Characteristics and Variations of Raindrop Size Distribution in Chengdu of the Western Sichuan Basin, China

Abstract

Knowledge of the microphysical characteristics of precipitation plays a significant role in meteorology, hydrology, and natural hazards management, especially in the western Sichuan Basin (WSB), which is located east of the Tibetan Plateau (TP) in southwestern China and thus has unique terrain conditions and weather systems. Nonetheless, the literature regarding raindrop size distribution (RSD) in the WSB is still very limited. This work investigates RSD characteristics and temporal variations in a site (Chengdu, CD) of the WSB by employing three years of quality-controlled RSD observation collected from a second-generation PARSIVEL disdrometer. The results show that RSD has noticeable seasonal and diurnal variations in CD. Specifically, the broadest mean raindrop spectra can be found in summer and the narrowest in winter, and the raindrop spectra of a day can be the narrowest during 1400–1500 BJT (Beijing Standard Time, UTC+8). In addition, the mass-weighted mean diameter ($D_m$) is lower in the daytime than in the nighttime, while the logarithm of the generalized intercept parameter ($lo{g}_{10}$N_w, the unit of the N_w is m⁻³ mm⁻¹) has a larger value in the daytime than in the nighttime. In addition, intercomparisons indicate that the mean $D_m$ of convective rains in CD is smaller than in South China and it is higher than in the eastern slope of TP, East China, and North China; on the other hand, the corresponding mean $lo{g}_{10}{N}_w$ is close to the value at the middle TP. Local empirical relations of shape–slope parameters ($\mu$–$\Lambda$) and reflectivity–rain rate (Z–R) are also presented to provide references for optimizing the RSD parameterization scheme and radar precipitation estimation in the local area.

1. Introduction

Raindrop size distribution (RSD), one of the most critical microphysical properties of natural precipitation, is the comprehensive result of raindrop generation, condensation, collision–coalescence, fragmentation, evaporation, etc. [1,2,3,4]. Since all bulk rainfall variables of interest can be derived as weighted moments of the RSD [5], observing the RSD is essential for exploring precipitation characteristics, mechanisms, and underlying physical processes [6,7]. Moreover, RSD information is beneficial for improving meteorological radar retrieval algorithms [8,9], correcting the deviation of satellite inversion of precipitation [10], and optimizing the parameterization scheme of numerical weather prediction (NWP) models [11,12], especially over areas with complex terrain conditions.

To date, many studies have revealed that the precipitation RSD can broadly vary in different geographical or climatic regions and can change along with seasons [6,13,14,15,16,17]. For instance, Kozu et al. (2006) [15], Radhakrishna et al. (2009) [16], and Chakravarty et al. (2013) [17] found that the RSD properties in southeast India are closely related to monsoon activities, that the precipitation consists of more small raindrops in the northeast monsoon area than in the southwest monsoon area, and that convections in pre-monsoon months can be stronger than those in monsoon seasons and produce more large raindrops. Ushiyama et al. (2009) [18] and Seela et al. (2018) [19] compared the precipitation over two islands of Palau and Taiwan and concluded that oceanic RSD also has apparent seasonal variations, namely, summer rain spectra typically have more small raindrops but fewer medium-to-large raindrops than winter. In addition, summer convections in Taiwan can produce more large raindrops than in Palau. The scenario in eastern China is slightly different; there, summer precipitation has not only the largest raindrops among the four seasons but also the highest concentration [20]. Under the influences of solar radiation, terrains, and different underlying surfaces, RSD also has diurnal variation. Kozu et al. (2006) [15] and Suh et al. (2016) [21] pointed out that with the effect of sea-land thermal forcing, the precipitation properties over Sumatra and Busan can be much different in different daily periods. Over the middle Tibetan Plateau, Chen et al. (2017) [22] and Chang et al. (2016) [23] also found that summer convection can produce larger raindrops in the daytime than in the nighttime, while the RSD generalized intercept is the opposite; moreover, raindrop spectra between 1700–1800 BJT are the widest during a whole day.

RSD properties are also closely related to rain types owing to experiences of different microphysical processes. Waldvogel (1974) [24] early pointed out that the raindrop concentration can significantly “jump” when the precipitation type transforms from stratiform to convective. Wen et al. (2019) [20] and Xie et al. (2020) [25] also confirmed that convective precipitation can produce wider RSDs than stratiform precipitation both in plain and plateau areas. Under the same rainfall intensity, Tokay et al. (1996) [26] demonstrated that stratiform precipitation contains more large raindrops but fewer small raindrops than convective precipitation. Bringi et al. (2003) [27] suggested that maritime convection can be characterized by relatively higher concentrations of small drops than continental convection. In addition, it has been found that typhoon precipitation consists of more small raindrops than non-typhoon precipitation [28].

As mentioned above, RSD varies significantly over different regions due to the differences in climates, seasons, precipitation types, etc., making investigating the variability and evolution of RSD in a specific region necessary. In this study, we focus on a site (Chengdu, CD) in the western Sichuan Basin (WSB), China (as shown in Figure 1), which is close to the eastern edge of the Tibetan Plateau (TP). Many unique and high-impact synoptic systems form and develop around this area, such as the TP trough and the southwest vortex, which can trigger heavy rainfall or other severe weather in the local or downstream cities. Rainstorms in CD of the WSB are mostly concentrated in summer as in other mid-latitude monsoon areas, while continuous rain happens in autumn [29,30], known as the “Autumn rain in West China”, and the “night rain” feature is very prominent [31].

To date, although RSD characteristics in different areas of China have been widely investigated [13,20,22,23,25,28], literature regarding precipitation microphysical characteristics in the WSB is still very limited, and it deserves further exploration. The main objective of this study is to employ the 3-year data collected with a disdrometer deployed in CD of the WSB, to reveal the RSD characteristics and variations in detail over this special area. This work is expected to provide foundations for improvements of local radar quantitative precipitation estimation (QPE), and also can be of great importance for parameterization scheme modifications of local numerical weather prediction (NWP) models. The remainder of this article is organized as follows. In Section 2, the observation site, used instrument, measurements, and methods of data quality control and postprocessing are described. Section 3 presents the results concerning the characteristics and variations of RSD found in CD of the WSB in detail. Discussions and conclusions of our findings are presented in Section 4 and Section 5, respectively.

2. Instrument, Data, and Methods

2.1. Observation Site, Instrument, and Measurements

The RSD data from 2018 to 2020 used in this study were collected from a second-generation PARSIVEL disdrometer (PARSIVEL²), which is deployed at the Chengdu national weather station (CD, 30.75° N, 103.86° E, 549 m ASL), located in the WSB, China. As shown in Figure 1, the east side of CD is a vast plain while its west side is the eastern edge of the enormous TP. The CD has a subtropical monsoon humid climate. Its average annual precipitation and temperature in the past decade are 1034.1 mm and 17.1 °C, respectively. The PARSIVEL² is a widely used laser-based disdrometer manufactured by OTT Hydromet. It can simultaneously obtain the equivalent volume diameter D (mm) and falling velocity V (m s⁻¹) of raindrops according to the signal attenuation and duration when raindrops pass through the laser beam. The raw measured data are raindrop counts reserved in 32 × 32 non-equidistant diameter and velocity classes. The measurable diameter and velocity range from 0.062 to 24.5 mm and 0.05 to 20.8 m s⁻¹, respectively. The sampling time interval is one minute.

Figure 1. The position and surrounding topography of the observation site of Chengdu (CD, 30.75° N, 103.86° E, 549 m ASL).

Figure 1. The position and surrounding topography of the observation site of Chengdu (CD, 30.75° N, 103.86° E, 549 m ASL).

2.2. RSD Data Quality Control and Postprocessing

Existing studies [32,33] have shown that the PARSIVEL² occasionally produces some problematic data due to its inherent limitations. Therefore, the following technologies were implemented to improve the raw data quality.

Firstly, considering the actual sensitivity of the instrument, raindrops in the first two diameter classes of RSDs were discarded [34]. Moreover, the RSD samples with any raindrops larger than 6 mm were deleted, because raindrops larger than 6 mm are mostly formed when multiple raindrops parallelly pass through the laser beam and they can pull down the quality of the entire rain spectrum [35,36]. Secondly, any RSDs where the rain rate was smaller than 0.1 mm h⁻¹ were filtered out, as implemented by Tokay and Short (1996), Jaffrain and Berne (2011), and Han et al. (2021) [26,37,38], to avoid noise from non-precipitation or to exclude too sparsely populated rain spectra. Thirdly, raindrops in RSDs that possessed an unmatched D–V (a normal D or V with an excessively large or small V or D) were also treated as unrealistic data, which can be produced under strong wind shear conditions or by raindrop splashings on the instrument surface. We compared the measured D–V of this kind of data with a theoretical relation proposed by Atlas et al. (1973) [39] and removed the raindrops when they were ±60% outside of the theoretical value, following Jaffrain and Berne (2011) [37]. Fourthly, the effective sampling area ($A_i$, mm²) was recalculated using an equation of $A_i=180 mm\times \left(30 mm-0.5D_i\right)$, where i is the order of diameter class [37]. Finally, RSD samples of non-liquid precipitation, including snow, sleet, and hail were excluded based on local artificial observations. After these quality-controlled steps, 70,957 RSD samples were selected during the observation period, among which 9.39% of total raindrop counts were eliminated.

The raindrop number concentration $N\left(D_i\right)$ (m⁻³ mm⁻¹) was calculated as follows:

$$N\left(D_i\right)={\displaystyle \sum }_{j=1}^{32}\frac{n_{ij}}{A_i·\Delta t·V_j·\Delta D_i},$$

(1)

where i and j represent orders of diameter and velocity classes, respectively. $n_{ij}$ is the drop count at the ith diameter class and the jth velocity class. $A_i$ (m²) stands for the effective sampling area for ith diameter class. $V_j$ (m s⁻¹) is the fall velocity for the jth velocity class and $\Delta D_i$ (mm) is the corresponding interval of the ith diameter class. $\Delta t$ (60 s) denotes the sampling time.

The RSD-integrated quantities, including rain rate R (mm h⁻¹), water content W (g m⁻³), radar reflectivity factor Z (mm⁶ m⁻³), and raindrop total concentration $N_T$ (m⁻³), were derived as follows:

$$R=\frac{\pi }{6}\underset{0}{\overset{\infty }{{\displaystyle \int }}}{D}^{3}N\left(D\right)dD=\frac{6\pi }{\mathrm{10,000}}{\displaystyle \sum }_{i=1}^{32}{\displaystyle \sum }_{j=1}^{32}{D}_i^3\frac{n_{ij}}{A_i·\Delta t},$$

(2)

$$W=\frac{\pi }{6}{\rho }_w\underset{0}{\overset{\infty }{{\displaystyle \int }}}{D}^{3}N\left(D\right)dD=\frac{\pi }{6000}{\rho }_w{\displaystyle \sum }_{i=1}^{32}{\displaystyle \sum }_{j=1}^{32}{D}_i^3\frac{n_{ij}}{A_i·\Delta t·V_j},$$

(3)

$$Z=\underset{0}{\overset{\infty }{{\displaystyle \int }}}{D}^{6}N\left(D\right)dD={\displaystyle \sum }_{i=1}^{32}{\displaystyle \sum }_{j=1}^{32}{D}_i^6\frac{n_{ij}}{A_i·\Delta t·V_j},$$

(4)

$$N_T=\underset{0}{\overset{\infty }{{\displaystyle \int }}}N\left(D\right)dD={\displaystyle \sum }_{i=1}^{32}{\displaystyle \sum }_{j=1}^{32}\frac{n_{ij}}{A_i·\Delta t·V_j},$$

(5)

where ${\rho }_w$ (g cm⁻³) is water density. The three-parameter Gamma function model is commonly used to represent the measured RSD, which can be expressed as [5]:

$$N\left(D\right)=N_0{D}^{\mu }\exp \left(-\mathsf{\Lambda }D\right)$$

(6)

where N₀ (m⁻³ mm^−1−μ), $\Lambda$ (mm⁻¹), and $\mu$ denote the intercept, shape, and slope parameters, respectively. The truncated moment method [40,41] was chosen to calculate the three parameters with the zeroth, first, and second moments as follows [42], where the nth-order moment is defined as:

$$M_n={{\displaystyle \int }}_0^{\infty }N\left(D\right)D^{n}dD=\frac{N_0\Gamma \left(n+\mu +1\right)}{{\Lambda }^{n+\mu +1}}$$

(7)

$$\eta =\frac{M_1^2}{M_0{M}_2},$$

(8)

$$\mu =\frac{1}{\left(1-\eta \right)}-2,$$

(9)

$$\mathsf{\Lambda }=\frac{M_0}{M_1}\left(\mu +1\right)$$

(10)

$$N_0=\frac{M_0{\Lambda }^{\mu +1}}{\Gamma \left(\mu +1\right)}.$$

(11)

Note that to ensure the estimation accuracy of the Gamma parameters, only RSDs with a total drop count greater than 100 were employed. The mass-weighted mean diameter $D_m$ (mm) was computed as the ratio of the fourth to the third moment of the RSD:

$$D_m=\frac{M_4}{M_3}=\frac{\sum N\left(D_i\right)D_i^4\Delta D_i}{\sum N\left(D_i\right)D_i^3\Delta D_i},$$

(12)

To solve the nonindependence problem of the parameters of the Gamma model, a normalization method has been proposed [6]. The normalized Gamma model makes it possible to compare RSDs regardless of the time scale and rain rate and accurately examine the substantial variations related to the physical rainfall regimes. The normalized Gamma model is defined as:

$$N\left(D\right)=N_{w}f\left(\mu \right){(\frac{D}{D_m})}^{\mu }\exp [-\left(4+\mathsf{\mu }\right)\frac{D}{D_m}]$$

(13)

where:

$$f\left(\mu \right)=\frac{6}{4^4}\frac{{\left(4+\mu \right)}^{\mu +4}}{\mathsf{\Gamma }\left(\mu +4\right)}$$

(14)

and the normalized intercept parameter $N_w$ (m⁻³ mm⁻¹) is related to the W and $D_m$ as follows:

$$N_w=\frac{4^4}{\pi {\rho }_w}\left(\frac{{10}^{3}W}{D_m^4}\right) ,$$

(15)

3. Results

3.1. RSD Seasonal Variation

In this section, we use quality-controlled data to analyze RSD seasonal variation. As summarized in

Table 1. Accumulated RSD sample number, accumulated rain amount, average rain rate, and rain rate ranges (5th to 95th percentiles) in four seasons during 2018–2020. The percentage against the all-seasons value is shown in parentheses, and rain rates herein were calculated from 1 min RSD using Equation (2).

Season	Accumulated RSD Sample Number	Accumulated Rain Amount (mm)	Averaged Rain Rate (mm h−1)	Rain Rate Range (mm h−1, 5th–95th Percentiles)
Spring	18,258 (25.7%)	336 (13.9%)	1.10	0.11–3.70
Summer	31,482 (44.4%)	1,682 (69.8%)	3.21	0.12–14.26
Autumn	17,451 (24.6%)	369 (15.3%)	1.27	0.11–3.91
Winter	3,739 (5.3%)	22 (1.0%)	0.34	0.11–9.23
All seasons	70,957	2,409	2.04	0.12–7.6

, during the three-year observation period, the total number of RSD samples after selection is 70,957, and the difference among seasons is noticeable. Summer has the largest percentage (44.4%), while winter has the smallest size (5.3%), mainly because winter’s rainfall processes were the fewest. It also can be seen that the seasonal change in accumulated rain amount and averaged rain rate is significant. Specifically, the rainfall amount in spring, summer, autumn, and winter contributes 13.9%, 69.8%, 15.3%, and 1.0% of the annual rain amount, respectively. In addition, the average rain rate in summer can be almost 1.5 times the average level in a whole year, while it is minimal in winter. Spring and autumn have the same level of either accumulated rain amount or rain rate in general.

Figure 2a shows the composite rain spectra and function curves fitted by normalized Gamma models as written in Equation (13) for four seasons during the observation period. To better quantify RSD differences among seasons, we also subtracted the composite RSDs of spring, summer, and autumn from that of winter, respectively, to form three kinds of deviations as curves (${\Delta }_{Spr}$, ${\Delta }_{Sum}$, and ${\Delta }_{Aut}$) drawn in Figure 2b. The sums and averages of ${\Delta }_{Spr}$, ${\Delta }_{Sum}$, and ${\Delta }_{Aut}$ for small raindrops (D < 1 mm) and medium-to-large raindrops (D ≥ 1 mm) were also listed. It can be seen that the number concentrations of all seasons decrease monotonically with the increase in raindrop size. Deviations indicate that the number concentrations of winter are the smallest among the four seasons at all diameter classes. Comparing the other three seasons, for small raindrops, spring generally has the highest number concentrations with a sum value of ${\Delta }_{Spr}$ being 2093 m⁻³ mm⁻¹ and an average of ${\Delta }_{Spr}$ being 262 m⁻³ mm⁻¹, followed by summer and autumn, respectively. By contrast, for medium-to-large raindrops, summer can possess the highest number concentrations, followed by spring and autumn, respectively. Spring and autumn have close number concentrations for raindrops within 1–2 mm. Whereas the former has higher number concentrations for raindrops smaller than 1 mm, it has lower number concentrations for raindrops larger than 2 mm than the latter. The observed RSDs can be formulized well by the normalized Gamma model, and correlation coefficients between observed and fitted results for spring, summer, autumn, and winter are 0.9842, 0.9990, 0.9972, and 0.9987. The fitted models for four seasons can be separately expressed as:

$$N\left(D\right)=\left\{\begin{array}{c}799.0D^{-1.2306}\exp \left(-2.105D\right), \text{for spring}, \\ 1090.8D^{-0.3728}\exp \left(-2.021D\right), \text{for summer},\\ 666.8D^{-0.9571}\exp \left(-2.0682D\right), \text{for autumn},\\ 783.0D^{-0.5498}\exp \left(-3.1122D\right), \text{for winter}.\end{array}\right.$$

(16)

Distributions of six additional RSD-integrated quantities and two Gamma parameters during the observation period were counted as shown in boxplots in Figure 3. Under the influence of more frequent convective activities (see details in Section 4.1), generally, summer shows the largest $D_m$ (Figure 3f), while winter shows the smallest. The seasonal variations of R, Z, and W (Figure 3a–c) also exhibit similar distributions since they are both highly related to the raindrop size. Note that averages can be larger than medians or even the 75th percentiles in Figure 3a,c,d,g,h. This is because most of these quantities have relatively small values. On average, spring has the largest total number concentration $N_T$ (Figure 3d), followed by summer and autumn, respectively; autumn has the largest normalized intercept $N_W$ (Figure 3e), followed by spring and summer, respectively; winter has the smallest $N_T$ and $N_W$. For the two Gamma parameters (Figure 3g,h), in general, autumn and winter can possess larger values than spring, and summer shows the smallest.

3.2. RSD Diurnal Variation

To investigate the diurnal variability of the microphysical properties of precipitation, the hourly average RSD, accumulated rainy sample number, accumulated rain amount R_a (mm), R, $D_m$, $N_w$, $N_{T }$, $\mu$ and $\Lambda$ were computed as shown in Figure 4. The result shows that diurnal variations in RSD and its integrated quantities are certainly significant in CD. Specifically, raindrop spectra during 1400–1500 BJT were the narrowest (Figure 4a), whereas they became the widest during 1100–1200 BJT. Moreover, a trend of raindrop spectrum broadening could be observed from afternoon to midnight. The log₁₀$N_T$ could reach 2.627–2.851 at 1100–1900 BJT (Figure 4f), which was significantly higher than that during other periods.

From the variations in the accumulated sample number, R_a, and R (Figure 4b,c), we can find that the duration and intensity of rainfall were longer and stronger at night than during the day, resulting in more significant cumulative rain amounts. The R from afternoon to evening was smaller than at other periods, and the minimum R of the day occurred around 1800–1900 BJT. The $D_m$ gradually decreased from 0600 BJT (Figure 4d), reached a minimum at 1900 BJT, and then increased again. However, variation trends of $\mu$ and $\Lambda$ (Figure 4g,h) were opposite to those of $D_m$. The $\Lambda$ was larger in the daytime, indicating that the number concentration of large raindrops decreases faster with the increase in diameter than in the night, especially in the afternoon. In addition, it can be found that the $D_m$ increased while $N_T$ and $N_w$ decreased with the increase in R, reflecting that the number of large raindrops increases with rainfall intensity. Generally, the rainfall in the daytime was mostly dominated by small raindrops (D < 1 mm), and medium-to-large raindrops (D ≥ 1 mm) can produce a larger contribution to nighttime rainfall.

To further compare the RSD in the daytime and nighttime, we divided RSD samples into two categories according to local sunrise and sunset time, i.e., daytime (0700–1900 BJT) and nighttime (2000–0600 BJT). The composite RSDs for the two periods are shown in Figure 5a. It can be seen that the number concentration decreased faster in the daytime than at night with the increase in raindrop diameter. Namely, the number of small raindrops (D < 1 mm) in the daytime was greater than that at night, while the situation for the number of medium-to-large raindrops (D ≥ 1 mm) was the opposite. The probability density distributions (PDFs) of $D_m$ and $lo{g}_{10}{N}_w$ observed in the two periods were counted as drawn in Figure 5b. Statistics reveal that the average of $D_m$ in the daytime (1.09 mm) was lower than at night (1.19 mm) and the average of $lo{g}_{10}{N}_w$ in the daytime (3.54) was larger than at night (3.33). The standard deviations (STDs) of $D_m$ and $lo{g}_{10}{N}_w$ being 0.45 mm and 0.7 in the daytime and 0.47 mm and 0.6 at night suggests a daily variation in raindrop size and concentration, which can be higher than that observed in eastern China [43]. In addition, we also find that PDFs of $D_m$ and $lo{g}_{10}{N}_w$ performed positive skewnesses (SKs) in both daytime and nighttime.

3.3. RSD Differences between Diverse Rain Types

To investigate the RSD differences between diverse rain types, we grouped all RSD samples into three categories, i.e., stratiform, convective, and the other, based on a method proposed by Bringi et al. (2003) [27]. Herein, only stratiform and convective precipitation are compared. After rain type division, for the whole dataset, accumulated RSD samples (percentages to the total) for stratiform and convective precipitation are 51,156 (72.09%) and 4681 (6.6%), respectively, and relevant rainfall amounts produced by the two types are 854 mm and 1371 mm, respectively. This suggests that stratiform precipitation is much more frequent than convective precipitation in CD of the WSB, while the former contributes much less rainfall than the latter. Comparisons among seasons also indicate that the proportion of summer convective precipitation is higher than that in other seasons, no convective rainfall occurs in winter, and the proportion of both rain types in spring and autumn is close.

Figure 6a shows the composite RSDs and Gamma fittings of the two rain types. It can be seen that under the same raindrop diameter, the number concentration of convective precipitation is higher than that of stratiform precipitation. The number concentration of stratiform precipitation can decrease faster than that of convective precipitation with the increase in raindrop diameter. As the rainfall in summer can be the most concerning, we built the normalized Gamma model individually for summer over the region of interest (CD) as:

$$N\left(D\right)=\left\{\begin{array}{c}1950D^{-0.0695}\exp \left(-3.1212D\right), \text{for stratiform}\\ 3632D^{0.9126}\exp \left(-2.2304D\right), \text{for convective}\end{array}\right.$$

(17)

Both of these are depicted in Figure 6b,c. The normalized Gamma distribution fits quite well for both rain types; the correlation coefficients between fitted values and measurements are 0.9994 and 0.9454 for stratiform and convective precipitation, respectively. The RSD distribution of stratiform precipitation in the CD behaves slightly concave, while it is slightly convex for convective precipitation. Furthermore, we compared summer RSD results in CD with several other similar-latitude regions of China, i.e., Naqu (NQ, located in the mid-Tibetan Plateau, Chen et al., 2017 [22]), Daocheng (DC, located in the eastern Tibetan Plateau, Wang et al., 2020 [13]), and Chuzhou (CZ, located in the east China, Jin et al., 2015 [35]), which are also illustrated in Figure 6b,c. Overall, both raindrops of stratiform precipitation are smaller than 4 mm, and RSD distributions of both two rainfall types are mostly unimodal in all regions. Although the RSD of stratiform precipitation distributes very similarly in CD and NQ, the number of small drops in NQ is less. DC has more raindrops than CD when the diameter is within 0.6–1.8 mm, while the opposite is true when the diameter is smaller than 0.6 or larger than 1.8 mm. The CZ has the largest number for raindrops within 0.5–1.6 mm among the four regions; however, the number of smaller or larger raindrops (D < 0.5 mm or D > 1.6 mm) is less than CD. The convective raindrop spectrum in the CD is broader than in other regions. In addition, it also can be observed that the number concentration for both rainfall types decreases fastest with raindrop size increase in DC.

3.4. Local Relationships of μ–Λ and Z–R

Previous studies [41,44,45] have confirmed that the Gamma parameters are not independent, among which $\mu$–$\Lambda$ is vital to microphysical parameterization schemes (e.g., bulk microphysical parameterization) [12]. Therefore, we analyzed the local $\mu$–$\Lambda$ relationship over the CD in this section.

According to the study of Zhang et al. (2003), relatively large errors happen in the $\mu$–$\Lambda$ relationship when the rain rate is lower than 5 mm h⁻¹ (light/drizzle rain) [41]. As a result, we choose the rule of $N_T$ > 500 ${\mathrm{m}}^{-3}$ and R > 5 mm h⁻¹ to screen whole data samples to obtain a more reliable $\mu$–$\Lambda$ relationship over the CD area. As RSD samples in winter were sparse after filtering, relationships for the other three seasons and the annual data were fitted as expressed in Equation (18) and results for the annual and summer were also drawn in Figure 7.

$$\Lambda =\left\{\begin{array}{c}0.0118{\mu }^2+1.182\mu +1.12, \text{for all seasons}\\ -0.0141{\mu }^2+1.436\mu +0.8125, \text{for spring}\\ 0.0187{\mu }^2+1.112\mu +1.195, \text{for summer}\\ -0.06409{\mu }^2+1.714\mu +0.5817, \text{for autumn}\end{array}\right.$$

(18)

Meanwhile, we present the results in the literature in which the study regions differ from this work for comparison. Overall, the $\mu$–$\Lambda$ relationship varies according to geographic location and climate. A closer look at Figure 7a shows that the slope of the $\mu$–$\Lambda$ curve gradually increases from CD (WSB), Chongqing (CQ, eastern Sichuan Basin, Liu et al. [46]) to Nanjing (NJ, eastern China, Wen et al. [20]). The $\mu$–$\Lambda$ curve of CD is more close to that of CQ, which may be related to the fact that their geographical locations are closer and they possess a more similar climate.

From Figure 7b, it can be found that CD (549 m, ASL) and DC (an upstream position of CD, 3800 m ASL, Wang et al. [13]) have relatively similar relationships in summer, while the curve slope of the former is slightly smaller. CD can generally possess smaller $\Lambda$ than NQ (4508 m ASL, Chen et al. [22]) under the same $\mu$, whereas their curve slopes are very close. When $\mu$ exceeds 2, the $\Lambda$ of CZ (103 m ASL, Jin et al. [35]) can be the smallest.

The Z–R relationship, in the form of $Z=A{R}^b$ is an essential foundation for radar quantitative precipitation estimation [47]. For instance, the standard relationship of $Z=300R^{1.4}$ [48] has been used in the Next Generation Weather Radar (NEXRAD) of the United States. Marshall and Palmer (1948) [49] proposed a form of $Z=200R^{1.6}$ which is more suitable for stratiform precipitation in mid-latitude regions. It has also been reported that A = 250 and b = 1.2 are beneficial for estimating tropical rainfalls [50]. These studies show that coefficients A and b vary much with geographical location and precipitation type [51], making the study of the scenario in the WSB of great importance.

Figure 8a,b show the Z–R relationships of the whole year and summer for stratiform precipitation in the CD area (solid black line). Meanwhile, results in other studies are plotted for comparison. As shown in Figure 8a, the Z–R relationship for the entire stratiform samples is $Z=342.8R^{1,368}$, which fits the dataset well. The Z–R relationship for stratiform rains in CD performs very similarly to the NEXRAD-operational $Z=300R^{1.4}$, whereas the $Z=200R^{1.6}$ proposed by Marshall and Palmer (1948) overestimates the rain rate in the region of interest. From Figure 8b, we can observe that parameter A of the Z–R relationship in summer over CD is smaller than the one fitted in a whole year. Moreover, comparisons among all Z–R equations in other regions indicate that cases in Yangjiang (YJ, southern China, $Z=403.9R^{1.25}$) [52] and CZ (eastern China, $Z=408R^{1.2}$) [35] are close to the situation in the CD area; by contrast, significant differences can be found for the cases in DC and NQ (east and middle TP, $Z=149R^{1.489}$ and $Z=170.7R^{1.31}$) [13,52].

The scenario for convective rain is depicted in Figure 8c,d. It can be seen from Figure 8c that there is an inconsistency between the relationship that we built in this study ($Z=461.8R^{1.327}$) and the NEXRAD operational relationship ($Z=300R^{1.4}$), although the trends are identical. The tropical used relationship ($Z=250R^{1.2}$) [50] performs worst in our study region. For summer, the intercomparison of four existing Z–R relationships with that of our study ($Z=452R^{1.331}$) in CD shows that the Z–R relationship in YJ (southern China, $Z=301R^{1.21}$) [52] has the most similar pattern and the Z–R relationships in East China has the most different pattern.

4. Discussion

4.1. Analysis of Temporal Variations in Atmospheric Conditions

The RSD is a comprehensive production of various precipitation physical processes. In this section, we discuss the differences in the atmospheric conditions in diverse seasons and diurnal periods to provide a macroscopical reference for understanding the precipitation variation in CD of the WSB.

Figure 9 and Figure 10 display the averaged specific humidity (Q, g kg⁻¹), horizontal winds at 850 hPa, and convective available potential energy (CAPE) in each season. From Figure 9d, we can find that in spring, the East Asian summer monsoon gradually established and developed northward, which increased the average Q to about 6 g kg⁻¹ over the CD area, providing necessary water vapor conditions for the formation and development of precipitation. In winter (Figure 9c), the Q in the CD area is around 4 g kg⁻¹, which is the lowest value among the four seasons. Moreover, the weather in the Sichuan Basin is mostly stable in winter [53,54], leading to unfavorable conditions for rainfall events. In addition, the average CAPE is close to 0, which makes for unfavorable conditions for the formation of convective rains in winter. In summer, on the one hand, the southerly component of the East Asian summer wind reaches the strongest in a year, which increases the Q in the CD to the maximum value (12 g kg⁻¹) (Figure 9a). On the other hand, CAPE increases significantly in this region, with an average value of 568 J kg⁻¹ and a maximum value of 4938 J kg⁻¹ (Figure 10). Under these conditions, more and stronger convections can happen to produce larger raindrops and wider rain spectra than in other seasons. Overall, the scenarios in autumn and spring differ slightly in terms of either Q or CAPE.

Horizontal winds and relative vorticity at 850 hPa at 2000 BJT, 0200 BJT, 0800 BJT, and 1400 BJT are plotted in Figure 11. During 2000–0200 BJT, the southerly flow from the Yunnan-Guizhou Plateau (as marked in Figure 1) to the eastern Sichuan Basin is significantly enhanced, and the horizontal wind in the Sichuan Basin exhibits cyclonic rotation. This cyclonic flow, strengthened at night, brings water vapor to the Sichuan basin [55] and enhances the convergence uplift at the eastern slope of the TP. The relative vorticity in the Sichuan Basin is below 0.4 × 10⁻⁵ s⁻¹ in the daytime and increases at night, reaching a maximum value of around 0.8 × 10⁻⁵ s⁻¹. In all, the increase in relative vorticity and water vapor at night benefits the diurnal variation in precipitation. In addition, the diurnal variation in precipitation is highly related to topography. At night, the TP turns from a heat source to a cold source, and the surface temperature is lower than that of the Sichuan Basin. On the one hand, the downslope wind blowing into the basin from the plateau’s eastern slope converges with the basin’s air, increasing the upward movement and the precipitation [56]. On the other hand, the cold air on the plateau moves over the warm and humid airflow in the basin at night, aggravating the instability of the atmospheric junction in the basin. This may make collision merging more efficient at night than during the daytime.

4.2. Comparison of $lo{g}_{10}{N}_w$–$D_m$

The $lo{g}_{10}{N}_w$–$D_m$ distribution can reflect the overall difference in raindrop diameter and number concentration of RSDs observed in different rain types and different climatological regions. The $lo{g}_{10}{N}_w$–$D_m$ distributions for total precipitation samples, stratiform precipitation, and convective precipitation observed in CD of the WSB are calculated as shown in Figure 12. It can be seen that the raindrop spectrum of stratiform precipitation and convective precipitation in the CD generally lie on the left and right sides of a dividing line proposed by Bringi et al. [27], respectively. The average of $D_m$ and $lo{g}_{10}{N}_w$ for stratiform precipitation in CD is 1.166 mm and 3.3776, respectively, which are below than 1.958 mm and 3.524 for convective precipitation. Moreover, $D_m$ distribution in stratiform precipitation is more concentrated than in convective rains, which is consistent with the results in Beijing (northern China) [38], though there are apparent differences in $D_m$ values. Compared with Bringi’s observation results of typical continental and maritime convective precipitation, convective rainfall in the CD area is more likely to be continental precipitation.

The mean values of $D_m$ and $lo{g}_{10}{N}_w$ for each precipitation type observed in various regions of China are summarized in

Table 2. Mean values of $D_{\mathrm{m}}$ and $lo{g}_{10}{N}_w$ for each precipitation type observed in various regions of China. The unit of $N_w$ is m⁻³ mm⁻¹.

Location	Chengdu (WSB)	Naqu (Mid-TP)	Daocheng (East TP)	Chongqing (Eastern Sichuan Basin)	Nanjing (East China)	Beijing (North China)	Zhuhai (South China)
Str. $D_m$ (mm)	1.166	1.084	0.932	1.13	1.3	1.02	1.53
Str. $lo{g}_{10}{N}_w$ (m−3 mm−1)	3.376	3.6	3.467	3.83	3.45	3.71	3.87
Con. $D_m$ (mm)	1.958	1.830	1.496	1.67	1.71	1.30	2.21
Con. $lo{g}_{10}{N}_w$ (m−3 mm−1)	3.524	3.5	3.437	3.92	3.8	4.16	4.36
All $D_m$ (mm)	1.252	1.3	―	1.13	1.4	―	1.47
All $lo{g}_{10}{N}_w$ (m−3 mm−1)	3.389	3.39	―	3.76	3.55	―	3.86
Reference	Present study	Chen et al. 2017 [22]	Wang et al. 2020 [13]	Liu et al. 2021 [46]	Chen et al. 2013 [43]	Han et al. 2021 [38]	Zhang et al. 2019 [57]

. For stratiform precipitation, the mean $D_m$ of the CD area is comparable to that of the eastern Sichuan Basin [46], smaller than that of East and South China [43,57], and larger than that of North China, East TP, and Middle TP [13,22,38]. Meanwhile, the mean $lo{g}_{10}{N}_w$ of the CD area is smaller than that of the other regions to different extents. For convective rains, the mean $D_m$ of the CD area is smaller than in south China and higher than in the other five regions. Mean $lo{g}_{10}{N}_w$ in the CD area has a similar value to Mid-TP, whereas it is slightly larger than in East TP and much smaller than in the other four regions.

5. Conclusions

This work focuses on the RSD variations and characteristics in the CD of WSB based on a three-year dataset. The main findings can be summarized as follows.

The local RSD exhibits apparent seasonal differences. Winter has the lowest raindrop concentration in all diameter classes. Spring has the highest concentrations of small raindrops (D < 1 mm), followed by summer and autumn; summer possesses the highest concentration of medium-to-large raindrops (D ≥ 1mm), followed by spring and autumn. Spring and autumn have similar concentrations when D is within 1–2 mm. On average, summer shows the largest D_m, while winter shows the smallest; spring possesses the largest N_T, and autumn has the largest N_W; the $\mu$ and $\mathsf{\Lambda }$ in cold seasons are larger than those in warm seasons. The normalized Gamma model can represent the observed RSDs of all seasons well.

Diurnal variations in RSD are also found. Generally, the RSD at night can be broader than in the daytime, and the raindrop spectrum is the narrowest during 1400–1500 BJT and the widest during 1100–1200 BJT. $D_{m }$ is lower in the daytime than in the nighttime while $lo{g}_{10}{N}_w$ has a larger value in the daytime than at night.

The investigation of RSD differences between different rain types suggests that stratiform precipitation is more frequent than convective precipitation in the CD of WSB. Meanwhile, it is found that the local convective rainfall is more likely to be continental precipitation. Intercomparisons show that the mean $D_m$ of convective rains in CD is smaller than in South China but it is higher than that in the eastern slope of TP, middle TP, eastern Sichuan Basin, and East and North China; meanwhile, $lo{g}_{10}{N}_w$ is close to the value at the middle TP. The local empirical relationships of $\mu$–$\Lambda$ and Z–R are also presented, which were expected to provide valuable references for optimizing the RSD parameterization scheme and quantitative precipitation estimation of different precipitation types in the WSB.