Raindrop Size Distribution Characteristics for Typhoons over the Coast in Eastern China

Abstract

This study investigates the characteristics of the raindrop size distribution (DSD) for five typhoons that made landfall or passed by Zhejiang on the eastern coast of China, from 2019 to 2022. Additionally, it examines the raindrop shape–slope (µ-Λ) relationship, as well as the local Z-R relationship for these typhoons. The DSD datasets were collected by the DSG1 disdrometer located in Ningbo, Zhejiang Province. Based on rainfall rate (R), the DSD can be categorized into convective and stratiform rainfall types. Some rainfall parameters can also be derived from the DSDs to further analyze the specific characteristics of rainfall. The histograms of the generalized intercept parameter (log₁₀N_w) exhibit negative skewness in both convective and stratiform rainfall, whereas the histograms of the mass-weighted mean diameter (D_m) of raindrops display positive skewness. During typhoon periods on the eastern coast of China, the DSD characteristic was composed of a lower number concentration of small and midsize raindrops (3.42 for log₁₀N_w, 1.43 mm for D_m in the whole dataset) as compared to Jiangsu in eastern China, Tokyo, in Japan, Miryang, in South Korea, and Thiruvananthapuram in south India, respectively. At the same time, the scatter plots of D_m and log₁₀N_w indicate that the convective rain during typhoon periods exhibits characteristics that are intermediate between “maritime-like” and “continental-like” clusters. Additionally, the raindrop spectra of convective rainfall and midsize raindrops in stratiform rainfall are well-represented by a three-parameter gamma distribution. The µ-Λ relation in this region is similar to Taiwan and Fujian, located along the southeastern coast of China. The Z-R relationship for eastern coastal China during typhoons based on filtered disdrometer data is Z = 175.04R^1.53. These results could offer deeper insights into the microphysical characteristics of different rainfall types along the eastern coast of China and potentially improve the accuracy of precipitation estimates from weather radar observations.

1. Introduction

China is ranked as one of the countries most significantly impacted by typhoons. The associated intense rainfall each year leads to a high number of natural disasters [1,2]. Exploring the characteristics and underlying physical mechanisms of typhoon-induced heavy rainfall is crucial for enhancing efforts in meteorological disaster prevention and mitigation [3,4]. The study of typhoon-induced heavy rainfall has been analyzed by numerous meteorologists who obtained valuable findings through synoptic diagnostic analysis, numerical simulations, and various approaches [5,6,7]. Current predictions of typhoons are significantly reliant on how numerical weather prediction (NWP) models depict microphysical processes, which remain subject to considerable uncertainties [7]. Therefore, it is imperative to know more about these microphysical processes. Acquiring a comprehensive understanding of these microphysical characteristics is key to enhance the precipitation parameterization schemes in numerical models [8,9,10,11]. The microphysical properties of various rain types (e.g., convective, stratiform, mixed, and light rainfall) within typhoon-induced rainfall exhibit unique characteristics [12,13,14]. The raindrop size distribution (DSD) is also pivotal in studying the microphysical structural characteristics of clouds [15,16,17,18]. By examining the concentration of raindrops per unit volume as a function of scale, rainfall integral parameters and the dual polarimetric radar variables can be calculated [3,16,19,20], which has significant implications for improving typhoon forecast and weather radar quantitative precipitation estimation (QPE). The precision of QPE hinges on the accuracy of the power-law Z-R relationship, denoted as Z = AR^b. Here, Z denotes the abstract radar reflectivity factor measured by single-polarization and dual-polarization radars, with R indicating the rainfall rate [21,22,23]. An accurate radar precipitation relationship can improve the precision of regional radar QPE and NWP.

The characteristics of ground-measured raindrop spectra are regularly influenced by factors such as regional climate, topography, and rainfall types [24,25,26,27]. Feng et al. [27] examined the DSDs of Typhoon Mangkhut during its landfall in southern China, discovering that its DSDs significantly varied from those observed in various Chinese regions and even from typhoons within the same region. Bao et al. [12] demonstrated that the characteristics of typhoon DSDs vary significantly with increasing rainfall rates across different convective rainbands. Their findings further suggest that the variations in DSD parameters could be affected by the considerable amount of water vapor transported from the ocean by the typhoon, coupled with the typhoon’s strong winds. Bringi et al. [24] conducted extensive research on the characteristics of DSDs across various global climatic regions using disdrometers and polarimetric radars. Their studies indicate that compared to continental convective rainfall, maritime convective rainfall contains a higher concentration of smaller-sized raindrops; they delineated convective rainfall into two distinct types: “maritime-like” and “continental-like” clusters. Chang et al. [23] studied the DSDs of typhoons landing in northern Taiwan and proposed that the interaction of these typhoons with the complex terrain of Taiwan causes convective rainfall to exhibit characteristics intermediate between “maritime-like” and “continental-like” clusters. However, the DSD characteristics during the landfall of seven typhoons in continental China (Guangdong and Jiangsu Provinces) tend to resemble those of a “maritime-like” cluster [13]. This is due to the smaller mean mass-weighted diameter (D_m) in the convective rainfalls compared to those observed in southeastern China [23,28] and the United States [4]. The D_m in northern Taiwan is slightly larger, attributed to the lifting effect of the Central Mountain Range [23].

Current research points to a trend of typhoon paths moving northward due to global warming [27,29]. Zhejiang province is located in east China, to the north of Taiwan, Guangdong, and Fujian. This suggests that Zhejiang is likely to witness a rise in the occurrence of typhoons making landfall. Despite extensive research about DSDs of typhoons in southern and southeastern China [13,21,22,23], there is a notable gap in studies focusing on the microphysical characteristics of rainfall in the Zhejiang coastal region, part of China’s eastern seaboard. It is not only located at a critical juncture connecting Southern and Northern China but also encompasses the most complex terrain within the Yangtze River Delta. This further drives us to investigate the characteristics of typhoon raindrop spectra along the eastern coast of China. The purpose of this study is to investigate the DSD of five typhoons that affected Zhejiang and its surrounding areas from 2019 to 2022. These typhoons include “Lekima” in 2019, “Hagubit” in 2020, “In-Fa” and “Chanthu” in 2021, and “Muifa” in 2022. In this study, we concentrate on analyzing the DSD characteristics, raindrop shape–slope relationship, and local Z-R relationship for the five typhoons along China’s eastern coast. This research may contribute to enhancing the predictive accuracy of regional models for typhoon precipitation and improve the precision of local radar QPE.

Following this introduction, Section 2 provides a concise overview of the datasets and methods used in this study. Section 3 examines the DSD characteristics of various typhoons, presenting detailed statistical analyses of DSDs across various rain types and contrasting their distinct characteristics. Finally, Section 4 summarizes the findings and draws conclusions based on observations.

2. Materials and Methods

2.1. Instruments and Datasets

Figure 1 illustrates that the eastern coast of China was impacted by the five typhoons from 2019 to 2022. The data for these typhoons were sourced from the Tropical Cyclone Data Center of the China Meteorological Administration (https://tcdata.typhoon.org.cn/zjljsjj.html, accessed on 21 May 2024). The DSD data, collected by an DSG1 disdrometer and processed by the Jiangsu Institute of Electronics and Information Technology Corporation of China, are used to reveal microphysical properties during the five typhoons. The DSG1 disdrometer is situated at the Ningbo Meteorological Observatory in Zhejiang Province, roughly a 10 m distance from the rain gauge. The disdrometer operates on a principle similar to the OTT PARSIVEL disdrometer, with both utilizing the attenuation of laser light by raindrops. This enables precise measurements of particle diameter, velocity, and rain rate at one-minute intervals [29,30,31]. Several studies have utilized the DSG1 to analyze DSD characteristics [29,30,31].

The DSG1 has a sampling area of 54 cm², with a sampling interval of 1 min [32]. It includes 32 size channels (median diameter spans from 0.062 to 24.5 mm) and 32 velocity channels (median velocity spans from 0.05 to 20.8 m s⁻¹). Since raindrops are generally non-spherical during their descent, it is necessary to correct the raindrop spectrum data for shape distortion to reduce errors [33,34,35]. According to the research results of Battaglia et al. [36], the shape distortion is considered negligible and the drops are assumed to be spherical with diameters below 1 mm. The raindrops are oblate ellipsoidal with an aspect ratio (ar, the ratio of particle height to width) ranging from 1 to 0.7 when the diameter is between 1 and 5 mm, that is, ar = 1.075 − 0.075D, where D is the raindrop diameter. Moreover, they are considered oblate ellipsoidal particles with an aspect ratio of 0.7 (ar = 0.7) when they have a diameter greater than 5 mm.

2.2. Methods

The accuracy of the disdrometer detection can be compromised by various factors, including sampling and noise effects, such as raindrop splashes and strong winds [37,38]. These instrument issues could lead to the misidentification of unrealistically large slow-falling raindrops and small fast-falling raindrops [16,39]. In this study, the following data quality control procedures were executed. (1) Since the signal-to-noise ratio is very low for the first two diameter bins in the disdrometer and raindrops larger than 8 mm are almost non-existent in natural rainfall, we remove data from the first two diameter bins with low signal-to-noise ratios (0.062 and 0.187 mm), as well as the sizes greater than 8 mm [3]. The final effective range of raindrop diameters is from 0.25 to 8.0 mm. (2) According to the Atlas et al. (1973), the relationship between the terminal velocity (V) of falling raindrops and diameter is V = 9.65 − 10.3exp(−0.6D) in the ideal conditions. However, the disdrometer tends to produce velocity errors when winds are stronger than 10 m s⁻¹. Therefore, it is necessary to exclude disdrometer data that deviate from the theoretical terminal velocity of raindrops by more than ±60% [3,13,30]. (3) Remove the noise data from the disdrometer that raindrop numbers are lower than 10 or R is less than 0.1 mm h⁻¹ within one minute. Moreover, precipitation events exceeding 10 min are deemed valid and shorter ones are excluded [21,22]. Finally, this study utilized 9218 one-minute DSD samples from the five typhoons. The rainfall can be categorized as stratiform and convective, according to the characteristics of R and its temporal variation from the previous studies [3,21,22]. It is of significant importance to investigate the characteristics and distinctions between these two rainfall types. According to the classification methodology outlined by Tokay et al. [40] and Chen et al. [3], stratiform rainfall is characterized by the R lies between 0.5 to 5 mm h⁻¹ from ti to ti + N and its standard deviation of R is less than 1.5 mm h⁻¹. Comparatively, convective rainfall is defined as when R exceeds 5 mm h⁻¹ and the standard deviation of R is over 1.5 mm h⁻¹. The other remaining data are categorized as mixed rainfall, which is not the primary focus of this study. The N is set to be ten samples in this study. Consequently, the dataset contains approximately 736 one-minute samples (7.98%) categorized as convective and 3363 one-minute samples (36.48%) classified as stratiform, respectively. Interestingly, during the five typhoon-induced precipitation events, 80.39% of the rainfall samples had an R below 5 mm h⁻¹, while 11.04% had an R between 5 and 10 mm h⁻¹.

The raindrop number concentration in the ith size class, denoted as N(D_i), and can be mathematically represented as follows:

$$\mathrm{N}({\mathrm{D}}_{\mathrm{i}})={\displaystyle \sum _{j=i}^{32}\frac{n_{ij}}{A\times \Delta t\times {\mathrm{V}}_j\times \Delta D_i}}$$

(1)

where N(D_i) (mm⁻¹ m⁻³) is the number concentration of raindrops per unit volume per unit size interval for raindrop diameter D_i (mm); n_ij is the total number of drops recorded at the ith size class and the jth velocity class; Δt is the sampling time (60 s); A(m²) is the sampling area; and V_j (m s⁻¹) is the falling velocity at the jth velocity class. Based on V(D), N(D_i), and the density of water (ρ_w, considered to be 1.0 g cm⁻³), various parameters can be calculated, such as the total concentration of raindrops (N_T, m⁻³), R (mm h⁻¹), liquid water content (W, g m⁻³), and radar reflectivity factor (Z, mm⁶ m⁻³), which are defined as follows:

$${\mathrm{N}}_{\mathrm{T}}={\displaystyle {\int }_{D_{\min }}^{{\mathrm{D}}_{\max }}\mathrm{N}(D)dD}$$

(2)

$$\mathrm{R}={\displaystyle \frac{6\pi }{{10}^4}}{\displaystyle {\int }_{D_{\min }}^{D_{\max }}{\mathrm{D}}^{3}N(D)V(D)dD}$$

(3)

$$\mathrm{W}={\displaystyle \frac{\pi {\rho }_{\mathrm{w}}}{6000}}{\displaystyle {\int }_{{\mathrm{D}}_{\min }}^{D_{\max }}{\mathrm{D}}^{3}N(D)dD}$$

(4)

$$\mathrm{Z}={\displaystyle {\int }_{{\mathrm{D}}_{\min }}^{D_{\max }}{\mathrm{D}}^{6}N(D)dD}$$

(5)

The three-parameter gamma function adeptly characterizes the raindrop spectra [41,42], and is expressed as

$$\mathrm{N}(D)=N_0{D}^{\mu }{e}^{-\Lambda D}$$

(6)

where N₀ represents the intercept parameter, μ denotes the shape parameter, and Λ indicates the slope parameter. The truncated moment method [26,43,44] is selected for calculating the three parameters (N₀, μ, and Λ), utilizing the 2nd, 4th, and 6th moments as follows. The nth-order moment can be described as

$${\mathrm{M}}_n={\displaystyle {\int }_0^{\infty }N(D)D^{n}dD}={\mathrm{N}}_0{\displaystyle {\int }_0^{\infty }{D}^{n+\mu }}{e}^{-\Lambda D}dD=N_0{\displaystyle \frac{\Gamma (n+1+\mu )}{{\Lambda }^{n+1+\mu }}}$$

(7)

$$\eta ={\displaystyle \frac{{\mathrm{M}}_4^2}{M_2{M}_6}}$$

(8)

$$\mu ={\displaystyle \frac{(7-11\eta )-{[{(7-11\eta )}^2-4(\eta -1)(30\eta -12)]}^{1/2}}{2(\eta -1)}}$$

(9)

$$\Lambda ={\left[{\displaystyle \frac{(4+\mu )(3+\mu )M_2}{M_4}}\right]}^{1/2}$$

(10)

$${\mathrm{N}}_0=M_2{\displaystyle \frac{{\Lambda }^{3+\mu }}{\Gamma (3+\mu )}}$$

(11)

The D_m (mm), which is pivotal in characterizing the DSD, involves computing the ratio of the 4th moment to the 3rd moment of the DSD. This mathematical expression is presented as follows:

$${\mathrm{D}}_{\mathrm{m}}={\displaystyle \frac{M_4}{M_3}}={\displaystyle \frac{{\displaystyle {\int }_{{\mathrm{D}}_{\min }}^{D_{\max }}{\mathrm{D}}^{4}N(D)dD}}{{\displaystyle {\int }_{{\mathrm{D}}_{\min }}^{D_{\max }}{\mathrm{D}}^{3}N(D)dD}}}$$

(12)

And the generalized intercept parameter (N_w, mm ⁻¹ m ⁻³) is computed as

$${\mathrm{N}}_w={\displaystyle \frac{4^4}{\pi {\rho }_w}}\left({\displaystyle \frac{W}{D_m^4}}\right)$$

(13)

3. Results

3.1. Overview of Typhoons

Figure 2 illustrates the temporal evolution of the DSD characteristics during the periods affected by five distinct typhoons. The DSG1 disdrometer recorded the raindrop spectrum data for the five typhoons that either made landfall or closely skirted Zhejiang (Figure 1). The specific description of the variations in DSD characteristics across different typhoons are as follows.

It can be seen that before 0800 LST (local standard time) on 9 August 2019, the Ningbo area may have been affected by the spiral rainband of typhoon Lekima and then the main rainband of the typhoon hit the area (Figure 2a). Raindrops can be classified into three categories according to their diameters: small raindrops (0.3~1 mm), medium raindrops (1~3 mm), and large raindrops (more than 3 mm) [4,45]. Most of Lekima’s raindrops are under 3 mm in diameter and the principal rainband features a significantly high concentration of small raindrops, with the number concentration exceeding a logarithmic value of 2.2 (log₁₀N(D)). In contrast, following its rapid decline in strength after making landfall, Typhoon Hagupit demonstrated less variability in its DSDs compared to Typhoon Lekima (Figure 2b). In addition, as illustrated in Figure 2b, it is evident that Typhoon Hagupit had two distinct impact processes on Ningbo. The first segment is characterized by intermittent precipitation with a short-duration high concentration of small drops, while the latter segment involves sustained precipitation with a comparatively lower number concentration. The R is relatively weak in both segments.

Typhoon In-Fa was the one among these five typhoons with the longest duration of rainfall, lasting about 7 days (Figure 2c). Initially, the rainfall intensity was weak with nearly all raindrops under 3 mm in size and a low number concentration. However, with the rapid increase in the concentration of small and midsize raindrops, the precipitation intensity quickly strengthened, resulting in some short-duration heavy rainfall events. The maximum R was 102.0 mm h⁻¹ at 0217 LST on 23 July 2021. During the occurrence of short-duration heavy rainfall, the concentration of small and midsize raindrops reached over logarithmic 2.7 (log₁₀N(D)), accompanied by the emergence of large raindrops exceeding 4 mm in diameter. The maximum drop diameter (7.5 mm) appeared at 0157 LST on 23 July 2021 with a corresponding R of 80.8 mm h⁻¹. Typhoon Chanthu had a shorter duration of impact compared to typhoon In-Fa. Additionally, due to its greater distance from China’s eastern coast (Figure 1a), Typhoon Chanthu had comparatively weaker wind and rain impacts. The short-duration heavy rainfall of Typhoon Chanthu mainly occurred around 1000 LST on 13 September 2021 but its intensity was much weaker than Typhoon In-Fa. The maximum rainfall rate was 30.1 mm/h at 1023 LST on 13 September 2021, with a maximum raindrop diameter of 4.75 mm, both of which are less than those recorded during Typhoon In-Fa. Additionally, the DSD characteristics of Typhoon Chanthu exhibited similarity to those of Typhoon Lekima, with a high concentration of small and midsize raindrops (Figure 2d). However, the impact duration of Chanthu was shorter. Throughout the period affected by Typhoon Chanthu, the majority of the rainfall was recorded on 13 September 2021.

During the period of influence of Typhoon Muifa, two distinct precipitation episodes were recorded on 13 and 14 September 2022, respectively. The Muifa brought only a small amount of rain on 12 September 2022, characterized primarily by sporadic light showers (Figure 2e). Subsequently, the intensity of the rainfall gradually increased, primarily due to a rising concentration of small- and medium-sized raindrops, along with increasing larger droplets. The peak R was about 46.6 mm h⁻¹ at 1753 LST on 13 September 2022. This was due to the high concentration of small- and medium-sized raindrops, accompanied by large raindrops exceeding 5 mm in diameter. Rainfall intensity gradually diminished from the evening of 13 September to the dawn of 14 September 2022. The intensity increased once more on the morning of the 14 September, continuing through to the evening of the same day. Note that a substantial number of small- and medium-sized raindrops reappeared during this period. The peak R on 14 September was recorded at 0957 LST, achieving 60.8 mm h⁻¹.

3.2. Distribution of D_m and N_w

Figure 3 presents the frequency histograms of D_m and log₁₀N_w with three commonly used indexes (mean, standard deviation (SD), and skewness (SK)) extracted from both the entire and individual datasets for each type of rain during typhoon periods. The mean values of D_m and log₁₀N_w along the eastern coast of China showcase the largest raindrops (1.43 mm for D_m) and the lowest concentrations (3.42 for log₁₀N_w), in contrast to other regions such as Jiangsu in eastern China (1.41 mm for D_m, 4.67 for log₁₀N_w) [13], Tokyo in Japan (1.25 mm for D_m, 3.74 for log₁₀N_w) [46], Miryang in South Korea (1.19 mm for D_m, 3.44 for log₁₀N_w) [47], and Thiruvananthapuram in southern India (1.21 mm for D_m, 3.66 for log₁₀N_w) [10]. The larger D_m and the lower N_w values may be attributed to the orographic effects of Zhejiang [23]. Moreover, Figure 3a highlights considerable variability in D_m and N_w across the whole dataset, evidenced by their high SD (D_m for 0.42 mm and log₁₀N_w for 0.43, respectively). Considering the two main types, the mean of D_m and log₁₀N_w values for stratiform rainfall are 1.33 mm and 3.33, respectively, which are lower compared to those for convective rainfall (1.99 mm and 3.58, respectively). Additionally, while the D_m for both stratiform and convective rainfall show positive skewness (1.95 and 1.67, respectively), their log₁₀N_w exhibit negative skewness (−0.31 and −0.90, respectively) from Figure 3b,c.

Figure 4 illustrates the distribution of log₁₀N_w-D_m scatter points for convective (orange) and stratiform (sky blue) rainfall during the typhoon periods. Bringi et al. [24] reported that convective rainfall systems characterized as “maritime-like” generally have a D_m of around 1.5–1.75 mm and a logarithmic N_w of approximately 4–4.5. In contrast, “continental-like” systems feature a D_m of 2–2.75 mm and a logarithmic N_w of 3–3.5, as illustrated by the two rectangles in Figure 4. As illustrated in Figure 4, the convective log₁₀N_w-D_m data in this study fall between the “maritime-like” and “continental-like” clusters, with only a portion of the convective log₁₀N_w-D_m data situated within the “continental-like” cluster and a minor fraction observed in the “maritime-like” cluster. The solid circle represents the average of convective log₁₀N_w-D_m taken from this study (Ningbo). Zheng et al. [8] and Feng et al. [27] conducted analyses on typhoon Kajiki (cross symbol) and Mangkhut (solid triangle) convective rainfall in the South China Sea and Guangdong, respectively, finding that the DSD characteristics in these regions lean toward the “maritime-like” cluster. The square boxes denoted the results of the four typhoon convective rainfalls in Jiangsu, eastern China, which were obtained by Wen et al. [13]. They found that the average values of D_m and log₁₀N_w for convective rainfall from the typhoons over Jiangsu (eastern China) were 1.28 mm and 4.55, respectively (solid square). Their results also show that the DSD characteristics of typhoons over eastern China lean toward the “maritime-like” cluster. These results further indicate that the convective precipitation of typhoons contains larger raindrop diameters and lower raindrop concentrations over the eastern coast of China. Chang et al. [23] revealed a slightly larger raindrop diameter (2 mm for D_m) and marginally higher concentration (3.8 for log₁₀N_w) for 13 typhoon convective rainfalls over northern Taiwan (plus sigh) compared to the eastern coast of China. These characteristics may be attributed to the more complex topography of Zhejiang. Note that the classification of convective DSDs as “maritime-like” or “continental-like” clusters depends on the geographical locations and mechanisms of the rainfall system.

The N_w and D_m values offered insights into the characteristics of the DSD and these parameters exhibited a unique relationship with the R [3,9]. As illustrated in Figure 5, scatter distributions of D_m-R and log₁₀N_w-R for the two rainfall types are depicted during the typhoon periods and the corresponding least squares fitted curves. The fitted exponent of both D_m-R and log₁₀N_w-R for convective and stratiform rainfall is positive, indicating that the values of D_m and N_w are positively correlated with the R. The log₁₀N_w-R relationship reveals that the exponent associated with stratiform rainfall is lower than that for convective rainfall, showing that with increasing rainfall intensity, the rate at which raindrop concentration rises is lower for stratiform rainfall compared to convective rainfall. Furthermore, the exponents for log₁₀N_w-R for both rainfall types are lower compared to those for D_m-R. This implies that the increase in rainfall for stratiform rainfall is mainly driven by the size of raindrops, whereas for convective rainfall, it is influenced by both the size and concentration of the raindrops. Nevertheless, the distribution of raindrop sizes narrows with increasing R. The D_m for convective rainfall stabilized at nearly 2.5 mm, while for stratiform rainfall, it leveled off at around 1.8 mm. This indicates that the size of the raindrops reaches an equilibrium state (attained through raindrop breakup and coalescence processes [48]). The further increase in rainfall rates is attributed to the elevated number concentration under the raindrop DSD equilibrium condition [49] and such behaviors were also reported for tropical cyclone rainfall [9,13,23,46,50].

3.3. Composite Raindrop Spectra

To further explore the microphysical processes during typhoon rainfalls, Figure 6 presents the composite raindrop spectra for the convective and stratiform rainfalls. Furthermore, the average rainfall parameters, meticulously detailed in

Table 1. Average parameters of the raindrop spectrum for various rain types.

Rain Types	NT	R	Dm	W	log10Nw
Convective	566	19.72	1.99	0.85	3.58
Stratiform	165	1.46	1.33	0.08	3.33
Whole	234	4.04	1.43	0.19	3.42

, are derived from the DSDs recorded during the five typhoons. As noted earlier, we apply the truncated moments to fit the three parameters of the DSDs of the convective and stratiform rainfall using a gamma distribution model. As illustrated in Figure 6, the DSDs for both rain types demonstrate different characteristics. Convective rainfall exhibits a broader spectrum width compared to stratiform rainfall, with maximum raindrop diameters exceeding 5 mm. The peak number concentration of convective rainfall primarily ranges from 0.44 to 1.05 mm. Moreover, the number of concentrations for different diameters in convective rainfall tends to be higher than those in stratiform rainfall. These analyses indicate that compared with stratiform rainfall, convective rainfall has a higher raindrop concentration, liquid water content, and rainfall rate (Table 1). Figure 6 clearly demonstrates that the three-parameter gamma distribution primarily matches the DSD characteristics of convective rainfall and aligns well with the medium diameter (1.0 to 2.3 mm) raindrops of stratiform rainfall, although its fit is less accurate for larger diameters. This study further demonstrates that the mathematically modeled gamma distribution might exhibit some discrepancies with the raindrop spectrum characteristics of stratiform rainfall. Zhang et al. [26] offer a detailed analysis of biases in DSD parameters, which were not accounted for in this study.

3.4. µ-Λ Relationship

Several studies indicate that the Gamma distribution is well-suited for characterizing DSD in different rain types, making it a widely utilized way in microphysical parameterization schemes [19,25,51]. Nevertheless, the shape parameter μ is typically assumed to be a constant [3,26]. The three parameters of the Gamma distribution function, N₀, μ, and Λ, are interdependent [5,19,52]. Understanding the relationship among them can enhance the parameterization scheme of the Gamma distribution in eastern coastal China. This is crucial for improving model forecasts and QPE using dual-polarization radar. Drawing on video-disdrometer data from Florida in the summer of 1998, Zhang et al. [26] established an empirical µ-Λ relationship for R greater than 5 mm h⁻¹ and raindrop numbers exceeding 1000. Additionally, Zhang et al. [26] also indicate that the µ-Λ relationship changes depend on climatological conditions, rain types, and geographical location. In recent years, different µ-Λ relationships have been reported at several different climate regimes, including Oklahoma [35], Scotland [53], Taiwan [9,23], Singapore [51], Palau islands [50], central China [31], northern China [20], South China Sea [54], and southern China [21,22]. Therefore, analyzing and determining the µ-Λ relationship for the eastern coast of China is essential. In this study, we utilized the methods outlined by Zhang et al. [26] to fit the DSD data that satisfied the specified criteria. Consequently, the µ-Λ relationship specific to convective rainfall during typhoons in eastern coastal China is as follows and is depicted with a black line in Figure 7.

Λ = 0.023μ² + 0.541μ + 1.594

(14)

Furthermore, upon comparing the μ-Λ relationships during typhoons in Taiwan (red dashed line), Fujian (orange dashed line), and continental China (Jiangsu and Guangdong; blue dashed line), it becomes evident that the μ-Λ relationship from this study closely aligns with those of Taiwan and Fujian, yet significantly diverges from those observed in continental China [13]. Notably, the μ-Λ relationship identified in our research exhibits a considerably higher μ value for a given Λ than those reported in the aforementioned studies. Ulbrich et al. [41] discovered that the relationship between μ and Λ could be expressed as ΛD_m = 4 + μ. The three gray lines correspond to D_m values of 1.0 mm, 1.5 mm, and 2.5 mm, respectively (Figure 8). The relationships identified within this study’s region, as well as those in Fujian and Taiwan, all reside within the relatively larger D_m region. Furthermore, Zhejiang is geographically proximate to Fujian and Taiwan, exhibiting comparable complex terrain characteristics. They are all susceptible to direct influence from similar typhoon systems in the western Pacific Ocean. Such factors may contribute to the similarity in microphysical processes during typhoons across these three regions, ultimately resulting in the formation of relatively large raindrop diameters. However, Wen et al. [13] reported that the continental regions of China (Guangdong and Jiangsu) feature higher concentrations of small raindrops during typhoons. This phenomenon could be attributed to the interplay between the vast amounts of water vapor from the ocean and the local anthropogenic aerosols, which might significantly influence the distinctive features of DSDs during typhoons [13]. However, it is important to note that exploring this topic is beyond the scope of the present study and remains a topic for future research. This further illustrates that the typhoon DSD characteristics in the eastern coast of China significantly differ from those in continental China [13]. Therefore, the aforementioned conclusions clearly demonstrate that the µ-Λ relationship varies depending on the specific location.

3.5. Z-R Relationship

The Z-R relationship (Z = aR^b) serves as the cornerstone for radar QPE. In the classic Z-R relationship for continental rainfall in the mid-latitude regions of the United States, it is expressed as Z = 300R^1.40 [55]. Numerous studies have illustrated the multifaceted influence of factors such as atmospheric conditions, climate, rainfall systems, geographical location, and topography on the Z-R relationship [5,10,34,35,50]. Therefore, it is imperative to derive a local Z-R relationship based on the DSD characteristics of eastern coastal China to enhance the precision of local radar QPEs.

Using the least squares method, we fitted the Z and R for whole rainfall derived from raindrop spectrum data, focusing on minute samples containing more than 1000 raindrop numbers. Consequently, we established the radar Z-R relationship for the eastern coastal China as Z = 175.04R^1.53. The exponent greater than 1 in the relationship equation may result from the collision and coalescence of raindrops [50,56]. Research indicates that in mid-latitude regions, the Z-R relationship for convective rainfall generally features a larger coefficient A and a smaller exponent b. Conversely, tropical regions tend to have a smaller coefficient A and a larger exponent b. This suggests that typhoon rainfall impacting eastern coastal China may be similar to tropical rainfall. To compare the Z-R relationships with those from other regions, Figure 8 illustrates the Z-R relationships for continental China (Jiangsu and Guangdong, shown with orange line) [13], southeastern coastal China (Fujian, depicted with green line) [28], and Taiwan (illustrated with purple line) [23]. The specific equations are detailed in

Table 2. Z-R relationship (Z = aR^b) coefficient (a) and power (b) over different regions.

Studies	Region	a	b
Fulton et al. [55]	NEXRAD	300	1.4
Chang et al. [23]	Taiwan, Southeastern China	206.83	1.45
Chen et al. [28]	Fujian, Southeastern China	308	1.32
Wen et al. [13]	Continental China (Jiangsu and Guangdong)	147.28	1.38
This study	eastern coast of China	175.04	1.53

. The Z-R fitting curve for eastern coastal China (depicted by the black solid line) closely resembles that of Taiwan and exhibits similarities to Fujian within the 10–30 mm h⁻¹ rainfall intensity (Figure 8). In comparison to the typhoon rainfall in the eastern coastal region, the Z-R relationship for Fujian tends to underestimate rainfall intensities below 10 mm h⁻¹ and overestimate those above 30 mm h⁻¹ for a given Z value. Additionally, the purple line (orange line) rests above (below) the black line, suggesting that the NEXRAD (continental China (Jiangsu and Guangdong)) has a tendency to underestimate (overestimate) typhoon rainfall in eastern coastal China. These findings further reveal that Z-R relationships can differ markedly across various regions, terrains, and climatic regimes.

4. Conclusions and Discussions

This research employs data from a DSG1 disdrometer in Ningbo to examine the characteristics of DSD during the five typhoons in eastern coastal China from 2019 to 2022. It further conducts a comparative analysis of Z-R relationships in various regions affected by typhoons. The key conclusions are summarized below.

(1)

Across all rainfall types, including stratiform and convective rainfall, log₁₀N_w shows negative skewness, while D_m shows positive skewness. The average D_m for the whole rainfall is 1.43 mm, with an average log₁₀N_w of 3.42. These values are larger than those found in stratiform rainfall (D_m = 1.33 mm, log₁₀N_w = 3.33) but smaller than those observed in convective rainfall (D_m = 1.99 mm, log₁₀N_w = 3.58). Compared to other regions, eastern coastal China experiences typhoon rainfall with lower concentrations and larger-sized raindrops. Therefore, the log₁₀N_w-D_m data for convective rainfall in the region lies within the range of the “continental” and “maritime” clusters;

(2)

By separately fitting the average diameter and corresponding mean number concentration of convective and stratiform rainfall, the results reveal that the raindrop spectra of convective rainfall closely match the three-parameter gamma distribution model, while the mid-sized raindrops of stratiform rainfall generally conform to the gamma distribution model. Additionally, the convective R substantially exceeds that of stratiform and whole rainfall, primarily driven by the larger diameter of raindrops in convective rainfall, along with higher liquid water content and concentration. The µ-Λ relationship for convective rainfall from typhoons on the eastern coast of China is represented by Λ = 0.023μ² + 0.541μ + 1.594. This finding closely resembles typhoon rainfalls in Taiwan and Fujian along the southeastern coastal China but exhibits notable disparities compared to typhoon rainfall in continental China (Jiangsu and Guangdong);

(3)

A least-squares fit is conducted on datasets where the number of raindrops in whole samples exceeded 1000, resulting in the Z-R relationship for eastern coastal China during typhoons being Z = 175.04R^1.53. This relationship closely aligns with the Z-R relationship observed in Taiwan. Using the Z-R relationship for Fujian tends to underestimate R below 10 mm h⁻¹ and overestimate those above 30 mm h⁻¹. Conversely, the NEXRAD system’s Z-R relationship generally underestimates typhoon rainfall in eastern coastal China, while the Z-R relationships from continental China (Jiangsu and Guangdong) tend to overestimate it.

This study is the first to analyze the DSD characteristics of different rainfall types during typhoons in eastern coastal China. It enhances understanding of the variations in microphysical characteristics of typhoon raindrop distributions caused by different precipitation processes. This is particularly significant for model microphysical parameterization and QPE using dual-polarization radar and rainfall measurement satellites. Because of varying DSD characteristics, the coefficients of Z-R relationships for different samples vary significantly. For a given radar echo, QPE values from different relationships can differ substantially. Although the study unearthed intriguing insights from the DSD characteristics during the typhoon periods, these findings could remain preliminary due to the limited number of precipitation episodes sampled and the absence of comprehensive observations across a sufficient number of surface sites. Long-term observations ought to be implemented, utilizing a greater amount of collected data during typhoon periods. Previous studies have shown significant differences in the DSD characteristics of various rainfall systems within the same region [3,13]. Therefore, further analysis of warm-season (non-typhoon) rainfall in eastern coastal China is warranted. Future studies should focus on comparing these properties to those observed during the warm season (non-typhoon), aiming to quantitatively discern the differences in DSD among distinct rainfall systems. Additionally, the thermal and dynamic processes in a typhoon’s spiral rainbands differ significantly from those in the eyewall, leading to notable differences in DSD characteristics at various stages of the typhoon [8,12]. Overall, eyewall rainfall exhibits a broader spectral width and higher raindrop concentration across all sizes compared to spiral rainbands [12,30]. Future research should focus on further analyzing the differences in DSD between spiral rainbands and eyewall regions of multiple typhoons in eastern coastal China. Furthermore, this study only suggests that topography may influence the DSDs of typhoons, without offering a detailed analysis. More comprehensive studies will likely require DSD data from various locations, radar observations, and numerical simulations.

The findings of this study suggest that the D_m is larger and the N_w is lower compared to continental China (Jiangsu and Guangdong) during typhoons, possibly due to topographical influences or potential measurement errors [23,57]. The principle of the DSG1 disdrometer is similar to the OTT that exhibits limitations in measuring small droplets compared to instruments like the meteorological particle spectrometer (MPS) and two-dimensional video disdrometer (2DVD) [13,21,22]. It has become crucial to secure more comprehensive DSD measurements through the utilization of more precise instruments, such as the MPS and 2DVD. Additionally, it is worth exploring the application of the drizzle mode reconstruction technique in this region. This initiative is slated for implementation in the near future.