3.1. DSD Variability in Different Areas of Beijing
The areas within the 6th Ring Road have dense infrastructure, heavy traffic, and frequent human activities. Over 90% of Beijing’s population lives and works in the areas inside the 6th Ring Road, while outside the 6th Ring Road, there are mostly farms, forests, and wastelands. The topography of Beijing is characterized by plains in the center and southeast and mountains in the west and north (
Figure 1). Accordingly, the 11 disdrometers used in this study were categorized into three groups based on their location: Urban stations (stations located within the 6th Ring Road, i.e., stations 399, 511, 513, and 594); suburban stations (stations located outside the 6th Ring Road with an elevation of less than 200 m above sea level, i.e., stations 398, 419, 424, and 431), and mountain stations (stations above 200 m above sea level, i.e., stations 406, 412, and 421).
The average DSD characteristics derived with all these 11 disdrometers are shown in
Figure 2.
Figure 2a shows the density scatter plot of
Dm versus
R, superimposed with the power–law relationship obtained using the least-square fit method.
Dm increases with the increase in
R (positive exponent in power–law relationship). As shown in the figure,
Dm increases rapidly when
R is less than 50 mm h
−1. This is because both the raindrop size and number concentration effectively increase within this rain rate range [
52]. The increase in
Dm becomes much slower (around 2.2~2.5 mm) when
R is greater than 50 mm h
−1. Apparently, the increase in the rain rate mainly relies on the increase in raindrop concentration rather than raindrop size. This fact implies that the accurate estimation of particle number concentration in numerical models is crucial for better forecasting of extreme precipitation events. In addition, the spread of
Dm becomes narrower with the increase in
R. Such a fact suggests that when the rain rate is small, the breakup and coalescence processes of raindrops may be unbalanced, resulting in a wide spread of
Dm. At a high rain rate, the breakup and coalescence are likely to reach a more balanced state. This result also explains why retrieving the rain rate using Equation (10) (traditional approach of QPE for single-polarimetric radar) is not accurate for small rain rate cases. Since parameters a and b in Equation (10) depend on DSD and there is a wide spread of DSD parameters with a small rain rate, if a fixed combination of a and b is used for QPE (the common approach for operational QPE), large errors will appear.
Figure 2b is the scatter plot of
Dm versus
Nw for convection and stratiform in Beijing, superimposed with BR03′s results. There is a clear boundary between convection and stratiform with some overlap of samples. For convection, only 4.23% and 13.1% of the samples lie in “maritime” and “continent” clusters in BR03, respectively. The mean value point of
Dm-
Nw lies between these two clusters, suggesting that the characteristics of convection in Beijing be different from those places recorded in BR03. As for the stratiform, the mean value point of
Dm-
Nw and 90% of samples lie on the left side of the least square fitting line of stratiform in BR03, indicating that the stratiform in Beijing has a smaller raindrop size and concentration. It is notable that DSD studies in other locations of China (Nanjing, eastern China; Guangzhou and Yangjiang, southern China; Naqu, Tibet Plateau) also suggest a lower raindrop size and concentration in the stratiform as compared to BR03 [
6,
7,
17,
18].
Figure 3 shows the variations of mean number concentration versus raindrop size in different areas of Beijing. The number concentration in mountain areas is lower than in the plains (i.e., urban and suburban areas) from the smallest raindrop size to up to 5 mm in diameter. The differences are most pronounced at the smallest sizes and around 3 mm. The urban and suburban curves are similar, but urban areas have a higher number concentration of raindrops less than 1 mm, and a lower number concentration of raindrops greater than 1 mm, indicating a smaller mean raindrop size.
Table 1 shows the mean values of DSD parameters in different areas of Beijing. Among these three areas, the urban average drop size (
Dm) is the smallest, and this value is comparable with previous studies based on urban disdrometer data in Beijing [
40,
41]. The average drop size in the suburban areas is the largest and between the two in the mountain areas. In terms of the average rain rate, the mountain areas have the smallest average rain rates, the suburban areas have the largest average rain rates, and the urban areas are in the middle. The distribution of R is consistent with previous works on the precipitation in Beijing based on rain gauge measurements [
38,
53,
54], which found that the average hourly precipitation intensity in the mountains is smaller than that in the plains, but the total precipitation hours are larger in the mountains, mainly because light rain occurs more frequently in the mountains of Beijing. This phenomenon might be related to the specific geographical location of Beijing. The southeast flow coming from the sea is the main moisture source for precipitation systems in Beijing. The mountain areas are located in the northwest part of Beijing, which means that the mountain areas of Beijing generally receive less moisture than the plain areas of Beijing. However, although the mountain areas receive less moisture, light precipitation can easily occur when the southeast flow is elevated by the mountains. In terms of the number concentration (
Nt), the mountain areas have the smallest average number concentration, the urban areas have the largest average number concentration, and the suburban areas are in the middle. In the mountain areas of Beijing, the smallest average number concentration may also be related to the frequent occurrence of light rain, as light rain is usually associated with fewer drop numbers. The comparison of these parameters in urban and suburban areas reveals that the urban environment modifies the precipitation microphysics, such that the drop size is suppressed while a greater number of drops are produced. This phenomenon may be related to the high aerosol emission in urban areas of Beijing due to human activities such as traffic. A high aerosol concentration tends to reduce the average drop size and increase the number concentration by providing more cloud condensation nuclei (CCN) [
15,
31,
55,
56].
Figure 4 shows the probability distribution functions (PDF) of
Dm,
R, and
Nt in different areas.
Dm in these areas all peak around 0.9 mm, with suburban areas having the highest frequency around the peak and urban areas having the lowest (
Figure 3a). The distribution of
Nt in the mountain areas is sharper and more symmetrical compared to those in the plains (i.e., urban and suburban areas). Both the urban and suburban areas have a broader distribution around the peak, and the frequency decreases faster toward the higher
Nt end than toward the lower
Nt end. In addition, urban areas have a higher distribution for
Nt larger than 10
3 and a lower distribution for
Nt from 10
2 to 10
2.5. As for the PDF for
R,
R less than 10
0.5 mm h
−1 is mainly responsible for the differences in different areas. There is a sharper and higher peak in mountain areas at the lower end of
R, indicating that light rain occurs more frequently in mountain areas than in plains. There is a higher frequency of rain rate from 10
0 to 10
0.5 and larger than 10
1.0 mm h
−1 in plains than in mountain areas, while the rain rate from 10
0.5–10
1.0 is quite close together. This result suggests that the mountains in Beijing may play a role in modifying precipitation microphysics mainly for precipitation with a rain rate less than 10
0.5 or larger than 10
1.0 mm h
−1. Light rain occurs more frequently in mountain areas because mountain areas receive less moisture than the plains in Beijing as the southeast wet flow travels further to reach the mountain areas in the western part of Beijing [
38,
53,
54]. As for the differences between urban and suburban areas, suburban areas have a high frequency of rain rate of less than 10
0.3 mm h
−1 and more than 10
1.3 mm h
−1, with a lower frequency in the middle.
Numerous studies have shown that
Dm,
R, and
Nt are larger in convection than in stratiform [
16,
17,
20], and other studies suggested that the terrain or urban environments can modify the microphysics processes in precipitation systems and change the DSD characteristics [
24,
57]. Consequently, there might be three causes responsible for the variation in DSD characteristics in different regions of Beijing: (1) The ratio of convection/stratiform might be different in different regions and the higher frequency of convection might lead to larger
Dm,
R, and
Nt; (2) for the same precipitation type, DSD characteristics in different regions might be different due to the terrain or urban effect; or (3) the combination of (1) and (2).
Accordingly, DSD observations were classified into convection and stratiform for further analysis. The DSD parameters, number of samples, and percentage of convection and stratiform in different areas of Beijing are shown in
Table 2. First, the difference between urban and suburban areas was analyzed. Although the average
Dm is larger in suburban areas than that in urban areas, it is surprising to see that the percentage of convection in suburban areas is almost identical to that in urban areas (8.58% versus 8.60%). Consequently, the differences in
Dm between urban and suburban areas are not likely due to differences in convection/stratiform ratios but rather are more likely due to differences in DSD characteristics for the same precipitation type. For both convection and stratiform,
Dm is smaller in urban areas than in suburban areas, perhaps due to the high aerosol concentration in urban areas of Beijing. High aerosol concentration usually causes smaller raindrop sizes by providing high CCN [
15]. A study on the spatial distribution of PM2.5 (particulate matter with aerodynamic diameters of less than 2.5 μm) in Beijing shows that the PM2.5 concentration is much higher in urban areas than in suburbs during rainy seasons [
58]. On the other hand, smaller raindrops tend to evaporate more quickly after falling out of the cloud, which may further lead to smaller raindrops in urban areas. Urban areas have smaller
R and
Nt for convection than suburban areas, but larger ones for stratiform. The result suggests urbanization affects convection and stratiform differently, whereby the urban environment tends to reduce the intensity of rain and the number concentration of raindrops in convection while positively influencing them in stratiform. It appears that the differences in DSD between urban areas and suburban areas are not due to differences in convection/stratiform ratios, but rather due to differences in DSD characteristics for the same precipitation types.
The convection/stratiform ratio in mountain areas is lower than that in the plains, and only 6.53% of the total precipitation is convection. For convection, Dm in mountain areas is almost the same as that in urban areas and smaller than that in suburban areas. However, for stratiform, Dm in mountain areas is larger than that in the plains. R and Nt for both convection and stratiform are smaller in mountain areas than in the plains. Therefore, smaller R and Nt values in mountain areas are the combined result of a smaller convection/stratiform ratio and smaller R and Nt values for the same precipitation types. Such a result may be related to the moisture conditions in Beijing. Beijing typically receives its moisture from the east (from the ocean), which travels hundreds of kilometers before reaching Beijing (the nearest ocean is 160 km away). The mountain areas on the west side of Beijing receive less moisture than the plain areas on the east, thereby reducing convection frequency, rain intensity, and number concentration.
3.2. Implication for QPE of Polarimetric Radar
Several X-band polarimetric radars (
= 3.2 cm) have been deployed in Beijing in recent years, aiming at providing better QPE products to meet the needs of meteorological and hydrological applications. These radars all operate in VCP 21 mode, which completes a volume scan in 3 min with radial and azimuth resolutions of 75 m and 0.95°, respectively. To study the X-band radar QPE using DSD data, the polarimetric radar variables of
ZH,
ZDR, and
Kdp were calculated from 1 min DSD observations. The parameters of a, b, and c in Equations (10)–(12) were then derived using the nonlinear least square fitting. The fitted parameters using DSD data collected in all locations, namely, urban, suburban, and mountain areas, are listed in
Table 3. As
Table 3 shows, these parameters vary in different regions of Beijing due to the DSD variability.
Figure 5 illustrates the scatter density plots of
R estimated from four estimators (
Table 3) versus R calculated directly from the 1 min DSD data. The statistical values of CC, RMSE and RMB are also shown. As shown in
Figure 5, the estimator R(
ZH) performs the worst (
Figure 5a) with the smallest CC and largest RMSE and RMB. The uncertainty of QPE increases greatly with the intensity of
R. The difference between
and
can be up to approximately 4 times (e.g., 30 mm h
−1 of
versus 120 mm h
−1 of
). When polarimetric variables of
ZDR and
Kdp are introduced, the accuracy of QPE is much better (
Figure 5b–c). Among these three estimators, R(
Kdp,
ZDR) performs the best, providing the most accurate estimation for light rain to heavy rain.
The results shown in
Figure 5 can be regarded as the theoretical upper limit of the performances of the estimators. When performing QPE estimators into operational radar, three aspects below affect the accuracy of the QPE result: Random observational errors of the radar variables, the systematic bias of the radar variables due to miscalibration, and the variability of the parameters of the QPE estimators due to DSD variability. It is well-known that the DSD variability in different climate regions significantly affects QPE accuracy. However, for city scales such as Beijing, it is unclear how much the DSD variability affects the QPE accuracy compared to radar variables measurement errors and bias. What is the dominant source of error for QPE? To find the answer, a series of experiments were performed using these DSD data.
The actual distribution of radar observational errors can be very complicated. However, for ideal experiments using DSD data, let us assume that the errors conform to the most general type of error distribution, the normal distribution , where and are the mean value and standard deviation. Approximately 68% and 95% of the total samples lie between to and to , respectively. Assuming that the radar observational variables follow the normal distribution, then the observational variables can be perturbed by multiplying to simulate measurement errors and systematic bias. For example, means measurement errors exist in Zh, while approximately 95% of the measured Zh are between 0.7 and 1.3 times the theoretical Zh; means both measurement errors and systematic bias exist in Zh, the mean observational Zh is stronger for 5% than the theoretical Zh, and approximately 95% of the measured Zh are between 0.75 to 1.35 time of the theoretical Zh.
Table 4 shows the experiment design of R(
ZH). All the DSD data collected by these 11 disdrometers are used in these experiments. In the control experiment, the rain rate is estimated using parameters obtained for the whole region of Beijing; it is the theoretical upper limit capability of applying R(
ZH) to perform QPE. In the DSD variability experiment, the rain rate is estimated using parameters obtained for the mountain region of Beijing. The purpose of this experiment is to find out how much the DSD variability can affect the accuracy of QPE when the parameters for specific regions (e.g., mountains) are used to estimate the rain rate for the whole region of Beijing. In the measurement error experiment, the
Zh is perturbed by multiplying
. This experiment aims to find out if there are measurement errors of
Zh between operational radar and disdrometer and how much the error can affect the accuracy of QPE. Furthermore, the systematic bias experiment is designed to find out how much the error and systematic bias (i.e., calibration issues) can affect the accuracy of QPE, and which of these above issues affect the accuracy of QPE the most.
Figure 6 shows the results of the R(
ZH) experiment. If inappropriate parameter values (DSD variability experiment,
Figure 6b) are used in QPE, such as using the parameters obtained in the mountain area to estimate the rain rate for the entire region of Beijing, it will lead to systematic bias in QPE. In this case, the rain rate is underestimated, as can be seen in
Figure 6b, where more dots appear in the lower right part. The RMSE does not change much, with the RMSE increasing from 3.75 mm h
−1 to 3.88 mm h
−1, and an even higher CC. The measurement errors affect the accuracy of QPE more significantly, as shown in
Figure 6c; even if 95% of the observational
Zh are within 10% measurement errors, the QPE accuracy drops significantly, especially for heavy precipitation. With a rain rate larger than 50 mm h
−1, the dots become much more scattered than in
Figure 6a, and RMSE rises to 4.23 mm h
−1. When both measurement errors and systematic bias of
Zh coexist, as shown in
Figure 6d, the QPE accuracy decreases even more. The QPE overestimates the rain rate by 38.82%, with more dots appearing in the upper right part and becoming more scattered, and the RMSE increases significantly to 5.26 mm h
−1. This result suggests that for a city-scale region such as Beijing, when R(
ZH) is used for QPE, the variability of DSD certainly affects the QPE accuracy, but the main influencing factors on QPE accuracy are the measurement errors and calibration of reflectivity, and they affect the QPE accuracy to a greater extent than the influence of the variability of DSD. Therefore, we should focus more on improving the quality of the reflectivity when utilizing R(
ZH) in operation.
Similarly, the experiment design of R(
Kdp) is shown in
Table 5. Since
Kdp is immune to calibration, the systematic bias experiment was discarded, and an additional measurement error experiment was added. The results are shown in
Figure 7. Some previous works have suggested that the R(
Kdp) estimator is relatively insensitive to the variability of DSD compared to R(
ZH) [
47,
59,
60], but by comparing
Figure 7a,b, it is clear that the variability of DSD does affect the accuracy of QPE using R(K
dp), at least for heavy precipitation. In this case, using parameters for the mountain region to estimate the rain rate for the entire region of Beijing results in the underestimation of heavy precipitation, as shown in
Figure 7b. More dots with a rain rate larger than 50 mm h
−1 appear in the lower right flank of the perfect line. The measurement errors, on the other hand, do not significantly affect the accuracy of QPE. Perturbing
Kdp by multiplying
does not degrade the performance much (
Figure 7c), with CC, RMSE, and RMB quite close to the control experiment. Even when perturbing
Kdp by multiplying
, which means assuming large measurement errors for
Kdp (approximately 32% of the
Kdp observation errors are larger than 15%), the QPE accuracy does not deteriorate significantly (
Figure 7d), and it is comparable to the result of
Figure 7b. This series of experiments on R(
Kdp) suggest that the variability of DSD even at the city scale could lead to systematic bias in QPE, especially for heavy precipitation. The variability of DSD may affect the accuracy of QPE even more than
Kdp measurement errors. Therefore, when utilizing R(
Kdp) to perform QPE in operational usage, special attention should be paid to obtaining appropriate parameters.
Experiments on R(
Kdp,
ZDR) are also performed using the design outlined in
Table 6, and the results are shown in
Figure 8. Similar to the R(
Kdp) experiment, although R(
Kdp,
ZDR) is relatively insensitive to the variability of DSD, the variability of DSD does affect the accuracy of R(
Kdp,
ZDR), at least for heavy precipitation above 50 mm h
−1. As shown in
Figure 8b, R(
Kdp,
ZDR) underestimates heavy precipitation above 50 mm h
−1 when inappropriate parameters are used. When Z
DR is assumed to have observational errors (
Figure 8c), the accuracy of QPE drops significantly, especially for heavy precipitation above 50 mm h
−1, resulting in more scattered dots. When both observational errors and systematic bias coexist (
Figure 8d), the accuracy of QPE becomes worse. In this case, the QPE systematically overestimates the rain rate, with more dots appearing in the upper left flank of the perfect line, and the dots become more scattered. These results suggest that the accuracy of R(
Kdp,
ZDR) may be more sensitive to observational errors and systematic bias rather than the representative parameters. It could be due to the negative parameter c, which puts ZDR in the denominator. Given that Z
DR is small in rain (generally less than 3 dB), a small fluctuation or deviation of Z
DR may lead to significant errors in QPE. Therefore, accurate Z
DR observation is crucial to the QPE accuracy for R(
Kdp,
ZDR) estimator. Therefore, accurate and well-calibrated Z
DR observations are crucial to ensure the accuracy of QPE using the R(
Kdp,
ZDR) estimator. Introducing Z
DR into QPE may not necessarily have a positive impact, but rather a negative impact on QPE accuracy if Z
DR is not measured accurately and well-calibrated.