Characteristics of Raindrop Size Distributions during Meiyu Season in Mount Lushan, Eastern China

Abstract

Meiyu front precipitation makes the region prone to frequent floods, mudslides, landslides, and other disasters and has been the focus of ongoing and challenging meteorological research. Investigation of the Raindrop size distribution (RSD) is essential for exploring the characteristics and underlying physical precipitation processes. In this study, the precipitation characteristics in Lushan mountainous areas during the Meiyu season were investigated using laser disdrometer observed RSD data from 2016 to 2020. For the average spectra of five rain rate classes, the concentrations of large raindrops (> 0.5 mm) increased with rain rate (R), whereas the concentrations of small raindrops (< 0.5 mm) increased only under rain rates higher than 10 mm h⁻¹. The gamma distribution parameters of N₀ (intercept parameter) and Λ (slope parameter) increased/decreased with rain rate, and the shape parameter µ exhibited negative values in different rain rate classes. The distribution pattern features were N(D) =721D^−1.79e^−1.20D. Distributions of the frequency for mass-weighted mean diameter (D_m) and the logarithm of the generalized intercept parameter (log₁₀ N_w) both showed a unique bimodal type, and an exceptionally high N_w (log₁₀N_w > 4.5) subset with small D_m was determined. The stratiform and convective rains of RSD were also investigated. D_m–R and N_w–R showed similar variations in two types of precipitation. The lower µ values resulted in higher primary and constant coefficients in the quadratic polynomial fitting for the µ–Λ relationship (Λ = 0.0347µ² + 1.180µ + 2.495). The Z–R relationship (Z for radar reflectivity factor) in stratiform precipitation characteristics was Z = 203R^1.59. Further investigations showed that high N_w values usually occurred in persistent precipitation. The RSD can be characterized as high concentrations of the first two diameter classes with a narrow spectrum width (< 1 mm), which were captured during in-cloud rain with a low but continuous rain rate (< 5 mm h⁻¹). The mountainous topography plays an important role in reshaping the characteristics of RSD and physical processes of precipitation.

1. Introduction

More accurate precipitation prediction and related physical mechanisms researches are vital for meteorology, climatology, and hydrology. Investigation of the raindrop size distribution (RSD) is essential for exploring the characteristics and underlying physical precipitation processes (Rosenfeld and Ulbrich 2003). The characteristics of RSD from ground-based observations are synthetic and address the microphysics and thermal dynamics within, or outside, precipitation clouds (Rosenfeld and Ulbrich 2003; Thomas et al. 2021). The parameterization of RSD is fundamental to improve the microphysics of clouds and precipitation in numerical model simulations (Haddad et al. 1996; Milbrandt and Yau 2005; Rotstayn 1997; Sun 2005; Tapiador et al. 2014, 2019). RSD researches have contributed to improving quantitative precipitation estimations (QPEs) for weather radar and satellite observations (Atlas et al. 1999; Chandrasekar and Bringi 1987; Chandrasekar et al. 2003; Rosenfeld and Ulbrich 2003; Seto et al. 2021; Tokay and Short 1996; Ulbrich and Atlas 1998; Zhang et al. 2001; Zhao et al. 2011).

The characteristics of RSD vary according to geographical locations (Chang et al. 2009; Chen, B. et al. 2017; Dolan et al. 2018; Luo et al. 2020; Niu et al. 2010; Radhakrishna et al. 2020; Sauvageot and Lacaux 1995; Zhao et al. 2011), climate regimes (Bringi et al. 2003; Yamaji et al. 2020), seasons (Chakravarty and Raj 2013; Seela et al. 2018; Wen et al. 2017), and rain types (Atlas and Ulbrich 2006; Chen et al. 2013, 2016; Thompson et al. 2015; Tokay and Short 1996). RSD characteristics and their variations may differ considerably between different disdrometer instruments (Angulo-Martínez et al. 2018) or even between the same instrument but within a short distance (Tapiador et al. 2010). Systematic RSD studies have been performed over the past two decades to better understand the characteristics of RSD in the East Asian monsoon region. Statistical studies of RSD, ranging from northern China to the Tibetan Plateau have been conducted, and the RSD characteristics significantly vary in different regions. Physical processes between stratiform and convective rains also exhibit obvious differences in different climate regimes (Chen, B. et al. 2013, 2017; Ji et al. 2019; Luo et al. 2020; Niu et al. 2010; Wen et al. 2016; Zhang et al. 2019).

Meiyu is a climatological phenomenon that affects the weather and climate in eastern Asia and usually induces abundant precipitation (Ding 1994). The Meiyu/Baiu front is characterized as a quasi-stationary front along the north edge of a subtropical high stretching from the Yangtze River basin to south Japan and presents unique weather systems during the Meiyu season. Previous research has shown that heavy precipitation events and related flood disasters are likely caused by the Meiyu/Baiu front (Tao and Ding 1981; Xu et al. 2008; Yasunari and Miwa 2006; Zhao et al. 2019). Additionally, it can influence extreme precipitation in Mount Lushan by adjusting the low-level jet (Li et al. 2012). Hashimoto and Harimaya (2003) analyzed the Baiu RSD data obtained in south Japan using principal component analysis and found two principal components of variation of RSD, which could be attributed to the difference between convective and stratiform precipitation. Different characteristics of RSD variation were obtained in their subsequent study, the major precipitation mechanism in the mature and dissipation stages of the Meiyu/Baiu convective clouds (Hashimoto and Harimaya 2005). Oue et al. (2010) and Oue et al. (2011) found and characterized different RSD with low echo-top and large Z_h (radar reflectivity) in stratiform and convective rain zones within the Meiyu/Baiu frontal rainband in the Okinawa region by simultaneously applying a C-band polarimetric radar and a disdrometer. Chen et al. (2013) found that the mass-weighted diameter (D_m) and generalized intercept parameter N_w in eastern China were lower than those reported in Japan (Bringi et al. 2003). Wen et al. (2016) studied the RSD characteristics and differences in convective, stratiform, and shallow rains, higher N_w and lower D_m values than those of Chen et al. (2013) were obtained. More recently, Fu et al. (2020) studied RSD characteristics in central China and demonstrated different N_w and D_m values and different µ–Λ and Z–R relationships. Although such studies have furthered the understanding of RSD in precipitation processes, few have focused on mountainous regions, and even less attention has been given to the impacts of mountainous topography on RSD characteristics and the related physical processes.

To understand the physical processes within the Meiyu precipitation concerning the high variety of RSD characteristics among different geographical locations, more RSD observations and studies are needed. The Lushan Mountains, with most peaks being more than 1000 m, are known as typical horst block mountains. They are in the northern Jiangxi Province, which faces Poyang Lake to the east and borders the Yangtze River in the north (Fig. 1a). The high mountainous topography of Mount Lushan can act as an elevated platform to investigate the interactions between aerosols, clouds, and precipitation because it is close to the cloud base or within the cloud directly (Duan et al. 2021; Guo et al. 2019). Continuous field observations of cloud and fog processes in Mount Lushan have been conducted since 2015 at the Lushan Cloud and Fog Experiment Station, and in this study, a laser precipitation monitor disdrometer was applied to observe the RSD characteristics. The long-term observed RSD dataset in Mount Lushan provides opportunities for investigating more comprehensive RSD characteristics and related physical processes under mountainous topographical conditions.

This study aims to explore the characteristics of RSDs during the Meiyu season in Mount Lushan from 2016 to 2020. This study is structured as follows: Section 2 describes the data and methods. Section 3 presents the characteristics of RSDs for different rain rates and rain types and the relationships between RSD parameters and gamma fitting parameters. Section 4 discusses the dataset with specific properties, and Section 5 summarizes the conclusions.

2. Data and methods

2.1 Observations

A Laser Precipitation Monitor (LPM) from Thies CLIMA was set at the observational platform of the Lushan Cloud and Fog Experiment Station in Mount Lushan (29.57°N, 115.97°E, 1080 m ASL) (Fig. 1). The LPM is a ground-based optical disdrometer with a sampling area of 45.6 cm² and a temporal resolution of 1 min. The RSD data were collected every 1 min in a 22 × 20 matrix that recorded the raindrop numbers of each diameter and velocity bin. The diameter ranged from 0.125 mm to larger than 8 mm, and the velocity ranged from 0 to 20 m s⁻¹.

Fig. 1.

Geographical location and surrounding topography of Mount Lushan (a), topographical features of Mount Lushan (b), overview of the observational platform (c), and the Thies CLIMA Laser Precipitation Monitor (LPM) (d). Locations of the observational platform (red pentagram) and Lushan Meteorological Bureau (blue pentagram) are marked in (b), and the position of the LPM (red arrow) is shown in (c).

2.2 Methods

a. LPM data quality control

The effective sampling area for laser optical sensors is affected by the border effects (Battaglia et al. 2010). In the ith size class, the effective sampling area is 228 × (20–D_i) mm² and D_i (mm), which is the mean diameter for the i th size diameter class (Jaffrain and Berne 2011). The incorrect records of small particles with high falling speed are named as the “margin fallers” and detected when they partially cross the sampling area (Yuter et al. 2006). Strong winds and splashing usually cause spurious particle recording, and according to previous studies, the empirical terminal velocity–diameter (V–D) relationship is constantly used to assess and eliminate spurious records (Chen, B. et al. 2013, 2017; Ji et al. 2019). In this study, we chose the empirical V–D relationship with the air density correction factor to assess the raindrop data (Atlas et al. 1973):   

where ρ₀ and ρ_a (1.20 kg m⁻³) are the air density at the observation level and sea level, respectively. The temperature and pressure data of the automatic meteorological station (AWS) of the Lushan Meteorological Bureau (29.57°N, 115.97°E, 1165 m) were used to retrieve the correction factor. Using the AWS data in June and the first half of July from 2016 to 2020, the average pressure and temperature during the Meiyu season were first calculated, and ρ₀/ρ_a was then derived through the ideal gas state equation (P = ρRT). Finally, a correction factor of 1.0655 was obtained. Thus, the terminal velocity V(D_i ) of each diameter bin D_i was achieved, and the particles out of the velocity range V(D_i) ± 0.6V(D_i) were removed (Friedrich et al. 2013; Jaffrain and Berne 2011) (Fig. 2).

Fig. 2.

Schematic diagram of quality control. The color blocks indicate the numbers of the sampled particles, and the solid line and dash lines show the corrected V–D relationship and the range of V(D_i) ± 0.6V(D_i). Particles falling outside the dash lines were removed.

b. Raindrop size distribution parameters

The raindrop size distribution is depicted as the number concentration of raindrops N (D_i) (m⁻³ mm⁻¹) per unit volume from D_i to D_i + ΔD_i in size class i and can be calculated using Eq. (2):   

where n_ij is the number of raindrops for the ith diameter bin and jth velocity bin, A_i (m²) is the effective sampling area, Δt is the sampling time interval (60 s for LPM), V_j (m s⁻¹) is the average velocity of the jth velocity bin, and ΔD_i (mm) is the width of each diameter bin.

The bulk microphysical parameters total number concentration N_T (m⁻³), rainwater content W (g m⁻³), rain rate R (mm h⁻¹), and radar reflectivity factor Z (mm⁶ m⁻³) were calculated as follows:   

  

  

  

where ρ_w is the density of water (1 g cm⁻³). The mass-weighted mean diameter D_m (mm) and generalized intercept parameter N_w (m⁻³ mm⁻¹) were introduced to describe the bulk characteristics of RSD, which could be calculated according to Eqs. (7) and (8).   

  

The gamma distribution proposed by Ulbrich (1983) was used to describe the distribution of the raindrop size, as shown in Eq. (9).   

where D (mm) is the diameter, N₀ (m⁻³ mm^−1−µ) is the intercept parameter, µ is the shape parameter, and Λ (mm⁻¹) is the slope parameter.

In this study, a rain event was defined as when there were continuous spectra with no less than 30 min, and two events with a less than 1 h rain-free period would be regarded as 1 (Chen, B. et al. 2017; Tokay and Bashor 2010). The spectra with a rain rate of less than 0.1 mm h⁻¹ or a total number of less than 10 would be treated as noise (Chen et al. 2013). During the Meiyu period from 2016 to 2020, a dataset of 186 rain events was derived from the quality-controlled observational data.

3. Results

3.1 RSD properties of different rain rates

The RSD of different rain rates has different characteristics (Chen, B. et al. 2013, 2017; Ji et al. 2019; Porcù et al. 2014). However, because of different geographic locations (e.g., Chen, B. et al. 2017; Ji et al. 2019) and rain types (e.g., Porcù et al. 2014; Chen et al. 2013), the RSD properties of different rain rates might vary. In this study, the rain rates were divided into five classes: 1) 0.1 ≤ R < 1 mm h⁻¹, 2) 1 ≤ R < 5 mm h⁻¹, 3) 5 ≤ R < 10 mm h⁻¹, 4) 10 ≤ R < 100 mm h⁻¹, and 5) R ≥ 100 mm h⁻¹. Samples with R < 5 mm h⁻¹ contributed 79 % to the total sample numbers and 22.74 % to the precipitation amount, and the samples with 5 ≤ R < 10 mm h⁻¹ and R ≥ 10 mm h⁻¹ were 10.25 % and 14.72 %, 10.74 %, and 62.54 %, respectively (Fig. 3). The percentages of sample counts and precipitation amounts were similar to the results for Nanjing, a city with a lower altitude in east China (Chen et al. 2013); however, there were more samples (0.32 %, 135 samples) with higher rain rates in Mount Lushan.

Fig. 3.

Accumulated sample numbers (blue) and precipitation amounts (orange) for each rain rate class in Mount Lushan from the Meiyu dataset. Numbers show the percentages (%) for each rain rate class.

For large raindrops (> 0.5 mm), the number concentration increases with the rain rate and spectra rise in parallel. For small raindrops (< 0.5 mm), when the rain rates are lower than 10 mm h⁻¹, the concentrations for smaller/larger than 0.0375 mm raindrops will decrease/increase, which concords with the “rotational movement” reported by Hashimoto and Harimaya (2003). When the rain rates exceeded 10 mm h⁻¹, the spectra tended to expand in parallel, and the concentrations of all diameter bins will rise with the rain rate. The average spectrum is like that of 5 ≤ R < 10 mm h⁻¹, but with a higher concentration at the smaller and larger ends of the diameter range, and a lower concentration at the middle diameter range (Fig. 4).

Fig. 4.

Average RSD spectra for different rain rate classes of 0.1 ≤ R < 1 mm h⁻¹ (blue), 1 ≤ R < 5 mm h⁻¹ (orange), 5 ≤ R < 10 mm h⁻¹ (yellow), 10 ≤ R < 100 mm h⁻¹ (purple), R ≥ 100 mm h⁻¹ (green), and all data (black).

To compare the spectral characteristics for different rain rate classes, the standard deviation of the mass spectrum σ_M = D_m/(4 + µ)^1/2 and normalized standard deviation of the mass spectrum σ_M/D_m, which were defined by Ulbrich and Atlas (1998), were used. To obtain the µ parameter from the RSD, the fitting methods were first compared. The maximum likelihood (ML) (Brawn and Upton 2007, 2008) and truncated moment (MM) (Ulbrich and Atlas 1998; Zhang et al. 2003) methods were used to estimate the parameters of the gamma distribution. The MM method fits better than the ML method in terms of RSD shape. For rain rates of < 10 mm h⁻¹, the ML method underestimates/overestimates the concentrations for large/small particles, and the ML method also slightly overestimates the larger diameter classes (diameter > 0.5 mm) for rain rates ≥ 10 mm h⁻¹. For the entire dataset average spectrum, the ML method overestimates the concentrations in the diameter range of 0.5–3 mm and smallest diameter class (0.125–0.25 mm) and underestimates the concentrations in the 0.25–0.5 and > 3.5 mm ranges (Fig. 5).

Fig. 5.

Fitting results of the ML method (dash lines) and the MM method (dotted lines) for average spectra of each rain rate class (a)–(e) and the entire dataset. Blue lines indicate the observed spectra.

Table 1 presents the correlation coefficient, absolute bias, relative bias, N_T, and W for the observation and fitting results for the two fitting methods. The absolute bias and relative bias were calculated following Tokay and Bashor (2010). The ML method shows significant advantages over the MM method according to the correlation coefficients and absolute biases and is similar to observed results in the Tibetan Plateau (Chen, J. et al. 2017). However, the MM method shows superior results in terms of relative biases. For N_T, ML obtains better results for smaller rain rate classes (< 10 mm h⁻¹), and MM obtains better results for larger rain rate classes (≥ 10 mm h⁻¹). For the entire dataset, the two methods exhibit similar results. For W, the MM method shows superior results to the ML method. The results will be based on the MM method to further discuss the characteristics of Meiyu precipitation because it has advantages in terms of describing the RSD shape and estimating the precipitation.

Table 2 presents parameters and fitting results of the average spectra for different rain rates. According to Table 1, the N_T and W both increase with rain rate, and in Table 2, the Z, D_m, and σ_M exhibit similar variations, meaning that the rising parameters have close relationships with diameter, spectra width, and rain rate. By contrast, log₁₀ N_w and σ_M/D_m, which address concentration, diameter, and spectra shape, scarcely vary with rain rate. For the fitting results, N₀ and Λ increase/decrease with rain rate, and µ varies little with rain rate and are negative for all rain rate classes. This differs from other observations (Chen, B. et al. 2013, 2016, 2017). The concentrations for small raindrops are slightly high and consequently lead to a left lower bending trend shape of the spectra, and negative µ values are derived (Figs. 4, 5).

3.2 Differences between stratiform and convective rains in Meiyu

a. Classification of stratiform and convective rains

It has been widely demonstrated that stratiform rains have quite different physical processes compared with convective rains (Bringi et al. 2003; Chang et al. 2009; Chen, B. et al. 2013, 2017; Ji et al. 2019; Zhang et al. 2019), as well as microphysical schemes and retrieval methods in remote sensing (Atlas and Ulbrich 2006; Chen, B. et al. 2017; Dolan et al. 2018; Rosenfeld and Ulbrich 2003; Ulbrich and Atlas 1998). To determine the differences between stratiform and convective rains, two classification schemes were considered, namely, the T01 scheme (Testud et al. 2001) and the B03 scheme (Bringi et al. 2003). For a rain rate time series {R_i}, in the T01 scheme, if R_k and adjacent 10 spectra (R_k−5–R_k+5) are all less than 10 mm h⁻¹, then the spectrum k will be classified as stratiform; otherwise, the spectrum k will be classified as convective. As to the B03 scheme, if the standard deviation (σ_R) of 10 consecutive spectra is no larger than 1.5 mm h⁻¹, then the 10 consecutive spectra will be classified as stratiform, whereas when the σ_R is larger than 1.5 mm h⁻¹ and the rain rate is no smaller than 5 mm h⁻¹, the spectrum will be classified as convective.

For the entire dataset (42,474 RSD samples), 33,518 (78.9 %) samples were classified as stratiform and 8956 (21.1 %) samples were classified as convective rain according to the T01 scheme. Using the B03 scheme, 30,127 (70.9 %) samples were classified as stratiform and 7866 (18.5 %) samples were convective. T01 is a proper way to classify all samples to stratiform or convective rain, but the B03 scheme allows a higher rain rate to be classified as stratiform rain. The convective sample ratios for the stratiform samples were 26.1 % and 26.7 % for the T01 and B03 schemes, respectively, which were almost the same.

Figure 6 displays the distributions of D_m and log₁₀N_w frequency of stratiform and convective RSD samples. For the entire dataset, the frequency of D_m peaks at 0.5–0.6 mm and 1.0–1.1 mm and the mean value, standard deviation, and skewness for D_m are 1.20 mm, 0.57 mm, and 1.03, respectively. Compared with the results of Chen et al. (2013) and Bringi et al. (2006), the mean D_m is smaller, whereas the standard deviation and skewness are larger in Mount Lushan. For log₁₀N_w, the peaks are 3.5–3.6 and 5.0–5.1, and the mean value, standard deviation, and skewness are 3.88, 0.80, and 0.74, respectively. The mean log₁₀N_w, which is close to the Marshall–Palmer value (8000 m⁻³ m⁻¹ for N_w), is similar to Chen et al. (2013), but has a higher standard deviation and skewness. The bimodal distribution of D_m frequency was reported by Wen et al. (2016) and is caused by shallow rain. Furthermore, the frequency of log₁₀N_w exhibits a second peak. This was also reported and attributed to shallow rain by Wen et al. (2016) and Fu et al. (2020). In the present study, the elevation of Mount Lushan will result in insufficient coalescence and thus, reduce the concentration of large raindrops. Also, it is easier for precipitating clouds to reach the ground because of the elevation, lack of evaporation in a saturated environment will increase the concentration of small raindrops. Hence, the second peak of log₁₀N_w in Mount Lushan can be affected jointly by shallow rain and the elevation of mountain topography. Moreover, the first peak in the present study differs from some Meiyu studies (Fu et al. 2020; Wen et al. 2016). The higher standard deviation and skewness also indicate significantly higher RSD variability in Mount Lushan during the Meiyu season.

Fig. 6.

Histograms of frequency for D_m (a) and log₁₀N_w (b). Gray shades, blue/red lines, and cyan/magenta lines represent the entire dataset, stratiform rains classified by the T01 and B03 scheme, and convective rains classified by the T01 and B03 scheme, respectively.

b. Distributions of D_m and log₁₀N_w in stratiform and convective rains

The stratiform–convective rain type classification methods of T01 and B03 were compared (Fig. 6), and the frequencies of D_m and log₁₀N_w for stratiform and convective rains of both methods exhibit similar results. The average value, standard deviation, and skewness of D_m of T01/B03 methods are 1.04/1.02 mm, 0.44/0.49 mm, 1.04/1.02, and 1.77/1.87 mm, 0.61/0.58 mm, 0.96/1.23 for stratiform and convective rains, respectively. For log₁₀ N_w, the average value, standard deviation, and skewness of T01/B03 methods are 3.91/3.93, 0.86/0.88, 0.70/0.70, and 3.76/3.77, 0.52/0.49, −0.24/−0.24 for stratiform and convective rains, respectively. There is no essential difference between the two methods; however, the B03 scheme displays more distinct stratiform/convective characteristics. Thus, here, the B03 scheme is considered as the classification method.

The difference between the stratiform and convective rains mainly manifests in the different peaks of the frequency distributions for D_m and log₁₀ N_w. However, different peaks and skewness of frequency distributions for D_m and log₁₀N_w have been found among different geographical locations (Bringi et al. 2006; Chen et al. 2013; Fu et al. 2020; Wen et al. 2016) in both stratiform and convective rains. Larger standard deviations for D_m and log₁₀N_w were obtained, indicating a more notable variety of RSD in Mount Lushan during the Meiyu season because of the mountainous topography.

The distribution between D_m and log₁₀N_w exhibits characteristics similar to those of other Meiyu RSD studies along the Yangtze River Valley (Fig. 7) (Chen et al. 2013; Fu et al. 2020; Wen et al. 2016), which is generally more stratiform-like. Compared with other Meiyu researches, there are more samples with larger log₁₀N_w and lower D_m values in the Mount Lushan dataset (Bringi et al. 2003; Chen et al. 2013; Fu et al. 2020; Wen et al. 2016). A larger standard deviation of log₁₀N_w for stratiform rain and a smaller standard deviation of D_m for convective rain were found in the present study, but the mean log₁₀N_w values were quite close. Compared with other related Meiyu precipitation studies (Chen et al. 2013; Fu et al. 2020; Wen et al. 2016), the present study obtained a smaller mean D_m for stratiform rain but a larger mean D_m for convective rain, indicating that the variety of D_m is larger in Mount Lushan. For the mean D_m–log₁₀N_w pairs of all data in each study, all studies are similar and fall along the stratiform rain line proposed by Bringi et al. (2003) in the D_m–log₁₀N_w coordinate. No significant tendency for maritime or continental characteristics can be found in the Meiyu precipitation (Bringi et al. 2003, 2009; Thompson et al. 2015).

Fig. 7.

Scatter plots of D_m vs log₁₀N_w for stratiform (light blue dots) and convective (pink dots) rain types and the average values and standard deviations for stratiform (blue line) and convective (red line) RSD. The horizontal and oblique dash gray lines indicate the stratiform-convective rain type separation lines from Thompson et al. (2015) and Bringi et al. (2009), and the Maritime and Continental rain type rectangles (gray rectangles) are from Bringi et al. (2003). Average D_m–log₁₀N_w pairs from the results of Bringi et al. (2006, ‘×’, ‘Bringi06’), Wen et al. (2016, ‘▼’, ‘Wen16’), Chen et al. (2013, ‘●’, ‘Chen 13’), and Fu et al. (2020, ‘◆’, ‘Fu20’) are also marked in the D_m–log₁₀N_w coordinate. Colors represent values of stratiform rain (blue), convective rain (red), and all data (black). S, C, and A represent stratiform, convective, and all, respectively.

The relationship between D_m–R and N_w–R was investigated (Fig. 8). D_m increases with rain rate for both stratiform and convective rains, and the power fitting results show little difference between the two rain types, which is similar to other Meiyu observations (Chen et al. 2013; Fu et al. 2020). The exponential fitting coefficients are higher than those of Chen et al. (2013) and Wen et al. (2016), indicating that D_m increases faster with R at higher rain rates. The N_w of stratiform rains shows little variation with rain rate, whereas for convective rains, N_w shows a rising trend at lower rain rates. Compared with other studies, the exponential fitting coefficients in the present study are quite low (Chen et al. 2013; Fu et al. 2020; Wen et al. 2016), particularly for stratiform rains.

Fig. 8.

Distributions of D_m and N_w with R for stratiform (a, b) and convective (c, d) rains. Blue and magenta lines indicate the power fitting results for stratiform and convective rains, and the fitting equations are also presented in corresponding diagrams. The light blue scatterplots represent the samples with log₁₀N_w > 4.5 and the cyan lines indicate their fitting results of corresponding samples.

D_m and N_w both show bimodal type distributions (Figs. 8a, b), which correspond to the frequency distributions of stratiform rains (Fig. 6). The high N_w peak (Fig. 8a) corresponds to the low D_m peak (Fig. 8b). To investigate the unique high N_w samples, a subset consisting of samples with log₁₀N_w > 4.5, was evaluated from stratiform rains for further analysis (Figs. 8a, b). The exponential fitting coefficients of the subset between D_m and R are the same as those of stratiform rain but with a lower primary coefficient, and N_w shows little variation with R.

The average spectra of the subset of log₁₀N_w > 4.5, log₁₀N_w < 4.5, and the entire stratiform rain are presented in Fig. 9. The concentrations of smaller/larger (divided by 0.875 mm) for the subset with log₁₀ N_w > 4.5 are higher/lower than those of log₁₀N_w < 4.5, and the subset with log₁₀N_w > 4.5, has a narrower spectrum width. Rosenfeld and Ulbrich (2003) summarized the processes that can modify the shape of RSD and stated that typically, coalescence and evaporation cause a decrease in small raindrops. For the samples with N_w > 4.5, the narrow spectrum width and high small raindrop concentrations are the result of a lack of coalescence. When precipitation occurs within a cloud, the RSD spectra will always be narrow and with high concentrations for small raindrops because of insufficient coalescence and the absence of evaporation. This type of precipitation is frequently seen in Mount Lushan, and therefore, it can be assumed that the high-N_w subset is the result of in-cloud precipitation.

Fig. 9.

Average RSD spectra of log₁₀N_w > 4.5 (cyan line), log₁₀N_w < 4.5 (magenta line), and all samples (blue line) in stratiform rains.

c. RSD spectra

The average spectrum of convective rain shows higher concentrations than stratiform rain, whereas the differential concentrations rise with diameter (Fig. 10) (Table 3). Compared with other studies conducted at lower altitudes along the Yangtze River Valley (Chen et al. 2013; Fu et al. 2020), the concentrations of raindrops in Mount Lushan are higher at the small diameter end than particle size velocity (Parsivel) measurements, and this can be attributed to raw particle size and fall velocity distribution differences estimated by two sensors (Angulo-Martínez et al. 2018, see in Table 4). Furthermore, compared with Chen et al. (2013) and Wen et al. (2016), higher raindrop concentrations at the large-diameter end were also obtained in Mount Lushan and may be related to the mountainous topography.

Fig. 10.

Average spectra (blue/orange dots) and fitting results (blue/red dash dotted lines) of stratiform/convective rains.

The gamma distribution fits quite well for both rain types, except for the underestimation of the first diameter bin class (Fig. 10). The N₀ and µ for stratiform rains are higher than convective rains, and the Λ for stratiform rains is smaller than convective rains. Compared with Chen et al. (2013), N₀ and Λ are significantly lower in Mount Lushan, and µ is negative for both rain types, indicating that the spectra are bent toward the left bottom. The differences between the present study and those of Chen et al. (2013) can be attributed to the high concentration of small raindrops resulting from the mountainous topography of Mount Lushan.

3.3 Relationships of gamma distribution parameters

Theoretical calculations and observational results both show that the parameters of gamma distribution are not independent (Atlas et al. 1973; Chandrasekar and Bringi 1987; Chen, B. et al. 2017; Haddad et al. 1996; Seela et al. 2018; Ulbrich 1983; Zhang et al. 2003). To investigate the relationships between the gamma distribution parameters and the distinctiveness of RSD in Mount Lushan, the relationships between µ–N₀ and µ–Λ were analyzed (Fig. 11).

Fig. 11.

Scatterplots of µ–N₀ (a) and µ–Λ (b) for stratiform (blue dots) and convective (orange dots) rains. The blue, red, and black solid lines indicate the exponential (a) and quadratic polynomial (b) fitting results of µ–N₀ and µ–Λ relationship for stratiform rains (S), convective rains (C), and the entire dataset (A). The fitting equations are also presented inside the diagrams. The black dashed line in (b) shows the µ–Λ fitting equation of Zhang et al. (2003), which is Λ = 0.0365µ² + 0.735µ + 1.935. All the data in Fig. 11 were filtered using the standard of N_t > 1000 m⁻³ and R > 5 mm h⁻¹ (Zhang et al. 2003).

It has been found theoretically and empirically that N₀ and µ have an exponential relationship of N₀ = C_N exp (3.2µ), where C_N is a constant (Ulbrich 1983). The distributions of the two parameters show an obvious exponential relationship, and the fitting equations for stratiform rain, convective rain, and the entire dataset are N₀ = 3720 exp (1.70µ), N₀ = 7406 exp (1.29µ), N₀ = 13043 exp (1.45µ), respectively (Fig. 11). Compared with Ulbrich (1983), the present study shows a lower exponential coefficient, but the C_N here is of the same order of magnitude. However, when compared with the dataset on the Tibetan Plateau (Chen, B. et al. 2017), the exponential coefficient is similar, but a higher C_N was found in Mount Lushan. The differences between the three studies indicate that although µ–N₀ has an exponential relationship, the fitting results vary significantly among different regions and rain types, and it is inconvenient to assess the varieties because N₀ will change with µ (Chen, B. et al. 2017).

Zhang et al. (2001) and Zhang et al. (2003) proposed a quadratic polynomial µ–Λ relationship (Λ = 0.0365µ² + 0.735µ + 1.935), which is thought to be a fundamental property of RSD, especially in convective rain (Seifert 2005). The µ–Λ relationship varies according to geographic location, climate regime, and synoptic system (Bringi et al. 2003; Chen et al. 2011; Chen, B. et al. 2013, 2016, 2017; Ji et al. 2019; Luo et al. 2020). The µ–Λ relationship for stratiform rain, convective rain, and the entire dataset of this study are presented in Fig. 11b. The fitting equations for three datasets are Λ = 0.0211µ² + 1.365µ + 2.374, Λ = 0.0533µ² + 0.974µ + 2.281, and Λ = 0.0347µ² + 1.180µ + 2.495, respectively. The µ–Λ of stratiform rain is similar to the results in the Tibetan Plateau, which is Λ = 0.0217µ² + 1.090µ + 1.706, but with a higher constant coefficient (Chen, B. et al. 2017). The µ–Λ of convective rain in Mount Lushan is similar to the result of a squall line case in eastern China, which is Λ = 0.0585µ² + 0.812µ + 1.934, also with a higher constant coefficient (Chen et al. 2016). Compared with the results of Zhang et al. (2003), the quadratic coefficient for the entire dataset here is similar, but the primary and constant coefficients are higher. However, in Chen et al. (2013), which is Λ = 0.0149µ² + 0.491µ + 2.015, all coefficients differ from Mount Lushan. The present study shows that under conditions using different instruments, the similarities of the µ–Λ relationship can still be assessed for different geophysical locations, climate regimes, and synoptic systems.

3.4 Z–R relationship

The Z–R relationship, in the form of Z = AR^b is an important criterion in radar QPE (Chen et al. 2013; Porcù et al. 2014; Tokay and Short 1996), and here, the Z–R relationship in Mount Lushan was investigated (Fig. 12). The Z–R relationship for the entire dataset is Z = 203R^1.59 (Fig. 12a), which is similar to the continental stratiform rain Z = 200R^1.6 (Marshall and Palmer 1948), and indicates that the Meiyu precipitation in Mount Lushan is typically stratiform-like. The Z–R relationships for stratiform and convective rains are Z = 194R^1.53 and Z = 198R^1.63, respectively, which are also similar to those of stratiform rain, although there are minute differences (Marshall and Palmer 1948). When comparing the operational WSR-88D Z = 300R^1.4 (Fulton et al. 1998) and Meiyu results in eastern China Z = 368R^1.21 (Chen et al. 2013), the rain rate R derived from Z will be overestimated/underestimated at lower/higher rain rate ranges (dividing rain rate approximately 5–10 mm h⁻¹) in Mount Lushan. The Meiyu precipitation in Mount Lushan can be generally characterized as typical stratiform rain.

Fig. 12.

Z–R scatterplots and fitting results for the Meiyu season at Mount Lushan: (a) the blue and orange scatter-plots represent the samples with log₁₀ < 4.5 and log₁₀N_w > 4.5 in the entire dataset and the power fitting results of samples with log₁₀N_w < 4.5, log₁₀N_w > 4.5, and the entire dataset are presented by red, blue, and magenta lines; (b) the blue and orange scatterplots indicate the stratiform and convective samples. Among the blue scatterplots, the light/deep blue color represents the samples with log₁₀N_w > 4.5/log₁₀N_w < 4.5. The red line, blue solid line, blue dash dotted line, and blue dotted line show the power fitting results of each dataset. The dash, dash dotted, and dotted black lines indicate the power laws of stratiform rain Z = 200R^1.6 (Marshall and Palmer 1948), operational WSR-88D Z = 300R^1.4 (Fulton et al. 1998), and Meiyu result in Eastern China Z = 368R^1.21 (Chen et al. 2013).

The samples with log₁₀N_w > 4.5 show significantly different characteristics, and therefore, the differences between samples with log₁₀N_w > 4.5 and log₁₀N_w < 4.5 were investigated. The Z–R scatterplots show a clear boundary between samples with log₁₀N_w > 4.5 and log₁₀N_w < 4.5, for the entire dataset (Fig. 12a) and the stratiform dataset (Fig. 12b). The Z–R relationships of samples with log₁₀N_w > 4.5 for the entire dataset and stratiform rain dataset are Z = 54R^1.47 and Z = 51R^1.41, respectively, showing little difference. The characteristics of the spectra and Z–R relationship for the high N_w samples are similar to the shallow rains diagnosed by Wen et al. (2016), and were attributed to warm rain processes. For those with log₁₀N_w < 4.5, the Z–R relationship for the entire dataset is Z = 306R^1.51, which is similar to that of WSR-88D (Fulton et al. 1998), but with a higher b value. The Z–R relationship for stratiform rain samples with log₁₀N_w < 4.5 is Z = 203R^1.59, which is very similar to continental stratiform rain (Marshall and Palmer 1948). The Z–R relationship for the high-N_w subset in the present study shows a higher rain rate at the same Z value. Yuter and Houze (1997) reported a bimodally distributed Z–R relationship in the Pacific Warm Pool, which corresponds to the populations of large and small drop spectra. The present study also revealed a similar bimodal distribution but with a significantly lower rain rate. The underlying reason should be further investigated.

4. Discussion

In Section 3, a typical dataset with high N_w (log₁₀N_w > 4.5) was assessed and showed quite different RSD characteristics. To investigate the characteristics and underlying reasons for the high N_w samples, a primary statistical analysis of the high N_w subset was conducted. Approximately one-third (60) of the rain events had high N_w samples with counts of more than 30. A further investigation of two long-lasting precipitation events of Meiyu found that high N_w samples always existed within continuous long-lasting precipitation processes (Fig. 13) that both lasted for more than 1 day, with few interruptions. The high N_w samples were normally obtained during the interval of two relatively heavy rain periods or in the dissipating period of the long-lasting precipitation (e.g., Figs. 13a, b). The samples with high N_w can be characterized as follows: 1) high concentrations in the first two diameter classes, 2) narrow spectrum width (no larger than 1 mm), and 3) low but continuous rain rate (mostly lower than 5 mm h⁻¹).

Fig. 13.

Two examples of precipitation processes with high N_w values. The first (a, b) is from 12:00 on June 28 to 07:40 on June 30, 2016, and the second is from 20:20 on July 15 to 06:00 July 17, 2019. The color maps and magenta lines in (a)/(c) represent the RSD and rain rate time series, and the blue and orange lines in (b)/(d) represent for the D_m and log₁₀N_w time series.

Mount Lushan is well known for its changeable clouds and fogs, and it is believed that in-cloud precipitation is frequently observed on the observational platform (Fig. 14). When a rain event occurs within the cloud in Mount Lushan, the absence of evaporation will cause a high concentration of small raindrops, and the low clouds will also lack sufficient coalescence. As such, a narrow spectrum with a high small raindrop concentration will be expected from in-cloud rain. To confirm this, a rain case was observed by the LPM, fog monitor (DMT FM-100), and visibility meter (Vaisala PWD22) (Fig. 15). Under similar rain rates, the N_w/D_m outside the cloud (before 09:00 on May 23, local solar time) was lower/higher than that inside the cloud (15:00–21:00 on May 23). When the rain began to dissipate, the N_w/D_m became higher/lower. Wen et al. (2016) reported the shallow rain type during the Meiyu season, which is like the high N_w subset and is regarded as forming through warm rain processes. However, in the present study, a more highlighted high N_w subset can be derived from the entire dataset (e.g., Figs. 6, 12), indicating that in-cloud rain, which is highly related to mountainous topography, plays an important role in generating a high-N_w RSD.

Fig. 14.

An example of in-cloud precipitation (taken on August 12, 2020).

Fig. 15.

(a) and (b) are the same as Fig. 13, but for the precipitation process from 00:00 May 23 to 16:00 on May 24, 2017, (c) shows the time series of drop size distributions from the fog monitor (color maps) and visibility (magenta line).

Although the topography of Mount Lushan is critical in generating in-cloud precipitation, to explain why the high-N_w samples always occur in long-lasting precipitation, the underlying dynamics and thermodynamics must be investigated in depth. Furthermore, the microphysical mechanisms of conversion from cloud/fog droplets to raindrops and the interaction between cloud/fog and precipitation also require investigation.

5. Conclusions

Using the RSD data collected by LPM in Mount Lushan from 2016 to 2020, the RSD characteristics of Meiyu precipitation in Mount Lushan were studied. The special RSD samples with high N_w were also discussed, and the results are as follows:

A dataset of 186 rain events was determined during the Meiyu season from 2016 to 2020 in Mount Lushan. For the entire dataset, lower rain rates (< 5 mm h⁻¹) contributed to the highest number of samples, whereas rain rates of 10–100 mm h⁻¹ contributed the highest precipitation amount. Extraordinarily high rain rates (> 100 mm h⁻¹) were found in Mount Lushan during the Meiyu season and contributed to quantitative precipitation (8.62 %) compared with its low frequency (0.32 %). For large-diameter ranges (> 0.5 mm), the concentrations for each diameter bin of the average spectra will increase with rain rate, whereas for small diameter ranges (< 0.5 mm), the concentrations for each diameter bin will rise only when the rain rates are higher (> 10 mm h⁻¹).

The performance of the two gamma fitting methods, namely, the ML and MM, were evaluated using the average spectra of each rain rate class for the Meiyu dataset. The ML method obtained better results for correlation coefficients and absolute biases, and the MM method obtained better results for relative biases and shapes of RSD. In simulating the RSD parameters, the MM method had good results for N_T and W. Thus, the MM method achieved good results for simulating the Meiyu RSD in Mount Lushan.

The RSD parameters of N_T, W, Z, D_m, and σ_M increased with rain rate, whereas N_w and σ_M/D_m varied little with rain rate. For the gamma distribution parameters of the average spectra for different rain rates, N₀ and Λ rose/decreased with rain rate, and µ had negative values for all rain rate classes. The gamma distribution for the average spectrum of the entire dataset was N(D) = 721D^−1.79e^−1.20D. The frequency distributions of D_m and log₁₀N_w both showed a special bimodal type. An exceptionally high-N_w (log₁₀N_w > 4.5) subset was diagnosed, which corresponds to the unique secondary peaks of D_m and log₁₀N_w, which has a narrower and steeper average spectrum with high concentrations for small raindrops (< 0.875 mm).

Two classification schemes (T01 and B03) for stratiform/convective rain were discussed, and the frequency distributions of D_m and log₁₀N_w for stratiform and convective rains showed little difference between the two schemes. The distribution of D_m–log₁₀N_w showed differences between the two rain types and no significant maritime/continental characteristics. The D_m–R and N_w–R relationships showed little difference between stratiform and convective rains, and N_w showed little variation with rain rate. The average spectra for stratiform and convective rains both had high concentrations of small raindrops, but the convective rains had larger raindrops. The gamma distribution parameters were also calculated (Table 3).

The relationships between the gamma distribution parameters of µ–N₀ and µ–Λ for stratiform and convective rain were examined. The µ–N₀ showed quite different characteristics for stratiform and convective rains, and the fitting equation for the entire dataset was N₀ = 13043 exp (1.45µ). The Meiyu dataset of Mount Lushan showed a similar µ–Λ relationship (Λ = 0.0347µ² + 1.180µ + 2.495) to other studies, but in the present study, the lower µ values resulted in higher primary and constant coefficients in the quadratic polynomial fitting results.

The Z–R relationship for the Meiyu season in Mount Lushan showed featured stratiform rain characteristics with a Z = 203R^1.59 fitting result. The Z–R relationships for stratiform and convective rains showed little difference, but the dataset of high N_w samples obtained a unique fitting result of Z = 54R^1.47.

The high-N_w subset was normally detected in long-lasting precipitation during the Meiyu season. The RSD can be characterized as high concentrations in the first two diameter classes, with narrow spectrum width (< 1 mm), and low but continuous rain rate (< 5 mm h⁻¹). Further investigations demonstrated that these samples can be attributed to in-cloud precipitation, which is related to the mountainous topography of Mount Lushan.

Acknowledgments

This work was jointly supported by the Chinese Academy of Meteorological Sciences Basic Research and Operation Fund (2019Z013, 2016Z004, 2020Y 010), S&T Development Fund of CAMS (2021KJ017), and the National Key R&D Program of China (2019 YFC1510300).

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