Statistical Characteristics of Raindrop Size Distribution in the Tibetan Plateau and Southern China

As the largest and highest plateau in the world, the average elevation over a large area of the Tibetan Plateau can reach up to the middle troposphere. The dynamic and thermodynamic forcing of the Tibetan Plateau exerts great impacts on atmospheric moisture and energy cycles and related convective activities, which subsequently affect ecological processes in the downstream areas of the Tibetan Plateau (Tao and Ding, 1981; Huang, 1985; Huang and Sun, 1994). (Shi et al., 2008a) argued that atmospheric moisture could be transported from the Tibetan Plateau to the Yangtze River Basin via the interaction between the orographic dynamical forcing and the abundant atmospheric moisture over the southern highlands around the Tibetan Plateau. The airflow originated from Tibet is forced to rise due to topographic obstruction and surface heating, triggering the development of convective activities and heavy rainstorms in southern China (He and Li, 2013; Li et al., 2014).

Over the past three decades, much attention has been paid nationwide to observations of raindrop size distribution (DSD). Great progress has been made in this regard, especially in the development of advanced measuring instruments and analytical approaches. (Chen and Gu, 1989) studied the characteristics of average DSD based on observations of heavy rainfall events in Changchun, Jilin Province. (Qing et al., 1994) summarized the DSD characteristics for a vortex-induced cloud system in Chengdu, Sichuan Province. (Niu et al., 2002) analyzed DSD parameters associated with various atmospheric circulation patterns and weather systems at seven stations in Ningxia Province. (Liu and Lei, 2006) summarized some preliminary characteristics of DSD for both stratiform and convective precipitation in the Beijing area, and described the mean diameters, DSD peaks and the relationships between reflectivity factor and rainfall rate (Z-R relationships). (Shi et al., 2008a) analyzed the DSD characteristics for convective precipitation, mixed precipitation, and stratiform precipitation around the Qilian Mountains during the summer of 2006. The particle diameters, Z-R relationships, and the distribution of fall velocity were revealed. (Zhang et al., 2009) summarized the differences in DSD among three precipitation systems in Menyuan, Qinghai Province, and analyzed their formation mechanisms. (Liao et al., 2011) investigated DSD characteristics for a typical typhoon precipitation event and a frontal precipitation event that occurred in the summer in the Pearl River Delta region. (Chen et al., 2013b) analyzed the spatio temporal variations of DSD during the mei-yu season over Jianghuai Basin. However, few studies have been conducted to investigate DSD characteristics with respect to the microphysical structure of precipitation over highland areas and their variations with rainfall rate, because of the scarcity of ground observations in such areas. Studies on the differences and similarities of rainfall characteristics between the Tibetan Plateau and southern China have received little attention so far. In terms of geographic location and climate over the Tibetan Plateau and southern China, it is well known that the precipitation in the pre-flood seasons is dominated by strong convective rain, while weak convective rain occurs frequently in northern Tibet with lower humidity and higher altitude. (Li and Su, 2014) compared conventional observations collected at 10 weather stations over the Tibetan Plateau and southern China and concluded air pollution could suppress light rainfall processes.

DSD observation is a key step for microphysical analysis of cloud and precipitation, which forms the basis for the development of microphysical parameterization schemes in numerical models. However, until the late 1990s, almost all microphysical schemes in numerical models used in China were actually developed abroad. The regional differences in cloud-precipitation characteristics and the specific characteristics of microphysical processes in China have been completely ignored in numerical weather prediction (NWP) studies (Fletcher, 1962; Kong et al., 1990; Guo et al., 2001). (Hu et al., 1998) developed a simplified explicit scheme to describe mixed-phase clouds and precipitation processes based on the warm cloud scheme. The Global Assimilation and Prediction System (GRAPES) has been under development by the China Meteorological Administration since 2001 (Chen et al., 2008; Xue et al., 2008). The GRAPES model includes a coupled cloud-precipitation scheme that can simulate precipitation well in the pre-flood season over southern China (Zhang and Liu, 2006). (Sun et al., 2008) coupled a complex microphysical scheme developed by CAMS (Chinese Academy of Meteorological Sciences) to simulate the hydrometeor distribution during the life cycle of a heavy rainstorm that occurred in northern China, and then investigated the DSD characteristics of the storm. Based on the above discussion, in order to improve the reliability and accuracy of NWP, it is necessary to incorporate microphysical properties of clouds and precipitation into numerical models.

The second Tibetan Plateau Experiment of Atmospheric Science (TIPEX) was conducted in the late 1990s and obtained valuable observations. Using the observations collected at Tibet (Nagqu) during TIPEX, (Ueno et al., 2001) investigated convective activities and cloud structures that were associated with weak and frequent monsoon precipitation. (Shimizu et al., 2001) detected a diurnal rainfall cycle on the Tibetan Plateau based on analysis of TRMM (Tropical Rainfall Measuring Mission) satellite information and revealed the mesoscale characteristics of stratiform clouds. (Uyeda et al., 2001) analyzed the characteristics of convective clouds measured by X-band Doppler radars. (Liu et al., 2002) summarized the diurnal precipitation variation over Tibet before and after monsoon onset and revealed their relationships with thermodynamic variables. However, DSD characteristics were not observed and analyzed in this experiment.

During the period from 1 July to 31 August 2014, the third TIPEX was carried out, in which microphysical variables related to clouds and precipitation were measured by advanced instruments in Nagqu, Tibet. In the same year, the southern China Monsoon Rainfall Experiment, funded by the Research and Development Project of the World Meteorological Organization, was conducted in Yangjiang, Guangdong Province. Measurements of DSD by ground-based disdrometers in Tibet and in Guangdong from April to August 2014 is used in this study. The purpose of the present study is to advance our understanding of DSD characteristics over the Tibetan Plateau and southern China. This knowledge would be useful for the evaluation of microphysical parameterization schemes in numerical models over regions in the future. The paper is organized as follows. A description of the dataset and methods is given in section 2. The classification of precipitation type, the average raindrop size distribution, and the parameters in Gamma distributions and their changes with rainfall rate and Z-R relationships over Tibet and southern China are analyzed in section 3. A summary and discussion are given in sections 4 and 5, respectively.

During the period from 24 April to 11 June 2014, DSD characteristics were measured at Yangjiang Meteorological Bureau [(21.84^°N, 111.98^°E); 90 m above mean sea level (AMSL)] with a particle size and velocity disdrometer called HSC-PS32. The disdrometer was also used to observe DSD characteristics at Nagqu Meteorological Bureau [(31.80^°N, 92.12^°E); 4508 m AMSL] from 24 June to 31 August in the same year. The HSC-PS32 disdrometer is a Chinese version of the OTT Parsivel disdrometer, which is a kind of ground-based optical disdrometer designed to count and measure the fall velocity and precipitation particle size simultaneously in a 32× 32 square. The main specifications of the HSC-PS32 disdrometer are shown in Table 1, and Table 2 gives the interval of each grade in rainfall rate. It should be noted that the raindrop diameter of larger than 5 mm has been excluded, considering its liquid particle size range and the unidentified overlapping particles in heavy precipitation events.

A total of 9430 and 6366 1-min DSD measurements were collected in Tibet and southern China, respectively. The raindrop number concentration per unit volume at a discrete instant could been calculated based on the disdrometer counts: \begin{equation} \label{eq1} n(D_i)=\sum_{j=1}^{32}\frac{A_{ij}}{V_j TS} , (1)\end{equation} where A_ij is the number of raindrops within the size bin i and velocity bin j; T(s) and S(m²) are the sampling time and area respectively; D_i (mm) is the raindrop diameter for the size bin I; and V_j (m s^-1) is the fall speed for the velocity bin j.

Thus, some integral rain parameters, such as radar reflectivity factor Z (dBZ), rainfall rate R (mm h^-1), total number density N _a (m^-3), and median volume diameter D₀ (mm) could be derived successively, as below. Rainfall rate has direct ratio relations with the third power of particle diameter and raindrop number, and reflectivity factor is proportional to the sixth power of particle diameter and raindrop number per unit volume. It should be noted that the reflectivity factor in Eq. (3) only applies to the Rayleigh scattering and S-band radars: \begin{eqnarray} \label{eq2} Z&=&10\lg(\sum_{i=1}^{32}n(D_i)D_i^6) ;(2)\\ \label{eq3} R&=&\frac{6\pi}{10^4}\sum_{i=1}^{32}\sum_{j=1}^{32}{n(D_i)D_i^3V_j} ;(3)\\ \label{eq4} N_{\rm a}&=&\sum_{i=1}^{32}{n(D_i)} ;(4) \end{eqnarray} \begin{eqnarray} \label{eq5} \sum_{i=0}^{D_{\max}}n(D_i)D_i^3=2\sum_{i=0}^{D_0}{n(D_i)D_i^3} . (5)\end{eqnarray}

The exponential distribution was widely assumed in many numerical parameterization schemes in the early days (Lin et al., 1983; Rutledge and Hobbs, 1983). The Gamma distribution, proposed by (Ulbrich, 1983), Eq. (7), has been proven to be a good description for instantaneous DSDs in many regions and rain types (Chen et al., 1998; Ulbrich and Atlas, 1998), while the exponential distribution is an exception of the Gamma distribution when μ=0: \begin{equation} \label{eq6} N(D)=N_0D^\mu\exp(-\lambda D) , \ \ (6)\end{equation} where N (m^-3 mm^-1) is the raindrop number concentration referring to the raindrop diameter D (mm). The Gamma distribution can be represented by an intercept parameter N₀ (m^-3 mm^-μ-1), a shape parameter μ, and a slope parameter Λ (m m^-1). However, these three parameters in a Gamma distribution are not mutually independent, and thus the standardized Gamma distribution is used to fit the DSD data, which is given by \begin{eqnarray} \label{eq7} N(D)=N_{\rm w}f(\mu)\left(\frac{D}{D_{\rm m}}\right)^\mu\exp\left[-(\mu+4)\frac{D}{D_{\rm m}}\right] ,\ \ \ (7)\\[-2mm]\nonumber \end{eqnarray} where N _w (m^-3 mm^-1) is a normalized intercept parameter, indicating the number concentration with exponential distributions that has the same median volume diameter and liquid water content (Liu et al., 2007), and the parameters D _m (mm) and μ are the mass-weighted mean diameter and the shape parameter, respectively.

Moment methods have been widely used to estimate raindrop spectrum parameters for cloud and precipitation in numerical models (Smith, 2003). The ith-order moment of DSD is given by Eq. (9). The three independent parameters N _w, μ and D _m could be calculated by the third, fourth and sixth moments of the DSD data described by (Kozu and Nakamura, 1991), and the parameters Γ(x), f(μ) and G are intermediate ones: \begin{eqnarray} \label{eq8} M_i&=&\sum_{i=1}^{32}{n(D_i)D^i} ;(8)\\ \label{eq9} N_{\rm w}&=&\frac{256}{6}\times\frac{M_3^5}{M_4^4} ;(9)\\ \label{eq10} D_{\rm m}&=&\frac{M_4}{M_3} ;(10)\\ \label{eq11} G&=&\frac{M_4^3}{M_3^2M_6} ;(11)\\ \label{eq12} \mu&=&\frac{11G-8+\sqrt{G(G+8)}}{2(1-G)} ;(12)\\ \label{eq13} \Gamma(x)&=&\sqrt{2\pi}e^{-x}x^{x-\frac{1}{2}} ;(13)\\ \label{eq14} f(\mu)&=&\frac{6}{256}\times\frac{(\mu+4)^{\mu+4}}{\Gamma(\mu+4)} .(14) \end{eqnarray}

The case study analysis casts light on some characteristics of the DSD for liquid precipitation regimes occurring over the Tibetan Plateau and southern China during 2014. The behavior of DSD is investigated using the 1-min DSD for selected precipitation types and rain rate intervals. A simple scheme is used to separate stratiform and convective precipitation types based on the standard deviation (σ_R) of the rainfall rate (R) over five consecutive 2-min DSD samples (Bringi et al., 2003), based on R≥ 0.5 mm h^-1 and σ_R≤ 1.5 mm h^-1 for stratiform precipitation, and R≥ 5 mm h^-1 and σ_R>1.5 mm h^-1 for convective precipitation. (Chen et al., 2013b) also adopted a similar concept to study DSD statistical characteristics in the mei-yu season over eastern China. The rain rate intervals are classified as follows (in mm h^-1): 0.1≤ R<1 (class 1); 1≤ R<2 (class 2); 2≤ R<5 (class 3); 5≤ R<10 (class 4); 10≤ R<20 (class 5); and R≥ 20 (class 6) (Porc\`ua et al., 2014). Table 3 shows the relative DSD distributions over the Tibetan Plateau and southern China in precipitation types and rain rate intervals. As can be seen, the stratiform precipitation over the Tibetan Plateau and southern China gives priority to class 1, and then generally decreases with an increase in rainfall rate, especially in the Tibetan Plateau, and there are no distributions of rainfall rate above 10 mm h^-1. For convective rain, with an increase in rainfall rate, the DSD distributions over southern China firstly decrease and then increase.

The average DSD for stratiform and convective rain over the Tibetan Plateau and southern China, obtained by averaging all the 1-min DSD data, is shown in Fig. 1. As can be seen, the average raindrop spectra appear to be one-peak curves; and, for stratiform precipitation (Fig. 1a), with an increase in diameter the raindrop number concentration in the Tibetan Plateau has a bigger decrease. Meanwhile, for convective precipitation (Fig. 1b), the raindrop number concentration over southern China is much higher than that over the Tibetan Plateau, with various diameters. The fluctuation of total raindrop number concentration is much more frequent in stratiform precipitation.

Figure 1.  Average raindrop spectra for (a) stratiform and (b) convective precipitation over the Tibetan Plateau and southern China, based on all the 1-min DSD data. The parameters N (m^-3 mm^-1) and D (mm) are the raindrop number concentration and raindrop diameter, respectively.

Figure 2.  Average raindrop spectra with rainfall rate for (a, c) stratiform and (b, d) convective precipitation over (a, b) the Tibetan Plateau and (c, d) southern China, based on all the 1-min raindrop data. The parameters N (m^-3 mm^-1) and D (mm) are the raindrop number concentration and raindrop diameter, respectively. The rainfall rate intervals are (in mm h^-1): 0.1≤ R<1 (class 1); 1≤ R<2 (class 2); 2≤ R<5 (class 3); 5≤ R<10 (class 4); 10≤ R<20 (class 5); and R≥ 20 (class 6).

Figure 2 shows the changes with average raindrop spectra and rainfall rate for stratiform and convective precipitation over the Tibetan Plateau and southern China. As can be seen, the number concentration for larger drops decreases much less in convective precipitation, especially over the Tibetan Plateau.

The exponential distribution and the standardized Gamma distribution are chosen to produce a better model for the raindrop size distribution, based on the moment methods provided in section 2.2. Relative error (RE) between the fitted raindrop number concentration (NC) and the raw raindrop number concentration (NR) is used for evaluation: $$ {\rm RE}=\frac{|{\rm NC}-{\rm NR}|}{{\rm NR}}\times 100\%.\ \ (15)$$

Relationships between the REs fitted by samples and the raindrop diameter for precipitation types over the Tibetan Plateau and southern China are shown in Fig. 3. It is noted that the standardized Gamma distribution can better describe the real raindrop spectra, especially for larger drops. For the same area, the fitted RE in convective precipitation is smaller; whereas, in the same rain type, the fitted RE over southern China is smaller.

Figure 3.  Plots of relative error (RE, %) fitted by DSD samples and diameter (D, mm) for (a, c) stratiform and (b, d) convective rain over (a, b) the Tibetan Plateau and (c, d) southern China. "M-P" and "Gamma" stand for the exponential distributions and the standardized Gamma distributions, respectively.

As three independent parameters in the standard Gamma distribution, the normalized intercept parameter N _w (m^-3 mm^-1), the shape parameter μ, and the mass-weighted mean diameter D _m (mm) can successfully represent the raindrop density, average diameter, and many other spectral characteristics. Table 4 gives the average values of parameters in the standardized Gamma distribution, indicating that all three independent parameters (N _w, μ and D _m), for stratiform rain over the Tibetan Plateau, are larger than those over southern China, especially N _w. Meanwhile, for convective precipitation, the N _w and μ in the Tibetan Plateau are less than those over southern China. Comparing the precipitation in the same area, the N _w and μ for stratiform rain are larger than those for convective rain, while its D _m is less; and the N _w and μ are much higher for stratiform precipitation than those for convective rain, while its D _m is less.

In order to study the relationships between raindrop spectral parameters and rainfall rate, the average value of N _w, μ and D _m in six rain rate intervals over the Tibetan Plateau and southern China, for stratiform and convective precipitation, are shown in Table 5. It is shown that the N _w and D _m for stratiform precipitation over the Tibetan Plateau increases with rainfall rate, but the μ does an opposite trend; and the N _w for stratiform precipitation over southern China decreases with rainfall rate, with its μ decreasing firstly and then increasing with increased rainfall rate, and its D _m increasing. Meanwhile, for the same rainfall rate, the three Gamma parameters for stratiform rain over the Tibetan Plateau are much higher. The N _w and μ for convective precipitation over the Tibetan Plateau decrease with rainfall rate, and the D _m would increase with rainfall rate. The N _w and μ for convective precipitation over southern China increases firstly and then decreases with increased rainfall rate, but the D _m decreases firstly and then increases with the increased rainfall rate. Meanwhile, for the same rainfall rate, the μ over Tibet for convective precipitation is smaller, while the D _m over the Tibetan Plateau for convective precipitation is higher.

The power-law relationship between reflectivity factor and rainfall rate, like Z=AR^b, is a longstanding problem in quantitative precipitation forecasting, and is strongly affected by altitude differences (Uijlenhoet, 2001). The coefficients A and b are closely related to the raindrop size distribution, particle diameter, radar signal attenuation, and so on (Rosenfeld and Ulbrich, 2003; Chandrasekar et al., 2003). High A values and low b values describe convective midlatitude precipitation, while the opposite is true for tropical precipitation (Tokay and Short, 1996; Caracciolo et al., 2006). Choosing the appropriate A and b based on precipitation types could improve regional rainfall estimation (Shi et al., 2004). The relationship Z=300R^1.4 for convective rain, proposed by (Fulton et al., 1998), has been widely used in NEXRAD (Next-Generation Weather Radar), while the relationship Z=200R^1.6 is commonly applied to midlatitude areas for stratiform rain (Marshall and Palmer, 1948). However, whilst studies on Z-R relationships in China have been conducted since the early 1990s (Xu et al., 1990; Xu, 1992; Liu et al., 2008), the relationships in Tibet have rarely been involved, let alone any comparisons made among regions. Scatter plots of Z-R relationships and fitted power-law relationships based on least-squares methods for rain types over the Tibetan Plateau and southern China are shown in Fig. 4. The results indicate that the coefficient A over the Tibetan Plateau is smaller than that over southern China, while its value of b is higher, especially for convective precipitation. When the rain type transfers from stratiform rain to convective rain, the coefficient A over the Tibetan Plateau decreases with rainfall rate, while its b increases. Meanwhile, the A and b over southern China increase with rainfall rate, which is different from the findings of previous studies (Hagen and Yuter, 2003). Comparing the results in similar areas, (Tokay and Short, 1996) found that (A=367, b=1.30) for stratiform cases and (A=139, b=1.43) for convective cases could describe tropical precipitation well; (Zhao et al., 2011) found markedly different values for A and b in the Heihe river basin (1500 m AMSL, in the northeastern part of the Tibetan Plateau), reporting (A=378, b=1.72) for stratiform rain and (A=244, b=1.79) for convective rain; Federico (Porc\`ua et al., 2014) carried out disdrometric campaigns in Lhasa (3600 m AMSL), Linzhi (3300 m AMSL) and Namco (4700 m AMSL) in the central-eastern part of the Tibetan Plateau, and reported results of A=247 (A=214) and b=1.15 (b=1.25) for stratiform (convective) precipitation. Possible reasons for such different values could be linked to the altitude/air density, physical properties, data quality control, data fitting, and so on (Cifelli et al., 2000).

Figure 4.  Scatter plots of radar reflectivity factor and rainfall rate for (a, c) stratiform and (b, d) convective precipitation over (a, b) the Tibetan Plateau and (c, d) southern China. The fitted power-law relationships, Z=AR^b, derived from the least-squares method, are also provided.

A comparison of raindrop characteristics between the Tibetan Plateau and southern China is discussed in this paper, using a total of 9430 and 6366 1-min raindrop spectra samples, respectively, which were collected by HSC-PS32 disdrometers from April to August 2014. The data are divided into stratiform precipitation and convective precipitation, and the rainfall rate in each rain type is classified into six classes. The main conclusions can be summarized as follows:

(2) The major rainfall rate interval for stratiform rain over the Tibetan Plateau and southern China is class 1, and then generally decreases with an increase in rainfall rate, especially in the Tibetan Plateau, and there are no distributions of rainfall rate above 10 mm h^-1. Additionally, the DSD distributions over southern China firstly decrease, and then increase, with an increase in rainfall rate.

(3) The average raindrop spectra seem to be one-peak curves. The raindrop number concentration for stratiform rain over the Tibetan Plateau has a bigger decrease with increased diameter. In convective precipitation, the raindrop number concentration over southern China is much higher than that over the Tibetan Plateau, with various diameters. Furthermore, the number concentration for larger drops has a much more significant increase with rainfall rate, especially in convective rain.

(4) The standardized Gamma distribution better describes real raindrop spectra, especially for larger drops. Compared with the precipitation in the same area, the fitted RE for convective rain is smaller; whereas, for the same rain type, the fitted RE over southern China is smaller.

(5) The three independent parameters for stratiform precipitation over the Tibetan Plateau are larger than over southern China, especially for N _w. Meanwhile, in convective precipitation, the N _w and μ in the Tibetan Plateau are less. The N _w and μ for stratiform rain are larger than those for convective rain, while its D _m is less; the N _w and μ are much higher for stratiform rain than those for convective rain, while its D _m is less.

(6) Referring to the standardized Gamma distribution parameter variation with rainfall rate, the mass-weighted diameter generally increases with rainfall rate, the normalized intercept parameter increases firstly and then decreases, and the shape parameter is inversely proportional to rainfall rate, whose parameter oscillation over southern China is much more frequent than that over the Tibetan Plateau. Meanwhile, the mass-weighted diameter and the shape parameter over the Tibetan Plateau for stratiform precipitation are less than those over southern China.

(7) In Z-R relationships, the coefficient A over the Tibetan Plateau is smaller, while b is higher. When the precipitation type transfers from stratiform to convective, the coefficients A and b over southern China increase gradually with an increase in rainfall rate, while the A over the Tibetan Plateau decreases.

Since convective precipitation over the Tibetan Plateau features small horizontal scales, short duration, and rapid change (Zhuang et al., 2013), the raindrop number concentration for convective ones over the Tibetan Plateau is less than that over southern China, while its shape parameter and particle diameter is larger, indicating the number of raindrops per unit volume is less and the raindrop concentration of larger particles decreases rapidly. The more raindrop splits over southern China for convective precipitation is one of the reasons, however, there would be much more evaporation in the Tibetan Plateau for its lower humidity (Niu et al., 2002). In Z-R relationships (Z=AR^b), the coefficients change with geographical location, weather conditions, and so on; However, referring to the discussed Z-R relationships, there are some considerable differences with previous studies, a subtle discrepancy in quality control, data fitting, raindrop physical properties are the possible reasons, such as, small raindrops tends to yield the smaller coefficients.