Statistical Characteristics of Raindrop Size Distribution during Rainy Seasons in Northwest China

Institute of Desert Meteorology, China Meteorological Administration, Urumqi 830002, China Center for Central Asian Atmosphere Science Research, Urumqi 830002, China Laboratory of Cloud-Precipitation Physics and Severe Storms, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China College of Earth Science, University of Chinese Academy of Sciences, Beijing 100049, China

From the tropics to mid-latitudes, many researchers have used observational data to obtain the characteristics of DSDs of different continental areas. Researchers have conducted extensive studies on Darwin in Australia [16], the Indian coast [17], South Korea [18], Taiwan [19], Singapore [20], Oklahoma [21], and south and east China [22][23][24], and the research conclusions are of great significance for understanding the characteristics of local DSDs and improving the level of QPEs. Some researchers have also used the observation data of ships on the ocean to obtain the characteristics of DSDs on the ocean [25][26][27]. Bringi et al. [28] compared the characteristics of DSDs of continental and ocean areas and pointed out that the mass-weighted average diameter (D m ) of marine rainfall is smaller than that of continental rainfall, and the normalized intercept parameter (log 10 N w ) of marine rainfall is larger than that of continental rainfall. Ma et al. [14] pointed out that in the rainy season from May to October in Beijing, D m of the rainfall in July is the largest and log 10 N w is the smallest. Wen et al. [13] studied DSDs in eastern China and found that the characteristics of DSDs show differences in different rainfall types and different seasons. e above-mentioned researches play a key role in fully understanding the characteristics of DSDs. However, it is clear that the past researches mainly focused on monsoon regions and humid regions, and less research on DSDs in arid regions has restricted the understanding of rainfall microphysical processes in arid regions. Simultaneously, it becomes difficult to improve the level of QPEs in arid areas.
Xinjiang is located in the central part of Asia, and far from the ocean and not directly affected by the monsoon system, so it is a typical arid climate zone [29]. e rain amount in Xinjiang is obviously lower than that in the monsoon regions of China, and the rainfall intensity is also lower than in eastern and southern China [30]. However, rainfall is of vital importance in the ecological environment, production, and life in Xinjiang [31]. In the past, the research on rainfall in Xinjiang mainly focused on the weather scale system [31], mesoscale system [32,33], and environmental conditions of rainfall [34,35], and there was a lack of research on the microphysical process of rainfall. Zeng et al. [36] used DSDs data from the spring of 2020 to study the diurnal variation characteristics of DSDs in the Xinyuan area of Xinjiang and found that the diurnal variation characteristics are related to the precipitation system, valley wind, and solar radiation. However, only the characteristics of DSDs of spring are obtained, but the research on the overall characteristics of the rainy season is lacking. is research focuses on DSDs and microphysical characteristics of rainfall during rainy seasons in Xinjiang. e conclusions of the study are conducive to strengthening the understanding of the microphysical process of rainfall in arid regions and improving the ability of QPEs in arid regions.

Study Area.
e area of this study is the Xinjiang region in northwestern China, which is also located in the northern Tibetan Plateau (Figure 1). is area is a typical arid area, with the famous Taklimakan Desert and the Gurbantungut Desert. Between the two desserts are the famous Tianshan Mountains. As the most rainfall-rich area in Xinjiang, the Tianshan Mountains are important for the regional weather and climate.

Data.
e disdrometer data of this study were collected by a disdrometer of Yining Meteorological Station of Xinjiang from July 2018 to August 2020 (April to October, November to March of the following year is mainly snowfall, regardless). e disdrometer in this study is a second-generation particle size and velocity (Parsivel) disdrometer, which was produced by the OTT Hydromet Company (Kempten, Germany). e disdrometer emits a 54 cm 2 laser beam, and the disdrometer provides counts per diameter (D) and velocity (V) classes of the drops that have passed through the laser beam in the last minute [37]. In order to reduce the sampling error caused by insufficient raindrops and too small rainfall intensity, this study abandoned samples with raindrops less than 10 or rain intensity less than 0.1 mm·h − 1 [12,26]. Additionally, raindrops with diameters greater than 6 mm and fall speed of 60% above or below the Atlas et al. [38] empirical fall velocity-diameter relation are discarded [39][40][41][42][43].

Methods.
In order to obtain other characteristics of physical quantities of raindrops, here we first calculate N(D i ) using the following equation [40,42]: where N(D i ) (m − 3 ·mm − 1 ) represents the number of raindrops per unit volume per unit diameter interval; Ai (m − 2 ) is the sampling area; here, the value is 0.0054 m − 2 ; nij is the number of raindrops within the size bin i and raindrop terminal velocity bin j; V j (m·s − 1 ) is the raindrop fall velocity of the j-th bin computed by Atlas et al. [38]; Δt (s) is the sample time, here is 60 s; ΔD i is the class spread of the i-th bin. rough DSDs data, the characteristic physical quantities of commonly used raindrops can be derived [41,42], mainly including rain intensity R (mm·h − 1 ), liquid water content LWC (g·m − 3 ), and radar reflectivity Z (mm 6 ·m − 3 ). e calculation formulas are as follows: where ρ w is the density of water, and the value is 1.0 g cm − 3 . e nth-order moment of the drop size distribution is expressed as follows [44]: e gamma model can describe the raindrop spectrum very well [45]. At the same time, it cannot be ignored that some researchers have put forward different opinions on this [46,47]. However, the gamma model has been applied and verified in many studies describing the raindrop spectrum [7,12,19,25,44,48,49], and its form is as follows: where N 0 (mm − 1− μ m − 3 ), μ, and Λ (mm − 1 ) represent the scale, shape, and slope parameters of the gamma distribution, respectively. e moment method with the third, fourth, and sixth moments to calculate N0, μ, and Λ is used in this study. , where the calculation formula of G is as follows: However, the three parameters in the gamma distribution are not completely independent. To solve the nonindependence problem of the parameters of the gamma DSD model, the normalized gamma distribution that can better represent the raindrop spectrum was proposed [50][51][52][53]. Its advantages have been confirmed in many studies [25,36,54,55]. e normalized gamma distribution formula is as follows: where N w (mm − 1 m − 3 ) is the normalized intercept parameter and D m (mm) is the mass-weighted mean diameter. N w , D m , and f(μ) are calculated according to formulas (8)-(10), respectively.

Distribution of DSD Parameters.
After excluding samples with raindrops less than 10 or rain intensity less than 0.1 mm·h − 1 , an effective sample of 17845 min was obtained. Figure 2 shows the frequency accumulation curve of rainfall intensity recorded. e samples smaller than 0.5 mm·h − 1 accounted for nearly half of the total samples, reaching 46.67%, and the samples smaller than 1 mm·h − 1 accounted for 69.64% of the total samples. e average rainfall intensity calculated by the 17845 min data is 0.93 mm·h − 1 (Table 1). It can be seen that for the arid area of Xinjiang, water vapor is seriously insufficient, and the rainfall process is mostly weak rainfall [30], which is consistent with the measurement of the rain gauge. Figure 3 shows the histogram of D m and log 10 N w for all samples. e three key statistics including mean, standard deviation (SD), and skewness (SK) are also indicated in Figure 3. e average values of D m and log 10 N w are 1.02 mm and 3.66, respectively. e D m histogram shows the characteristics of highly positive skewness, and the skewness of log 10 N w is − 0.37, indicating that the distribution of log 10 N w is more symmetrical. At the same time, the standard deviation of D m and log 10 N w reach 0.43 mm and 0.49, respectively, which show that D m and log 10 N w have high variability. In addition to this, the three key feature statistics of R, W, and Z are also shown in Table 1.

DSD Characteristics for Different Rainfall Types.
In the subsection, the characteristics of raindrop spectra of different rainfall types based on the classification of rainfall as convective precipitation and stratiform precipitation are studied. In the past, many researchers have developed some classification schemes based on disdrometer. For example, Tokay and Short [12] used the N 0 − R relationship to distinguish between convective precipitation and stratiform precipitation. Testud et al. [53] developed a scheme to distinguish different types of precipitation by R. Bringi et al. [28] divided rainfall into convective rainfall and stratiform rainfall based on the standard deviation of R and R, this classification method has been applied in many studies, and this research also uses a similar Advances in Meteorology classification method. Specifically, R of continuous rain for 10 minutes is 0.5 mm·h − 1 ≤ R ≤ 0.5 mm h − 1 , and the standard deviation of R is ≤ 1.5 mm·h − 1 , which is considered as stratiform precipitation; R of continuous rainfall for 10 minutes is R ≥ 5 mm·h − 1 , and the standard deviation of R is >1.5 mm·h − 1 , which is considered to be convective precipitation. rough this classification method, 236 convective precipitation samples and 5479 stratiform precipitation samples are obtained. It can be seen that the convective precipitation samples are significantly less than the stratiform precipitation samples, which is mainly due to the fact that the prevalence of minutes of stratiform rain is a quite common feature. Figure 4 shows the histogram of D m and log 10 N w of convective and stratiform rain. D m of both types of rainfall is positive skewness, while the log 10 N w of convective rainfall is negative skewness. e average D m of convective rainfall and stratiform rainfall is 1.62 mm and 1.09 mm, respectively, while the average log 10 N w of the two types of rainfall is 3.73 and 3.80, respectively. e standard deviation of D m and log 10 N w of convective rainfall is greater than that of stratiform rainfall, indicating that convective rainfall has more extensive changes. In order to more clearly see the difference between the two types of rainfall, Table 2 gives some statistics of convective rainfall, stratiform rainfall, and the overall Parameters  rainfall of the two, respectively. It can be seen that the mean R of convective rainfall and stratiform rainfall is 7.77 mm·h − 1 and 1.51 mm·h − 1 , respectively. However, due to the fact that there are obviously more stratiform precipitation samples than convective rainfall samples, the average R for overall of the two is only 1.73 mm·h − 1 , it is closer to the characteristics of stratiform precipitation, and other statistics have similar trends.
In order to further obtain the relationship between D m and R in different rainfall types, we fitted the D m − R relationship curves of the two types of rainfall as shown in Figure 5. Figure 5 also shows the scatter density plot for D m − R. As shown in Figure 5, D m and R of convective rainfall are concentrated in 1.0-2.0 mm and 5.0-6.0 mm·h − 1 , respectively, while D m and R of stratiform rain are concentrated in 0.6-1.6 mm and 1.0-2.0 mm·h − 1 , respectively. Both types of rainfall increase as R increases, D m increases (the exponents of the power-law fitting equations are positive), and the distribution of D m becomes narrower. Under higher rainfall intensity R, the value of D m tends to be stable, which may be due to the accumulation and rupture of raindrops close to equilibrium [56], and the increase in R in this case may be due to the increase in concentration [57]. Figure 6 shows the scatter plot of log 10 N w versus D m for the two rain types, as well as statistical results from different parts of China. e two black rectangles correspond to the maritime and continental convective clusters, and the yellow dashed line is the log 10 N w − D m relationship for stratiform rain reported by Bringi et al. [28]. For convective rainfall and stratiform rainfall, there is a difference in the concentration of scattered points. Specifically, the log 10 N w and D m of convective rainfall are concentrated in 3.3-4.3 and 1.0-2.0 mm, respectively, and the value of stratiform rainfall is concentrated in 3.1-4.5 and 0.6-1.6 mm; although there are some overlapping areas, the boundary between the two types of rainfall is clear. For convective rainfall, although there are a few points in the "Continental cluster", most points are neither in the "Continental cluster" nor in the "Maritime cluster" and tend to be close to stratiform rainfall. For stratiform rainfall, most points appear on the left side of the "stratiform line". Comparing the statistical results of DSDs in different regions of China, we got interesting conclusions. In order to reduce the error caused by the measurement of different instruments, we only compared the results measured using the Parsivel disdrometer. e conclusion is that for stratiform rainfall, D m of northern China (Beijing) [14] and northwestern China (Yining) is smaller than that of eastern China (Nanjing) [24], and D m of southern China (Zhuhai) [48] is the largest. At the same time, for stratiform rainfall, although Beijing and Yining have similar D m , and log 10 N w in Yining is larger than that in Beijing. For convective rainfall, D m in Yining is the smallest, D m in Zhuhai is the largest, and log 10 N w in Zhuhai is also the largest. is result shows that the characteristics of DSDs are highly dependent on specific geographic locations and climatic conditions. Figure 7 shows DSDs of the two rainfall types. ere is a big difference in the distribution of DSDs of the two types of rainfall.
e peaks of DSDs of convective rainfall and stratiform rainfall are located at 0.7 mm and 1.2 mm in diameter, respectively. When the diameter is less than 0.7 mm, DSDs of the two types of rainfall basically coincide, Table 2: Statistics of DSD parameters for convective rainfall, stratiform rainfall, and an overall average of the two.
Parameters   Advances in Meteorology but when the diameter is greater than 0.7 mm, the DSD of convective rainfall is located above the stratiform rain. It can be seen that there are larger raindrops in convective rainfall than stratiform rainfall, and these large raindrops contribute more to rainfall intensity.

DSD Characteristics in Different Rainfall Rate Classes.
Previous studies have shown that DSDs of different rainfall intensities show different properties [12,58], and Chen et al. [7] divided DSDs measured on the Qinghai-Tibet Plateau into 5 classes according to R. Seela et al. [26] compared DSDs of Palau and Taiwan and divided DSDs into 12 classes according to R. Ma et al. [14] divided the rainfall into 8 classes when studying the nature of DSDs in Beijing. In order to further understand the nature of DSDs under different rainfall intensities in Xinjiang, drawing on the classification criteria previously studied, and combining the fact that Xinjiang rainfall is mainly weak rainfall [30], DSDs are divided into 6 classes according to R: C1, 0.1 ≤ R < 0.5 mm·h − 1 ; C2, 0.5 ≤ R < 1 mm·h − 1 ; C3,  Figure 6: Scatterplot of log 10 N w versus D m for convective rains (red filled circles) and stratiform rains (blue filled circles). e two black rectangles correspond to the maritime and continental convective clusters, and the yellow dashed line is the log 10 N w − D m relationship for stratiform rain reported by Bringi et al. [28]. e squares represent the averaged values in this study. e triangles, circles, stars, and diamonds represent the averaged values obtained in previous studies by Chen et al. [24], Ma et al. [14], and Zhang et al. [48] for different parts of China. e colors of these symbols represent different rains: green for stratiform rains and brown for convective rains.   1 ≤ R < 2 mm·h − 1 ; C4, 2 ≤ R < 5 mm·h − 1 ; C5, 5 ≤ R < 10 mm h − 1 ; C6, R ≥ 10 mm h − 1 . e statistics of sample numbers and R for each rain rate class are summarized in Table 3. Figures 8(a) and 8(b) show the changes in log 10 N w and D m of the six rainfall rate classes in the form of box-andwhisker plots, respectively. D m increases with the increase of R, while log 10 N w shows a trend of first increasing and then decreasing. In order to see more clearly the changing trend of the two with the increase of R, Figure 8(c) shows the variation of mean log 10 N w (along with ±1 standard deviation) with D m in different rain classes. It can be seen that the average value of D m has a wider range of variation than the average value of log 10 N w , and the variation is more significant under heavy rainfall classes. At the same time, Table 4 shows the specific average values and standard deviations of D m and log 10 N w for the six rainfall rate classes. e average value of D m varies from 0.92 to 2.18 mm, and the average value of log 10 N w varies from 3.34 to 3.81. In addition, a scatterplot of log 10 N w versus D m for different rain rate classes is shown in Figure 8(d), and the black dashed line is the log 10 N w − D m relationship for stratiform rain reported by Bringi et al. [28]. It can be seen that with the increase of R, D m shows an increasing trend, and the dispersion of scattered points strengthens. e scattered points of C3 and C4 are closer to the black dashed line, and the corresponding rainfall rate is 1-5 mm.
To facilitate the comparison of the average DSDs between different rainfall rate classes, the average DSDs for different rain rate classes are superimposed on the same graph ( Figure 9). It can be clearly seen that as R increases, the spectrum width of the DSDs increases, and the diameter corresponding to the peak of DSDs increases. In the range of smaller diameters (less than 0.6 mm), the corresponding concentrations of different rainfall rate classes are similar, and when the diameter is greater than 0.6 mm, the corresponding concentrations of high rainfall rate classes show an increasing trend. It can be seen that there are particles with smaller diameters in each rainfall rate class, and the main factor that increases the rainfall rate is to have more particles with larger diameters.

Z-R Relationship.
e power-law relationship Z � A · R b obtained by Z and R is the most widely used algorithm in QPEs of single-polarization radar (including the radar currently used in Yining). However, many researchers have pointed out that the coefficient A and the index b in the relationship have strong variability. e continental stratiform rain relation reported by Marshall and Palmer [59] is Z � 200.00 R 1.60 , and in the United States, the default Z − R relationship in the operational Weather Surveillance Radar-1988 Doppler (WSR-88D) systems is Z � 300.00 R 1.40 [60]. In the past, some researchers have carried out localized Z − R relationship studies in different regions of China using the Parsivel disdrometer, which has a certain significance for improving local precipitation quantitative estimation capabilities [14,24,48,61,62]. In this study, we used the least square method to derive the Z − R relationship of different rainfall types in the Yining area, with the purpose of providing a reference for quantitative estimation of precipitation in this area. Figure 10 is a scatter plot of the Z − R relationship between convective precipitation and stratiform precipitation and the corresponding fitting curves. For comparison, the default Z − R relationship in WSR-88D [60] and the continental stratiform rain relation reported by Marshall and Palmer [59] are also indicated in Figure 10. For stratiform rain, most of the continental stratiform rain relation reported by Marshall and Palmer [59] will overestimate the rainfall fitting from this study, and this overestimation is more obvious under high reflectivity conditions. e default Z − R relationship in WSR-88D will underestimate stratiform precipitation with lower reflectance values and overestimate stratiform precipitation with higher reflectance values. As for convective rainfall, the overall trend is overestimated. In addition, in order to compare with different regions in China, we also plot the Z − R relationship of convective precipitation and stratiform precipitation in different regions of China, including Nagqu in western China [63], Yangjiang in southern China [63], Nanjing in eastern China [62], and Beijing in northern China [64].  Diameter (mm) Figure 9: Average size spectra for different rain rate classes. 8 Advances in Meteorology Obviously, the differences in Z − R relationship in various regions are significant, which also shows that localized research is very necessary.
3.5. μ − Λ Relationship. e fact that the μ − Λ relationship can better describe the variability of DSDs during natural rainfall has been widely proven [21,24,49,65]. A large number of previous studies have shown that this relationship is different under different climatic conditions [66][67][68][69]. erefore, it is necessary to study the Yining area of Xinjiang located in a typical arid area. Figure 11 shows scatterplots of μ − Λ values in the Yining area. e gray solid circles are points from all the data, the dispersion of these scattered points is very large, so in order to reduce the dispersion, refer to Chen et al. [7] processing method, that is, DSD data are filtered by allowing only those with total drop counts >300, these data points are represented by black circles, and the corresponding fitted quadratic polynomials are as follows: Comparing the research results of Chen et al. [7], it can be seen that in the smaller value part, the two fitting curves overlap better, but in the larger value part, the divergence of the two curves becomes obvious. is also further shows that under different climate conditions, the variability of precipitation microphysics is obvious.

Discussion
e nature of DSD changes accordingly with the differences in climate regions, topography, and rainfall types [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. In the past, a large number of studies have been carried out on DSDs of many continental and ocean areas, and the research conclusions are of great help in improving the understanding of the microphysical process of rainfall [16][17][18][19][20][21][22][23][24][25][26][27][28]. However, past studies have mainly focused on monsoon regions with abundant rainfall and have paid less attention to arid regions. For example, for China, past research mainly focused on the southern, eastern, and northern regions of China, which are humid regions controlled by the monsoon system [2,13,14,[22][23][24], while there is less research on arid regions in China. At present, for the arid regions of China, researchers pay more attention to the raindrop spectrum of the Qinghai-Tibet Plateau [7,63] and lack research on Xinjiang. erefore, the conclusions of this study are conducive to understanding the microphysical properties of rainfall in Xinjiang. rough comparison, some differences between Xinjiang and humid regions of China have been found. For example, regardless of stratiform rainfall or convective rainfall, D m of Xinjiang is smaller than that of humid areas of China, which shows that the particles in Xinjiang are smaller during rainfall. At the same time, the Z − R relationship we deduced is also different from that of humid areas of China, which has reference value for improving QPE in Xinjiang. is study has obtained the overall DSD properties of the annual rainfall. However, DSDs of e magenta solid line denotes the continental stratiform rain relation reported by Marshall and Palmer [59]. e purple solid line denotes the default NEXRAD relation reported by Fulton et al. [60]. e red, green, blue, and wine red lines represent the Z − R relations obtained in previous studies by Wu et al. [63], Wu et al. [63], Huang et al. [62], and Ji et al. [64] for different parts of China. e different line types represent different rains: solid lines for stratiform rains, and dashed lines for convective rains. different seasons and different months are also different, which will be further carried out in future work.

Conclusions
In this study, we used the raindrop spectrum data of Yining of Xinjiang during the rainy season (April to October) from July 2018 to August 2020 to study the nature of DSD in Xinjiang in arid areas. e main findings are as follows: (1) For all rain samples, rainfall appears in the form of weaker intensity, and nearly 70% of the rainfall rate is less than 1 mm h − 1 , and the DSD parameter (D m ) and bulk variables (R, W and Z) have a positive skewness, indicating a low frequency of high values and a high frequency of low values in Yining. e larger standard deviations of these parameters indicate that the rainfall variability is stronger. (2) e statistically obtained convective rainfall samples are significantly less than the stratiform rainfall samples. e mass-weighted average diameter D m and R of convective rainfall are concentrated in 1.0-2.0 mm and 5.0-6.0 mm·h − 1 , respectively, while D m and R of stratiform rain are concentrated in 0.6-1.6 mm and 1.0-2.0 mm·h − 1 , respectively. As R increases, D m increases, and the distribution of D m becomes narrower. Convective rainfall in the Yining area is neither in the "Continental cluster" nor in the "Maritime cluster" and tends to approach stratiform rain. For stratiform rain, most points appear on the left side of the "stratiform line". e peaks of the raindrop spectra of convective rain and stratus rain are located at 0.7 mm and 1.2 mm in diameter, respectively. When the diameter is less than 0.7 mm, DSDs of the two rainfalls basically coincide, but when the diameter is greater than 0.7 mm, DSDs of convective rainfall are located above that of the stratiform rain. (3) According to different rainfall intensities, the raindrop spectrum is divided into 6 classes. It is found that D m increases with the increase of R, and the standardized intercept parameterlog 10 N w shows a trend of first increasing and then decreasing. As R increases, the spectrum width of DSDs increases, and the diameter corresponding to the peak of DSDs increases. In the range of smaller diameters (less than 0.6 mm), the corresponding concentrations of different rainfall rate classes are similar, and when the diameter is greater than 0.6 mm, the corresponding concentrations of high rainfall rate classes show an increasing trend. (4) We deduced the Z − R relationship in the Yining area and found that the default Z − R relationship in WSR-88D will underestimate stratiform precipitation with lower reflectance values and overestimate stratiform precipitation with higher reflectance values. As for convective rainfall, the overall trend is overestimated. We also deduced the μ − Λ relationship, compared with Chen et al. (2017), the two fitted curves agree better in the smaller value part, and when the value is larger, the two curves are more different.

Data Availability
Data used in this paper can be obtained from Yong Zeng (15099610397@163.com) upon request.

Conflicts of Interest
e authors declare no conflicts of interest.