# Geometric and Physical Characteristics of Precipitation Clouds in Tibetan Plateau

Authors: Kunyu Teng; Hongke Cai; Xiubin Sun; Quanliang Chen
Journal: Advances in Meteorology
 (2022)

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## Abstract

This paper examines the basic geometric and physical characteristics of precipitation clouds over the Tibetan Plateau, based on the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) data from 1998 to 2015, using the minimum bounding rectangle (MBR) method. The results show that about 60% of the precipitation clouds occur with a scale of approximately 18 km (length) and 15 km (width), and the proportion of precipitation clouds with a length longer than 100 km and a width wider than 90 km is less than 1%. Most of the precipitation cloud exhibits a shape between square and long strips in the horizontal direction and lanky in the vertical direction. The average rainfall intensity of precipitation clouds is between 0.5 and 6 mm h−1. The average length and width of precipitation clouds show a logarithmic, linear relationship. The distribution of raindrops in precipitation clouds is relatively compact. With the expansion of the area, the precipitation clouds gradually become squatty. The relationship between physical and geometric parameters of precipitation clouds shows that with the precipitation cloud area expanding, the average rainfall rate of precipitation clouds also increases. Heavy convective rainfall is more likely to occur in larger precipitation clouds. For the precipitation clouds of the same size, the area fraction and contribution of convective precipitation are lower than that of stratiform precipitation.


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## Body

## 1. Introduction

Cloud is an important indicator of weather and climate changes. It plays an important role in the global energy and water cycle, which is called the “regulator” of radiation balance in the earth-atmosphere system. Clouds can change the local atmospheric energy balance and affect the atmospheric circulation and energy cycle by reflecting and absorbing solar short-wave radiation and absorbing and emitting Earth long-wave radiation [1–4]. During the formation of different types of clouds, the thermodynamic and microphysical processes are different, which can result in different radiative forcing and climate feedback [5, 6]. Among them, the study of precipitation clouds is particularly critical. At first, the precipitation clouds were usually considered as circular precipitation areas, and their rainfall rates (or radar reflectivity) were equal to or greater than the threshold rainfall rates (or radar reflectivity) [7]. Capsoni et al. [8] defined precipitation clouds as regions with rain rates (RR) greater than 5 mm h−1 observed by S-band radar near Milan during April–October 1980. In addition, the formulas of spatial numerical density and cumulative rainfall rate distribution of precipitation clouds are obtained. In 1989, Awaka [9] revised the formulas and set the threshold of rainfall rate at 0.4 mm h−1. Studies about the characteristics of precipitation clouds is typically important for in-depth studies of the formation mechanism of precipitation, the simulation of the impact on future climate changes, the weather forecast, and the water resources forecast. Moreover, understanding the structure of precipitation clouds is also of great significance to carry out operations of influencing weather in scientific and artificial approaches.For a long time, many scholars have been studying the climatic characteristics of clouds in China and its surrounding areas by using ground observation data and various satellite observation data. The results pointed out that the annual average total cloud coverage in southern China is more than that in northern China. And the east and west sides of the Tibetan Plateau have high annual average total cloud coverage. The distribution characteristics of low clouds are consistent with the total cloud coverage, and the distribution of cloud optical thickness and water vapor content is also similar to that of total cloud coverage. In all types of clouds in China and its surrounding areas, except cumulus, stratocumulus, and rain layer clouds, the cloud thickness of southern China is greater than that of northern China. The largest average thickness among all types of clouds is the deep convective cloud, and the smallest one is the stratocumulus. The occurrence probability of cloudy sky in southern mainland China is higher than in northern mainland China, and the occurrence probability of single-layer clouds is significantly higher than that of multilayer clouds. The occurrence probability of clouds of summer and autumn is higher than that of spring and winter. In summer, the cloud height has the maximum value for each layer of clouds [10–12]. Cirrus clouds are the most common in Northwest China. The optical thickness and cloud water path can have maximum value for the following clouds: water layer cloud, ice layer cloud, water rain layer cloud, ice rain layer cloud, and the deep convective cloud. The high-value areas of cloud coverage are located in the areas of Tianshan-Kunlun-Qilian Mountains and southern Shanxi province, which are beneficial to artificial water enhancement [10, 13]. In southern China’s summer time, the frequency of stratospheric precipitation is more than twice as much as that of convective precipitation, and the intensity of convective precipitation is at least 4 times as much as that of stratospheric precipitation, and convective precipitation mainly occurs in the afternoon [14].The Tibetan Plateau, known as the “roof of the world”, is the largest plateau in China and the highest in the world. It is the birthplace of many rivers in China, with high-mountain rivers, steep and changeable terrain, and complex topography. The Tibetan Plateau is in the middle and upper troposphere, and its atmospheric activity is intense and frequent, which has a significant impact on climate change locally and globally. Due to the complex topography and the thermodynamic structure, the weather and the climate phenomena of the Tibetan Plateau and their corresponding mechanisms have been attracting a number of scholars. Two large-scale scientific experiments were carried out in China in 1979 and 1998 (the third is 2014–2021, which is still ongoing), and remarkable results have been achieved. The relevant studies on the Tibetan Plateau show that the Tibetan Plateau is dominated by convective clouds in summer, which is mainly distributed in the central and eastern parts of the plateau and southeastern Tibet [15]. The precipitation on the Tibetan Plateau is mainly concentrated in southeastern Tibet, and the maximum near-surface precipitation rate is greater than 100 mm h−1 [16]. The water vapor content in the UTLS (upper troposphere to lower stratosphere) region of the southern Qinghai-Xizang Plateau is higher than that of the northern Qinghai-Xizang Plateau [17, 18]. The frequency of deep convection on the southern slope of the plateau is higher than that on the plateau. And the deep convection mainly occurs from July to August [19].The average altitude of the Tibetan Plateau is more than 4000 m. Its complex topography and thermodynamic structure make the clouds on the plateau unique. Therefore, many scholars have done a lot of research on plateau clouds. The initial research can only be based on the ground observation data to study the basic parameters such as cloud coverage and height. The results show that the distribution of total cloud coverage in the plateau decreases from southeast to northwest, and there is a significant downward trend when we analyze it year by year or season by season. Strong convective clouds have the highest frequency in summer and the lowest frequency in winter [20, 21]. After the emergence of satellite data, the studies of plateau clouds are not limited to cloud coverage and cloud height. The results show that the clouds on the top of the Tibetan Plateau are higher than those of the surrounding area [22]. There are few clouds on the north and south sides of the plateau, and the optical thickness of the cloud is also small [23]. The optical thickness of the cloud is large in the areas with more clouds on the western and southeastern Tibetan Plateau [24]. The total cloud coverage in the eastern plateau is more than that in the central and western plateau, and the total cloud coverage of the southern Tibetan Plateau is more than that in the northern Tibetan Plateau. The total cloud coverage of the edge of the plateau is more than that of the main part of the plateau [25]. The distribution of total cloud coverage on the plateau shows a decreasing trend from southeast to the northwest of the plateau [26]. The optical thickness of clouds, cloud water path, and cloud top temperature on the plateau have all increased significantly [27].Studies about the macro and microcharacteristics of precipitation clouds on the plateau play an important role in understanding the thermal-dynamic and microphysical processes, water vapor transportation, and climate changes in the formation of precipitation clouds on the plateau. Many scholars have used various satellite data to study precipitation clouds on the plateau. Fu et al. [28] studied the precipitation cloud structure in a valley and its nearby areas in the southeast of the Tibetan Plateau by using the TRMM satellite precipitation radar. The results show that topographic forcing is an important external factor for the formation of this precipitation cloud cluster. The maximum length of the precipitation cloud system is more than 100 km, and its width is about 40 km. It is a strong convective cloud cluster. Other research has shown that the summer precipitation on the plateau is dominated by deep and weak convective precipitation, followed by shallow and thin precipitation, and deep and strong convective precipitation is the least. In summer, the frequency and intensity of precipitation on the Tibetan Plateau gradually increase from west to east, while the heights of cloud tops and precipitation echo tops have exactly the opposite trend. The main precipitation on the plateau in summer is dominated by ice precipitation, and the plateau clouds are dominated by single-layer clouds [29, 30].Summarizing the previous studies, it can be found that the research on the plateau precipitation cloud is mainly focused on the investigation of the summer season. And most of the research is related to the horizontal distribution, vertical structure, and microphysical characteristics, but there is still a lack of research on other aspects, such as the geometric characteristics of precipitation clouds, the relationship between geometric size and precipitation, and the contribution of different types of precipitation to the same precipitation clouds. Therefore, this paper is using TRMM/PR data from 1998 to 2015 to study the geometric and physical characteristics of precipitation clouds in the Tibetan Plateau.


## 2. Data and Methodology

### 2.1. Introduction

In this study, the standard dataset of TRMM 2A25 at version 7 from January 1998 to December 2015 (https://trmm.gsfc.nasa.gov/data_dir/data.html) was used. The Tropical Rainfall Measuring Mission (TRMM) is the first Earth Science mission dedicated to studying tropical and subtropical rainfall. The Japanese space agency (JAXA) launched the satellite on an H-II rocket from Tanegashima Space Center on November 27, 1997. It is a nonsun-synchronous, about 16 orbits every day, with an inclination of 35 degrees to the Equator, and a precession period of about 46 days for the orbit nodes with respect to the Sun. The main parameters of PR are as follows: scans across a swath 215 km (245 km after boost) wide, vertical and horizontal resolutions of 250 m and 4.3 km at nadir (5.0 km after boost), the detection height is from the surface up to a height of about 20 kilometers. According to TRMM’s precipitation algorithm, the 2A25 precipitation profile data also provides precipitation type information, which is divided into convective precipitation, stratiform precipitation, and other types of precipitation. To put it simply, the identification of the precipitation type is based on whether the radar echo has a bright band and whether the echo intensity exceeds 39 dBZ. The bright band is a sign of identifying stratiform clouds, and 39 dBZ is the standard for identifying convective precipitation. Nonconvective and nonstratigraphic precipitation are defined as “other” types of precipitation. The scope and topography of the research area are shown in Figure 1.Figure 1
Topographic map of the Tibetan Plateau (The red line represents the 3000-meter contour).


### 2.2. Research Methods

Regarding the research methods of precipitation clouds, most scholars use the ellipse-fitting approach to filter precipitation clouds and to determine the orientation angle and the length of the major and minor axes of precipitation clouds. Comparative analysis of precipitation cloud systems in tropical and subtropical, ocean and land [31–33]. However, this method has some limitations in the identification of precipitation clouds and errors due to swath truncation effect.In 2020, Fu et al. [34] used the minimum bounding rectangle (MBR) method to identify precipitation clouds and then obtained the shape parameters of precipitation clouds, which effectively avoided the swath truncation effect and was an effective screening for precipitation clouds method. It showed that MBR method is an effective method of identifying precipitation clouds. Therefore, this study uses the Minimum Bounding Rectangle (MBR) method to identify precipitation clouds. The precipitation pixel track truncation identification will be performed first, that is, whether the precipitation pixels are traversed close to the edge of the track. If there are precipitation pixels at the edge of the track, these precipitation clouds will be defined as truncated precipitation clouds and will be eliminated. The study of Hirose et al. showed that due to the radial distortion of TRMM PR scanning, the geometric distortion of edge pixels is more significant than that of the near nadir pixels, but the land deviation is smaller [35]. Moreover, we eliminate edge pixels, which reduce the impact of pixel distortion on the results, so our research is still very meaningful. Then, it is necessary to rotate the minimum bounding rectangle to fit the spatial distribution of target precipitation clouds to ensure accurate precipitation clouds are identified. The length (L) of the rain cell is the distance between the two ends of the target precipitation cloud along the direction with the longer edge of the smallest bounding rectangle. Similarly, the other direction along the smallest bounding rectangle is defined as the width (W) of the precipitation cloud. Both L and W are the horizontal dimensions of precipitation cloud. The MBR method is used to identify precipitation clouds, which can be relatively easily applied to search for tens of thousands of rain pixels in PR swath. At the same time, compared with the ellipse-fitting approach, the MBR method can improve the inclusion integrity of the rain pixels in the target precipitation cloud. To describe the three-dimensional geometric characteristics of precipitation clouds, this paper gives a series of parameters based on the study of Fu et al. [34], including length (L), width (W), height (Havgc and Havgs), area (S), and others. The geometric parameters are shown in Table 1.Table 1
The definition of geometric parameters of precipitation clouds.
SymbolGeometric meaningL(km)The length of precipitation cloudW(km)The width of precipitation cloudαα describing horizontal shape of precipitation cloud, α = W/LS(km2)The area of precipitation cloud, sum of all area of rain pixelsβThe filling ratio of precipitation cloud, the ratio of precipitation cloudS to the fitted MBR areaHmax(km)The maximum echo top height among rain pixels in precipitation cloudHavg(km)The mean echo top height averaged among rain pixels in precipitation cloudγmaxThe maximum spatial morphology,γmax = Hmax/LγavgThe mean spatial morphology,γavg = 2 ∗ Havg/(L + W)In addition, the physical parameters of precipitation clouds are defined as well. Based on rain types, rain rate profiles and near-surface rain rate supplied at version 7 2A25, those physical parameters of the precipitation cloud are shown in Table2. These parameters are important for expressing the intensity, inhomogeneity, and evolution stages of precipitation clouds.Table 2
The definition of physical parameters of precipitation clouds.
SymbolPhysical meaningRRavg(mm·h−1)Mean rain rate obtained averaged by all rain rate within precipitation cloudRRmax(mm·h−1)The maximum rain rate among rain pixels of precipitation cloudRRavgc(mm·h−1)Mean convective rain rate averaged by all convective rain rate within precipitation cloudRRavgs(mm·h−1)Mean stratiform rain rate averaged by all stratiform rain rate within precipitation cloudRRmaxc(mm·h−1)The maximum rain rate among convective pixels of precipitation cloudRRmaxs(mm·h−1)The maximum rain rate among stratiform pixels of precipitation cloudCAF(%)Fraction of convective area to total precipitation area within precipitation cloudSAF(%)Fraction of stratiform area to total precipitation area within precipitation cloudCPC(%)Convective precipitation contribution to total precipitation within precipitation cloudSPC(%)Stratiform precipitation contribution to total precipitation within precipitation cloudFor example, Figure1 shows two precipitation clouds selected by the MBR method, namely June 15, 1998 and August 7, 1998. Table 3 shows the calculated geometric and physical parameters of the two precipitation clouds displayed in Figure 2.Table 3
The calculated (horizontal and vertical) and physical parameters of the first/second case.
Geometrical parametersPhysical parametersL (km)155.08/188.44RRavg(mm·h−1)2.57/1.95W (km)134.60/63.33RRmax(mm·h−1)124.85/69.88Α0.87/0.34RRavgc(mm·h−1)10.00/7.76S (km2)8438.75/4199.75RRavgs(mm·h−1)1.59/1.41β0.52/0.45RRmaxc(mm·h−1)124.85/69.88Hmax (km)16.25/8.5RRmaxs(mm·h−1)11.54/5.00Havg (km)10.10/5.92CAF(%)11.86/8.5γmax0.11/0.045SAF(%)86.51/91.5γavg0.07/0.047CPC(%)46.19/33.91SPC(%)53.46/66.09Figure 2
Near-surface rain rate of two precipitation clouds occurred on Tibetan Plateau ((a) 15 June 1998; (b) 7 August 1998) measured by PR.
(a)(b)The first case (Figure2(a)) is a mesoscale precipitation cloud. Its length is 155.08 km, and its width is 134.6 km, and its area is 8438.75 km2. The average echo top height is 10.1 km, and the maximum echo top height is 16.25 km. Since α = 0.87, we can know that the precipitation cloud is a quasisquare precipitation cloud. In addition, since β = 0.52, we can see that the distribution of raindrops in the precipitation clouds is relatively compact. From the perspective of spatial morphology, the precipitation cloud has γmax = 0.11 and γavg = 0.07, indicating that its spatial morphology is “squatty,” and the vertical scale is much smaller than that in the horizontal direction. CAF = 11.86%, SAF = 86.51%, indicating that the stratiform precipitation in this precipitation clouds occupies a large area fraction. However, CPC = 46.19% and SPC = 53.46% indicate that although the area occupied by convective precipitation is smaller, the contribution of convective precipitation is greater. In this case, RRavg = 2.57 mm h−1, RRmax = 124.85 mm h−1, RRavgc = 10 mm h−1, RRavgs = 1.59 mm h−1, RRmaxc = 124.85 mm h−1, RRmaxs = 11.54 mm h−1.For the second case (Figure2(b)), the precipitation cloud has a length of 188.44 km, width of 63.33 km, and area of 4199.75 km2. The average echo top height is 5.92 km, and the maximum echo top height is 8.5 km. Different from the first case, its α = 0.34 shows that the precipitation cloud is long strip shape. Its β = 0.45 shows that the distribution of raindrops in the precipitation cloud is not as compact as the first case. From the perspective of spatial morphology, the precipitation cloud has γmax = 0.045 and γavg = 0.047, which shows that its spatial morphology is also “squatty,” but its vertical scale is smaller than the first case. In addition, the CAF = 8.5% and SAF = 91.5% of this precipitation cloud indicate that the area fraction of stratiform precipitation in this precipitation cloud is larger than that of the first case. CPC = 33.91% and SPC = 66.09% indicate that although the contribution of convective precipitation is larger than that of the occupied area, the contribution of stratiform precipitation is still greater. In this precipitation cloud, RRavg = 1.95 mm h−1, RRmax = 69.88 mm h−1, RRavgc = 7.76 mm h−1, RRavgs = 1.41 mm h−1, RRmaxc = 69.88 mm h−1, RRmaxs = 5 mm h−1.We can conclude from the above two examples that the geometric and physical parameters of the two different types of precipitation clouds are different, and these parameters are well described by the MBR method. In this study, a total of 300,320 precipitation clouds were identified in the Tibetan Plateau from January 1998 to March 2015. The geometric and physical characteristics of these precipitation clouds will be discussed below.


## 2.1. Introduction

In this study, the standard dataset of TRMM 2A25 at version 7 from January 1998 to December 2015 (https://trmm.gsfc.nasa.gov/data_dir/data.html) was used. The Tropical Rainfall Measuring Mission (TRMM) is the first Earth Science mission dedicated to studying tropical and subtropical rainfall. The Japanese space agency (JAXA) launched the satellite on an H-II rocket from Tanegashima Space Center on November 27, 1997. It is a nonsun-synchronous, about 16 orbits every day, with an inclination of 35 degrees to the Equator, and a precession period of about 46 days for the orbit nodes with respect to the Sun. The main parameters of PR are as follows: scans across a swath 215 km (245 km after boost) wide, vertical and horizontal resolutions of 250 m and 4.3 km at nadir (5.0 km after boost), the detection height is from the surface up to a height of about 20 kilometers. According to TRMM’s precipitation algorithm, the 2A25 precipitation profile data also provides precipitation type information, which is divided into convective precipitation, stratiform precipitation, and other types of precipitation. To put it simply, the identification of the precipitation type is based on whether the radar echo has a bright band and whether the echo intensity exceeds 39 dBZ. The bright band is a sign of identifying stratiform clouds, and 39 dBZ is the standard for identifying convective precipitation. Nonconvective and nonstratigraphic precipitation are defined as “other” types of precipitation. The scope and topography of the research area are shown in Figure 1.Figure 1
Topographic map of the Tibetan Plateau (The red line represents the 3000-meter contour).


## 2.2. Research Methods

Regarding the research methods of precipitation clouds, most scholars use the ellipse-fitting approach to filter precipitation clouds and to determine the orientation angle and the length of the major and minor axes of precipitation clouds. Comparative analysis of precipitation cloud systems in tropical and subtropical, ocean and land [31–33]. However, this method has some limitations in the identification of precipitation clouds and errors due to swath truncation effect.In 2020, Fu et al. [34] used the minimum bounding rectangle (MBR) method to identify precipitation clouds and then obtained the shape parameters of precipitation clouds, which effectively avoided the swath truncation effect and was an effective screening for precipitation clouds method. It showed that MBR method is an effective method of identifying precipitation clouds. Therefore, this study uses the Minimum Bounding Rectangle (MBR) method to identify precipitation clouds. The precipitation pixel track truncation identification will be performed first, that is, whether the precipitation pixels are traversed close to the edge of the track. If there are precipitation pixels at the edge of the track, these precipitation clouds will be defined as truncated precipitation clouds and will be eliminated. The study of Hirose et al. showed that due to the radial distortion of TRMM PR scanning, the geometric distortion of edge pixels is more significant than that of the near nadir pixels, but the land deviation is smaller [35]. Moreover, we eliminate edge pixels, which reduce the impact of pixel distortion on the results, so our research is still very meaningful. Then, it is necessary to rotate the minimum bounding rectangle to fit the spatial distribution of target precipitation clouds to ensure accurate precipitation clouds are identified. The length (L) of the rain cell is the distance between the two ends of the target precipitation cloud along the direction with the longer edge of the smallest bounding rectangle. Similarly, the other direction along the smallest bounding rectangle is defined as the width (W) of the precipitation cloud. Both L and W are the horizontal dimensions of precipitation cloud. The MBR method is used to identify precipitation clouds, which can be relatively easily applied to search for tens of thousands of rain pixels in PR swath. At the same time, compared with the ellipse-fitting approach, the MBR method can improve the inclusion integrity of the rain pixels in the target precipitation cloud. To describe the three-dimensional geometric characteristics of precipitation clouds, this paper gives a series of parameters based on the study of Fu et al. [34], including length (L), width (W), height (Havgc and Havgs), area (S), and others. The geometric parameters are shown in Table 1.Table 1
The definition of geometric parameters of precipitation clouds.
SymbolGeometric meaningL(km)The length of precipitation cloudW(km)The width of precipitation cloudαα describing horizontal shape of precipitation cloud, α = W/LS(km2)The area of precipitation cloud, sum of all area of rain pixelsβThe filling ratio of precipitation cloud, the ratio of precipitation cloudS to the fitted MBR areaHmax(km)The maximum echo top height among rain pixels in precipitation cloudHavg(km)The mean echo top height averaged among rain pixels in precipitation cloudγmaxThe maximum spatial morphology,γmax = Hmax/LγavgThe mean spatial morphology,γavg = 2 ∗ Havg/(L + W)In addition, the physical parameters of precipitation clouds are defined as well. Based on rain types, rain rate profiles and near-surface rain rate supplied at version 7 2A25, those physical parameters of the precipitation cloud are shown in Table2. These parameters are important for expressing the intensity, inhomogeneity, and evolution stages of precipitation clouds.Table 2
The definition of physical parameters of precipitation clouds.
SymbolPhysical meaningRRavg(mm·h−1)Mean rain rate obtained averaged by all rain rate within precipitation cloudRRmax(mm·h−1)The maximum rain rate among rain pixels of precipitation cloudRRavgc(mm·h−1)Mean convective rain rate averaged by all convective rain rate within precipitation cloudRRavgs(mm·h−1)Mean stratiform rain rate averaged by all stratiform rain rate within precipitation cloudRRmaxc(mm·h−1)The maximum rain rate among convective pixels of precipitation cloudRRmaxs(mm·h−1)The maximum rain rate among stratiform pixels of precipitation cloudCAF(%)Fraction of convective area to total precipitation area within precipitation cloudSAF(%)Fraction of stratiform area to total precipitation area within precipitation cloudCPC(%)Convective precipitation contribution to total precipitation within precipitation cloudSPC(%)Stratiform precipitation contribution to total precipitation within precipitation cloudFor example, Figure1 shows two precipitation clouds selected by the MBR method, namely June 15, 1998 and August 7, 1998. Table 3 shows the calculated geometric and physical parameters of the two precipitation clouds displayed in Figure 2.Table 3
The calculated (horizontal and vertical) and physical parameters of the first/second case.
Geometrical parametersPhysical parametersL (km)155.08/188.44RRavg(mm·h−1)2.57/1.95W (km)134.60/63.33RRmax(mm·h−1)124.85/69.88Α0.87/0.34RRavgc(mm·h−1)10.00/7.76S (km2)8438.75/4199.75RRavgs(mm·h−1)1.59/1.41β0.52/0.45RRmaxc(mm·h−1)124.85/69.88Hmax (km)16.25/8.5RRmaxs(mm·h−1)11.54/5.00Havg (km)10.10/5.92CAF(%)11.86/8.5γmax0.11/0.045SAF(%)86.51/91.5γavg0.07/0.047CPC(%)46.19/33.91SPC(%)53.46/66.09Figure 2
Near-surface rain rate of two precipitation clouds occurred on Tibetan Plateau ((a) 15 June 1998; (b) 7 August 1998) measured by PR.
(a)(b)The first case (Figure2(a)) is a mesoscale precipitation cloud. Its length is 155.08 km, and its width is 134.6 km, and its area is 8438.75 km2. The average echo top height is 10.1 km, and the maximum echo top height is 16.25 km. Since α = 0.87, we can know that the precipitation cloud is a quasisquare precipitation cloud. In addition, since β = 0.52, we can see that the distribution of raindrops in the precipitation clouds is relatively compact. From the perspective of spatial morphology, the precipitation cloud has γmax = 0.11 and γavg = 0.07, indicating that its spatial morphology is “squatty,” and the vertical scale is much smaller than that in the horizontal direction. CAF = 11.86%, SAF = 86.51%, indicating that the stratiform precipitation in this precipitation clouds occupies a large area fraction. However, CPC = 46.19% and SPC = 53.46% indicate that although the area occupied by convective precipitation is smaller, the contribution of convective precipitation is greater. In this case, RRavg = 2.57 mm h−1, RRmax = 124.85 mm h−1, RRavgc = 10 mm h−1, RRavgs = 1.59 mm h−1, RRmaxc = 124.85 mm h−1, RRmaxs = 11.54 mm h−1.For the second case (Figure2(b)), the precipitation cloud has a length of 188.44 km, width of 63.33 km, and area of 4199.75 km2. The average echo top height is 5.92 km, and the maximum echo top height is 8.5 km. Different from the first case, its α = 0.34 shows that the precipitation cloud is long strip shape. Its β = 0.45 shows that the distribution of raindrops in the precipitation cloud is not as compact as the first case. From the perspective of spatial morphology, the precipitation cloud has γmax = 0.045 and γavg = 0.047, which shows that its spatial morphology is also “squatty,” but its vertical scale is smaller than the first case. In addition, the CAF = 8.5% and SAF = 91.5% of this precipitation cloud indicate that the area fraction of stratiform precipitation in this precipitation cloud is larger than that of the first case. CPC = 33.91% and SPC = 66.09% indicate that although the contribution of convective precipitation is larger than that of the occupied area, the contribution of stratiform precipitation is still greater. In this precipitation cloud, RRavg = 1.95 mm h−1, RRmax = 69.88 mm h−1, RRavgc = 7.76 mm h−1, RRavgs = 1.41 mm h−1, RRmaxc = 69.88 mm h−1, RRmaxs = 5 mm h−1.We can conclude from the above two examples that the geometric and physical parameters of the two different types of precipitation clouds are different, and these parameters are well described by the MBR method. In this study, a total of 300,320 precipitation clouds were identified in the Tibetan Plateau from January 1998 to March 2015. The geometric and physical characteristics of these precipitation clouds will be discussed below.


## 3. Results and Discussion

### 3.1. Statistical Characteristics of Geometric and Physical Parameters

First, we show the statistical characteristics of precipitation clouds. The result indicates that the probability distribution functions (PDFs) ofL reaches the peak of 60% when L is at 18 km, that is, the occurrence frequency of precipitation clouds with 18 km in length is 60% (Figure 3(a)). When L is greater than 18 km, the occurrence probability of precipitation clouds decreases with the increase of L. When L is greater than 100 km, the occurrence probability of precipitation clouds drops rapidly to below 1%. Similarly, the PDF of W reaches the peak of 60% when W is 15 km (Figure 3(b)). When W is greater than 90 km, the occurrence probability of precipitation clouds is very low, less than 1%. From the PDF of L and W, more than 60% of precipitation clouds appear on the scale of 18 km in length and 15 km in width. The statistics in Table 4 show that the average length of precipitation clouds in the Tibetan Plateau is 34.74 km and the average width is 19.91 km.Figure 3
The probability distribution functions (PDFs) of the horizontal geometrical parameters forL (a), W (b), S (c), α (d), and β (e) on Tibetan Plateau calculated from 1998 to 2015.
(a)(b)(c)(d)(e)Table 4
The calculated mean geometrical (horizontal and vertical) and physical parameters of precipitation clouds.
Geometrical parametersAveragePhysical parametersAverageL (km)34.74RRavg(mm·h−1)1.54W (km)19.91RRmax(mm·h−1)5.60α0.62RRavgc(mm·h−1)7.22S (km2)373.67RRavgs(mm·h−1)1.20β0.55RRmaxc(mm·h−1)13.61Hmax (km)9.69RRmaxs(mm·h−1)2.60Havg (km)8.36CAF(%)19.29γmax0.39SAF(%)94.13γavg0.42CPC(%)44.16SPC(%)86.39In terms of the level of precipitation clouds, the occurrence probability of precipitation clouds decreases with the increase of precipitation clouds areaS (Figure 3(c)). When S is greater than 1000 km2, the occurrence probability of precipitation clouds is less than 1%. The statistics in Table 4 show that the average area of precipitation clouds is 373.67 km2.The probability distribution function of the parameterα describing the horizontal shape of the precipitation cloud is shown in Figure 3(d). The results show that the occurrence probability of “long strip” (α < 0.4) and “square” (α > 0.8) precipitation clouds is relatively low, less than 15%. The rest precipitation clouds are featured between the two shapes. As shown in Table 4, the average α of precipitation clouds is 0.62. It can be seen that the average horizontal shape of most precipitation clouds is between square and long strips.The PDF ofβ mainly varies between 0.25 and 0.75, with a peak value close to 0.7 (Figure 3(e)), and more than half of the precipitation clouds have β greater than 0.5. In fact, the average β of precipitation clouds in Table 4 is 0.55. These precipitation clouds almost fill more than half of the minimum bounding rectangle (MBR), which shows that the MBR method in this study is effective for identifying precipitation clouds.The PDFs of vertical geometrical parameters of precipitation clouds over Tibetan Plateau calculated from 1998 to 2015 are plotted in Figure4. The results show that the PDF of Hmax has a peak at 9 km above the plateau (Figure 4(a)), with a range of 4–18 km. The average Hmax of precipitation clouds is 9.69 km (Table 4). From the PDF of Havg (Figure 4(b)), it can be seen that the Havg value varies from 3 km to 13 km, and the peak appears at 9 km above the plateau. The statistical calculations in Table 4 show that the average Havg of precipitation clouds is 8.36 km.Figure 4
The PDFs of vertical geometrical parameters forHmax (a), Havg (b), γmax (c), and γavg (d) on Tibetan Plateau calculated from 1998 to 2015.
(a)(b)(c)(d)γmax and γavg are parameters that reflect the spatial morphology of precipitation clouds, that is, the “squatty” appearance or “lanky” appearance of precipitation clouds. The variation range of γmax and γavg is in 0.05–0.95, and both reach the peak value at 0.4 (Figures 4(c) and 4(d)). The mean γmax and γavg are 0.39 and 0.42. It can be seen that the spatial morphology of precipitation clouds in the Tibetan Plateau is still dominated by “lanky” appearance.Figure5 shows the PDFs of these physical parameters of precipitation clouds in the Tibetan Plateau. The results show that the RRmax of precipitation cloud varies from 0.5 to 20 mm h−1, with a peak at 1.5 mm h−1 (Figure 5(a)). The RRavg of precipitation cloud varies from 0.5 to 6 mm h−1, with a peak at 1 mm h−1 (Figure 5(b)). It can be seen from Figure 4(b) that the probability of heavy rain (RRavg greater than 4 mm h−1) on the plateau is much smaller than that of light rain (RRavg less than 1.5 mm h−1), and about 75% of precipitation clouds have RRavg between 1.5 mm h−1 and 4 mm h−1.Figure 5
The PDFs of physical parameters for RRmax (a), RRavg (b), RRmaxc (c), RRavgc (d), RRmaxs (e), RRavgs (f), CAF (g), CPC (h), SAF (i), and SPC (j) on Tibetan Plateau from 1998 to 2015.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)Figures5(c)–5(f) show the PDFs of RRmaxc, RRavgc, RRmaxs and RRavgs. It can be seen that the difference between convective and stratiform precipitation is very obvious, and the variation range of convective precipitation is obviously larger than that of stratiform precipitation. The variation range of RRmaxc is 0.5–40 mm h−1, the variation range of RRavgc is 0.5–20 mm h−1, and the variation range of RRmaxs and RRavgs is only 0.5–9 mm h−1 and 0.5–3.5 mm h−1. Both the RRmaxc and RRavgc peaked at 6.5 mmh−1, while the RRmaxs and RRavgs peaks were at 2mmh−1 and 1mmh−1, respectively. In Table 4, the statistical results show that the average precipitation cloud of RRmaxc, RRavgc, RRmaxs and RRavgs are 13.61 mm h−1, 7.22 mm h−1, 2.60 mm h−1 and 1.20 mm h−1, respectively.Through CAF or SAF, the area fraction of convective precipitation and stratiform precipitation, it also reflects the nature of precipitation clouds to a certain extent. For example, the raindrops in precipitation clouds are mostly convective or stratified. In Table4, the average CAF and SAF of precipitation clouds is 19.29% and 94.13%. Figures 5(g) and 5(i) show the PDFs of CAF and SAF. The results show that the PDF decreases sharply with the increase of the CAF in the precipitation cloud, while the PDF increases sharply with the increase of the SAF in the precipitation cloud. The CAF in 50% of the precipitation clouds on the plateau is less than 10%, but for the precipitation clouds with 80% CAF, it is only 1% on the plateau. On the contrary, the precipitation cloud with 40% SAF on the plateau is only 1%, but the precipitation cloud with 80% SAF has about 30%.Figures5(h) and 5(j) are the PDFs of CPC and SPC. The results show that when CPC increases to 20%, the PDF of CPC rises to more than 10%, and then as CPC increases to 100%, the PDF of CPC drops to below 10%. It can be seen that the contribution of convective precipitation in the same precipitation cloud is relatively low. When the SPC increases to 65%, the PDF of SPC rises from 1% to 7%. When the SPC increases to 75%, the PDF of SPC drops slightly. When the SPC increases to 100%, the PDF of SPC rises to the highest but still less than 10%. It can be seen that the contribution of stratiform precipitation in the same precipitation cloud is lower than that of convective precipitation.The analysis of the above PDF shows that the MBR method can accurately identify precipitation clouds, and most precipitation clouds are 18 km in length and 15 km in width. The precipitation cloud with a length of more than 100 km, a width of more than 90 km, and an area of more than 1,000 km2 is less than 1%. In contrast, the horizontal form of most precipitation clouds is long strip shape. From the vertical direction, the height of precipitation clouds is mostly 9 km above the plateau, and the spatial shape is mainly lanky appearance. The PDF of physical parameters indicates that the occurrence probability of light rain on the plateau is greater than heavy rain. The difference between convective and stratiform precipitation is very obvious. The area fraction of stratiform precipitation is greater than convective precipitation, but the contribution of precipitation is smaller than that of convective precipitation.


### 3.2. The Relationship among the Geometric Parameters

In this study, a total of about 300,000 samples of precipitation cloud geometric parameters were obtained. To increase the reliability of statistical results, the approach of equal sample statistics is adopted. This approach has been used to calculate the mean and standard deviation of rain rate variation with altitude [36]. Specifically in this study, an independent variable (x axis) is divided into 40 intervals, 2.5% of the total samples in each interval, and then the values of a dependent variable (y axis) are averaged within each interval.First, the relationship betweenL (x axis) and W (y axis) is shown in logarithmic coordinates in Figure 6. The results show that when L is greater than 25 km, L and W have a log-linear relationship, which can be expressed by the equation logW=a+b×logL. Here, a = 0.0798 and b = 0.8264. When L is less than 25 km (W is less than 17 km), that is, a small precipitation cloud, the relationship between these two parameters is more complicated. For these precipitation clouds, these two parameters are geometrically affected by various combinations of raindrop positions, which may indicate that the horizontal geometric parameters at the initial stage of precipitation cloud formation have undergone strong physical changes.Figure 6
The relationship between W and L on Tibetan Plateau from 1998 to 2015 based on the statistical principle of same samples in each interval atx axis.In order to better understand the horizontal structure of precipitation clouds, the relationship between horizontal morphological parameters (α, β) and horizontal geometric parameters (L, W, S) is analyzed. As shown in Figure 7(a), as L increases from 10 km to 25 km, the parameter α decreases rapidly from 1.0 (square precipitation cloud) to 0.6 (quasisquare precipitation cloud). When L continues to increase from 25 km to around 300 km, α slowly decreases from 0.6 to around 0.5 (relatively long precipitation clouds). This confirms the characteristic of the ratio change between L and W shown in Figure 6; they generally follow a log-linear relationship. As shown in Figure 7(b), when W is greater than 17 km, the parameter α changes less. When W is less than 17 km, α increases with the increase of W, and α increases from 0.3 (long precipitation cloud) to 0.6 (quasisquare precipitation cloud).Figure 7
The relationship betweenα and L (a), α and W (b), α and S (c), β and L (d), β and W (e), and β and S (f) on Tibetan Plateau from 1998 to 2015 based on the statistical principle of same samples in each interval at x axis.
(a)(b)(c)(d)(e)(f)The change in the ratio ofL to W also determines that when S is less than 300 km2, the parameter α (W/L) decreases with the increase of the precipitation cloud area S, which means that when the precipitation cloud area increases to 300 km2, the shape of the precipitation cloud is very easy to change from a square shape to a relatively long strip shape. When S is greater than 300 km2, α is almost unchanged. The above results show that the parameter α combined with the length and width of the precipitation area is also a parameter describing the horizontal shape of the precipitation cloud.The parameterβ is the ratio of the area of S to MBR. As shown in Figures 7(d)–7(f), when L is greater than 25 km, W is greater than 17 km, or S is greater than 300 km2, β decreases with the increase of L, W and S, respectively. This means that the precipitation clouds on the plateau become loose when their horizontal geometric parameters are increased. For those precipitation clouds with small horizontal geometric parameters (L is less than 25 km, W is less than 17 km, or S is less than 300 km2), the β of these precipitation clouds changes around 0.6 or above, indicating that the distribution of raindrops in these precipitation clouds is relatively compact.Figure8 shows the relationship between the vertical geometric parameters (Hmax and Havg) and the horizontal geometric parameters (L, W, and S) of precipitation clouds in the Tibetan Plateau. The results show that when L is less than 30 km, W is less than 18 km, and S is less than 200 km2, there is no law for the change of Hmax and Havg, that is, the relationship between vertical geometric parameters and horizontal geometric parameters is more complicated. When L is greater than 30 km, W is greater than 18 km, and S is greater than 200 km2, both Hmax and Havg tend to be stable, Hmax is about 10 km and Havg is about 8 km. Although the changing trends of Hmax and Havg are roughly the same, Havg can more effectively express the relationship between the precipitation cloud range and the horizontal scale because it reduces the error caused by random values or extreme values.Figure 8
The relationship betweenHmax and L (a), Hmax and W (b), Hmax and S (c), Havg and L (d), Havg and W (e), and Havg and S (f) on Tibetan Plateau from 1998 to 2015 based on the statistical principle of same samples in each interval at x axis.
(a)(b)(c)(d)(e)(f)The relationship between spatial morphology (γmax and γavg) and S (Figure 9) shows that when S is less than 200 km2, both parameters are greater than 0.3, which means that small precipitation clouds on the plateau tend to be a lanky appearance. Both parameters decrease with the increase of S, which indicates that as the area increases, the precipitation cloud gradually becomes a squatty appearance. This phenomenon is physically reasonable, because as the horizontal area of the precipitation cloud becomes larger, there is not enough energy to support its overall vertical development.Figure 9
The relationship betweenγmax and S (a) and γavg and S (b) on Tibetan Plateau from 1998 to 2015 based on the statistical principle of same samples in each interval at x axis.
(a)(b)


### 3.3. The Relationship between Physical and Geometric Parameters

The physical properties of precipitation clouds generally determine its geometric properties. Naturally, they are more concerned about the relationship between the physical parameters and geometric parameters of precipitation clouds. The relationship between RRmax (RRavg) and S of precipitation clouds is shown in Figure 10. Relatively speaking, as S increases, the RRmax in the precipitation cloud increases (Figure 10(a)). It illustrates that in the larger precipitation cloud, the probability of extreme precipitation is greater. Compared with the relationship between RRmax and S, the relationship between RRavg and S can more effectively understand the influence of precipitation cloud area on precipitation intensity. Because RRavg is a parameter that normalizes all raindrops in a precipitation cloud, it reduces the influence of the unequal number of raindrops in different precipitation clouds. Figure 10(b) shows that, relatively speaking, as S increases, the precipitation cloud RRavg increases. When S is greater than 500 km2, RRavg seems to remain at 1.7 mm h−1.Figure 10
The relationship between RRmax and S (a) and RRavg and S (b) on Tibetan Plateau from 1998 to 2015 based on the statistical principle of same samples in each interval at x axis.
(a)(b)Figure 11
The relationship between RRmaxc and S (a), RRmaxs and S (b), RRavgc and S (c), and RRavgs and S (d) on Tibetan Plateau from 1998 to 2015 based on the statistical principle of same samples in each interval at x axis.
(a)(b)(c)(d)The relationship between the precipitation cloud areaS and the average rain rate and maximum rain rate of convective or stratiform precipitation, RRmaxc, RRmaxs, RRavgc and RRavgs, is obtained as plotted in Figure 11. Relatively speaking, RRmaxc and RRmaxs both increase with the increase of S. Both RRavgc and RRavgs also increase with the increase of S, but the increase of RRavgs is not obvious. However, the growth rates of RRmaxc and RRmaxs exceed RRavgc and RRavgs, respectively.Figure12 shows the relationship between CAF (SAF) and S in the precipitation cloud and the relationship between CPC (SPC) and S in the precipitation cloud. When S is less than 400 km2, CAF is relatively high, which may be the initial development period of precipitation clouds. Then CAF gradually decreases to about 20%, which means that the precipitation cloud has entered a period of dissipation. In contrast, the relationship between SAF and S is significantly different from CAF. Figure 12(b) shows that as S increases from 50 to 5000 square kilometers, the value of SAF is almost all above 80%, indicating that the area fraction of stratiform precipitation is greater than convective precipitation and as much as 4 times larger. From Figures 12(c) and 12(d), it can be seen that the trend of CPC and SPC is roughly the same as CAF and SAF. When S is less than 400 km2, CPC is relatively high, and then gradually decreases to about 40%. When S is less than 300 km2, SPC tends to increase gradually, and then reaches about 80% steadily. Individually, the contribution of stratiform precipitation is also greater than convective precipitation. However, from the perspective of CAF and SAF, the contribution of convective precipitation is much greater than the area fraction of convective precipitation. It can be seen that the precipitation intensity of convective precipitation is still very large.Figure 12
The relationship between CAF andS (a), SAF and S (b), CPC and S (c), and SPC and S (d) on Tibetan Plateau from 1998 to 2015 based on the statistical principle of same samples in each interval at x axis.
(a)(b)(c)(d)


### 3.4. The Spatial Frequency Distribution of Rain Cells in Different Parameters

In order to understand the geometric and physical parameters of the above precipitation cloud, we further investigate the spatial frequency distribution of the precipitation cloud corresponding to the three different parameters. The first example is the spatial frequency distribution of precipitation clouds in differentα, as shown in Figure 13. Based on the probability distribution function of α shown in Figure 3(c), three α ranges are selected, namely α ≤ 0.4, 0.4 < α ≤ 0.7 and α > 0.7. Figure 13(a) shows that precipitation clouds tend to be long (α ≤ 0.4) in the central and eastern plateau, and the frequency of such precipitation clouds is about 8%. The precipitation clouds on the southern slope of the plateau are mostly square (α > 0.7), and the frequency of these precipitation clouds exceeds 56%, but the frequency of these precipitation clouds in the plateau is relatively low, only about 40% (Figure 13(c)). Precipitation clouds whose shapes tend to be between long strip and square shape (0.4 < α ≤ 0.7) are mainly distributed inside the plateau. The frequency of precipitation clouds is more than 54% (Figure 13(b)). By comparing the three situations shown in Figure 13, it is found that the long strip precipitation cloud accounts for the smallest proportion, followed by the square, and the precipitation cloud between the long strip and the square shape has the largest proportion. This is consistent with the result in Figure 3(c).Figure 13
The spatial frequency distributions of precipitation clouds with (a)α ≤ 0.4, (b) 0.4 < α ≤ 0.7, and (c) α > 0.7. The red line represents the 3000-meter contour.
(a)(b)(c)The second example is the spatial frequency distribution of precipitation clouds in differentγavg. Based on the γavg probability distribution function shown in Figure 4(d), it is divided into three ranges: γavg ≤ 0.1, 0.1<γavg ≤ 0.5, and γavg > 0.5. Figure 14(a) shows that precipitation clouds in squatty appearance (γavg ≤ 0.1)are mainly distributed in the marginal area of the eastern plateau, and the frequency of such precipitation clouds is about 16%. The precipitation clouds in lanky appearance (γavg > 0.5, Figure 14(c)) are concentrated in the southwestern part of the plateau, with a frequency of about 13%. Figure 14(b) shows that precipitation clouds that are neither squatty nor lanky appearance (0.1<γavg ≤ 0.5) mainly appear inside the plateau, with a frequency of more than 86%, which is consistent with the situation in Figure 4(d).Figure 14
The spatial frequency distributions of precipitation clouds with (a)γavg ≤ 0.1, (b) 0.1 < γavg ≤ 0.5, and (c) γavg > 0.5. The red line represents the 3000-meter contour.
(a)(b)(c)The third example is the spatial frequency distribution of precipitation clouds for different RRavg, as shown in Figure 15. The results show that precipitation clouds with relatively small precipitation intensity (RRavg ≤ 1.5 mm·h−1) dominate the plateau precipitation clouds, mainly distributed in the interior and east of the plateau, and the frequency of such precipitation clouds exceeds 60% (Figure 15(a)). Precipitation clouds with high precipitation intensity (RRavg > 4 mm·h−1) mainly appear in the southwest and eastern edges of the plateau, with a frequency of about 17% (Figure 15(c)). Precipitation clouds with moderate precipitation intensity (1.5<RRavg ≤ 4 mm h−1) mainly appear on the southern slope of the plateau, with a frequency of more than 42% (Figure 15(b)). In summary, it is consistent with the result in Figure 5(b).Figure 15
The spatial frequency distributions of precipitation clouds with (a) RRavg ≤ 1.5 mm h−1, (b) 1.5<RRavg ≤ 4 mm h−1, and (c) RRavg > 4 mm h−1. The red line represents the 3000-meter contour.
(a)(b)(c)From the comprehensive analysis of Figures13–15, precipitation clouds with moderate precipitation intensity mainly appear on the southern slope of the plateau and most of these precipitation clouds are square. Some precipitation clouds with lower precipitation intensity appear in the eastern plateau, and these precipitation clouds are mostly having a long strip shape and its spatial shape tends to be squatty appearance; some appear in the interior of the plateau, and the horizontal shape of these precipitation clouds tends to be between square and long strip shape. Its spatial shape tends to be between the squatty appearance and lanky appearance. It can be seen that the geometric and physical parameters of precipitation clouds defined in this study are of great significance for revealing the spatial distribution characteristics and regional differences of precipitation clouds.


## 3.1. Statistical Characteristics of Geometric and Physical Parameters

First, we show the statistical characteristics of precipitation clouds. The result indicates that the probability distribution functions (PDFs) ofL reaches the peak of 60% when L is at 18 km, that is, the occurrence frequency of precipitation clouds with 18 km in length is 60% (Figure 3(a)). When L is greater than 18 km, the occurrence probability of precipitation clouds decreases with the increase of L. When L is greater than 100 km, the occurrence probability of precipitation clouds drops rapidly to below 1%. Similarly, the PDF of W reaches the peak of 60% when W is 15 km (Figure 3(b)). When W is greater than 90 km, the occurrence probability of precipitation clouds is very low, less than 1%. From the PDF of L and W, more than 60% of precipitation clouds appear on the scale of 18 km in length and 15 km in width. The statistics in Table 4 show that the average length of precipitation clouds in the Tibetan Plateau is 34.74 km and the average width is 19.91 km.Figure 3
The probability distribution functions (PDFs) of the horizontal geometrical parameters forL (a), W (b), S (c), α (d), and β (e) on Tibetan Plateau calculated from 1998 to 2015.
(a)(b)(c)(d)(e)Table 4
The calculated mean geometrical (horizontal and vertical) and physical parameters of precipitation clouds.
Geometrical parametersAveragePhysical parametersAverageL (km)34.74RRavg(mm·h−1)1.54W (km)19.91RRmax(mm·h−1)5.60α0.62RRavgc(mm·h−1)7.22S (km2)373.67RRavgs(mm·h−1)1.20β0.55RRmaxc(mm·h−1)13.61Hmax (km)9.69RRmaxs(mm·h−1)2.60Havg (km)8.36CAF(%)19.29γmax0.39SAF(%)94.13γavg0.42CPC(%)44.16SPC(%)86.39In terms of the level of precipitation clouds, the occurrence probability of precipitation clouds decreases with the increase of precipitation clouds areaS (Figure 3(c)). When S is greater than 1000 km2, the occurrence probability of precipitation clouds is less than 1%. The statistics in Table 4 show that the average area of precipitation clouds is 373.67 km2.The probability distribution function of the parameterα describing the horizontal shape of the precipitation cloud is shown in Figure 3(d). The results show that the occurrence probability of “long strip” (α < 0.4) and “square” (α > 0.8) precipitation clouds is relatively low, less than 15%. The rest precipitation clouds are featured between the two shapes. As shown in Table 4, the average α of precipitation clouds is 0.62. It can be seen that the average horizontal shape of most precipitation clouds is between square and long strips.The PDF ofβ mainly varies between 0.25 and 0.75, with a peak value close to 0.7 (Figure 3(e)), and more than half of the precipitation clouds have β greater than 0.5. In fact, the average β of precipitation clouds in Table 4 is 0.55. These precipitation clouds almost fill more than half of the minimum bounding rectangle (MBR), which shows that the MBR method in this study is effective for identifying precipitation clouds.The PDFs of vertical geometrical parameters of precipitation clouds over Tibetan Plateau calculated from 1998 to 2015 are plotted in Figure4. The results show that the PDF of Hmax has a peak at 9 km above the plateau (Figure 4(a)), with a range of 4–18 km. The average Hmax of precipitation clouds is 9.69 km (Table 4). From the PDF of Havg (Figure 4(b)), it can be seen that the Havg value varies from 3 km to 13 km, and the peak appears at 9 km above the plateau. The statistical calculations in Table 4 show that the average Havg of precipitation clouds is 8.36 km.Figure 4
The PDFs of vertical geometrical parameters forHmax (a), Havg (b), γmax (c), and γavg (d) on Tibetan Plateau calculated from 1998 to 2015.
(a)(b)(c)(d)γmax and γavg are parameters that reflect the spatial morphology of precipitation clouds, that is, the “squatty” appearance or “lanky” appearance of precipitation clouds. The variation range of γmax and γavg is in 0.05–0.95, and both reach the peak value at 0.4 (Figures 4(c) and 4(d)). The mean γmax and γavg are 0.39 and 0.42. It can be seen that the spatial morphology of precipitation clouds in the Tibetan Plateau is still dominated by “lanky” appearance.Figure5 shows the PDFs of these physical parameters of precipitation clouds in the Tibetan Plateau. The results show that the RRmax of precipitation cloud varies from 0.5 to 20 mm h−1, with a peak at 1.5 mm h−1 (Figure 5(a)). The RRavg of precipitation cloud varies from 0.5 to 6 mm h−1, with a peak at 1 mm h−1 (Figure 5(b)). It can be seen from Figure 4(b) that the probability of heavy rain (RRavg greater than 4 mm h−1) on the plateau is much smaller than that of light rain (RRavg less than 1.5 mm h−1), and about 75% of precipitation clouds have RRavg between 1.5 mm h−1 and 4 mm h−1.Figure 5
The PDFs of physical parameters for RRmax (a), RRavg (b), RRmaxc (c), RRavgc (d), RRmaxs (e), RRavgs (f), CAF (g), CPC (h), SAF (i), and SPC (j) on Tibetan Plateau from 1998 to 2015.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)Figures5(c)–5(f) show the PDFs of RRmaxc, RRavgc, RRmaxs and RRavgs. It can be seen that the difference between convective and stratiform precipitation is very obvious, and the variation range of convective precipitation is obviously larger than that of stratiform precipitation. The variation range of RRmaxc is 0.5–40 mm h−1, the variation range of RRavgc is 0.5–20 mm h−1, and the variation range of RRmaxs and RRavgs is only 0.5–9 mm h−1 and 0.5–3.5 mm h−1. Both the RRmaxc and RRavgc peaked at 6.5 mmh−1, while the RRmaxs and RRavgs peaks were at 2mmh−1 and 1mmh−1, respectively. In Table 4, the statistical results show that the average precipitation cloud of RRmaxc, RRavgc, RRmaxs and RRavgs are 13.61 mm h−1, 7.22 mm h−1, 2.60 mm h−1 and 1.20 mm h−1, respectively.Through CAF or SAF, the area fraction of convective precipitation and stratiform precipitation, it also reflects the nature of precipitation clouds to a certain extent. For example, the raindrops in precipitation clouds are mostly convective or stratified. In Table4, the average CAF and SAF of precipitation clouds is 19.29% and 94.13%. Figures 5(g) and 5(i) show the PDFs of CAF and SAF. The results show that the PDF decreases sharply with the increase of the CAF in the precipitation cloud, while the PDF increases sharply with the increase of the SAF in the precipitation cloud. The CAF in 50% of the precipitation clouds on the plateau is less than 10%, but for the precipitation clouds with 80% CAF, it is only 1% on the plateau. On the contrary, the precipitation cloud with 40% SAF on the plateau is only 1%, but the precipitation cloud with 80% SAF has about 30%.Figures5(h) and 5(j) are the PDFs of CPC and SPC. The results show that when CPC increases to 20%, the PDF of CPC rises to more than 10%, and then as CPC increases to 100%, the PDF of CPC drops to below 10%. It can be seen that the contribution of convective precipitation in the same precipitation cloud is relatively low. When the SPC increases to 65%, the PDF of SPC rises from 1% to 7%. When the SPC increases to 75%, the PDF of SPC drops slightly. When the SPC increases to 100%, the PDF of SPC rises to the highest but still less than 10%. It can be seen that the contribution of stratiform precipitation in the same precipitation cloud is lower than that of convective precipitation.The analysis of the above PDF shows that the MBR method can accurately identify precipitation clouds, and most precipitation clouds are 18 km in length and 15 km in width. The precipitation cloud with a length of more than 100 km, a width of more than 90 km, and an area of more than 1,000 km2 is less than 1%. In contrast, the horizontal form of most precipitation clouds is long strip shape. From the vertical direction, the height of precipitation clouds is mostly 9 km above the plateau, and the spatial shape is mainly lanky appearance. The PDF of physical parameters indicates that the occurrence probability of light rain on the plateau is greater than heavy rain. The difference between convective and stratiform precipitation is very obvious. The area fraction of stratiform precipitation is greater than convective precipitation, but the contribution of precipitation is smaller than that of convective precipitation.


## 3.2. The Relationship among the Geometric Parameters

In this study, a total of about 300,000 samples of precipitation cloud geometric parameters were obtained. To increase the reliability of statistical results, the approach of equal sample statistics is adopted. This approach has been used to calculate the mean and standard deviation of rain rate variation with altitude [36]. Specifically in this study, an independent variable (x axis) is divided into 40 intervals, 2.5% of the total samples in each interval, and then the values of a dependent variable (y axis) are averaged within each interval.First, the relationship betweenL (x axis) and W (y axis) is shown in logarithmic coordinates in Figure 6. The results show that when L is greater than 25 km, L and W have a log-linear relationship, which can be expressed by the equation logW=a+b×logL. Here, a = 0.0798 and b = 0.8264. When L is less than 25 km (W is less than 17 km), that is, a small precipitation cloud, the relationship between these two parameters is more complicated. For these precipitation clouds, these two parameters are geometrically affected by various combinations of raindrop positions, which may indicate that the horizontal geometric parameters at the initial stage of precipitation cloud formation have undergone strong physical changes.Figure 6
The relationship between W and L on Tibetan Plateau from 1998 to 2015 based on the statistical principle of same samples in each interval atx axis.In order to better understand the horizontal structure of precipitation clouds, the relationship between horizontal morphological parameters (α, β) and horizontal geometric parameters (L, W, S) is analyzed. As shown in Figure 7(a), as L increases from 10 km to 25 km, the parameter α decreases rapidly from 1.0 (square precipitation cloud) to 0.6 (quasisquare precipitation cloud). When L continues to increase from 25 km to around 300 km, α slowly decreases from 0.6 to around 0.5 (relatively long precipitation clouds). This confirms the characteristic of the ratio change between L and W shown in Figure 6; they generally follow a log-linear relationship. As shown in Figure 7(b), when W is greater than 17 km, the parameter α changes less. When W is less than 17 km, α increases with the increase of W, and α increases from 0.3 (long precipitation cloud) to 0.6 (quasisquare precipitation cloud).Figure 7
The relationship betweenα and L (a), α and W (b), α and S (c), β and L (d), β and W (e), and β and S (f) on Tibetan Plateau from 1998 to 2015 based on the statistical principle of same samples in each interval at x axis.
(a)(b)(c)(d)(e)(f)The change in the ratio ofL to W also determines that when S is less than 300 km2, the parameter α (W/L) decreases with the increase of the precipitation cloud area S, which means that when the precipitation cloud area increases to 300 km2, the shape of the precipitation cloud is very easy to change from a square shape to a relatively long strip shape. When S is greater than 300 km2, α is almost unchanged. The above results show that the parameter α combined with the length and width of the precipitation area is also a parameter describing the horizontal shape of the precipitation cloud.The parameterβ is the ratio of the area of S to MBR. As shown in Figures 7(d)–7(f), when L is greater than 25 km, W is greater than 17 km, or S is greater than 300 km2, β decreases with the increase of L, W and S, respectively. This means that the precipitation clouds on the plateau become loose when their horizontal geometric parameters are increased. For those precipitation clouds with small horizontal geometric parameters (L is less than 25 km, W is less than 17 km, or S is less than 300 km2), the β of these precipitation clouds changes around 0.6 or above, indicating that the distribution of raindrops in these precipitation clouds is relatively compact.Figure8 shows the relationship between the vertical geometric parameters (Hmax and Havg) and the horizontal geometric parameters (L, W, and S) of precipitation clouds in the Tibetan Plateau. The results show that when L is less than 30 km, W is less than 18 km, and S is less than 200 km2, there is no law for the change of Hmax and Havg, that is, the relationship between vertical geometric parameters and horizontal geometric parameters is more complicated. When L is greater than 30 km, W is greater than 18 km, and S is greater than 200 km2, both Hmax and Havg tend to be stable, Hmax is about 10 km and Havg is about 8 km. Although the changing trends of Hmax and Havg are roughly the same, Havg can more effectively express the relationship between the precipitation cloud range and the horizontal scale because it reduces the error caused by random values or extreme values.Figure 8
The relationship betweenHmax and L (a), Hmax and W (b), Hmax and S (c), Havg and L (d), Havg and W (e), and Havg and S (f) on Tibetan Plateau from 1998 to 2015 based on the statistical principle of same samples in each interval at x axis.
(a)(b)(c)(d)(e)(f)The relationship between spatial morphology (γmax and γavg) and S (Figure 9) shows that when S is less than 200 km2, both parameters are greater than 0.3, which means that small precipitation clouds on the plateau tend to be a lanky appearance. Both parameters decrease with the increase of S, which indicates that as the area increases, the precipitation cloud gradually becomes a squatty appearance. This phenomenon is physically reasonable, because as the horizontal area of the precipitation cloud becomes larger, there is not enough energy to support its overall vertical development.Figure 9
The relationship betweenγmax and S (a) and γavg and S (b) on Tibetan Plateau from 1998 to 2015 based on the statistical principle of same samples in each interval at x axis.
(a)(b)


## 3.3. The Relationship between Physical and Geometric Parameters

The physical properties of precipitation clouds generally determine its geometric properties. Naturally, they are more concerned about the relationship between the physical parameters and geometric parameters of precipitation clouds. The relationship between RRmax (RRavg) and S of precipitation clouds is shown in Figure 10. Relatively speaking, as S increases, the RRmax in the precipitation cloud increases (Figure 10(a)). It illustrates that in the larger precipitation cloud, the probability of extreme precipitation is greater. Compared with the relationship between RRmax and S, the relationship between RRavg and S can more effectively understand the influence of precipitation cloud area on precipitation intensity. Because RRavg is a parameter that normalizes all raindrops in a precipitation cloud, it reduces the influence of the unequal number of raindrops in different precipitation clouds. Figure 10(b) shows that, relatively speaking, as S increases, the precipitation cloud RRavg increases. When S is greater than 500 km2, RRavg seems to remain at 1.7 mm h−1.Figure 10
The relationship between RRmax and S (a) and RRavg and S (b) on Tibetan Plateau from 1998 to 2015 based on the statistical principle of same samples in each interval at x axis.
(a)(b)Figure 11
The relationship between RRmaxc and S (a), RRmaxs and S (b), RRavgc and S (c), and RRavgs and S (d) on Tibetan Plateau from 1998 to 2015 based on the statistical principle of same samples in each interval at x axis.
(a)(b)(c)(d)The relationship between the precipitation cloud areaS and the average rain rate and maximum rain rate of convective or stratiform precipitation, RRmaxc, RRmaxs, RRavgc and RRavgs, is obtained as plotted in Figure 11. Relatively speaking, RRmaxc and RRmaxs both increase with the increase of S. Both RRavgc and RRavgs also increase with the increase of S, but the increase of RRavgs is not obvious. However, the growth rates of RRmaxc and RRmaxs exceed RRavgc and RRavgs, respectively.Figure12 shows the relationship between CAF (SAF) and S in the precipitation cloud and the relationship between CPC (SPC) and S in the precipitation cloud. When S is less than 400 km2, CAF is relatively high, which may be the initial development period of precipitation clouds. Then CAF gradually decreases to about 20%, which means that the precipitation cloud has entered a period of dissipation. In contrast, the relationship between SAF and S is significantly different from CAF. Figure 12(b) shows that as S increases from 50 to 5000 square kilometers, the value of SAF is almost all above 80%, indicating that the area fraction of stratiform precipitation is greater than convective precipitation and as much as 4 times larger. From Figures 12(c) and 12(d), it can be seen that the trend of CPC and SPC is roughly the same as CAF and SAF. When S is less than 400 km2, CPC is relatively high, and then gradually decreases to about 40%. When S is less than 300 km2, SPC tends to increase gradually, and then reaches about 80% steadily. Individually, the contribution of stratiform precipitation is also greater than convective precipitation. However, from the perspective of CAF and SAF, the contribution of convective precipitation is much greater than the area fraction of convective precipitation. It can be seen that the precipitation intensity of convective precipitation is still very large.Figure 12
The relationship between CAF andS (a), SAF and S (b), CPC and S (c), and SPC and S (d) on Tibetan Plateau from 1998 to 2015 based on the statistical principle of same samples in each interval at x axis.
(a)(b)(c)(d)


## 3.4. The Spatial Frequency Distribution of Rain Cells in Different Parameters

In order to understand the geometric and physical parameters of the above precipitation cloud, we further investigate the spatial frequency distribution of the precipitation cloud corresponding to the three different parameters. The first example is the spatial frequency distribution of precipitation clouds in differentα, as shown in Figure 13. Based on the probability distribution function of α shown in Figure 3(c), three α ranges are selected, namely α ≤ 0.4, 0.4 < α ≤ 0.7 and α > 0.7. Figure 13(a) shows that precipitation clouds tend to be long (α ≤ 0.4) in the central and eastern plateau, and the frequency of such precipitation clouds is about 8%. The precipitation clouds on the southern slope of the plateau are mostly square (α > 0.7), and the frequency of these precipitation clouds exceeds 56%, but the frequency of these precipitation clouds in the plateau is relatively low, only about 40% (Figure 13(c)). Precipitation clouds whose shapes tend to be between long strip and square shape (0.4 < α ≤ 0.7) are mainly distributed inside the plateau. The frequency of precipitation clouds is more than 54% (Figure 13(b)). By comparing the three situations shown in Figure 13, it is found that the long strip precipitation cloud accounts for the smallest proportion, followed by the square, and the precipitation cloud between the long strip and the square shape has the largest proportion. This is consistent with the result in Figure 3(c).Figure 13
The spatial frequency distributions of precipitation clouds with (a)α ≤ 0.4, (b) 0.4 < α ≤ 0.7, and (c) α > 0.7. The red line represents the 3000-meter contour.
(a)(b)(c)The second example is the spatial frequency distribution of precipitation clouds in differentγavg. Based on the γavg probability distribution function shown in Figure 4(d), it is divided into three ranges: γavg ≤ 0.1, 0.1<γavg ≤ 0.5, and γavg > 0.5. Figure 14(a) shows that precipitation clouds in squatty appearance (γavg ≤ 0.1)are mainly distributed in the marginal area of the eastern plateau, and the frequency of such precipitation clouds is about 16%. The precipitation clouds in lanky appearance (γavg > 0.5, Figure 14(c)) are concentrated in the southwestern part of the plateau, with a frequency of about 13%. Figure 14(b) shows that precipitation clouds that are neither squatty nor lanky appearance (0.1<γavg ≤ 0.5) mainly appear inside the plateau, with a frequency of more than 86%, which is consistent with the situation in Figure 4(d).Figure 14
The spatial frequency distributions of precipitation clouds with (a)γavg ≤ 0.1, (b) 0.1 < γavg ≤ 0.5, and (c) γavg > 0.5. The red line represents the 3000-meter contour.
(a)(b)(c)The third example is the spatial frequency distribution of precipitation clouds for different RRavg, as shown in Figure 15. The results show that precipitation clouds with relatively small precipitation intensity (RRavg ≤ 1.5 mm·h−1) dominate the plateau precipitation clouds, mainly distributed in the interior and east of the plateau, and the frequency of such precipitation clouds exceeds 60% (Figure 15(a)). Precipitation clouds with high precipitation intensity (RRavg > 4 mm·h−1) mainly appear in the southwest and eastern edges of the plateau, with a frequency of about 17% (Figure 15(c)). Precipitation clouds with moderate precipitation intensity (1.5<RRavg ≤ 4 mm h−1) mainly appear on the southern slope of the plateau, with a frequency of more than 42% (Figure 15(b)). In summary, it is consistent with the result in Figure 5(b).Figure 15
The spatial frequency distributions of precipitation clouds with (a) RRavg ≤ 1.5 mm h−1, (b) 1.5<RRavg ≤ 4 mm h−1, and (c) RRavg > 4 mm h−1. The red line represents the 3000-meter contour.
(a)(b)(c)From the comprehensive analysis of Figures13–15, precipitation clouds with moderate precipitation intensity mainly appear on the southern slope of the plateau and most of these precipitation clouds are square. Some precipitation clouds with lower precipitation intensity appear in the eastern plateau, and these precipitation clouds are mostly having a long strip shape and its spatial shape tends to be squatty appearance; some appear in the interior of the plateau, and the horizontal shape of these precipitation clouds tends to be between square and long strip shape. Its spatial shape tends to be between the squatty appearance and lanky appearance. It can be seen that the geometric and physical parameters of precipitation clouds defined in this study are of great significance for revealing the spatial distribution characteristics and regional differences of precipitation clouds.


## 4. Conclusion

The precipitation system controlled by the weather system usually consists of precipitation clouds of various sizes. These precipitation clouds have complex shapes and different properties. It is important to understand the geometric and physical parameters of precipitation clouds, and the relationship between these parameters to have a deeper insight of the most basic characteristics of precipitation clouds. The studies of precipitation clouds are critical to the investigation of atmospheric circulation and latent heat. Meanwhile, the basic characteristics of precipitation clouds also provide observational basis for future weather forecasts. In this paper, the MBR method is used to identify precipitation clouds, and then the horizontal geometric parameters, vertical geometric parameters, and physical parameters are inverted to describe the basic characteristics of precipitation clouds.The PDF of geometric parameters shows that about 60% of precipitation clouds appear on the dimension of 20 km in length and 15 km in width. The horizontal shapes of precipitation clouds tend to be between square shape and long strip shape. There are not many large precipitation clouds on the plateau. The average echo top height of precipitation clouds varies from 3 km to 13 km, and the peak appears at 9 km above the plateau. The clouds on the plateau are generally higher. The spatial morphology of precipitation clouds is mainly in lanky appearance.The PDF of physical parameters shows that the probability of heavy rain on the plateau is much smaller than that of light rain. The difference between convective and stratiform precipitation is obvious. The probability distribution function of CAF decreases sharply as the CAF in the precipitation clouds increases, while the probability distribution function of SAF increases sharply as the SAF in the precipitation clouds increases. The contribution of convective precipitation in the same precipitation clouds is relatively low.The relationship between geometric parameters shows that whenL is greater than 25 km, there is a logarithmic linear relationship between the length L and the width W of the precipitation clouds. From the relationship between L, W, S, and α, we can conclude that the larger the horizontal scale of the precipitation clouds is, the closer its horizontal geometric shape is to quasisquare. As the horizontal scale increases, the horizontal structure of precipitation clouds becomes looser. The spatial morphology of precipitation clouds gradually changes from lanky appearance to squatty appearance as the area expands.The relationship between physical parameters and geometric parameters shows that the average rainfall rate and maximum rainfall rate of precipitation clouds increase with the expansion of the area. When the raining area is larger than 500 km2, the average rainfall rate remains at about 1.6 mm h−1. The maximum and average rainfall rate of convective precipitation in the precipitation clouds increases with the expansion of the precipitation cloud area. For raining areas of the same size, the area fraction of convective precipitation and the contribution rate of the total precipitation are not as large as those of the stratiform precipitation.The results also show that the precipitation clouds with moderate precipitation intensity mainly appear on the southern slope of the plateau and most of these precipitation clouds are square. Some precipitation clouds with lower precipitation intensity appear in the eastern plateau, and these precipitation clouds are mostly having a long strip shape and its spatial shape tends to be squatty appearance; some appear in the interior of the plateau, and the horizontal shape of these precipitation clouds tends to be between square and long strip shape. Its spatial shape tends to be between the squatty appearance and lanky appearance. In summary, the southern slope of the plateau is a large-value area where various types of precipitation clouds appear.



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*Source: 9181219-2022-01-10.xml*