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The Parsivel laser raindrop spectrometer (OTT Parsivel Co., Germany) utilizes laser measurement, and it calculates the size of precipitation particles and measures their velocity through the blocking of the laser band by particles during falling. This instrument enables monitoring of precipitation types, precipitation particle number concentration, rain rate, and accumulated precipitation (Löffler-Mang and Joss, 2000). It can identify eight precipitation types, i.e., drizzle, rain, sleet, snow, snow grains, freezing rain, and hail. In addition, this instrument has 32 particle scale channels of 0.2–25 mm and 32 particle velocity channels of 0.2–20 m s−1, with a sampling area of 54 cm2 and a sampling time of 60 s (Yuter et al., 2006). According to the method used in the study by Chen et al. (2013), the detected DSD samples (1 min) with a total number of raindrops less than 10 or a rainfall rate less than 0.1 mm h−1 were deemed to be noise and eliminated from the data.
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Raindrops are mostly ellipsoidally distributed during their falling under gravity, while the raindrop spectrometer can only measure the raindrop scale in the horizontal direction (the long-axis diameter of ellipsoidal raindrops), which can cause the raindrops to be measured as larger than they really are. For this reason, the method from Battaglia et al. (2010) is used to correct the deformation of raindrops in this study (Eq. 1).
where D denotes the corrected equivalent spherical diameter of raindrops, and Dpar indicates the measured raindrop diameter.
Parsivel observations are the number of raindrops that pass through the sampling area during the sampling time. Therefore, the raindrop number concentration (mm−1 m−3) is calculated as follows (Eq. 2).
where N(Di) (mm−1 m−3) represents the number concentration of raindrops with diameters between Di and Di+
$ \Delta $ Di, nij represents the number of raindrops at the ith size class and the jth velocity class, Vj (m s−1) is the measured falling speed for the jth velocity class, A (m2) represents the effective sampling area for the ith size class, and$ \Delta t $ represents the sampling time interval.The rain rate (R, mm h−1), rainwater content (W, mg m−3), and radar reflectivity factor (Z, mm6 m−3) are calculated by the following equations (Eqs. 3–5).
Marshall and Palmer (1948) proposed a widely used exponential raindrop size distribution, i.e., the M-P distribution (Eq. 6).
By introducing a shape parameter μ into the M-P function, Ulbrich (1983) derived the gamma droplet size distribution. The nth moment of the DSD can be expressed as follows (Eq. 7).
where Γ(x) denotes the complete gamma function, and D (mm) represents the equivalent spherical diameter. N0 (m−3 mm−1−μ), μ (dimensionless), and λ (mm−1) indicate the three control parameters of the gamma model, the intercept, shape, and slope parameters, respectively. In this study, the three control parameters are derived from the gamma DSD by using the M246 truncated moment fitting method (Vivekanandan et al., 2004).
In addition to the rainfall integral parameters, another parameter of interest is the mass-weighted mean diameter Dm (mm) (Eq. 8).
The generalized intercept parameter (Nw, mm−1 m−3) defined by Bringi et al. (2003) is also used in this research (Eq. 9). M3 and M4 are the third moments and fourth distances of the DSD in Eq. (8).
where ρw (1.0 g cm−3) denotes the water density.
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The six laser raindrop spectrometers used in this study are located in the northeastern part of the TP (Fig. 1), and the observation stations include Xining, Henan, Zeku, Dari, Longbao, and Yushu. The altitude of the observation stations ranges from 2434 m to 4202 m, with a difference of nearly 2000 m.
In this study, we refer to the method from Testud et al. (2001) to classify precipitation types as stratiform and convective precipitation. From ti−N5 to ti+N5 (N5 is the 5-minute sampling time of five samples), if the rain intensity is less than 0.5 mm h−1 at any moment in the period with a standard deviation of less than 1.5 mm h−1, this sample is defined as stratiform precipitation. Otherwise, it is convective precipitation.
Since precipitation on the TP is more concentrated from May to October, this period was chosen as the observation time. The spectral distribution of raindrops varies greatly between different precipitation types. The specific observation time and sample profiles are shown in Table 1. Throughout the observation period, the sample number of stratiform precipitation is more than that of convective precipitation.
Location Altitude (m) Date No. of Stratiform No. of Convective Xining 2434 Jun 2017–Jul 2017, May 2020–Jun 2020 4627 864 Henan 3500 Jul 2017–Sep 2017 3007 2761 Zeku 3663 Aug 2019–Oct 2019, May 2020–Jun 2020 2197 1692 Dari 3967 Jun 2018–Oct 2018 4295 1563 Longbao 4202 May 2019– Oct 2019 6744 2494 Yushu 4290 May 2014–Sep 2014 4478 2325 Table 1. General features of raindrop spectral samples.
To investigate the DSD characteristics under different precipitation conditions on the TP, we use the method from Chen et al. (2017) to divide the entire dataset into five rain rate grades, i.e., R<0.1 mm h−1, 0.1≤R<1 mm h−1, 1≤R<5 mm h−1, 5≤R<10 mm h−1, and R≥10 mm h−1. Figure 2 presents the frequency of stratiform and convective precipitation with different rain intensities at the six observation stations and their accumulated contribution to the total precipitation. Overall, at Xining, Henan, and Longbao stations, the samples with R of less than 0.1 mm h−1 and 0.1≤R<1 mm h−1, accounting for 70%–80% of the total samples, are the ones with the largest contribution to the stratiform precipitation. However, at Zeku, Dari, and Yushu stations, the top two largest contributions are the samples with rain rate of 0.1≤R<1 mm h−1 and 1≤R<5 mm h−1, which account for about 80% of the total samples. In addition, the smallest contributions are from the samples with rain rate of 10 mm h−1. The contribution of precipitation with the rain rate of 1≤R<5 mm h−1 to the total rainfall is the largest at 51% in the Northeastern TP. Comparing the contribution of rain rate of 1≤R<5 mm h−1 to the total precipitation of each station, Yushu contributed 71% to the total precipitation of stratiform cloud precipitation, which was the station with the highest contribution to precipitation. The contribution of Henan Observation station of 35% was the lowest. In the convective precipitation, the contribution of 1≤R<5 mm h−1 rain rate to the total precipitation was 59% at Xining station and 36% at Yushu station, which were the two stations with the highest contribution and the lowest contribution, respectively. The precipitation with the R ≥10 mm h−1 in Yushu station contributes 54% to the total precipitation, although its sample number only accounts for 7% of the total samples.
Figure 2. Frequency distributions of stratiform and convective precipitation with different rain intensities and their accumulated contributions to total precipitation.
Note that from the lowest altitude site (Zeku, 3663 m) to the highest altitude site (Yushu, 4290 m), the contribution of the precipitation with the rain rate of 1≤R<5 mm h−1 gradually increases to stratiform precipitation and decreases to convective precipitation (Figs. 2e, 2f). The trends of stratiform precipitation and convective precipitation with the R≥10 mm h−1 are opposite to those of 1≤R<5 mm h−1, and the contribution for the R ≥10 mm h−1 gradually decreases to stratiform precipitation and gradually increases to convective precipitation. The contribution for the rain rate of 1≤R<5 mm h−1 to stratiform precipitation gradually increases with increasing altitude, while the situation is the opposite in convective precipitation. For R ≥10 mm h−1 from Zeku to Yushu, the contribution of R to stratiform precipitation gradually decreased, but it gradually increases to convective precipitation. However, this feature was not obvious in Xining and Henan (Figs. 2g, 2k).
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As shown in Table 2, the raindrop scale and number concentration of convective precipitation were larger than those of stratiform precipitation. The R of convective precipitation increases with elevation, while other microphysical parameters do not show an obvious upward or downward trend with the change of altitude, indicating local differences in DSDs. Among the six stations, the difference of the raindrop particles between stratiform precipitation and convective precipitation is the most obvious at Yushu station, with average differences of 2.14 mm h−1 in R and 0.09 mg m−3 in W. In addition, there is no major difference in N(D) between the two precipitation types, but high altitude areas (such as Yushu and Longbao) have higher D and Dms, suggesting that the larger particles are responsible for the higher rain rate and rainwater content at Yushu station.
Location Rain type R (mm h−1) N(D) (m−3 mm−1) D (mm) Dms (mm) W (mg m−3) Xining Stratiform 0.44 1635.40 0.67 0.70 0.03 Convective 1.31 1914.00 0.80 0.86 0.07 Henan Stratiform 1.52 2901.70 0.69 0.73 0.10 Convective 1.76 3272.50 0.75 0.79 0.11 Zeku Stratiform 0.82 2267.30 3.30 3.47 0.06 Convective 2.09 2406.00 3.55 3.74 0.11 Dari Stratiform 1.02 2486.90 3.39 3.57 0.07 Convective 1.61 2907.40 3.87 4.08 0.10 Longbao Stratiform 1.06 1803.90 5.01 5.12 0.07 Convective 2.16 2462.30 5.15 5.34 0.12 Yushu Stratiform 1.01 2601.50 5.71 4.76 0.07 Convective 3.42 2630.50 5.91 5.00 0.16 Table 2. Microphysical parameter values for raindrop spectra during different rainfall events. R denotes the rain rate (mm h−1), N(D) the number concentration (m−3 mm−1), D the mean particle diameter (mm), Dms the root-mean-square diameter (mm), and W the rainwater content (mg m−3).
The raindrop spectrum on the northeastern TP (Fig. 3) shows a single-peaked distribution with the average peak particle size value around 0.31 mm. There are obvious differences in the actual raindrop spectrum distributions between different precipitation types. At the same altitude, the spectrum width of stratiform precipitation is narrower than that of convective precipitation, and both number concentration and spectrum width increase accordingly with the gradual increase of rain rate.
Figure 3. Variations of the mean raindrop number concentration with the different raindrop diameters for different rain rate grades at the four disdrometer stations.
The spectrum width of convective precipitation gradually becomes wider as the altitude increases. In terms of individual observation stations, the spectrum patterns for different rain intensities are basically the same at Henan station. The changes of the raindrop spectra at Zeku, Dari, Longbao, and Yushu stations are the same, i.e., the spectrum width gradually widens with the increased rain rate, and the number concentration gradually increases when the mean particle diameter is less than 5 mm. However, note that the particle concentrations for the R of 5≤R<10 mm h−1 are larger than those for R≥10 mm h−1 when the mean particle diameter is less than 1.06 mm. Overall, the greater the rain rate, the higher the number concentration, and the wider the spectrum width. The droplet spectrum width for R≥10 mm h−1 changes with increasing altitude. When R≥10 mm h−1, the higher the altitude, the broader the droplet spectrum. For the characteristics of raindrop spectrum variation at high altitudes (Zeku, Dari, Longbao, and Yushu stations), Chen et al. (2017) found a similar pattern at Naqu station in the TP region and concluded that the observation instruments might underestimate the number of small-scale raindrops at high rain rates.
The raindrop spectrum distributions of stratiform and convective precipitation on the northeastern TP (Fig. 4) show a single-peaked pattern, with a peak particle size between 0.31–0.50 mm. The peak particle size and number concentration of stratiform precipitation and convective precipitation are basically the same at the same altitude, but convective precipitation has a broader spectrum and a higher concentration of large-scale particles. The maximum spectrum widths of stratiform precipitation particles are between 4 mm and 5 mm, while the maximum spectrum widths of convective precipitation particles range from 4 mm to 8 mm. With the gradual increase of altitude, the difference of particle spectrum width between convective and stratiform precipitation gradually becomes more obvious.
The M-P distribution and the Gamma distribution are currently the main analytic functions describing the spectrum distribution of raindrops, and both methods are widely used in precipitation detection and numerical model parameterization schemes (Marshall and Palmer, 1948). As shown in Fig. 4, the fitting performance of the Gamma distribution is better than that of the M-P distribution. The fitted results of the Gamma distribution for convective precipitation of D<3 mm at Longbao and Yushu stations are smaller than the actual droplet spectrum distribution. The fitting results for both precipitation types of D<1 mm by both fitting methods are inaccurate at Zeku station.
Table 3 presents the values of each parameter fitted by the M-P distribution and Gamma distribution for different precipitation types. The M-P distribution and the Gamma distribution performed well in fitting both precipitation types, especially the Gamma distribution, with correlation coefficients of R2≥0.97 and R2≥0.98, respectively. The slope parameter (λ) can directly reflect the slope of the fitted curves of raindrop spectra, indicating that a decreasing rate of raindrop particle concentration corresponds with an increasing diameter. On the eastern TP, the λ of stratiform precipitation is larger than that of convective precipitation in both M-P and Gamma distributions, which is also consistent with the narrower spectrum width of stratiform precipitation than that of convective precipitation. Since the gamma fit introduces the μ parameter, the λ parameters of the M-P distribution and the Gamma distribution cannot be compared directly.
Location Rain type M-P distribution Gamma distribution N0 λ R2 N0 λ μ R2 Xining Stratiform 3874.65 3.67 0.99 123067.75 7.90 1.86 0.99 Convective 1842.29 1.88 0.97 11069.49 3.93 0.96 0.99 Henan Stratiform 5418.73 3.00 0.98 130507.98 7.20 1.52 0.99 Convective 3809.32 2.42 0.99 15318.88 4.15 0.70 0.99 Zeku Stratiform 14385.24 5.02 0.99 1725.21 1.91 0.98 0.99 Convective 8486.81 3.68 0.99 775.81 1.61 1.70 0.99 Dari Stratiform 15199.6 4.87 0.99 5571.18 2.84 0.33 0.99 Convective 9473.33 3.43 0.99 1253.69 1.95 1.45 0.99 Longbao Stratiform 2464.81 2.15 0.96 52191.86 5.54 1.79 0.98 Convective 2727.85 1.85 0.96 34538.64 4.48 1.58 0.99 Yushu Stratiform 3168.49 2.35 0.99 17872.71 4.46 0.88 0.99 Convective 2371.97 1.76 0.98 7766.41 3.04 0.66 0.99 Table 3. Mean spectrum parameters fitted by the Gamma and M-P distribution and their correlation coefficients. R2 is the correlation coefficient.
The Gamma distribution can better reflect the bending characteristics of the actual raindrop spectrum fitting line due to the introduction of the shape parameter μ. A smaller μ indicates a broader spectrum width of raindrops, suggesting that the variation range of raindrop diameter increases with increasing altitude. Thus, the raindrop diameter is larger at high altitudes. The curve bends upward when μ>0 and bends downward when μ<0. It has been pointed out that μ<0 indicates mainly precipitation in mountainous regions, which has more small raindrops and broader spectrum width (Ulbrich, 1983). μ>0 represents thunderstorm and stratiform precipitation, and μ is variable but basically positive. μ of both stratiform and convective precipitation in the study area is greater than 0, indicating that the precipitation in this area is dominated by large raindrops.
Dm denotes the average diameter of all raindrops in a certain period, and Nw represents the number concentration of all raindrops. These two parameters are used in combination to reflect the variations of raindrop size and number concentration at a certain rainwater content (Testud et al., 2001). The lgNw-Dm scatter distribution (Fig. 5) shows that lgNw decreases as Dm increases. The concentration area of precipitation moves downward and to the right in Fig. 5 with increasing altitude, and the number concentration of raindrop particles increases while the average diameter becomes larger. Moreover, with an increase of altitude, compared with stratiform precipitation, the convective precipitation has more samples with R >5 mm h−1, and the lgNw-Dm distribution has an obvious “rightward and downward” trend, which demonstrates that the convective precipitation is more intense in the northeastern TP.
Figure 5. The lgNw-Dm scatter plot for different rain rate grades at four disdrometer stations. Dm represents the average diameter of all raindrops in a certain period, and Nw denotes the number concentration of all raindrops.
Figure 6 shows the lgNw-Dm scatter distribution of convective and stratiform precipitation. The cloud droplet spectrum distributions are dispersed at all stations. For stratiform precipitation, the average lgNw is 2.60 mm−1 mm−3, and the Dm is 0.86 mm. In terms of convective precipitation, the average lgNw is 2.39 mm−1 mm−3, and the Dm is 1.22 mm. Compared with convective precipitation, the lgNw of stratiform precipitation is high at the same altitude, and the Dm is small, indicating that stratiform precipitation particles have smaller sizes and higher concentrations than the convective precipitation particles.
Figure 6. The lgNw-Dm scatter distribution of convective and stratiform precipitation particles. Dm represents the mass-weighted mean diameter of raindrops. The two outlined rectangles correspond to the maritime and continental convective clusters reported by Bringi et al. (2003), and the dashed straight line indicates the results of Bringi et al. (2003) for stratiform precipitation.
The results of our study are similar to those of Chen et al. (2017) and Wang et al. (2021) on the lgNw-Dm distribution characteristics of stratiform precipitation located in the southern part of the TP in Naqu and Motuo. Precipitation particles in the northern TP have higher Nw values and lower Dm values than those in the tropical ocean (Thompson et al., 2015). In the study of Chen et al. (2017), the convective precipitation from Motuo was characterized by small raindrops with high concentration, which is Maritime-like precipitation. In Motuo, the convective precipitation with warm and humid water vapor conditions, where ice processes may be weaker or less effective in the cloud, results in a large number of small particles. While the six stations are located in the northern part of the TP, the high mountains to the north and south of the TP will block the water vapor transport from both sides, making the warm and humid conditions in this region less than those in the Motuo and Naqu areas. This may be the reason for the lower convective precipitation lgNw at the six stations.
The falling velocity of precipitation particles plays an essential role in the precipitation formation. Precipitation particles with different sizes, phases, and shapes have different falling velocities, which can lead to collisions, merging, and charge redistribution inside the particles (Tang et al., 2014). The distribution of raindrop number with diameter and falling velocity at six stations on the northeastern TP (Fig. 7) indicates that raindrops at each size scale correspond to a falling velocity range, and the falling velocity range is slightly larger for convective precipitation than for stratiform precipitation at the same particle size scale, indicating that the falling velocity of raindrops is not only influenced by the particle size, but also related to many other factors. The updraft and downdraft in and under the precipitation cloud will have different falling velocities for water droplets of the same size (Battan, 1964). Air density (Niu et al., 2010), raindrop breakup/coalescence (Montero-Martínez et al., 2009), and turbulence (Pinsky and Khain, 1996) also affect the falling speed of raindrops.
Figure 7. The number of raindrops as a function of the drop diameter and falling velocity. The solid black line is the fitted curve of the falling terminal velocity of raindrops under standard conditions measured by Atlas et al. (1973)
The solid black line in Fig. 7 is the fitted curve of the falling terminal velocity of raindrops under standard conditions measured by Atlas et al. (1973), representing the falling terminal velocity of raindrops at sea level height under standard conditions, and the curve corresponds to an air density of 1.23 kg m−3 (Eq. 10).
where V denotes the falling velocity of precipitation particles, and D represents the particle diameter.
There is an underestimation of the falling velocity of raindrops after the standard curve fitting throughout the observation period (Fig. 7). The relationship between the diameter and falling velocity (black scattered points) in the actual sample is refitted (red line), and the curve correlation after fitting the average falling velocity is above 0.9. The lower air density and special topography in the northeastern TP may be the main reasons for the observed velocity being higher than its falling velocity. Simultaneously, the falling velocity of raindrops is affected by various factors such as raindrop collision and merging, vertical motions of air, and turbulence. For Xining and Henan stations, the relationship between the diameter and falling velocity is basically the same, while for the remaining four observation stations, the falling velocity of convective precipitation particles with D ≥2 mm is higher than that of stratiform precipitation particles. At Longbao station, although the particle size is less than 0.3 mm, there are also higher values of falling velocity (4.4–4.7 m s−1), which differs from the situation at other stations.
The generally accepted influences on the falling velocity of raindrops include air density (Atlas et al., 1973), turbulence (Pinsky and Khain, 1996), raindrop merging and fragmentation (Villermaux and Bossa, 2009), and instrumental measurement errors (Niu et al., 2010). The air density decreases as the altitude rises. The two types of precipitation at the six stations are not characterized by changes in raindrop velocity as the air density decreases, indicating that air density is not a single influential factor affecting the falling velocity of raindrops in the northern TP. Pinsky and Khain (1996) demonstrated through numerical simulations that raindrop fall velocity is influenced by wind shear and inertial acceleration of particles in atmospheric turbulence. Niu et al. (2010) suggested that atmospheric turbulence may have an effect on the vertical velocity of small raindrops despite the 25% measurement error of the Parsivel disdrometer for small raindrops. Convective activity over the TP is a major source of heat in the Asian monsoon region (Yanai and Li, 1994; Ueda et al., 2003), and atmospheric turbulent activity and subsurface specificity exacerbate the local specificity of the raindrop spectrum in this region.
The relationship between radar reflectivity intensity and rain rate (Z-R relationship) is the basis of radar QPE. However, the uncertainty of the Z-R relationship is also the main contributor affecting the accuracy of radar QPE. There is a power exponential relationship between R and Z, i.e., Z = aRb, where a is the relationship coefficient, and b is the exponent. The values of a and b vary greatly with regions, seasons, precipitation types, and raindrop spectrum types. The magnitudes of Z and R are closely related to the raindrop spectrum distribution, and the Z-R relationship varies for different precipitation types.
The fitted Z-R relationships for different precipitation types at six stations on the eastern TP are shown in Fig. 8. For stratiform precipitation, the coefficient a ranges from 352 to 443, with a mean value of 401, and the index b varies between 1.26 and 2.36, with a mean value of 1.91. In terms of convective precipitation, the coefficient a ranges from 396 to 513, with a mean value of 454, and the index b varies between 1.50 and 2.17. Overall, the Z-R relationship in the eastern TP is Z = 401R1.91 for stratiform precipitation and Z = 454R1.89 for convective precipitation. Compared with the conventional QPE formula (Z = 300R1.4) used by the new generation weather radar in current meteorological operations, the relationship coefficient a and index b on the eastern TP in this study are large. Thus, using the conventional radar estimation method would lead to an underestimation of precipitation in this region.
Location | Altitude (m) | Date | No. of Stratiform | No. of Convective |
Xining | 2434 | Jun 2017–Jul 2017, May 2020–Jun 2020 | 4627 | 864 |
Henan | 3500 | Jul 2017–Sep 2017 | 3007 | 2761 |
Zeku | 3663 | Aug 2019–Oct 2019, May 2020–Jun 2020 | 2197 | 1692 |
Dari | 3967 | Jun 2018–Oct 2018 | 4295 | 1563 |
Longbao | 4202 | May 2019– Oct 2019 | 6744 | 2494 |
Yushu | 4290 | May 2014–Sep 2014 | 4478 | 2325 |