Microphysical Characteristics of Rainfall Based on Long-Term Observations with a 2DVD in Yangbajain, Tibet

The Tibetan Plateau (TP), recognized as the “third pole” of the Earth, is situated in southwestern China with an average elevation of over 4000 m. Its distinctive high altitude, surface features, and climate profoundly influence the climate and water cycle not only in China and Asia but also globally, earning it the title “Water Tower of Asia” (Chen et al., 2017). The water vapor on the TP mainly comes from the Indian Ocean monsoon and the westerly wind belt, in addition to its own water cycle (Yuan et al., 2023). The precipitation on the TP significantly impacts the water cycle of the plateau itself and the middle and lower reaches of the Yangtze River. Due to the harsh environment and limited observation data available on the TP, research is lacking on the precipitation characteristics in this region. However, due to the special nature and importance of the TP, we need to carry out long-term observations of precipitation on the TP to obtain long-term, accurate, and representative results.

Drop size distribution (DSD) is crucial for studying the microphysical properties of precipitation. Marshall and Palmer (1948) measured the mean distribution spectrum (M-P distribution) of raindrops in detail. Ulbrich (1983) proposed a three-parameter Gamma distribution function for the raindrop size distribution, which is widely used as the main method for characterizing the DSD in mesoscale models. Milbrandt and Yau (2005) showed that cloud and precipitation properties simulated with fixed shape parameters are highly sensitive to the values of the shape parameter since the shape parameter plays an important role in determining sedimentation and microphysical growth rates. Notably, polarization radars make use of oblateness to measure the difference in backscatter reflectivity and propagation phase. A small error in the axis ratio can lead to significant errors in the estimated DSD and rainfall rates (Chandrasekar et al., 1988; Thurai and Bringi, 2005). Many researchers have studied the microphysical properties of different types of precipitation based on DSD (Tokay and Short, 1996; Bringi et al., 2003; Brandes et al., 2004; Williams et al., 2007; Thurai et al., 2016). Studying the microphysics of clouds and precipitation also drives improvements in numerical models (Lu et al., 2023; Zhu et al., 2024). It has been shown that the characteristics of DSD vary across time, region, and topography (Bringi et al., 2003; Kozu et al., 2006; Ulbrich and Atlas, 2007; Tokay et al., 2008; Bumke and Seltmann, 2012; Chakravarty and Raj, 2013). Therefore, it is necessary to continue rainfall observations in YBJ or other regions of the TP, both now and in the future.

Over the past few decades, DSD observations have been conducted over a variety of regions in China using various disdrometers (Chen et al., 2013, 2016; Wen, et al., 2016 Wen et al., 2017; Lyu et al., 2022; Lü et al., 2023). So far, precipitation information obtained on the TP through professional instruments is still very limited. Previous studies on clouds and precipitation on the TP mainly used satellite observations to statistically analyze the macroscopic characteristics of clouds (Fu et al., 2006; Ma et al., 2017). In recent years, some researchers have also studied the microphysical characteristics of precipitation and raindrops on the TP (Porcù et al., 2014; Chen et al., 2017; Chang et al., 2019; Wang et al., 2021). Chang et al. (2019) conducted aerial measurements during the third atmospheric science experiment on the TP and suggested that the significant diurnal variation in summer clouds and precipitation on the TP is caused by the intense solar radiation on the TP. Chen et al. (2017) analyzed the DSD characteristics of the hinterland of the TP using a 2nd generation OTT Particle Size Velocity (OTT Parsivel²) disdrometer in Nagqu (4500 m elevation with a straight-line distance from YBJ of approximately 210 km). The DSD characteristics of stratiform rain were less affected by day–night changes, whereas those of convective rain exhibited significant day–night variations, with more small raindrops and fewer large raindrops at night compared to daytime. Wang et al. (2021) measured the raindrop size distribution with an OTT Parsivel² disdrometer in Medog (1275 m), located on the southeastern Tibetan Plateau. However, the fact that Medog is located to the south of the Himalayas deems this data unrepresentative of the precipitation characteristics of the hinterland of the TP.

At present, most research on the TP uses the OTT Parsivel² for droplet spectrum measurement, which has the advantages of low cost, easy installation, and convenient maintenance. However, previous studies have shown that compared to the two-dimensional video disdrometer (2DVD), OTT Parsivel² underestimates the number of small droplets and overestimates the number of large droplets (Tokay et al., 2013; Wen et al., 2016). The short continuous observation time and large instrumental errors are the main factors that constrain the acquisition of accurate DSD observation data on the TP. As the most accurate disdrometer currently available, the 2DVD is superior to OTT Parsivel² in terms of measurement accuracy for both small and large raindrops, and can measure the axis ratio of raindrops (Wen et al., 2016; Luo et al., 2021).

The Institute of Atmospheric Physics, Chinese Academy of Sciences (IAP, CAS) has established the Atmospheric Profiling Synthetic Observation System (APSOS) in YBJ (Lu et al., 2018). One of its main objectives is to detect data on clouds and precipitation over the TP and obtain statistical characteristics of raindrop spectra in the hinterland of the TP, which will be of great help in studying the microphysical processes of clouds and precipitation, further aiding the improvement the microphysical parameterizations in present-day weather and climate models. This study used a 2DVD to conduct fixed-point long-term continuous observations in the YBJ area. Our observations spanned 27 months and three rainy seasons from July 2021 to September 2022, which were not available in previous studies. The study of raindrop size distribution contributes to understanding the microphysical characteristics of precipitation, thereby improving quantitative precipitation estimation (QPE) (Wen et al., 2016, 2020; Chen et al., 2017; Wen et al., 2017), and enhancing the accuracy of numerical forecasting in the hinterland of the TP. The China Meteorological Administration has deployed C-band radar in Lhasa, Linzhi, Rikeze, and Nagqu, but due to the obstruction of high mountains, the effective detection range of the radar is greatly limited. Therefore, the detection advantage of precipitation satellites on the TP is extremely obvious. Currently, a dual-frequency precipitation radar (DPR) is mainly used for this purpose, which is a primary instrument aboard the Global Precipitation Measurement (GPM) Mission Core Observatory satellite. On 16 April 2023, China’s first precipitation measurement satellite, FengYun-3G (FY-3G) was successfully launched, carrying a precipitation measurement radar (PMR), which will greatly promote the study of precipitation on the TP. The FY-3G PMR consists of a Ku-band precipitation radar (13.35 GHz) and a Ka-band precipitation radar (35.55 GHz), which, allows us to improve the precipitation retrieval algorithm for dual-frequency precipitation radars in the hinterland of the TP aboard the the FY-3G and GPM satellites.

Here, we analyze the microphysical characteristics of rainfall in the region, along with a statistical analysis of DSD parameters and the axis ratio. The remainder of this paper is organized as follows. The data and methodology adopted in this study are described in section 2. Section 3 presents the DSD properties of different rain rates and precipitation types. Section 4 obtains the empirical relationship between the equivalent reflectivity of Ka and Ku band radars and improves the precipitation inversion algorithm of TP hinterland dual-frequency precipitation radar. The summary and conclusion are provided in section 5.

The YBJ Observatory is located in the town of YBJ, Damxung County, Lhasa City, Tibet Autonomous Region. It is backed by the Nyenchen Tanglha Mountains, with an elevation of 4300 m, a latitude and longitude of 30°05′N, and 90°33′E. The red star marker in Fig. 1 shows the location. The instruments used in this paper include the third-generation 2DVD developed by Joanneum Research, Austria, which has been set up at the YBJ Observatory, and a Total Rain Weighing Sensor (TRWS204).

Figure 1.  Map of the YBJ Observatory (red star) and the other stations (blue circle), with the Yangtze River represented by a red line. The picture also shows actual shots of some instruments at the YBJ station.

The 2DVD used in present observations is a particle imaging system consisting mainly of two orthogonal high-speed line scan cameras with crossed optical paths, with an effective sampling area of 10 × 10 cm², which can obtain front and side profiles, drop velocities, precise time stamps, rain rate, drop size distribution, and other data (Huang et al., 2015). Small particles can be measured in the 2DVD more accurately than with the OTT Parsivel² (Zhang et al., 2011; Thurai et al., 2014), which is an advantage for this study.

To ensure the proper functioning of the 2DVD and the reliability of the acquired data, the calibration should be performed in strict accordance with the manufacturers’ calibration steps after the installation of the instrument and whenever the lamps are replaced. Calibration is achieved by releasing calibration balls (0.5, 1.0, 1.5, 2, 3, 4, 5, 6, 8, and 10 mm in diameter). Schönhuber et al. (2007) concluded that the measurement accuracy of individual particles was determined by averaging 100 calibration sphere readings and that the results usually did not deviate from the established values by more than 1%. Diameter tests are conducted using calibration spheres of 0.5 mm and larger, while height and width ratios are assessed with calibration spheres of 2 mm and larger. The 2DVDs used in this study were calibrated at regular intervals, and the calibrated results were consistent with the findings reported by Schönhuber et al. (2007).

From July 2021 to September 2023, long-term and continuous fixed-location observations were conducted. The accuracy of the 2DVD is mainly affected by the strong wind interference and splash during measurement (Nešpor et al., 2000).

Considering the uniqueness of precipitation on the TP, we adopt the diameter terminal velocity model with an air density correction proposed by Atlas et al. (1973) as a filter to remove the raindrops with velocities outside the ±60% range. Figure 2a shows the relationship between the falling terminal velocity and particle size, with the diameter terminal velocity model and the ±60% range lines indicated.

Figure 2.  (a) Heatmap of the number of raindrops with different particle sizes and terminal velocity classifications. The black solid line is the V-D empirical formula proposed by Atlas et al. (1973) after correcting for air density, and the dotted line represents the terminal velocity boundary of the ± 60% empirical formula. (b) Comparison of 2DVD pre- and post-quality control data and rain gauge rainfall rates and (c) accumulated rainfall. The solid green line is the rain gauge (TRWS204), the solid red line is before the 2DVD quality control and the solid blue line is after the quality control.

In this study, samples with a total of less than 10 raindrops within a minute were also filtered out, including potential non-rainfall samples caused by flying insects entering the detection area (Tokay et al., 2013). After quality control, a total of 26980 1-minute precipitation samples was obtained to evaluate the effectiveness of instrument measurement and quality control of the 2DVD data.

Figures 2b and 2c show the comparison of the rain rate and accumulated rainfall calculated from DSD data measured by the 2DVD before and after quality control, and the data obtained from a rain gauge on 5 August 2021. The objective is to verify the effectiveness of quality control and further study the microphysical characteristics of precipitation in the YBJ area. The rain rate and accumulated rainfall from all three datasets are generally consistent. The 2DVD DSD data is also sensitive to low rain rates, although it slightly underestimates the peak rain rate. Schönhuber et al. (2007) suggested that for volumetric parameters such as rainfall, the rate of difference between the 2DVD and rain gauges compared to rainfall is typically less than 10%. Figure 2c shows that the deviation of the accumulated rainfall between the rain gauge data and the measurements before and after the quality control of 2DVD data at YBJ Station is 5.3 and 3.6%, respectively. The deviation between the 2DVD quality control data and the rain gauge data is well below 10%. Therefore, the revised data is of better quality.

In this paper, the raindrop diameters collected by the 2DVD are divided into 41 isometric particle size bins, and the velocities are divided into 41 non-isometric velocity bins (Cao et al., 2008). Therefore, the number of raindrop concentrations for the i-th particle size channel $N\left( {{D_i}} \right)$ (mm^–1 m^–3) can be expressed as:

where ${D_i}$ (mm) is the median equivalent volume diameter of the i-th particle size channel, and $\Delta t$ (mm) is the effective sampling interval, set to 60 s in this study. ${A_j}$ (m²) is the effective sampling area, set to 0.01 m² in this study. $\Delta D$ (mm) is the bin size (0.2 mm) (Luo et al., 2021). ${M_i}$ is the number of raindrops in the i-th particle size bin during the effective sampling time. ${V_j}$ (m s^–1)is the terminal fall speed for velocity class j.

When $N\left( {{D_i}} \right)$ is given, the rain rate $R$ (mm h^–1), liquid water content $W$(g m^–3), total raindrop concentration ${N_T}$ (m^–3), and radar reflectivity factor $Z$ (mm⁶ mm^–3) are calculated as follows:

where $ L $ is the total number of bins and ${V_i}$ is the end velocity of the raindrop at a particle size of $ {D}_{i} $. ${\rho _w}$ (1 g cm^–3) is the density of pure water.

It is widely accepted that using a three-parameter Gamma distribution function can effectively represent the distribution of the raindrop size distribution, which is expressed as:

where $D$ (mm) is the raindrop diameter. ${N_0}$ (${\mathrm{m}}^{-3}\;{\mathrm{mm}}^{-1-\mu} $) is the intercept parameter. $\mu $ is the shape parameter. ${{\Lambda }}$ (mm^–1) is the slope parameter.

In this paper, we use the method of order moments to fit the parameters of the Gamma distribution function, and the n-th-order moment $ {M}_{n} $ is defined as follows (Tokay and Short, 1996):

The mass-weighted average diameter can be obtained using the method of order moments $ {D}_{m} $ (mm) and the normalized intercept parameter $ {N}_{w} $ (m^–3 mm^–1) (Bringi et al., 2003):

The three parameters ${N_0}$, $\mu $, and $ \text{ Λ } $ of the gamma distribution function are fitted using the 2nd, 4th and 6th moments of the DSD observation, respectively (Zhang et al., 2003).

Existing research has shown that precipitation with different rain rates can exhibit distinct DSD characteristics, and it is necessary to study the classification of precipitation by rain rate in Tibetan areas. This paper uses the classification proposed by Chen et al. (2017) in Nagqu to classify precipitation into five classes in the YBJ: (1) R1: 0 < R < 0.1 mm h^–1, (2) R2: 0.1 ≤ R < 1 mm h^–1, (3) R3: 1 ≤ R < 5 mm h^–1, (4) R4: 5 ≤ R < 10 mm h^–1, (5) R5: R ≥10 mm h^–1. As shown in Fig. 3a, R1 and R2 have the longest total rainfall duration, accounting for 86% of the total rainfall time. R3 contributes the most to the total rainfall, representing approximately 49%. Overall, there is a 99% probability of light rain (R< 5 mm h^–1) occurring in YBJ.

Figure 3.  Average raindrop size spectra. (a) Histograms of accumulated rain amount (orange) and rain duration (blue) for the five rain rate classes. (b) Average raindrop size spectra for five different rain rates. (c) Average raindrop size spectra for stratiform and convective rain.

Figure 3b shows the average spectra of the five rain rates in the YBJ. The DSD spectra for different classes are similar. When D > 1 mm, the concentration and spectral width of raindrops increase with the increase in rain rate. The raindrop spectra of the five precipitation grades all exhibit singular peaks, and the maximum concentration of the droplet particles occurs at a particle diameter of 0.3 mm. The concentration of small raindrops in R5 is close to, or even slightly less than, that in R4. This phenomenon may be attributed to the 2DVD being affected by errors resulting from the oversampling of small raindrops caused by wind-induced turbulence near the optical camera and the splash contamination (Kruger and Krajewski, 2002; Chang et al., 2009).

The integral rain parameters calculated from the average DSD are shown in Table 1. As the rainfall rate increases, the liquid water content $W$, total raindrop concentration ${N_T}$, radar reflectivity factor $Z$, and mass-weighted mean diameter $ {D}_{m} $ calculated from the average spectrum also increase.

To study the characteristics of the raindrop spectra of different types of precipitation, precipitation is typically categorized into two main groups, stratiform rain and convective rain. The formation mechanisms of these two types of precipitation are different, resulting in different microphysical characteristics (Stout and Mueller, 1968). Therefore, studying the microphysical characteristics of precipitation requires classifying precipitation in advance (Tokay and Short, 1996; Bringi et al., 2003; Chen et al., 2013, 2017; Wen et al., 2020). Many studies have used ground-based disdrometer data to classify stratiform and convective rain based on rain rate. Chen et al. (2017) proposed a classification method based on the Bringi et al. (2003) method, which relies on the rainfall rate (R) and its standard deviation (σR). This method requires ensuring that the first and second five minutes are continuous: (1) σR ≤ 1.5 mm h^–1 is classified as stratiform and (2) R ≥ 5 mm h^–1 and σR ≥1.5 mm h^–1 is classified as convective. We identified 19272 (98.4%) 1-min data as stratiform and 310 (1.6%) 1-min data as convective. The statistical results show that stratiform precipitation accounts for 80% of the total rainfall, while convective rainfall accounts for 20%.

The average raindrop spectra for the stratiform rain and convective rain are presented in Fig. 3c. The integral rain parameters calculated from the average raindrop spectra for stratiform and convective rain are provided in Table 2. The mean spectra for both stratiform and convective rain exhibit peaks at a particle size of 0.3 mm, although the maximum drop size varies, being 3.9 mm for stratiform and 6.3 mm for convective rain.

The frequency histograms showing the occurrence of ${D_m}$ and ${{\mathrm{l}}} {\text{g}}{N_w}$ for stratiform and convective rain types, along with their mean, standard deviation, and skewness, are also presented in Fig. 4. The ${D_m}$ values for stratiform and convection rain fall within the range of 0.4–1.1 mm and 0.8–1.6 mm, respectively, with average values of 0.81 mm and 1.47 mm. The ${{\mathrm{l}}} {\text{g}}{N_w}$ values for stratiform rain are concentrated between 3.0 and 4.2, while for convective rain, they are concentrated between 3.3 and 4.8, resulting in a higher STD for convective rain compared to stratiform rain. The histograms of ${D_m}$ and ${{\mathrm{l}}} {\text{g}}{N_w}$ for convective rain tend to shift toward larger values relative to that of the stratiform rain histogram, indicating that convective rain exhibits higher ${D_m}$ and ${{\mathrm{l}}} {\text{g}}{N_w}$ values.

Figure 4.  The bar distribution of ${D_m}$ and ${} {\text{lg}}{N_w}$ for (a) stratiform rain and (b) convective rain. The mean (Mean), standard deviation (STD), and skewness (SK) for both parameters are given in the figure.

To compare the mean values of ${D_m}$ and ${} {\text{lg}}{N_w}$ with those of other climate regimes, Fig. 5 gives the ${D_m} - {} {\text{lg}}{N_w}$ distribution for stratiform and convective rain. The boundary between stratiform rain and convective rain, as defined by Bringi et al. (2003), is also given. The clusters, as defined by Bringi et al. (2003), correspond to maritime- and continental-like convective rain. These are overlaid on a scatterplot with two black rectangles. The figure also shows the results for other regions of the TP (Nagqu and Medog) and eastern China. We further conduct a fitting analysis of the ${D_m} - {} {\text{lg}}{N_w}$ relationship for stratiform and convective rain as follows:

Figure 5.  The distribution of ${D_m} $−${} {\text{lg}}{N_w}$ for stratiform rain (blue) and convective rain (red). The square marks represent the results from YBJ, while the circular marks show the result from Medog (Wang et al., 2021), the star marks represent Nagqu (Chen et al., 2017), and the triangular marks correspond to East China (Wen et al., 2016). The black rectangles correspond to the maritime and continental convective clusters defined by Bringi et al. (2003), and the dotted line denotes the stratiform cases.

It is obvious that the convective rain of YBJ, Medog, and Nagqu are all near the line.

Our results indicate that the summer convective rain in YBJ exhibits more maritime characteristics, while its stratiform rain is very similar to other regions. The convective rain in YBJ is comparable to that in the other areas. However, there are some differences. Unlike the abundant warm and humid atmospheric conditions in Medog and eastern China (Wang et al., 2021), the YBJ and Nagqu regions have high altitudes and are relatively dry. Research conducted by Chang et al. (2019) suggests that summer clouds on the TP may primarily consist of mixed-phase cumulus clouds that formed due to intense solar heating, and the 0°C-layer bright band is lower than that in East China. This could result in a relatively shorter condensational growth distance for raindrops, potentially leading to a higher number of small raindrops. However, further research is needed to validate these observational findings.

The $\mu $−$ {{\Lambda }}$ relationship can provide insights into the DSD characteristics of different regions, as demonstrated in previous studies (Zhang et al., 2003; Chen et al., 2013; Thurai et al., 2014; Wen et al., 2016). The YBJ region is a representative area in the TP hinterland, making it essential to study the $\mu $−$ {{\Lambda }}$ relationship. We employ the method described in Chen et al. (2017) to filter out data with particle numbers fewer than 300. This not only improves data dispersion but also helps eliminate, to some extent, unreasonable data resulting from measurement and calculation errors. A least squares fit was employed to derive the $\mu $−$ {{\Lambda }}$ relationship:

and

The fitted coefficients are similar to the results of previous studies (Cao et al., 2008; Chen et al., 2017; Wang et al., 2021), but they are not identical. Figure 6a shows the YBJ area’s µ–Λ scatterplot and gives the fitted curves. Figure 6b is a comparison plot of the µ–Λ relationship. In this case, the values of Chen et al. (2017) and Wang et al. (2021) were observed using the OTT Parsivel² in Nagqu and Medog, respectively; while those of Cao et al. (2008) were observed using the 2DVD in Oklahoma. The fitted relationship of YBJ is closer to the relationship reported by Cao et al. (2008) compared to other relationships. For a given Λ, the relationship proposed by Chen et al. (2017) and Wang et al. (2021) has higher µ values compared to our relationship. Previous studies (Tokay et al., 2013; Wen et al., 2016) have shown that higher µ values can be partially attributed to the underestimation of small drops by the OTT Parsivel². Similarly, with the same Λ value, the m value of YBJ is smaller, indicating a higher concentration of small raindrops in the YBJ. As Λ increases, the three curves in TP tend to become more scattered. In addition to measurement errors resulting from the use of different instruments, this scattering may also be influenced by the unstable convective activity in the boundary layer of the TP.

Figure 6.  Scatterplots of µ–Λ with DSD. (a) The µ–Λ relationship scatter density heatmap. The red solid line represents the µ–Λ relationship fitted using the least squares method. (b) Comparison plot of the µ–Λ relationship. The green, black, and blue solid lines represent the µ–Λ relationship for Chen et al. (2017) in Nagqu, Wang et al. (2021) in Medog, and Cao et al. (2008) in the Oklahoma report, respectively.

The shape of a raindrop during its fall is nearly an oblate spheroid, with its symmetrical axis closely aligned with its vertical axis, and there is a monotonic relationship between its axis ratio and raindrop size (Thurai and Bringi, 2005). Polarimetric radar uses the axis ratio to measure backscattering and propagation phase differences, so the shape parameters of the raindrops play a crucial role in retrieving rain DSD by polarimetric radar and in the quantitative estimation of precipitation. In this paper, we use the 2DVD to measure the axis ratio of raindrop particles on the TP, which can improve the application of polarimetric radar in this region.

Figure 7a shows the distribution information for the number of raindrops at 0.2 mm diameter intervals and 0.02 axis ratio intervals. The white error bars indicate the mean value of the axis ratio at each equivalent particle size interval and their respective standard deviations (±1σ). The detection of axis ratios for raindrop particles with a particle diameter of less than 0.5 mm is inaccurate and is generally attributed to the limitations of the instrument itself (Kim et al., 2016; Luo et al., 2021). We have adopted the recommendation of Chang et al. (2019), who suggested that particles with diameters less than 0.5 mm are nearly spherical (with an axis ratio close to 1). Figure 7a shows that the measured axis ratio of raindrop particles with large particle diameters oscillates as the particle diameter increases. This subset of the raindrop particles has fewer measured samples and is more susceptible to wind influence. Therefore, only particles with particle diameters less than 3 mm are considered for fitting to minimize the impact of clutter on the fitted relationship.

Figure 7.  Distribution of the drop number density (log scale) as a function of drop diameter and axis ratio (b/a). (a) The distribution plot of raindrop number density with equivalent diameter and axis ratio, with the mean and error indicated by the white error bars and the red solid line showing the fitted relationship between diameter and axis ratio. (b) A comparison of the diameter and axis ratio relationship from previous studies and the relationship in YBJ.

The fourth-order polynomial relationship for the mean axis ratio of raindrops in the YBJ region of the TP is given by:

where a and b are the long and short axes of the raindrop, respectively, and D represents the equivalent diameter of the raindrop.

In Fig. 7b, the relationship between the equivalent diameter of raindrops and the axis ratio in the YBJ is plotted as a red solid line, and it is compared to axis ratio relationships from three previous studies (Beard and Chuang, 1987; Wen et al., 2017; Luo et al., 2021). This comparison reveals that as the equivalent diameter increases, the raindrop shapes in the YBJ tend to approach that of a spheroid. This phenomenon may be influenced by factors such as low air density, low air buoyancy, and horizontal winds in plateau areas.

This section proposes a radar-based quantitative precipitation estimation (QPE) algorithm based on the DSD characteristics observed during the three rainy seasons (2021–23) at the YBJ station. The Z-R relationship in the form of a power law function ($Z = a{R^b}$) is widely used for QPE (Zhang et al., 2001; Brandes et al., 2002; Ryzhkov et al., 2005; Lee, 2006; Cao et al., 2010). Variations in atmospheric dynamics and microphysical processes across different regions can alter the coefficients of the Z-R relationship (Tokay et al., 2008). Table 3 provides the fitted Z-R relationships for stratiform and convective rain.

Figure 8 shows the scatterplots and fits of the Z−R relationship for stratiform rain and convective rain. The Z−R relationship for YBJ is on the left side of Medog, indicating that the rainfall rate of YBJ is lower than that of Medog at the same Z value. The Z−R relationship of stratiform rain in YBJ and Nagqu is highly consistent. For a given R-value, the Z of convective rain in YBJ is greater. This may be related to the abundance of small raindrops in YBJ.

Figure 8.  Z-R logarithmic distributions for stratiform rain (gray circles) and convective rain (black dots), along with their fitted relationships shown as solid red lines. In addition, the green and blue lines represent the Z−R relationship of Nagqu and Medog, respectively (Wu and Liu, 2017; Wang et al., 2021).

Based on the above analysis results concerning the statistical characteristics of the YBJ DSD, we will generalize and apply them to improve the rainfall retrieval algorithms of the satellite dual-frequency precipitation radar in the hinterland of the TP. It should be noted that the data from FY-3G has been made publicly available. However, the current accumulation of rainfall data in the hinterland of the TP, as documented by FY-3G, is very limited. Nevertheless, we will try to provide some rainfall retrieval algorithms for the FY-3G data using the long-term 2DVD data shown in previous sections as a preliminary result. The effective radar reflectivity factor $ {Z_e} $ (mm⁶ mm^–3) for a specific wavelength can be expressed as follows:

where $\lambda $ is the radar wavelength and $\sigma \left( {{D_i},\lambda } \right)$ is the backscattering cross-section of a water drop with diameter ${D_i}$, which is directly calculated according to Mie theory. ${\left| {{K_w}} \right|^2}$ is the dielectric factor, which is related to the complex refractive index of water and is taken to be 0.93 by convention (Zhang et al., 2001). The Z_e −R relationship of Ka band radar reflectivity (Z_Ka) and Ku band radar reflectivity (Z_Ku), as calculated by the T-matrix (Mishchenko et al., 1996) and rainfall rate was fitted. The results are presented in Table 4.

The weak precipitation with rainfall intensity less than 1 mm h^–1 in the YBJ area accounts for nearly 86% of the total precipitation time (Fig. 3a). Millimeter wave cloud radar has a higher detection ability for non-precipitating and weak precipitating clouds than centimeter wave weather radar due to its short wavelength. Its high sensitivity and spatial resolution enable it to effectively detect the structure and physical characteristics of small particles (Kollias et al., 2007). Therefore, we use the difference in the radar equivalent reflectivity factor between two frequencies (dual-frequency ratio referred to as DFR) of the FY-3G PMR (DPR), as well as the radar reflectivity at the Ku or Ka bands to estimate the parameters N_w and D_m, and then derive the rainfall rate.

The DFR (dB) is defined as:

where ${Z_{{\text{Ku}}}}$ and ${Z_{{\text{Ka}}}}$ are the radar equivalent reflectivity factors at the Ku and Ka frequencies obtained from Eq. (15), respectively. Previous research has shown that when the DFR is positive, there is a one-to-one relationship between the DFR and ${D_m}$, while when the DFR is negative, one DFR value corresponds to two ${D_m}$ values (Chen et al., 2017; Wang et al., 2021). Figure 9a indicates that due to the small diameter of raindrops in YBJ, there is still a dual value problem in this study. To avoid the dual value problem, this study adopted Liao and Meneghini (2019) modified DFR (DFR*) method in Fig. 9b. The DFR* (dB) is defined as:

Figure 9.  Scatterplots showing the relationships of ${D_m}$ with DFR, DFR (*), and $ {Z_e} $. The top panels show the relationship between ${D_m}$ and (a) the dual-frequency ratio (DFR) and (b) the modified DFR (DFR*). Scatterplots of ${D_m}$ and $ {Z_e} $ in the (b) Ku and (c) Ka bands. The solid red line represents the fitted curve.

where $\gamma $ is a scale factor with a value ranging from 0 to 1 (Liao and Meneghini, 2019). The $\gamma $ for this study is taken as 0.7. We also used $ {Z_e} $ to obtain the empirical relationship of ${D_m}$. To eliminate scatter, the ${D_m} $−$ {Z_e} $ scatterplots for the data sets with ${N_T}$ > 300 in YBJ are shown in Figs. 9c and 9d. ${D_m}$ tends to increase with the increase of $ {Z_e} $. We found that ${D_m}$ was highly correlated with $ {Z_e} $. Using a least squares fitting, we derive the following quadratic polynomial relationship:

Because ${D_m}$ and ${N_w}$ are related, the empirical ${D_m} $−$ {N_w}$ relationship for stratiform and convective rain can be established as shown in Eqs. (10) and (11). As long as D_m and N_w are exported, the given μ can be used to reconstruct the DSD and ultimately estimate the rainfall rate (Chen et al., 2017).

This paper uses a 2DVD to analyze the microphysical characteristics of raindrops in precipitation, establishing a valuable set of cloud precipitation research and quantitative precipitation estimation models for the TP hinterland.

The microphysical characteristics of precipitation in YBJ suggest that convective rain exhibits more maritime characteristics compared to Nagqu. Convective rain with maritime characteristics is mainly characterized by a high numerical concentration of small raindrop sizes, predominantly generated within mixed-phase and warm clouds. The main source of water vapor in YBJ during summer is the warm and humid airflow transported from the Bay of Bengal to Lhasa. The airflow is obstructed by the mountains, and the uplift can easily cause terrain rain. These factors collectively result in the predominantly maritime nature of convective rain in YBJ. Additionally, the prevalent cloud formations over the TP during summer, characterized by mixed-phase cumulus clouds due to strong solar heating, contribute to the unique characteristics of summer convective rain in YBJ.

The main findings are as follows:

(1) The DSD was divided into five rainfall rate categories. A comparison of the spectral shape and width of the five average DSDs revealed that the average spectral shape is similar for different rain rates, with the spectral width increasing with rain rate. Statistical results indicate that 86% of the precipitation in YBJ falls into the weak precipitation category (R< 1 mm h^–1).

(2) Precipitation was classified into convective and stratiform types. YBJ exhibited similar ${D_m}$ and $\lg {N_w}$ values to those in North China, resembling those documented by Nagqu and Medog for stratiform precipitation. It was found that convective rain could be identified as maritime-like and was characterized by a high numerical concentration of small raindrop sizes. We conducted the fitting analysis for the $ {D_m} $−$ \lg {N_w} $ relationship of stratiform and convective precipitation and found the mean values of YBJ, Medog, and Nagqu are all close to the lines.

(3) We derived empirical second-degree polynomials of the μ–Λ relationship in YBJ. For a given Λ, the µ value in this study is less than that derived from Nagqu. This paper also gives the relationship between the equivalent diameter and axis ratio of raindrops in the YBJ. Compared to low-altitude areas, the raindrop shapes in YBJ are closer to spherical as the equivalent particle diameter increases.

(4) We derived Z−R relationships for stratiform and convective rain and compared them with Nagqu and Medog. Convective rain in YBJ exhibited greater Z-values for a given R-value. Rainfall estimation algorithms, $ {Z_{{\text{Ka}}}} $−R and $ {Z_{{\text{Ku}}}} $−R were derived and discussed in terms of improving the precipitation inversion algorithm for the TP hinterland’s dual-frequency precipitation radar. In addition, we used a modified DFR to improve the FY-3G (or GPM DPR) rainfall retrieval algorithm over the TP.

Acknowledgements. The authors would like to thank Prof. Congzeng HAN for polishing the article and Prof. Yuejian XUAN for the 2DVD calibration. The authors thank the reviewers for their great help on the article during its review progress. This research was funded by the second Tibetan Plateau Scientific Expedition and Research Program (2019QZKK0604).