset are listed before and after the '/' in row 5. Angle bracket stands for the sample mean.

Figure 4 shows the scatterplot of log10 *Nw* versus *D*<sup>0</sup> for convective (C\_All, orange) and stratiform (S\_All, lime) rain types, as well as the corresponding relative occurance frequency. The mean (MEAN), standard deviation (STD) and skewness (SKEW) are also indicated in Figure 4. Here, C\_All (S\_All) dataset equals to the dataset of C\_BR09 (S\_BR09) denoted in Table 2. Equation (13) are superimporsed in the scatterplot panel (dashed line). Meanwhile, another C−S separation line suggested by Thompson et al. [53] (hereafter referred to as TH15) for oceanic, tropical rain regions is also superimposed (dot-dashed line) for reference. Equation (14) shows the formula of TH15,

$$
\log\_{10} N\_w^{\text{TH15}} = 3.85. \tag{14}
$$

Stratiform samples (S\_All) are concentrated near the MEAN values of *D*<sup>0</sup> = 1.01 mm and log10 *Nw* = 3.57, whereas convective samples (C\_All) are sparsely distributed above the BR09 line. It results in larger STD of *D*<sup>0</sup> and log10 *Nw* for convective than stratiform rain. The *D*<sup>0</sup> histograms for both rain types are positively skewed, whereas the log10 *Nw* histograms for convective rain exhibit a negative skewness of −0.93. Compared with stratiform rain, the *D*<sup>0</sup> and log10 *Nw* histograms for convective rain tend to shift toward larger values, which are in agreement with previous studies for other climate regimes [10,11,51]. Similar variation tendencies of *D*<sup>0</sup> and log10 *Nw* histograms between "Total" dataset (blue) and stratiform rain can be found, which are due to the dominant role of stratiform rain.

**Figure 4.** Scatterplot of log10 *Nw* vs. *D*<sup>0</sup> for stratiform (S\_All, lime) and convective (C\_All, orange) rain in the bottom left panel, as well as the corresponding relative frequency histograms in the top and bottom right panels. The unit of *Nw* is m−<sup>3</sup> mm<sup>−</sup>1. Rain types were classified by BR09 scheme. The C\_All (S\_All) dataset equals to the dataset of C\_BR09 (S\_BR09) denoted in Table 2. Blue curves in each histogram indicate the relative frequency of the entire dataset for log10 *Nw* and *D*0. The mean (MEAN), standard deviation (STD) and skewness (SKEW) for the entire dataset, stratiform rain and convective rain are shown in colors in each histogram panel, whereas the MEAN values of log10 *Nw* vs. *D*<sup>0</sup> together with the respective ±1 × STD values are plotted as error bars. The dashed and dot-dashed grey lines represent the C−S separation lines of BR09 and TH15, respectively.

The normalized frequency of DSD sample occurrence is shown in Figure 5. Note that the TH15 line in *W*–*D*<sup>0</sup> domain (Figure 5b) can be generated by combining Equation (7) and (14). The highest frequency of occurrence is in the ranges of *D*<sup>0</sup> about 0.8–1.1 mm and log10 *Nw* about 3.2–4.1, corresponding to rainwater content *W* within 0.02–0.11 g m<sup>−</sup>3. The distribution of normalized frequency of DSD in both log10 *Nw*–*D*<sup>0</sup> and *W*–*D*<sup>0</sup> domains are similar to the analyses in Dolan et al. [46] (their Figure 2b,e) in the midlatitudes. Therefore, this study provides new evidence from midlatitude Asian (northern China) to further support such analysis.

**Figure 5.** Normalized occurrence frequency of DSD sample in (**a**) log10 *Nw* − *D*<sup>0</sup> and (**b**) *W* − *D*<sup>0</sup> domains. The dashed and dot-dashed lines represent the C−S separation lines from BR09 and TH15, respectively.

In Figure 6, the log10 *Nw* − *D*<sup>0</sup> pairs are color coded by rain rate *R* and *ZH* to investigate the interrelations among them. Similar patterns can be found in Figure 6a,b that the increases of both *R* and *ZH* are proportional to the increases of log10 *Nw* and *D*0, illustrating the internal relation between rain rate and radar reflectivity, or the *Zh*–*R* relationship that will be discussed in Section 4. The TH15 line crosses all levels of *R* and *ZH*, whereas BR09 line is almost equivalent to a threshold of *R* (8.6 mm h<sup>−</sup>1) or *ZH* (36.8 dBZ). Similar conclusion has been drawn for tropical, maritime regions with *R* = 10 mm h−<sup>1</sup> and *ZH* = 40 dBZ [53], which are slightly higher than our results.

**Figure 6.** Scatterplots of log10 *Nw* vs. *D*<sup>0</sup> color coded by (**a**) *R* and (**b**) *ZH*. The units of *R* and *ZH* are in mm h−<sup>1</sup> and dBZ, respectively. The dashed and dot-dashed lines represent the C−S separation lines from BR09 and TH15, respectively.

Interestingly, fewer DSD samples fell within log10 *Nw* > 4 and *D*<sup>0</sup> > 1 mm (see Figures 4–6) compared to the results observed during the Asian Summer Monsoon Season in Eastrn [14] (their Figure 6) or Southern China [54] (their Figure 6), and in tropical, oceanic islands [53] (their Figure 14a,b). In addition, more DSD samples exist in the range above BR09 line but below TH15 line. Referring to Dolan et al. [46] and Bringi et al. [51], warm rain with the collision-coalescence process has a great contribution to the precipitation in Eastern and Southern China during the Asian Summer Monsoon Season and tropical, oceanic regions. On the contrary, mixed phase precipitaiton processes may dominante the rainfall microphysics near the disdrometer site in Beijing. The enhanced mixed phase precipitation processes can produce larger raindrops when the ice-based hydrometers melt, which need to be further investigated in future.

*Remote Sens.* **2019**, *11*, 1479

Datasets for convective and stratiform rain are further divided into months, as shown in the log10 *Nw*–*D*<sup>0</sup> domain in Figure 7, to see the monthly variations in DSD and better compare with previous findings. For stratiform rain, the MEAN values of log10 *Nw* and *D*<sup>0</sup> in each month are all concentrated near the highest frequency of occurrences (Figure 5a), which corresponds to the "ambiguous" area in Figure 12 shown in reference [46]. For convective rain, those values are distributed in a larger range from the mixed area to the ice-based area (from April to August), as well as aggregation/riming area (September and October) in Figure 12 from Dolan et al. [46]. Note that for convective rain the MEAN values of log10 *Nw*–*D*<sup>0</sup> pairs in months from May to August are almost all around the value of 3.61 and 2.03 mm for C\_All dataset with minor variations. Their STD values are also similar, which means similar microphysical processes dominated the precipitation during these months. However, such characteristics are not observed in other months. Relatively larger log10 *Nw* and smaller *D*<sup>0</sup> indicate relatively more warm rain processes in April, while in September and October obviously lower log10 *Nw* and larger *D*<sup>0</sup> indicate the relatively intense ice-based processes, such as aggregation and riming that sharply exhausting the number of small size hydrometers but slowly increasing the size of drops. Such analyses demonstrate the seasonal variation of dominating microphysical processes in Beijing. Overall, all MEAN values for both rain types in each month are below the TH15 line, illustrating that different microphysical processes are dominating the precipitation between midlatitude and Eastern and Southern China during the Asian Summer Monsoon Season, as well as tropical, oceanic regions.

**Figure 7.** The MEAN values of log10 *Nw* vs. *D*<sup>0</sup> together with the respective ± 1 × STD values plotted as error bars for convective (triangle) and stratiform (square) rain. The dataset for both rain types, including all data, are plotted in black, whereas the monthly results are indicated by different colors. The dashed and dot-dashed lines represent the C−S separation lines from BR09 and TH15, respectively.
