**3. Result**

### *3.1. Statistical Characteristics*

Table 3 shows the maximum, mean and standard deviation (SD) of *R*, *D*m and *N*T calculated by using 1 min DSD disdromter samples in different seasons. The maximum rainfall rate of 56.643 mm h−<sup>1</sup> was in the premonsoon season, indicating that the strongest convective precipitation occurred in the premonsoon season. The mean *R* was highest in the monsoon season, followed by the premonsoon season, and the weakest in winter. The sequence was in line with that of the accumulated rainfall amount in the four seasons. The low value of SD in all the seasons indicated a small variation in precipitation intensity in Mêdog. The lowest SD in winter may be related to uniform stratiform precipitation and minimal convective precipitation. The higher SD was more or less in the premonsoon and monsoon seasons, showing that convective precipitation mainly occurred in the two seasons.


**Table 3.** Maximum, mean and standard deviation of *R*, *D*m and *N*T during the four seasons.

The maximum, mean and SD of *D*m were found to be larger in the premonsoon season, which indicates stronger convective actions. During the monsoon season, the mean and SD of *D*m were smaller, probably due to precipitation dominated by warm rain processes and the relative consistency of precipitation [3,24]. The maximum, mean and SD of *N*T were the highest in the monsoon season, which indicates that the raindrop concentration was the highest with larger dispersion.

In general, the monsoon exhibited the largest values for the mean and SD of *R*, the smallest values for the mean and SD of *D*m, and the highest values for the maximum, mean and SD of *N*T. All these features showed that rainfall during the monsoon period is characterized by abundant, smaller drops, which may be attributed to the sufficient warm and humid air flows from the Indian Ocean. In addition, the *D*m of premonsoon precipitation registered larger values in the maximum, mean and SD, as well as the highest value of the maximum *R*. Therefore, stronger convective activities probably occurred in the premonsoon season.

### *3.2. Seasonal Variation in DSDs*

Figure 4 shows the DSDs of different seasons from mean spectra. Drops with *D* ≤ 1 mm were regarded as small raindrops, *D* > 3 mm as large raindrops, and 1 < *D* ≤ 3 mm as medium raindrops [18]. As seen from Figure 4, the DSDs in Mêdog exhibited bimodal distribution with peaks at 0.4 mm and 1.1 mm. This characteristic of the multipeak raindrop spectrum has been discussed [35]. In terms of small raindrops, the highest concentration was in the monsoon season and the lowest was in winter, and the premonsoon season was similar to the postmonsoon season. As raindrop diameter increased, the concentration of medium raindrops was slightly higher in the monsoon and premonsoon seasons than in the postmonsoon and winter seasons. The concentration of large raindrops was the highest (lowest) in the premonsoon (monsoon) season. The results showing that the concentration of large (small) raindrops was the highest in the premonsoon season (monsoon) were consistent with those found in tropical coastal areas, which are also dominated by the Indian Ocean monsoon in summer [3]. Unlike the SCS, Zeng et al. [18] reported that small drops predominate in precipitation during the premonsoon period, while large drops prevail in the postmonsoon season.

To further analyze the DSD characteristics in different seasons, the DSD data used in this study were divided into six categories, as shown in Table 2. The DSDs of different rainfall rate categories from mean spectra for different seasons are shown in Figure 5. As the rainfall rate increased, the spectra width in all seasons became wider, and the difference in DSDs among the four seasons gradually increased. For *R* ≤ 5 mm h−<sup>1</sup> (usually corresponding to stratiform precipitation [13]), the concentration of large raindrops was the highest in winter. Precipitation with *R* ≥ 10 mm h−<sup>1</sup> (usually corresponding to convective rainfall [36,37]) occurred mainly in the premonsoon and monsoon seasons. The concentration of large raindrops in the premonsoon season was significantly greater than that in the monsoon season, indicating stronger convective rainfall in the premonsoon season.

**Figure 4.** Averaged DSDs during the four seasons.

**Figure 5.** Averaged DSDs for different rain rate categories. (**a**) R1: 0.1 ≤ *R* < 1 mm <sup>h</sup>−1, (**b**) R2: 1 ≤ *R* < 2 mm <sup>h</sup>−1, (**c**) R3: 2 ≤ *R* < 5 mm <sup>h</sup>−1, (**d**) R4: 5 ≤ *R* < 10 mm <sup>h</sup>−1, (**e**) R5: 10 ≤ *R <* 20 mm h−<sup>1</sup> and (**f**) R6: *R* ≥ 20 mm h−1.

Table 4 gives the average rainfall microphysical parameters for each of the six rainfall rate categories from 1 min DSD samples in different seasons. The mean values of *Z*, LWC, *N*T and *D*m increased with increasing rain rate in all seasons. The log10(*N*w) tended to decrease with the increasing rain rate in winter, indicating that the increase in precipitation intensity was mainly attributed to the increase in raindrop size. During other periods, log10(*N*w) tended to increase with increasing rain rate until *R* > 20 mm h−1. For the same rainfall rate categories, monsoon precipitation was characterized by the smallest mean *D*m value and the highest mean log10(*N*w) value.


**Table 4.** Average rainfall microphysical parameters for each of the six rainfall rate classes in the winter, premonsoon, monsoon and postmonsoon seasons.

### *3.3. Distribution of Dm, R, and NT*

Figure 6 shows the percentage of occurrence (bar) and relative contribution to the total rainfall (line) for the different *D*m bins in the four seasons. Mêdog rainfall in all the seasons was dominated by raindrops with *D*m < 2 mm. The distribution of the occurrence frequency of *D*m was similar in all seasons except for a slight difference in the premonsoon season. The occurrence frequency of Dm1 was the highest, followed by Dm2 for all four seasons. During the winter, monsoon and postmonsoon seasons, the occurrence percentage of Dm1 was more than 60%, whereas it was less than 60% during the premonsoon period. On the other hand, the percentage occurrence of Dm2 was more than 40% in the premonsoon season, while it was approximately 30% in the other three seasons. The deceased Dm1 in the premonsoon season was compensated by the increase in Dm2. This result indicated that the occurrence frequency of larger raindrops was higher in the premonsoon season than in the other three seasons.

The distribution of the relative contribution to the rainfall totals was different from that of the occurrence frequency. The Dm2 category produced a greater contribution to rainfall by 50–70%, although it had a lower occurrence frequency than the Dm1 category. The rainfall rate was proportional to the third power of raindrop diameter. The larger raindrops with 2 ≤ *D*m < 3 mm only contributed to the total rainfall by approximately 5% in the winter and premonsoon seasons, and there were hardly any larger raindrops with 2 ≤ *D*m < 3 mm during the monsoon and postmonsoon periods.

**Figure 6.** Percentages of occurrence (bar) and relative contributions to the total rainfall (line) from the different *D*m bins in the four seasons: winter (**a**), premonsoon (**b**), monsoon (**c**) and postmonsoon (**d**).

The percentage of occurrence (bar) and relative contribution to the total rainfall (line) from the different rain rate categories in the four seasons are shown in Figure 7. Weak rainfall with *R* < 1 mm h−<sup>1</sup> was dominant in the four seasons, which was evident from the occurrence frequency of the R1 category exceeding 60%, especially more than 80% in the winter season. The occurrence frequencies of R2 and R3 were higher in the monsoon season than in the other three seasons. Considering the relative contribution to total rainfall, the relative contribution to rainfall by R1 was largest and exceeded 60% in the winter season. Similarly, the R1 category also made the largest relative contribution to rainfall in the postmonsoon season. However, the relative contributions to rainfall by the R1, R2, and R3 categories were comparable in the premonsoon season. During the monsoon season, the R3 category made the highest contribution to total rainfall, although its occurrence frequency was lower than that of the R1 and R2 categories.

**Figure 7.** Percentages of occurrence (bar) and relative contributions to the total rainfall (line) from the different *R* bins in the four seasons: winter (**a**), premonsoon (**b**), monsoon (**c**) and postmonsoon (**d**).

Figure 8 shows the percentage of occurrence (bar) and relative contribution to the total rainfall (line) from the different *N*T classes in the four seasons. The occurrence frequencies decreased with the increase in drop number, and the NT1 class predominated in the four seasons. The drop concentration in Mêdog was mostly below 250 m<sup>−</sup>3, followed by 250–500 m<sup>−</sup>3, and a drop concentration of more than 1000 m<sup>−</sup><sup>3</sup> rarely occurred. The occurrence frequency of NT1 was lower in the monsoon season (approximately 57%) than in the other three seasons (an average of approximately 88%), and the occurrence frequency of NT2 in the monsoon season (approximately 30%) was higher than in the other three seasons (an average of approximately 9.5%). The relative contribution to the total rainfall

monotonically decreased with increasing *N*T in all seasons except the monsoon season. During the monsoon season, NT2 made a larger relative contribution (38%) to the total rainfall than the NT1 class (28%).

**Figure 8.** Percentages of occurrence (bar) and relative contributions to the total rainfall (line) from the different *N*T bins in the four seasons: winter (**a**), premonsoon (**b**), monsoon (**c**) and postmonsoon (**d**).

### *3.4. Characteristics of DSDs in Stratiform and Convective Rainfall*

Previous studies have shown that the microphysical process of stratiform rainfall is significantly different from that of convective rainfall [34,38]. Therefore, the 1 min DSD samples were classified into stratiform rainfall and convective rainfall. Consequently, the stratiform/convective precipitation samples/percentages were 6130/5 (99.6%/0.1%), 24,155/286 (97.1%/1.1%), 33,468/763 (94.2%/2.1%) and 6930/69 (97.1%1.0%) in the winter, premonsoon, monsoon and postmonsoon seasons, respectively. Considering only five samples, the DSD of convective rainfall in winter was not considered.

Figure 9 shows the DSDs of stratiform rainfall and convective rainfall from mean spectra during different periods. Compared to stratiform rainfall, convective rainfall had a broader spectrum width and a higher concentration of drops. Bimodal distribution could also be seen in both DSDs of stratiform rain and convective rain, and the concentration of the second peak at 1.1 mm was comparable to that of the first peak at 0.4 mm for convective rainfall.

**Figure 9.** The mean DSDs of stratiform rain (**a**) and convective rain (**b**) for different seasons.

For stratiform rainfall (Figure 9a), the DSD peaked at 0.4 mm in all four seasons and then decreased rapidly. The precipitation in the monsoon season (winter) was characterized by a higher (lower) concentration of drops with sizes less than 1.1 mm. The winter and premonsoon precipitation had higher concentrations of drops with sizes larger than 2.1 mm than the monsoon and postmonsoon precipitation. The precipitation in the four seasons had comparable concentrations of drops with diameters of 1.1–2.1 mm. For convective rainfall (Figure 9b), the highest concentration of raindrop diameters less than 1.1 mm occurred in the monsoon season, and the highest concentration of drops larger than 1.7 mm appeared in the premonsoon season. On the other hand, convective rain in the monsoon season had the lowest concentration of larger drops with *D* > 2 mm, and the lowest concentration of small drops occurred in the premonsoon season. The concentrations of raindrops with sizes of 1.1–1.7 mm were very similar for the three seasons considered.

The average microphysical parameters of stratiform rain and convective rain from 1 min DSD samples during the four periods are given in Table 5. For stratiform rain, the mean LWC, *N*T, *R*, *N* w and *μ* were the highest in the monsoon season. The largest mean *D* m value was observed in the premonsoon season, followed by the winter season, and the smallest mean *D* m value was observed in the monsoon season. The highest mean *Z* in the premonsoon season was mainly attributed to the largest *D* m because the reflectivity factor is proportional to the sixth power of drop diameter. During the winter period, the lowest mean *R* and LWC were probably related to the lowest concentration of drops. For convective rain, the mean *R*, *Z*, LWC and *D* m were the largest in the premonsoon period. The highest mean values of *N*T, *N* w and *μ* were found in the monsoon period, followed by the postmonsoon period, and the lowest mean values of *N*T and *N* w were found in the premonsoon period.

**Table 5.** The average microphysical parameters of stratiform rain and convective rain in different seasons.


Figure 10 shows the average log10(*N* w) versus average *D* m value (along with ±σ SD bars) for stratiform rain and convective rain during different periods. The two outlined squares represent the maritime-like and continental-like convective events reported by Bringi et al. [34]. In general, the average *D* m versus average log10(*N* w) showed evident seasonal differences in Mêdog. In terms of convective rain, monsoon precipitation had the smallest (highest) mean *D* m (log10(*N* w)) value of 1.26 mm (4.14), while premonsoon precipitation was characterized by the largest (lowest) mean *D* m (log10(*N* w)) value of 1.67 mm (3.70). Convective rain in the monsoon and postmonsoon seasons was similar to maritime-like events, exhibiting smaller *D* m and higher log10(*N* w). The convective precipitation during the monsoon and postmonsoon seasons also conformed to the C–S separation line from Thompson et al. [5] for the tropics. Convective events during the premonsoon period were considered to be between maritime- and continental-like events. For stratiform rain, the average *D* m versus log10(*N* w) values appeared on the left side (underside) of the C–S separation line, as reported by Bringi et al. [34] (Thompson et al. [5]). The differences in the mean *D* m values among the four seasons were relatively slight, whereas the mean log10(*N* w) displayed an evident discrepancy. For example, the mean

log10(*N*w) value of 3.75 in the monsoon season was much higher than that in the winter period, with a value of 3.28.

**Figure 10.** Scatterplots of averaged log10(*N*w) versus *D*m (along with ±σ standard deviation bars) for stratiform (blank symbols) and convective (full symbols) precipitation in Mêdog (circles), SCS (squares), Nanjing (diamond) and Beijing (star) during the winter (green), premonsoon (purple), monsoon (red) and postmonsoon (blue) seasons. The two outlined squares represent (left) the maritime and (right) continental types of convective systems reported by Bringi et al. [34]. The dotted line and dashed lines represent the C–S separation line by Bringi et al. [34] and Thompson et al. [5].

For comparison with other regions in China, Figure 10 is also superimposed with the mean *D*m and log10(*N*w) values of different seasons from previous studies, including the SCS [18], Nanjing [39] and Beijing [40]. Compared with these regions, the stratiform precipitation in Mêdog showed smaller mean *D*m and mean log10(*N*w) values in all seasons, except the monsoon season, which had a similar mean log10(*N*w) value. The mean *D*m value of the premonsoon convective precipitation in Mêdog was similar to that in the SCS, and the mean log10(*N*w) value was similar to that in Beijing. Mêdog convective rain in the monsoon season was similar to Nanjing, which may have been due to abundant water vapor in the two regions during this period. The mean *D*m (log10(*N*w)) of Mêdog convective rain was much smaller (higher) than that in the SCS and Beijing in the monsoon season. This finding was probably related to the predominant warm (cold) rain processes in Mêdog (SCS and Beijing). Similarly, the postmonsoon convective cluster in Mêdog was similar to Nanjing but had a smaller (higher) *D*m (log10(*N*w)) than Beijing and the SCS.

### *3.5. The μ–*Λ *Relationships*

The *μ*–Λ relationship is closely related to the DSD and varies with rain types, climatic characteristics and terrain [38,41]. Zhang et al. [38] proposed the quadratic fitting formula in Florida as follows:

$$
\Lambda = 0.0365 \,\mu^2 + 0.735 \,\mu + 1.935 \,\tag{16}
$$

To minimize the scatter, the samples in Mêdog with rain rates > 5 mm h−<sup>1</sup> and drop counts > 300 were used to derive *μ* and Λ [15,38]. Figure 11 shows the scatterplots of *μ* and Λ for three seasons due to minimal convective precipitation in winter. The fitted *μ–*Λ relationships for the premonsoon, monsoon and postmonsoon periods are given as follows:

$$
\Lambda = 0.0148 \,\mu^2 + 0.786 \,\mu + 1.916 \,\tag{17}
$$

$$
\Lambda = 0.0056 \,\mu^2 + 0.949 \,\mu + 1.716,\tag{18}
$$

and

$$
\Lambda = 0.0250 \,\mu^2 + 0.665 \,\mu + 2.674. \tag{19}
$$

The *μ*–Λ relationships in Mêdog exhibited little variation among the different periods, especially for Λ < 13. The shape factor *μ* in the postmonsoon season gradually became lower than that in other seasons when Λ > 13, which may be related to the few samples of convective precipitation with increasing Λ during the postmonsoon period. Notably, the *μ*–Λ relationships in different seasons were similar to the Florida (subtropical environment) relationship reported by Zhang et al. [38]. This finding might indicate that climatic characteristics may play an important role in the determination of the *μ*–Λ relationship.

**Figure 11.** Scatterplots of *μ* versus Λ and the empirical fitting relationships for samples with rain rates > 5 mm h−<sup>1</sup> and drop counts > 300 during the premonsoon, monsoon and postmonsoon seasons. The colored solid lines are the fitted empirical *μ*–Λ relationships in different seasons, and the gray solid line represents the empirical *μ*–Λ relationship of Zhang et al. [38].

### *3.6. Quantitative Precipitation Estimation (QPE)*

An important application of DSD is quantitative precipitation estimation (QPE). The power-law relationship of *Z* = A*R*<sup>b</sup> is widely used in radar meteorology and changes with rainfall type, atmospheric conditions and geographic location [42]. The new-generation weather radar system in China uses the empirical relationships of *Z* = 300*R*1.4 and *Z* = 200*R*1.6 to describe midlatitude convection [43] and stratiform precipitation [44], respectively. Wu and Liu [16] proposed that coefficient A (exponent b) is 170.7 (1.31) and 69.83 (1.83) for summer convection precipitation and stratiform precipitation in Nagqu, respectively, based on disdrometer measurements. Wang et al. [24] gave the relationships of *Z* = 114.79*R*1.34 and *Z* = 53.69*R*1.71 for convection precipitation and stratiform precipitation in rainy seasons in Mêdog, respectively. The equivalent radar reflectivity factor (*Z*e, in mm<sup>6</sup> m<sup>−</sup>3) based on observed DSDs can be expressed according to Zhang et al. [45]:

$$Z\_{\mathfrak{c}} = \frac{4\lambda^4}{\pi^4|K\_{\mathfrak{w}}|^2} \int\_{D\_{\text{min}}}^{D\_{\text{max}}} \left| f(D) \right|^2 N(D) dD \tag{20}$$

where *λ* indicates the radar wavelength and was set to 5 cm, considering that C-band Doppler weather radars were deployed over the TP. *K*w is the water dielectric factor, and |*Kw*|<sup>2</sup> is set to 0.93 by convention. *f* (*D*) is the backscattering amplitude for a raindrop of size *D*, which is calculated by using the extended boundary condition method (EBCM) [46].

Considering the evident seasonal variation in DSD characteristics in Mêdog, the *Z*–*R* relationships for the four seasons are discussed in this section. Figure 12 shows the scatter plots of *Z* and *R* superimposed with the fitted *Z*–*R* relationships using the least squares method for stratiform rain and convective rain, respectively. The fitted coefficient A and exponent b for different rainfall types in the four seasons are given in Table 6. Following Zeng et al. [18], the normalized mean biases (NBs) of the fitted *Z*–*R* relations and empirical relations at midlatitudes for different precipitation types were calculated to evaluate the accuracies of different *Z*–*R* relationships (Table 7).

**Figure 12.** Scatterplots of radar reflectivity factor (*Z*) and rain rate (*R*) and fitted *Z*–*R* relationships using the least squares method (solid lines) for stratiform rain (**a**) and convective rain (**b**).


**Table 6.** Fitted radar reflectivity and rain rate (*Z–R*) relationships for stratiform and convective rain types in the four seasons.

**Table 7.** NB (%) values of the fitted *Z–R* relationships and empirical relationships for different precipitation types in the four seasons.


For stratiform precipitation, a small discrepancy in fitted *Z*–*R* relationships among the different seasons could be noted. Winter precipitation had larger A and b values than those of the empirical relationship in midlatitudes, while precipitation in other seasons had smaller A and b values. This result may be related to the fact that winter stratiform precipitation had more (less) large (small) drops than in other seasons. The empirical relationship of *Z* = 200 *R*1.6 underestimated rainfall in the premonsoon, monsoon and postmonsoon seasons by 1.74%, 27.24%, and 14.32%, respectively, while it overestimated winter rainfall by 21.51%. The fitted *Z*–*R* relationships reduced the NB to less than 10% for all of the considered seasons.

For convective precipitation, the fitted coefficient A (exponent b) in the premonsoon, monsoon and postmonsoon seasons was much less (larger) than that of the empirical relation at midlatitudes. Monsoon precipitation had a minimum coefficient A (50.91) and exponent b (1.70), which might have been attributed to the large number of small raindrops during this period. That is, the same reflectivity factor would derive the highest rain rate in the monsoon season. Given a radar reflectivity factor value of 40 dBZ, the corresponding rainfall rates were 15.24 mm <sup>h</sup>−1, 22.33 mm h−<sup>1</sup> and 18.20 mm h−<sup>1</sup> in the premonsoon, monsoon and postmonsoon seasons, respectively. The empirical relationship of *Z* = 300 *R*1.4 underestimated convective rainfall up to 51.38% in the monsoon season, followed by 26.87% in the postmonsoon season and then 12.27% in the premonsoon season. However, the fitted *Z*–*R* relationships significantly reduced the NB in all of the considered seasons. In particular, the NB decreased from 51.38% to 2.98% in the monsoon season. The distinct seasonal variation in DSDs in Mêdog convective rain determined the evident discrepancy in *Z*–*R* relationships among the different seasons. Therefore, the fitted *Z*–*R* relationships for different seasons could significantly improve the accuracy of radar-based QPEs.
