*3.2. Microphysical Characteristics of Precipitation in Di*ff*erent Seasons*

Figure 5 is the distribution of different diameters with varying velocities obtained in different seasons. In spring, summer and autumn, the majority of raindrop particles are in an area close to the theoretical curve proposed by Beard [45]; in winter, the data is accumulated in low levels of both *v* and *D*. Data are overall lying over the theoretical curve in spring, summer and autumn; in winter, however, the velocities are underestimated compared to the theoretical curve in winter. This is because the type of rainfalls during winter was mainly snow (regarded as solid rainfalls) and could cause deviation in call speed, and the raindrop data with D > 6 mm are excluded as shown in Section 2.3.

**Figure 5.** Plots of measured raindrop terminal velocity-diameter relationships in different seasons. The red curve is derived by Beard [45] in 1976, giving the relationships between *v* and *D*, and used as the reference line for the *v-D* distribution in each season (**a**) spring; (**b**) summer; (**c**) autumn; (**d**) winter.

Figure 6 shows the histogram of *Dm* and log10*Nw* in different seasons and precipitation types. The yearly average *Dm* and log10*Nw* are 1.41 and 3.91 mm, respectively. The average *Dm* of stratiform (convective) rain from small to large is 1.38 mm (1.46 mm) in summer, 1.46 mm (1.52 mm) in spring and 1.51 mm (1.57 mm) in autumn. However, there is less variation in average log10*Nw* data among the three seasons. The average log10*Nw* of stratiform rain from small to large is 3.88 mm in summer, 3.89 mm in autumn and 3.92 in spring. However, the maximum of the average log10*Nw* of convective rain is 4.28 in summer. This reflects the micro-physical characteristics of rainfall in Yulin area: according to the results shown in Section 3.1, the average rainfall intensity is larger in summer than in spring and autumn. According to Equation (5), the rain intensity is related to raindrop diameter and DSD. The average *Dm* of different precipitation types in different seasons shows that for stratiform rain, *R* is affected more by the raindrop diameter; for convective rain, *R* is affected more by DSD. The average value of *Dm* is slightly less than that of in southern China (1.46 mm) [10].

Besides the average value, standard deviation and skewness of different *Dm* and log10*Nw* were also calculated. The standard deviation of *Dm* in stratiform and convective rain among different seasons varies from 0.19 mm to 0.26 mm. The skewness of *Dm* and *Nw* in stratiform and convective rain are less than 0 in spring and autumn, illustrating the frequency of the data below the *Dm* mean (*Nw* mean) is less than data above the *Dm* mean (*Nw* mean). However, the skewness of *Dm* and *Nw* in stratiform and convective rain in summer are larger than 0, illustrating the frequency of the data below the *Dm* mean (*Nw* mean) is more than data above the *Dm* mean (*Nw* mean).

**Figure 6.** Frequency histogram of mass-weighted median diameter *Dm* and the denary logarithm of *Nw* in different precipitation types and different seasons calculated from the data measured by OTT Parsivel-2. (**a**) Histogram in stratiform rain in spring; (**b**) Histogram in convective rain in spring; (**c**) Histogram in stratiform rain in summer; (**d**) Histogram in convective rain in summer; (**e**) Histogram in stratiform rain in autumn; (**f**) Histogram in convective rain in autumn. The average value, standard deviation and skewness are also given for *Dm* and *Nw* in each plot.

Figure 7 shows the *Nw-R* relationships in different seasons and precipitation types. The base-10 logarithm of *Nw* is used to fit the relationship curves log10*Nw* = c*R*d, in which c and d are parameters fitted by measured data. For the error bars in each panel, *R* in the range (0.5, 5) (for stratiform rain) are divided into nine intervals evenly, and in the range (5, 35) (for convective rain) are divided into five intervals (5 < *R* < 10, 10 < *R* < 15, 15 < *R* < 20, 20 < *R* < 25 and *R* >25 mm·h−1), and error bars are used for each interval. The error bars for each interval are based on the mean value of *R* and log10*Nw*, with the ±1 Stdev (standard deviation), respectively. A significance analysis of fitting results is also proposed [46]. The p-values in each panel of Figure 7 are derived from the fitting tests of the power function. The p-values show that the fits for stratiform rain are statistically relevant and sound (shown in Figure 7a,c,e). When comparing the disparity in precipitation types, parameters c and d have a smaller range in variability in different seasons. Figure 7a,c,e indicate that for stratiform rain, the difference of parameter c among different seasons ranges in 3.73–3.79 (*p* < 0.05). However, the parameter c for convective rain varies in a larger range of 3.86–4.14 (*p* < 0.1). For each season, the parameter a of stratiform rain is smaller than that of convective rain. The difference in parameter d is small among different seasons, and the d of stratiform rain is larger than that of convective rain.

**Figure 7.** *Nw*-*R* relationships for different precipitation types in different seasons. The fitted power formula based on the least-squares method is also shown in each plot: (**a**) stratiform rain in spring; (**b**) convective rain in spring; (**c**) stratiform rain in summer; (**d**) convective rain in summer; (**e**) stratiform rain in autumn (**f**) convective rain in autumn.

#### *3.3. Z-R Relationships in Di*ff*erent Rainfall Events*

Three rainfall events were selected to illustrate the differences between the data measured by OTT Parsivel-2 Disdrometer and four TE525MM Rainfall Gauges. The three events are, respectively, chosen from each season, regarding their representation of different levels of rainfall intensity (all of the three events last for > 4h and include stratiform and convective records).

Table 2 shows the precipitation characteristics of these rainfall events. S/C records show the relative rates of amounts of the stratiform and the convective records during the selected rainfall events, for which Event 1, 2 and 3 are 662%, 888% and 753%, respectively. The results correspond to the average rainfall intensity *<sup>R</sup>* of each rainfall event. Event 2 is with the least *<sup>R</sup>* (2.42 mm·h<sup>−</sup>1), while Event 1 is with the highest *<sup>R</sup>* (3.07 mm·h<sup>−</sup>1).


**Table 2.** Precipitation characteristics of selected three rainfall events.

\* Derived from disdrometer-measured raindrop spectra. See in Equation (5). \*\* Obtained by the four rainfall gauges and averaged.

Figure 8 shows the difference in *Z-R* relationships of the three rainfall events of spring, summer and autumn, and the results are *Z* = 109.6*R*2.1 (Event 1), *Z* = 119.0*R*1.8 (Event 2) and *Z* = 78.3*R*1.9 (Event 3). The parameter a of each of the three rainfall events is less than the parameter a of the default *Z-R* relationship [47] (*Z* = 300*R*1.4, where parameter a is equal to 300). Parameter b in *Z* = a*R*<sup>b</sup> has only slight difference among different rainfall events, and ranges in 1.8–2.1 (*p* < 0.05). This is consistent with previous studies [48–51], that parameter b in *Z* = a*R*<sup>b</sup> varies in the range of 1–2.87 (*p* < 0.05). The raindrop spectra have obvious changes for different precipitation types, causing the parameters of *Z-R* relationships to vary. It is clear that the *Z-R* relationships of rainfall events vary depending on the season and the precipitation types. The rainfall events with a higher S/C rate tend to have a higher average rainfall intensity. Therefore, precipitation estimates for different types should be treated as such. The results indicate that there is a need to utilize modified *Z-R* relationships in different seasons when calculating the rainfall intensity by the QPE method.
