An Investigation of the Characteristics of the Mei–Yu Raindrop Size Distribution and the Limitations of Numerical Microphysical Parameterization

Abstract

This study examines a Mei-Yu rainfall event using rain gauges (RG) and OTT Parsivel disdrometers to observe precipitation characteristics and raindrop size distributions (RSD), with comparisons made against Weather Research and Forecasting (WRF) model simulations. Results show that Parsivel-derived rain rates (RR) are slightly underestimated relative to RG measurements. Both observations and simulations identify 1–3 mm raindrops as the dominant precipitation contributors, though the model overestimates small and large drop contributions. At low RR, decreased small-drop and increased large-drop concentrations cause corresponding leftward and rightward RSD shifts with decreasing altitude—a pattern well captured by simulations. However, at elevated rainfall rates, the simulated concentration of large raindrops shows no significant increase, resulting in negligible rightward shifting of RSD in the model outputs. Autoconversion from cloud droplets to raindrops (ATcr), collision and breakup between raindrops (AGrr), ice melting (MLir), and evaporation of raindrops (VDrv) contribute more to the number density of raindrops. At 0.1 < RR < 1 mm·h⁻¹, ATcr dominates, while VDrv peaks in this intensity range before decreasing. At higher intensities (RR > 20 mm·h⁻¹), AGrr contributes most, followed by MLir. When the RR is high enough, the breakup of raindrops plays a more important role than collision, leading to a decrease in the number density of raindrops. The overestimation of raindrop breakup from the numerical parameterization may be one of the reasons why the RSD does not shift significantly to the right toward the surface under the heavy RR grade. The RSD near the surface varies with the RR and characterizes surface precipitation well. Toward the surface, ATcr and VDrv, but not AGrr, become similar when precipitation approaches.

1. Introduction

Precipitation is one of the most common and watched weather phenomena among various meteorological events, and rainstorm and flood disasters account for nearly 40% of the losses caused by natural disasters worldwide. China is one of the regions most frequently affected by rainstorms and flood disasters [1,2]. In China, the Mei-Yu front is known as a typical quasi-stationary front around the Yangtze and Huaihe rivers that occurs every year from June to July. With long durations, long wind ranges, and intense and concentrated rainfall, the Mei-Yu rainfall is highly prone to causing flood disasters [3,4,5]. Raindrops, the final products of complex macro- and microlevel processes within clouds, inevitably directly cause surface precipitation. The raindrop size distribution (RSD) describes the variation in the number of raindrops with a certain diameter per unit volume. Research on RSD can provide in-depth insights into the dominant microphysical processes within clouds, such as collision-coalescence, breakup, and evaporation, and how these processes vary with rainfall intensity and environmental conditions [6,7,8].

Two primary categories of RSD measurements established through electronic technologies have been used worldwide [9,10,11]. The first type comprises near-surface detection such as impact-type Joss-Waldvogel Disdrometer (JWD), the laser-optical OTT Parsivel disdrometers, and the two-dimensional video disdrometers (2DVDs). The second type comprises vertical detectors such as the vertically pointing Micro Rain Radar (MRR).

Benefiting from these measurement methods, many studies on RSD have been conducted worldwide. These studies have focused on the statistical characteristics of different climate zones, precipitation types, precipitation intensities, and underlying surfaces. For example, Bringi et al. [12] analyzed the microphysical characteristics of different precipitation types in various global climate zones. They reported that the characteristics of stratiform precipitation are generally similar across different climate zones and that the characteristics of convective precipitation are divided into “maritime” and “continental” categories by climate zones, with the “maritime” type predominantly characterized by high concentrations of small raindrops, whereas the “continental” type is characterized primarily by low concentrations of large raindrops. Using 2DVD data, Bang et al. [13] compared the RSD differences between the southern Korean Peninsula (KOR) and Norman, Oklahoma, United States (OKL), and reported that the number of large (small) raindrops was smaller (higher) in KOR than in OKL. Han et al. [14] found a maritime nature of convective precipitation throughout the warm season in China. Some studies have focused specifically on RSD observations during the Mei-Yu season, investigating the statistical features in various geographical locations [15,16].

Owing to insufficient measurement site density and limitations in detection technology [17], the detection data exhibit distinct shortcomings in temporal–spatial resolution. Numerical models can parameterize the RSD to elucidate complex microphysical processes through quantitative calculations and then provide high temporal–spatial resolution outputs. Therefore, to deeply and clearly understand the microphysical process, it could be helpful to combine observations from measurements and numerical simulations. Gao et al. [18] examined the microphysical features of convective precipitation over the Tibetan Plateau with ground-based millimeter cloud radar (MMCR, advanced disdrometer HSC-PS32) and microphysical parameterization schemes in the WRF model. Wang et al. [19], using radar observations, investigated the capabilities of four microphysical schemes in simulating typhoons and reported that the Thompson scheme performed better.

In summary, most of the previous studies have primarily focused on either observational statistics or comparison of numerical model schemes. However, observations remain an essential means for model validation. Thus, research on how to integrate observations to uncover the limitations of microphysical parameterizations is highly valuable, and it provides a reliable approach for the regional adaptation of these schemes. Based on a Mei-Yu event, this study employed data from RG and Parsivel to validate both the macroscopic precipitation distribution and the microphysical raindrop size distribution in numerical models, thereby investigating the limitations of the microphysics parameterizations. The remainder of this paper is organized as follows: Section 2 introduces the Mei-Yu rainfall event. Section 3 introduces the datasets, methods, and numerical experiments; Section 4 analyzes the precipitation, raindrop size distribution and microphysical processes; and Section 5 and Section 6 provide a summary and discussion, respectively.

2. Study Case

Figure 1 shows the large-scale circulation at 0000 UTC on 5 July 2020, from the European Centre of Medium-Range Weather Forecasts Reanalysis v.5 global reanalysis (ERA5). A short-wave trough at 500 hPa was located behind the middle and lower reaches of the Yangtze River, which was between the 300 hPa upper-level jet exit and the 850 hPa low-level jet entrance. The 850 hPa cross section lying at 30°N was stable, with strong convergence at a low level. With the 588-gpdm contour, which indicates subtropical high pressure and was located near 20°N, a large amount of water vapor was transported from the South China Sea to the middle and lower reaches of the Yangtze River, and the vapor flux at 925 hPa was clearly visible.

It is essential to examine whether the precipitation of this event exhibits characteristic Mei-Yu front rainfall distribution patterns. The distribution of the 24 h accumulated precipitation at observation stations in the middle and lower reaches of the Yangtze River is displayed in Figure 2. As Figure 2 shows, precipitation occurred mainly in Hubei, Anhui, Jiangsu, and Zhejiang Provinces. The rain belt was distributed in a typical Mei-Yu quasi-east–west direction. Seven stations accumulated surface rainfall exceeding 125 mm day⁻¹ in total, and the maximum rainfall was located at Xiantao in Hubei Province, with a value of 151 mm·day⁻¹.

3. Datasets, Model Experiments and Methods

3.1. Observational Datasets

The surface precipitation data observed via RG at automatic weather stations were downloaded from the “Meteorological Big Data Cloud Platform-Tianqing” [20]. The data with a 1 h resolution have been quality controlled by the “Meteorological Data Operation System (MDOS)”, with a data availability rate of 100%, and are widely utilized in various weather analyses.

The parsivel, an laser OTT second-generation particle size and velocity distrometer, measures the diameters and terminal velocities of particles based on the attenuation amplitude of the laser beam signal and the duration of signal changes when particles fall through the laser beam sampling area. Both the volume equivalent diameters and terminal velocities are measured in 32 bins per minute, with diameters ranging from 0.25 to 25 mm and velocities ranging from 0.2 to 22.4 m·s⁻¹ [16,21]. Quality control was performed as follows. Initially, the first two bins of velocity and diameter with low signal-to-noise ratios were excluded [21]. Second, particles larger than 8 mm were removed because of the rarity of raindrops larger than 8 mm in the natural atmosphere [22]. Next, particles exceeding the 60% range of the expected theoretical velocity–diameter relationship ($V=9.65-10.3e^{-0.6D}$) were removed [23,24]. Finally, samples with particle counts less than 10 or detected RR < 0.1 mm·h⁻¹ were excluded [25].

With the measured volume equivalent diameter class I (D_i), the number of raindrops in diameter class I (N(D_i), m⁻³·mm⁻¹) is given by

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

(1)

where n_ij is the number of raindrops in diameter class i and velocity class j; A is the effective measuring area (54 cm²); ∆t is the measuring time interval (60 s); V_j is the fall velocity of raindrops in class j (m·s⁻¹); and ∆D_i is the width in diameter class I (mm).

Based on N(D_i), the precipitation parameters, such as the rain rate distribution R_D(D), RR (mm·h⁻¹), and liquid water content Lwc (g·cm⁻³), are defined as follows [26,27]:

$$R_D\left(D\right)={\displaystyle \frac{6\pi }{{10}^4}}{D_{\mathrm{i}}}^{3}N(D_i)V(D_i)$$

(2)

$$RR={\displaystyle \frac{6\pi }{{10}^4}}{\displaystyle \sum _{\mathrm{i}=1}^{32}{D_{\mathrm{i}}}^{3}N\left(D_i\right)V\left(D_i\right)}\Delta D_{\mathrm{i}}$$

(3)

$$Lwc={\displaystyle \frac{\pi }{6000}}{\displaystyle \sum _{i=1}^{32}{D_{\mathrm{i}}}^{3}N\left(D_i\right)\Delta D_i}$$

(4)

Moment methods are commonly applied to determine the parameters of the RSD. The nth-order moment of RSD (M_n) can be expressed as follows:

$$M_n={\displaystyle \sum _{\mathrm{i}=1}^{32}{D_i}^{n}N\left(D_i\right)\Delta D_i}$$

(5)

The third and fourth moments are utilized for calculating the mass-weighted mean diameter D_m (mm) and the normalized number concentration N_w (mm⁻³·mm⁻¹) [28,29]:

$$D_m={\displaystyle \frac{M_4}{M_3}}$$

(6)

$$Nw={\displaystyle \frac{4^4}{\pi {\rho }_w}}\left({\displaystyle \frac{{10}^3{L}_{wc}}{{D_m}^4}}\right)$$

(7)

where ρ_w (1.0 g·cm⁻³) is the water density.

3.2. Model Experiments

3.2.1. Model Experimental Design

The Weather Research and Forecasting (WRF) model (version 4.1.1) was employed to conduct the simulation. The experiment was configured with two nested grids of 9 and 3 km horizontal grid spacing. The model refined the near-ground layers in the vertical direction to analyze the near-surface microphysical characteristics, with a total of 51 vertical levels and a model top of 10 hPa. The physics schemes used were the Morrison two-moment bulk microphysical scheme [30], the Kain–Fritsch cumulus scheme (not used in the 3 km domain) [31], the RRTM longwave, and the Dudhia shortwave radiation scheme [32,33], the ACM2 planetary boundary layer scheme [34], and the unified Noah land-surface scheme [35]. The simulation was started at 1200 UTC on 4 July 2020 and integrated for 24 h, ending at 1200 UTC on 5 July 2020. Numerical data were output at 1-min intervals to match the temporal resolution of the Parsivel data. ERA5 reanalysis data with a 1 h temporal resolution and 0.25° horizontal resolution provided the initial and boundary conditions [36].

3.2.2. Model Methods

(1) Raindrop Size Distribution

The three-parameter Gamma distribution [37,38] or two-parameter Marshall-Palmer (M-P) distribution [18,39] is generally used in numerical models to describe the RSD. The mathematical form of the Gamma distribution is as follows:

$$N\left(D\right)=N_0{D}^{\mu }{\mathrm{e}}^{-\lambda D}$$

(8)

where D (mm) represents the volume equivalent diameter and N(D) (m⁻³·mm⁻¹) represents the number concentration of raindrops at diameter D per unit diameter range, as expressed in Equation (1). N₀ (mm^−1-u·m⁻³), λ (mm⁻¹), and μ are the intercept, slope, and shape parameters, respectively.

μ is defined as 0 in the Morrison scheme so that the RSD becomes the M–P, and λ and N₀ are calculated by the mass mixing ratio of raindrops Qr (kg·m⁻³) and number density of raindrops Nr (kg·kg⁻¹) as follows:

$$\lambda ={\left(\pi \cdot 997\cdot {\displaystyle \frac{N_{\mathrm{r}}}{Q_r}}\right)}^{{\displaystyle \frac{1}{3}}}$$

(9)

$$N_0=N\mathrm{r}\cdot \lambda$$

(10)

Later, the simulated RSD is obtained by substituting λ and N₀ into Formula (8). In this study, D_m and N_w of the simulation were calculated using Formulas (5)–(7), as Parsivel did.

(2) Raindrop Budget

Formulas (11) and (12) are the source and sink terms of Qr and Nr, respectively, in the Morrison microphysical scheme. The microphysical terms in the formulas are shown in

Table 1. List of microphysical processes.

Symbol	Description
ATcr	Autoconversion from cloud droplets to rain drops
CLcr	Accretion of cloud droplets by rain drops
MLir	Melting of ice hydrometeors (ice, snow and graupel) to rain drops
CLri	Accretion of rain drops by ice hydrometeors
VDrv	Evaporation of rain drops to water vapor
AGrr	Self-collection and breakup of rain drops

. It is clear that ATcr, MLir, CLri, and VDrv contribute to both Qr and Nr, but CLcr contributes only to Qr, and AGrr contributes only to Nr.

$$SQr=ATcr+CLcr+MLir+CLri+VDrv$$

(11)

$$SN\mathrm{r}=ATcr+AGrr+MLir+CLri+VDrv$$

(12)

3.3. Methods

In this study, data from the RG are utilized to characterize the observed precipitation distribution and validating the precipitation from the Parsivel disdrometer and the WRF model, thereby ensuring the reliability of the results. Subsequently, the RSD measured by the Parsivel disdrometer is employed to verify the RSD in the numerical model, which helps to identify the limitations of the RSD parameterization scheme. Additionally, an analysis of raindrop sources and sinks is conducted to explore the underlying reasons for these limitations.

4. Results

4.1. Test of the Parsivel Hourly Rainfall Rate

To ensure the reliability of the Parsivel data after quality assurance, Figure 3 compares the hourly RR values derived from the Parsivel measurements and RG. In particular, the RR values from the Parsivel measurements were averaged over the preceding 60 min, as specified in Formula (3). The precipitation data were generated from 1800 UTC on 4 July to 1200 UTC on 5 July 2020 at all five stations. Overall, Figure 3a shows that the RR values from the Parsivel measurements exhibit a similar temporal evolution trends to those from the RG. With a total of 125 samples, the RR values from the Parsivel measurements were slightly underestimated compared with the RR values from the RG, with a mean bias (BIAS) of 0.83 mm and a root mean square error (RMSE) of 1.94 mm. Compared with the RSD statistical characteristics summarized by Zhou et al. [25] and Fu et al. [16] with Parsivel measurements, the BIAS and RMSE values in this study fall within acceptable ranges, confirming the reliability of the Parsivel data.

4.2. Simulated Precipitation

First, it is necessary to verify the precipitation forecasts from numerical models. Figure 4 shows the distribution of simulated 24 h accumulated surface rainfall from 1200 UTC on 4 July to 1200 UTC on 5 July 2020. The simulated rain belt, ranging from 29.5 to 31.5°N, exhibits an east–west orientation similar to that of the observations. Compared with the observed rainfall belt shown in Figure 2, the simulated belt is narrower in the north–south direction, and the rainfall in the eastern region tends to be positioned more southerly. Notably, two heavy rainfall centers (>150 mm·day⁻¹), located in central and eastern Hubei Province, were identified in the simulation. The maximum rainfall amount of 392 mm·day⁻¹ occurred in eastern Hubei, which is westward and larger than the observed value. The accumulated 24 h rainfall values at the five Parsivel stations fall within the range of from 25 to 150 mm·day⁻¹.

4.3. Simulated Raindrop Size Distribution and Microphysical Processes

4.3.1. Surface Raindrop Size Distribution

To better match the RR values from the Parsivel measurements, the surface RR values from the simulation are calculated using the same method as employed by the Parsivel disdrometer. It should be noted that the simulated values at each of the five stations represent an average within a 3 km radius around the station locations. This spatial averaging approach was adopted to mitigate potential representativeness errors associated with using single grid-point values. Specifically, the RSD values from the simulation are evaluated using Formulas (8)–(10) first, followed by the calculation of RR values via Formula (3). Finally, the RR values on sigma levels are interpolated to the 50 m level using the linear interpolation method. In this section, raindrops are classified into three categories: small raindrops (D < 1 mm), medium raindrops (1 < D < 3 mm), and large raindrops (D > 3 mm).

First, a comparative analysis was conducted on the ground-based raindrop size distributions between the simulation and Parsivel observations. Figure 5 presents the temporal and spatial mean ground-based raindrop size distributions log₁₀N(D) from the Parsivel measurements and simulation under different rain rate grades. The RSD values from the Parsivel measurements exhibit a Gamma distribution with a single peak, whereas the simulated RSD curves follow the M-P distribution. For RR < 5 mm·h⁻¹, the simulated raindrop number concentration is lower than that from the Parsivel measurements, indicating that the model results generally underestimate light precipitation within narrow precipitation range, consistent with the observations shown in Figure 3. As RR increases, both the number concentration and diameter of raindrops increase. For the same RR grade, the simulated number concentration of large (medium and small) raindrops is greater (less) than that from the Parsivel measurements. This indicates that fewer small raindrops and more large raindrops are produced, leading to overestimation of heavy rainfall and underestimation of light precipitation.

Similarly, Gao et al. [18] reported that the numerical model produced fewer small raindrops and more large raindrops in convective clouds over the Tibetan Plateau. Furthermore, the spatially averaged RSD values over the five stations are essentially consistent with those averaged over the precipitation belt, except for RR < 1 mm·h⁻¹ and RR > 40 mm·h⁻¹. These statistical characteristics are consistent with our results. Therefore, the vertical characteristics of the mean RSD are further analyzed.

Figure 6 shows the temporal and spatial mean rain rate distributions (R_D(D)) with the particle diameter (D) from the Parsivel measurements and simulations under different rain rate grades. R_D(D) represents the contribution of raindrops with varying diameters to total precipitation. R_D(D) from the Parsivel measurements and simulation show that medium raindrops contribute the most to precipitation, which is consistent with the conclusions of Zhou et al. and Tokay et al. [21,25]. As the RR increases, the R_D(D) from the Parsivel measurements shifts to the right toward the surface, with the maximum contribution raindrop diameter increasing from 0.9 mm to 2.8 mm. However, with increasing RR, the simulated R_D(D) shifts rightward for RR < 20 mm·h⁻¹. As a result, the Parsivel measurements remain upright, with the maximum contribution raindrop diameter remaining at approximately 2.2 mm for RR > 20 mm·h⁻¹. Additionally, compared with the R_D(D) from the Parsivel measurements, the simulated result exhibits a broader distribution and lower peak values under most rain rate grades, except for RR > 40 mm·h⁻¹. This results in greater contributions from small and large raindrops to total rainfall in the simulation.

4.3.2. Vertical Raindrop Size Distribution

The vertical RSD is comprehensively influenced by various microphysical processes, such as collision, melting, and evaporation. The investigation on the vertical RSD contributes to a better understanding of these complex microphysical processes. Raindrops are predominantly found below the melting layer (at approximately 5.5 km), and this study focuses on microphysical processes below 5.5 km. The vertical profile of RSD typically varies with different precipitation intensities. D_m and N_w are commonly used to characterize the overall features of the raindrop spectrum. Figure 7 shows the mean vertical profiles of D_m and log₁₀N_w from simulations under different rain rate grades. Below the melting level, the increase in the rain rate RR corresponds to increases in D_m and log₁₀N_w. However, the magnitudes of increase differ across various heights. For example, as the RR increases, the increase in log₁₀N_w below 4 km is more remarkable, indicating that microphysical processes have a greater impact on the RSD in the lower layer than in the upper layer.

Based on aircraft observations, Geoffroy et al. [40] reported that the mean diameter of raindrops tends to increase, whereas the number concentration tends to decrease during their fall. In general, the numerical model in this study basically simulates raindrop growth, namely, D_m increases gradually, and log₁₀N_w first increases but then decreases with decreasing altitude. Notably, for RR < 20 mm·h⁻¹, D_m exhibits a significant positive correlation with height, while log₁₀N_w shows a substantial negative correlation with height, suggesting abundant growth of raindrops as they fall. For RR > 20 mm·h⁻¹, conversely, both D_m and log₁₀N_w change slightly as height decreases below 1.5 km, indicating a decelerated rate of raindrop growth.

In addition, the D_m and N_w from the simulation generally vary with RR. However, for RR > 20 mm·h⁻¹, this pattern no longer holds near the surface, potentially because the breakup effects, such as raindrop growth, limit D_m in a specific range, although it allows N_w to rise. Above 4.5 km, owing to the complexity of cloud microphysical processes, N_w no longer increases significantly and even begins to decrease for RR > 20 mm·h⁻¹.

The vertical profiles of raindrop size spectra under various rain rate grades provide insights into the differences in cloud microphysical processes associated with varying precipitation regimes. Figure 8 shows the mean vertical distributions of the raindrop size distribution log₁₀N(D) from simulations under different rain rate grades. Under the weak precipitation grade (RR ≤ 1 mm·h⁻¹), the vertical RSD tends to be narrow and primarily consists of raindrops smaller than 3 mm. From the melting level to a height of approximately 4 km, the raindrop log₁₀N(D) increases with decreasing altitude. Below 4 km, as the altitude decreases, the log₁₀N(D) with D < 1.5 mm significantly decreases, causing the vertical raindrop spectrum of small raindrops to shift leftward, and the log₁₀N(D) with D >2 mm significantly increases, leading to a rightward shifting of the rain spectrum of large raindrops (Figure 8a). With increasing RR, the log₁₀N(D) under the same diameter grade increases notably; for example, for RR > 40 mm·h⁻¹, the log₁₀N(D) of raindrops with 2 mm diameters is approximately four times greater than that under RR ≤ 1 mm·h⁻¹ grade. Additionally, the raindrop size distribution broadens significantly, and the log₁₀N(D) with D > 6 mm also increases. Notably, below 3 km, the log₁₀N(D) of large raindrops (D > 3 mm) changes less dramatically toward the surface, so the vertical RSD does not indicate a rightward tilt trend and remains upright.

A vertical raindrop spectrum with leftward shifting trends in small raindrops and rightward trends in large raindrops are observable in the studies conducted by Song et al. [41] and Zhou et al. [25] using MMR data. They assumed that the evaporation of raindrops into water vapor and the self-collection of raindrops results in a decrease in the concentration of small raindrops and an increase in the concentration of large raindrops. However, for RR > 20 mm·h⁻¹ from the simulation in this study, as the altitude decreases, the relatively upright trend of the RSD and slowing down of the D_m and log₁₀N_w ratios notably differ from the observations from Song et al. [41] and Zhou et al. [25]. the underlying reasons for these discrepencies will be explained through an analysis of microphysical processes contributing to raindrop growth in the subsequent sections.

4.3.3. Microphysical Processes

Figure 9 shows the mean vertical profiles of microphysical process rates for the raindrop mass mixing ratio Qr under different rain rate grades via Equation (11). Specifically, ATcr, CLcr, MLir, VDrv, and CLri are the dominant pathways for the mass mixing ratio of raindrops. The first three terms are source terms, the last two terms are sink terms, and the total term is the sum of the sink and source terms.

As shown in Figure 9, the rates of different microphysical processes vary significantly with altitude under different rain rate grades. Above 4 km, MLir and CLcr contribute the most to Qr, MLir is significantly stronger than CLcr for RR < 20 mm·h⁻¹, whereas CLcr is significantly greater than MLir for RR > 40 mm·h⁻¹. Below 4 km, CLcr, MLir, and VDrv contribute the most to Qr.

As RR increases, all processes become stronger. For 0.1 < RR ≤ 1 mm·h⁻¹, VDrv reaches its maximum of approximately −0.2 ×10⁻³ g·m⁻³·s⁻¹ at approximately 4 km, and the maximum number concentration of small droplets lies at nearly 4 km in Figure 8a, indicating that the evaporation process conducted by small raindrops is quite active to the extent that small raindrops usually cannot grow into larger droplets. Subsequently, with increasing RR, the three dominant processes exhibit certain variations. Specifically, VDrv increases toward the surface when the RR > 40 mm·h⁻¹ (Figure 9f). CLri leads to a reduction in Qr, mainly above the melting layer, and the ratio of CLcr to MLir first increases and then decreases as the altitude decreases until CLcr contributes more to Qr closer to the ground.

In conclusion, three microphysical processes (i.e., CLcr, MLir, and VDrv) dominate the mass mixing ratio of raindrops, and they all intensify with increasing RR. The importance of CLcr and MLir varies with RR. The total source-sink ratio values of Qr below 1 km are negative under all rain rate grade values, indicating the more important effect of evaporation.

Moreover, ATcr, MLir, CLcr, and VDrv play large roles in raindrop number density Nr in addition to AGrr. Figure 10 shows the mean vertical profiles of the microphysical process rates for Nr under different rain rate grades.

The relative contributions of VDrv and MLir show comparable effects on Nr and Qr. In other words, as RR increases, VDrv intensifies with decreasing altitude and contributes more to Nr near the surface. Meanwhile, the contribution of MLir to Nr first increases and then weakens as altitude decreases. Notably, ATcr and CLri exert a more significant influence on Nr than they do on Qr. In general, both AGrr and CLri increase with rainfall rate, with CLri remaining the smallest contributor on Nr. At 0.1 < RR < 1 mm·h⁻¹, ATcr dominates, while VDrv peaks in this intensity range before decreasing. At higher intensities (RR > 20 mm·h⁻¹), AGrr contributes most, followed by MLir. Notably, MLir and ATcr reach their maxima at 10 < RR < 20 mm·h⁻¹ and 20 < RR < 40 mm·h⁻¹, respectively, then decline. Below 2 km altitude, the magnitudes of key source/sink terms for raindrop number concentration decrease significantly.

Moreover, AGrr, the process that involves self-collection and breakup of raindrops, is quite complex [42]. When falling, larger raindrops collect smaller raindrops, resulting in an increase in the mean diameter and a decrease in the number concentration. Then, the grown raindrops upon reaching a certain size threshold will break up, leading to a decrease in the mean diameter and an increase in the number concentration. For RR < 20 mm·h⁻¹, a negative AGrr ratio from upper levels to the surface means that self-collection processes are stronger than breakup processes, leading primarily to a negative impact on Nr. Therefore, more large raindrops are generated, resulting in a noticeable rightward trend of RSD toward the surface, as shown in Figure 7a and Figure 8a–d. When RR > 20 mm·h⁻¹, the ratio of AGrr near the surface is positive and leads to an increase in Nr. The breakup of large raindrops contributes more than the accretion of small raindrops by large raindrops, leading to a decrease in the concentration of large raindrops. As a result, the distribution of RSD near the surface shows negligible variation (Figure 7a and Figure 8e,f). In addition, log₁₀N_w shows little variation with decreasing altitude (Figure 7b). In conclusion, the simulation tends to overestimate the breakup process when rainfall is strong, which may lead to the simulated number concentration of large raindrops not shifting to the right significantly under heavy RR grades near the surface, as results from the Parsivel measurements show.

4.3.4. Relationships Between the RSD and Surface Precipitation

The relationship between the RSD and surface precipitation is analyzed with respect to microphysical processes and surface rainfall at the Wuhan station, where the simulated hourly RR evolution was closest to the observations. First, the RR evolution is shown in Figure 11a. There are three RR peaks from 0100 to 0300 UTC on 5 July 2020. The RR reaches its peak value at T2, followed by a decrease at T3. The RR values at T4 and T5 are comparable. Next, the evolution of the ground-based raindrop size distribution, expressed as log₁₀N(D), is shown in Figure 11b. The surface raindrop number concentration first increases but then decreases synchronously with the evolution of RR during the T1 to T3 period. Moreover, the surface number contribution values at T4 and T5 are similar, indicating that the surface raindrop spectrum can characterize surface precipitation well.

To investigate the characteristics of the vertical raindrop spectrum, Figure 12 presents the evolution of the vertical profiles of D_m and log₁₀N_w from the simulation at the Wuhan station. During the period from T1 to T3, D_m and log₁₀N_w first increase and then decrease; that is, both D_m and log₁₀N_w increase with the rising RR from T1 to T2 and then decrease as the RR decreases from T2 to T3. However, even though the RSD values are similar at T4 and T5, the profiles of D_m and log₁₀N_w differe significantly.

Figure 13 shows the evolution of the vertical profiles of the Nr budget terms. From T1 to T3, RR increases first and then decreases, both the total term and VDrv exhibit similar trends, with VDrv remaining consistently negative. ATcr continues to decrease and contributes positively to Nr on a consistent basis. AGrr makes negative contributions during the enhancement stage T1 and attenuation stage T3, but positive contributions during peak stage T2 due to the breakup of large raindrops, which further confirms the significant breakup process during heavy precipitation, as analyzed in Section 4.3.3. At T4 and T5, ATcr and VDrv values become closer near the surface, but the dominant AGrr term differs significantly, resulting in a substantial difference in the total source and sink balance.

5. Conclusions

In this study, based on RG, Parsivel measurements, and model results, we investigated the characteristics of the raindrop size distribution of a Mei-Yu rainfall event and the limitations of RSD parameterization and microphysical mechanisms. The conclusions are as follows:

(1) Although slightly underestimated, the RR values from Parsivel measurements trend are consistent with that from RG.

(2) The RSD values from the Parsivel measurements follow a Gamma distribution, whereas the RSD from the simulation follows the M-P distribution. The simulation tends to produce more large raindrops and fewer small raindrops to overestimate heavy precipitation and underestimate light precipitation. Parsivel measurements and simulations indicate that medium raindrops (1 ≤ D < 3 mm) contribute the most to precipitation. With increasing RR, the raindrop size contributing the most to precipitation continues to increase in the Parsivel measurements, and it remains relatively constant when the RR reaches a certain intensity in the simulation. In addition, simulated small and large raindrops exhibit higher contributions to rainfall than observational counterparts

Some studies using MRR have shown that the number concentration of small raindrops decreases and large raindrops increase with decreasing altitude. This leads to a leftward shift in the RSD of small raindrops and a rightward shift in large raindrops near the surface. The simulation in this study shows that RSDs present similar left and right shifting trends except for under the heavy rain rate grades when the RSDs of large raindrops remain upright.

(3) The contributions of different microphysical processes vary significantly with altitude under different rain rate grades. For Qr, CLcr, MLir, and VDrv contribute the most, and they all become stronger as RR increases. Near the surface, CLcr and VDrv contribute more to Qr, and the lower the height is, the larger the contribution of VDrv. ATcr, AGrr, and VDrv play important roles in Nr. At 0.1 < RR < 1 mm·h⁻¹, ATcr dominates, while VDrv peaks in this intensity range before decreasing. At higher intensities, AGrr contributes most, followed by MLir. When rainfall is strong, the overestimated breakup process in the simulation may lead to the number concentration of large raindrops not shifting to the right significantly near the surface, as in some studies conducted with MRR.

(4) The surface RSD varies with the RR to characterize surface precipitation well. The vertical distributions of the RSD and microphysical processes are pretty complex. For Nr, the breakup processes contribute more under the strong rain rate grades, whereas the self-collision process plays a more important role under the slight rain grades. When the RR values are similar, the differences among the ATcr, and VDrv values tend to diminish with decreasing altitude, especially close to the surface. In addition, AGrr has a very different distribution than the other terms.

6. Discussion

In Figure 7, For rainfall rates of 1–10 mm·h⁻¹, Dₘ is smaller than those among other RR intervals, rendering these drops particularly susceptible to collection by larger raindrops. Source-sink term analysis reveals this range exhibits the strongest evaporation effects where potential overestimations of drop evaporation and collection by large drops, coupled with underestimated cloud-to-rain autoconversion, collectively contribute to systematic underestimations of small drop concentrations. Notably, ice-phase processes (raindrop collection by ice particles and ice melting) demonstrate negligible impacts on drop concentration within this rainfall rate regime.

Cloud-to-rain autoconversion (ATcr) requires supersaturation conditions that are rarely met in the near-surface layer, forcing cloud droplets to ascend to higher altitudes for conversion. Following raindrop formation, subsequent growth occurs primarily through collision-coalescence at these elevated levels. Consequently, both ATcr and cloud droplet collection (CLcr) become negligible in the boundary layer, appearing effectively absent in magnitude-based distributions. Below the freezing level, ATcr and CLcr emerge as dominant source terms, governing raindrop formation and evaporation patterns. This results in vapor deposition (VDrv) distributions that closely track these processes across most rainfall rate (RR) regimes. Enhanced raindrop breakup processes under high rainfall rates (RR > 40 mm·h⁻¹) generate abundant small droplets in the near-surface layer, significantly intensifying vapor deposition on rain (VDrv) within affected altitude bands. This mechanism may lead to overestimated raindrop number concentration and consequently reduce the mean volume diameter near the surface, ultimately altering the vertical structure of raindrop size distributions. These results emphasize the importance of refined breakup parameterizations in microphysical schemes for accurately simulating heavy rainfall events.

As noted in previous studies [43,44], the treatment of raindrop collision-breakup processes primarily depends on droplet diameter, where breakup is assumed when diameters exceed a threshold range. However, model results suggest that additional physical constraints should be incorporated to enhance the universality of simulations, such as utilizing observational data (particularly microphysical retrievals from dual-polarization radar data) to constrain model parameters and adopt more advanced or empirically robust physical process parameterization, including next-generation artificial intelligence (AI)-based approaches that explicitly resolve microphysical process interactions, to improve model fidelity. These measures may highlight a critical direction for model improvement for flood forecasting.

In addition, while multiple cloud microphysics parameterization schemes exist with distinct characteristics, our analysis specifically employs the Morrison scheme for a single case study, thus limiting generalizability. Whether this limitation found in the Morrison scheme also exists in other microphysical schemes (e.g., MY, WDM6) requires further systematic comparative investigation. Future work should incorporate: (1) multi-scheme intercomparisons, (2) observational validations across diverse cases, and (3) enhanced breakup criteria to advance microphysical representation.

Additionally, it should be noted that the changing of breakup processes may exert feedback on the thermodynamic structure within clouds. For example, the breakup of large raindrops into numerous smaller droplets substantially increases the total surface area, thereby enhancing evaporation efficiency. This evaporation process induces localized air cooling through latent heat absorption, which under specific atmospheric conditions can lead to cold pool formation with temperature depressions exceeding 2–3 °C. These cold pools subsequently modulate convective development through outflow boundary generation, enhanced low-level convergence, and inhibition of warm inflow, ultimately influencing storm organization and precipitation distribution. When raindrop breakup is weakened, the number of small droplets decreases. Therefore, the weakening of raindrop breakup effects reduces evaporation cooling, thereby inducing opposing changes in the thermodynamic fields mentioned above. In future studies, we will systematically examine how raindrop breakup modulates both thermal and dynamic processes within precipitation systems.