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Table 1 shows several averaged RSD parameters for the three periods, including the rain rate R, radar reflectivity Z, average diameter Da, mass-weighted mean diameter Dm, median diameter D0, average maximum diameter Dmax, total number concentration of raindrops Nt, and normalized intercept parameter Nw. In addition, the contribution of raindrops with diameters less than 1 mm to Nt (N1 / Nt), R (R1 / R) and Z (Z1 / Z) is also given, which can be expressed by:
Period No. samples (min−1) R
(mm h−1)Z (dBZ) Da (mm) Dm (mm) D0 (mm) Dmax (mm) Nt (m−3) lg(Nw)
(mm−1 m−3)N1 / Nt
(%)R1 / R
(%)Z1 / Z
(%)PRM 220 5.42 32.31 0.89 1.40 0.93 2.40 904.29 3.80 81.11 7.86 1.44 MON 293 12.25 38.61 0.92 1.75 1.47 3.16 834.67 3.72 71.93 5.12 0.65 POM 282 4.86 32.27 0.84 1.45 1.07 2.54 631.02 3.66 75.65 8.53 0.94 All 795 8.39 35.21 0.88 1.55 1.23 2.82 754.19 3.71 76.74 6.29 0.83 Table 1. Averaged microphysical parameters of RSD for the pre-monsoon (PRM), monsoon (MON), and post-monsoon (POM) periods. These parameters include the rain rate R, radar reflectivity Z, average diameter Da, mass-weighted mean diameter Dm, median diameter D0, average maximum diameter Dmax, total number concentration of raindrops Nt, and normalized intercept parameter lg(Nw).
According to Table 1, the total average number concentration of raindrops and the percentage of raindrops with diameters less than 1 mm in the pre-monsoon period is 904.29 m−3 and 81.11%, respectively. This suggests that small raindrops (D ≤ 1 mm) are prevalent in the pre-monsoon period. The average diameter Da, mass-weighted mean diameter Dm, and average maximum diameter Dmax in the monsoon period are the largest in the three periods. Thus, medium- and large-sized drops are expected to be prevalent during the monsoon period. This feature can also be deduced from the smallest contribution of raindrops with diameters less than 1 mm in the monsoon period. The post-monsoon period has the lowest average drop concentration Nt and the smallest average diameter Da. This indicates the significant contribution of small raindrops to precipitation in this period, which can also be deduced from the largest R1 / R ratio (8.53%). In addition, the larger mass-weighted mean diameter Dm and median diameter D0 in the post-monsoon period than those in the pre-monsoon period suggests that there may also be some big raindrops in this period.
The median volume diameter D0 in the monsoon period is 1.47 mm, which is very close to the value of 1.5 mm measured during the Australian monsoon season as reported by Penide et al. (2013). This similarity may be related to the influence of both of them by the warm and humid air currents from the ocean. Compared with the precipitation of the pre-monsoon, summer monsoon, and post-monsoon seasons observed at the tropical coastal station of Thiruvananthapuram (Sreekanth et al., 2017), the total concentration of raindrops Nt and the mass-weighted mean diameter Dm during the same season over the SCS are both much larger. The average maximum diameter Dmax of precipitation in the pre-monsoon period is close to that observed in Taiwan (Seela et al., 2017), but the mean Dmax in the other two seasons is both larger. The Nw values of precipitation in the pre-monsoon and monsoon periods are very close to the values during autumn and winter in East China, whereas they are smaller than those in summer and spring (Wen et al., 2019). The Dm values in the SCS are much larger than those in East China, which indicates there are fewer small drops but more large drops observed in precipitation over the SCS. The average Nt of precipitation over the SCS is higher than the summer precipitation over northern China, whereas the average Dm over northern China is much larger (Wen et al., 2017). Considering the also smaller median diameter D0 over the SCS, we infer that small drops are more abundant over the SCS than over northern China in the summer season. This might be attributable to the sufficient water vapor supply in the SCS summer monsoon period over the SCS.
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Figure 2 presents the average raindrop spectra for the three different monsoon periods. The concentration of small drops (D ≤ 1 mm) is the highest in the pre-monsoon period, and the concentration of medium-sized raindrops (1−3 mm) is the highest during the monsoon period. The post-monsoon period has the smallest concentration of raindrops, with a diameter below 3 mm. However, the concentration of raindrops with diameters greater than 4 mm is higher during the post-monsoon period than those during the other two periods. This further confirms the presence of several big raindrops in the post-monsoon period.
Figure 2. Spectra for the pre-monsoon (PRM), monsoon (MON), and post-monsoon (POM) precipitation periods.
The concentration of drops observed during the SCS summer monsoon period is higher than that during the South India summer monsoon season as reported by Chakravarty et al. (2013). Compared to the raindrop spectrum reported by Wen et al. (2016), also using a Parsivel disdrometer, the concentration of raindrops with diameters greater than 3 mm is higher in the SCS summer monsoon period.
To further discern the RSD differences among the three periods, the observed RSDs were further divided into six classes with respect to rain rate (mm h−1)—namely, R ≤ 2 mm h−1, 2 < R ≤ 5 mm h−1, 5 < R ≤ 10 mm h−1, 10 < R ≤ 20 mm h−1, 20 < R ≤ 40 mm h−1, and R > 40 mm h−1.
Table 2 shows the statistical values of RSD parameters in the six rain-rate classes. With an increase in rain rate, there is an increase in Nt and Da for precipitation in the pre-monsoon and monsoon periods. The mean Dm values all increase with the rain rate in the three periods. The lg(Nw) observed in the pre-monsoon period tends to increase, whereas it tends to decrease in the post-monsoon period. From low-intensity precipitation to high-intensity precipitation, no significant change in lg(Nw) values is observed in the monsoon period. Overall, the values of RSD parameters N0 and λ tend to decrease with the increasing rain rate during the three periods. For the shape parameter μ, it decreases with the rain rate increasing in the pre-monsoon period. However, there is no orderliness to the change of parameter μ with rain rate in the monsoon and post-monsoon periods.
Class
(mm h−1)No. samples (min−1) R
(mm h−1)Nt
(m−3)Da (mm) Dm (mm) lg(Nw)
(mm−1 m−3)lg(N0)
(m−3 m−1 − μ)μ λ (mm−1) PRM R ≤ 2 91 1.10 396.67 0.74 1.12 3.60 8.12 9.97 13.18 2< R ≤5 43 3.16 455.40 0.81 1.43 3.63 4.97 4.54 5.81 5 < R ≤ 10 35 7.02 626.00 0.84 1.56 3.68 4.60 3.55 4.57 10 < R ≤ 20 28 13.79 1759.2 0.85 1.72 3.98 4.77 2.92 4.24 20 < R ≤ 40 18 31.16 2317.8 0.88 2.05 3.96 4.36 2.19 3.09 R > 40 5 50.09 3242.2 0.90 2.08 4.13 4.21 1.70 2.75 MON R ≤ 2 70 0.89 850.90 0.67 1.16 3.81 6.88 6.88 10.43 2 < R ≤ 5 45 3.89 777.16 0.81 1.45 3.79 5.06 3.90 5.67 5 < R ≤ 10 84 7.75 848.16 0.94 1.69 3.68 4.69 4.05 4.86 10 < R ≤ 20 55 14.03 946.87 0.98 1.91 3.69 4.48 3.63 4.17 20 < R ≤ 40 28 26.91 1065.9 1.06 2.17 3.71 4.25 3.83 3.67 R > 40 11 52.39 1881.1 0.95 2.47 3.73 3.97 2.81 2.76 POM R ≤ 2 103 1.05 543.95 0.73 1.20 3.60 5.79 5.33 8.36 2 < R ≤ 5 72 3.09 714.25 0.86 1.51 3.62 5.62 6.22 7.47 5 < R ≤ 10 55 7.41 720.28 0.95 1.74 3.64 4.93 5.65 5.64 10 < R ≤ 20 27 13.82 667.83 1.00 2.09 3.52 4.25 4.37 4.15 20 < R ≤ 40 19 31.60 701.80 1.23 2.70 3.35 3.64 4.78 3.37 R > 40 6 41.66 390.74 1.45 3.05 3.20 3.10 6.42 3.24 Table 2. Averaged microphysical parameters for each of six rain-rate intervals of precipitation in the pre-monsoon, monsoon, and post-monsoon period. Except for the parameters in Table 1, the RSD parameters including intercept parameter lg(N0), shape parameter μ, and slope parameter λ are also presented in Table 2.
As shown in Fig. 3, with the rain rate increasing, the width of the RSD spectra in different monsoon periods broadens. The concentration of drops with diameter less than 2 mm increases in the pre-monsoon period but decreases in the post-monsoon period. For R < 10 mm h−1, the disagreement among the three curves diminishes with the rain rate increasing. For R ≥ 10 mm h−1, the disagreement among the three curves increases with the rain rate increasing. It is clear that there is a sharp increase in the small raindrop concentration during the pre-monsoon period. The concentration of large (small) drops is the highest (lowest) during the post-monsoon period. This pattern is consistent with the largest mean Dm for the same rain rate classes in the post-monsoon period and the highest Nw in the pre-monsoon period for R ≥ 10 mm h−1, as shown in Table 2.
Figure 3. Averaged RSDs for each of the six class intervals in the pre-monsoon (green), monsoon (red) and post-monsoon (blue) periods.
The value of rain rate is usually proposed to be a discriminator for types of precipitation. Tokay and Short (1996) took R = 10 mm h−1 as a critical value for the classification of rain types. Thus, the previous analysis might indicate the differences in RSD for precipitation with different types, which will be analyzed further below.
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In the present study, the classification criteria of stratiform and convective precipitation based on rain rate and its standard deviation by Bringi et al. (2003) were adopted. For 10 consecutive 1-min RSD samples, samples with R ≥ 0.5 mm h−1 and σR ≤ 1.5 mm h−1 were classified as stratiform rain and samples with R ≥ 5.0 mm h−1 and σR ≥ 1.5 mm h−1 were convective rain.
Figure 4 compares the RSDs of stratiform and convective rainfall in the three periods. As depicted in Fig. 4a, the stratiform rainfall in the pre-monsoon period is characterized by a high concentration of small raindrops with diameter below 1 mm. The stratiform rainfall in the monsoon period has the highest concentration of raindrops with diameter between 1 mm and 5 mm. The concentration of raindrops in different particle sizes during the post-monsoon period is almost the minimum. In Fig. 4b, for convective rainfall, the highest concentration of drops with diameter less than 2 mm occurs in the pre-monsoon period. The concentration of drops with diameter greater than 4 mm for convective rainfall is the highest in the post-monsoon period. Relatively, the drops with diameter between 2 mm and 4 mm in monsoon precipitation are much more abundant.
Figure 4. Variations of mean raindrop concentration with rain type for (a) stratiform and (b) convective precipitation. PRM, MON, and POM stand for the pre-monsoon, monsoon, and post-monsoon periods, respectively, while-Str and -Con denote the results from stratiform and convective precipitation, respectively.
Table 3 shows the statistical values of RSD parameters for stratiform and convective rainfall during the three periods. For stratiform rainfall, the mean Nt, mean Da, and mean lg(Nw) are all the largest in the pre-monsoon period. The mean Dm is the largest in the monsoon period, followed by the post-monsoon period. The three gamma shape parameters of stratiform rainfall are all the largest in the pre-monsoon period, but are the smallest in the monsoon period. In comparison with the stratiform precipitation of the summer and winter seasons observed over northern Taiwan (Seela et al., 2018), larger Dm but smaller lg(Nw) are observed over the SCS. However, their mean gamma distribution parameters, μ and λ, are very close. The stratiform precipitation during the three periods over the SCS has a higher number concentration of raindrops Nt and larger mass-weighted mean diameter Dm than that over northern China (Wen et al., 2017). This suggests that RSDs for stratiform precipitation over the SCS have a higher concentration of bigger-sized drops than those over northern China.
Rain types M R (mm h−1) Nt (m−3) Da (mm) Dm (mm) lg(Nw) (mm−1 m−3) lg(N0) (m−3 m−1 − μ) μ λ (mm−1) PRM-Str 170 3.00 836.42 0.90 1.43 3.65 5.27 4.72 6.60 MON-Str 188 6.07 639.51 0.84 1.51 3.59 4.63 3.36 5.01 POM-Str 203 2.83 479.37 0.78 1.45 3.52 4.77 3.81 5.90 PRM-Con 50 17.35 1575.6 0.94 1.70 4.02 5.03 3.86 4.84 MON-Con 105 18.49 940.02 1.00 1.90 3.77 4.76 4.55 4.75 POM-Con 79 17.20 635.30 1.06 2.00 3.61 4.91 6.62 5.74 Table 3. Averaged microphysical parameters for convective and stratiform rain types. The stratiform and convective precipitation types are denoted as “Str” and “Con”, respectively.
For convective rainfall, the largest (smallest) Nt and lg(Nw) have also been found in the pre-monsoon (post-monsoon) period. However, the average Da and Dm of post-monsoon convective rainfall are the largest, which indicates the occurrence of large raindrops in this period. The slope parameter λ is also much larger in the post-monsoon period than in the other two periods. The average number concentration of raindrops Nt for convective precipitation in the post-monsoon period is very close to the value observed in a coastal city of South China, Yangjiang (Tang et al., 2014). However, the mean Dm [lg(Nw)] of precipitation during the post-monsoon period is larger (smaller) than that in Yangjiang. The difference may be related to the existence of large raindrops in the post-monsoon period over the SCS.
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To further reveal the characteristics of RSD, the distributions of Dm and lg(Nw) are analyzed in this section. The mean lg(Nw) versus Dm values, with standard deviation, for the stratiform and convective rain types are depicted in Fig. 5. The maritime-like and continental-like convective clusters reported by Bringi et al. (2003) are also shown in the figure. In addition, Fig. 5 also provides comparative results from other studied regions. From Fig. 5, we can see that the mean Dm and Nw of stratiform rainfall in the three periods are near the right-hand side of the “stratiform line” given by Bringi et al. (2003). Relatively, the Dm (Nw) of stratiform rainfall in the monsoon (pre-monsoon) period is slightly larger.
Figure 5. Average value of lg(NW) versus average Dm (along with ±σ standard deviation bars) for stratiform and convective rainfall during the three periods. The two outlined squares represent (left) the maritime and (right) continental types of convective systems reported by Bringi et al. (2003). The dashed line is the result for their stratiform rain. The suffixes -Str and -Con denote the results from stratiform and convective precipitation, respectively. The blue triangles indicate results observed in other geographic locations.
Convective precipitation in the pre-monsoon period is very close to the “maritime cluster”, whereas convective precipitation in the post-monsoon period is closer to the “continental cluster”. The convective monsoon precipitation is not similar to either maritime or continental convective precipitation. The figure shows a clear shift in the RSD from the “maritime” to the “continental” cluster from the pre-monsoon to post-monsoon period.
Figure 5 also provides comparative results from other studied regions. The stratiform and convective precipitation over the SCS show larger Dm but smaller Nw in comparison with those observed in East China (Wen et al., 2016) and Taiwan and Palau (Seela et al., 2017). The average Nw (Dm) of stratiform precipitation over the SCS is slightly smaller (much larger) than that over northern China reported by Wen et al. (2017). The average Dm and Nw of stratiform precipitation over the SCS are both much larger those in the South Korean coastal region (Suh et al., 2016) (not shown in the figure). However, the average Dm and Nw of convective precipitation observed in the South Korean coastal region are just located between the values of the pre-monsoon convective precipitation and monsoon convective precipitation. This similarity may be related to the fact that all the three observation areas are located in coastal areas, where the precipitation is affected by warm and humid air currents from the sea.
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One of the key RSD applications is QPE, because it can provide proper relations for rainfall retrieval algorithms (Lee and Zawadzki, 2005; Chapon et al., 2008; Chen et al., 2017). In this section, the power-law relationship Z = ARb, widely used in radar meteorology, is firstly studied based on the observed datasets. Then, several empirical relationships used in polarimetric radar are also derived. Finally, the relationships of Dm−Zku, Dm−Zka, and lg(Nw)−Dm, used in the construction of the dual-frequency precipitation radar (DPR) rainfall retrieval algorithm, are also fitted, to improve the inversion accuracy of marine precipitation with GPM.
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Figure 6a presents scatterplots of radar reflectivity factor Z and rain rate R, as well as the results of Z−R fittings by using the least-squares method. The results show that the coefficient A is the largest (smallest) and the exponent b is the smallest (largest) in the pre-monsoon (post-monsoon) period. There is a clear inverse relationship between the coefficient A and exponent b in the three periods. Testud et al. (2001) noted that the Z−R relationship could be approximately set to Z ∝
$ N_{\rm{w}}^{ - 0.5}{R^{1.5}}$ , which means that the coefficient A is proportional to$ N_{\rm{w}}^{ - 0.5}$ if exponent b is close to 1.5. The changes in coefficient A during the three periods are shown to be consistent with the previous statistical results of lg(Nw) (as in Table 1). Uijlenhoet et al. (2003) proposed that the exponent b in the Z−R relation can reflect the different mechanisms of the formations of precipitation particles. Thus, the difference in the values of exponent b infers that the microphysical processes occurring during different monsoon periods are different (Seela et al., 2017). Comparing the current results with those obtained in Taiwan and Palau, the coefficient A over the SCS is slightly higher. The exponent b during the pre-monsoon period is very close to that in Taiwan and Palau (Seela et al., 2017). The coefficient A and exponent b in the pre-monsoon period are also close to the values of southwest monsoon precipitation at Gadanki, reported by Rao et al. (2001). Compared with the values of southwest monsoon precipitation observed at another tropical station, Kadapa, which is located in the southern part of India (Jayalakshmi and Reddy, 2014), the coefficient A of precipitation during the three periods over the SCS is all larger. The exponent b in the pre-monsoon period is slightly smaller than that at Kadapa, while the exponent b in the monsoon period and post-monsoon period are both slightly larger. These comparisons further illustrate the need to study the localized Z−R relationships.Figure 6. (a) Scatterplots of the Z−R values for precipitation during different monsoon periods and the fitted power-law relationships, Z = ARb, where A is the coefficient and b is the exponent, derived from the least-squares method. (b) Scatterplots and the fitted power-law relationships of the total stratiform (black dashed line) and convective (red solid line) rain types observed in the SCS. The relation for mei-yu convective rain, Z = 368R1.21 (Chen et al., 2013); the standard NEXRAD Z−R relationship, Z = 300R1.40 (Fulton et al., 1998); and the tropical Z−R relationship, Z = 250R1.20 (Rosenfeld et al., 1993) are also shown (green, blue and yellow lines, respectively).
The NEXRAD weather radar quantifies the default equation for the precipitation using Z = 300R1.40. However, Rosenfeld et al. (1993) recommend Z = 250R1.20 to estimate the precipitation in the tropics. Scatterplots between Z and R for the total stratiform and convective precipitation over the SCS are presented in Fig. 6b with cross symbols and gray dots, respectively. The results of correlation fitting are also given in this figure. The coefficient A is larger and exponent b is smaller for stratiform precipitation than convective precipitation, which indicates the need for different relationships to estimate different types of precipitation. The Z−R relationship for stratiform precipitation over the SCS has a larger coefficient A but smaller exponent b than those observed at Kadapa (Jayalakshmi and Reddy, 2014) and Gadanki (Rao et al., 2001). This difference may be related to the higher Dm but lower Nw of stratiform precipitation over the SCS than those at the two Indian stations.
The A and b values of the Z−R relationship for convective precipitation over the SCS are 384 and 1.38, respectively, which are similar to those of the standard relationship, Z = 300R1.40, but differ from those of the standard tropical relationship, Z = 250R1.20. The tropical relation underestimates the intense precipitation over the SCS. The coefficient A of precipitation over the SCS is very close to that observed during the mei-yu season, whereas the exponent b in the SCS is much bigger. Compared to the Z−R relationship derived from summer monsoon at Zhuhai (Z = 498R1.3), the convective precipitation over the SCS shows a smaller coefficient A (Zhang et al., 2019). But, their exponent b is much closer, which may result from the fact that they are both affected by the warm and wet currents from the tropical ocean region. Compared with the convective precipitation observed in Taiwan and Palau (Seela et al., 2017), the coefficient A in the SCS is also higher, but their exponent b values are very close, which may be related to the fact that they are all in the western Pacific region. The coefficient A and exponent b for convective precipitation in the SCS are both larger than those during southwest monsoon convective precipitation at Kadapa (Jayalakshmi and Reddy, 2014). These results reconfirm previous opinion that there is a need to adopt modified Z−R relations in the estimation of rainfall in different regions (Seela et al., 2018).
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In addition to conventional weather radar, polarimetric radar has also been used in rainfall estimation for several years (Zhang et al., 2001; Cao et al., 2010; You et al., 2014). Cao and Zhang (2009) demonstrated that polarimetric measurements, such as differential reflectivity ZDR and specific differential phase Kdp, can provide valuable information caused by DSD variability, hail contamination, beam blockage, and other sources of error, which is conducive to resolving problems. To improve precipitation estimation with polarimetric radar, several empirical relationships, such as R(ZH, ZDR), R(Kdp), R(ZH), and R(ZDR, Kdp), also needed to be constructed (Zhang et al., 2017).
In this paper, the widely used R(ZH, ZDR) relationship was derived, which can be expressed as follows:
where a is the coefficient. b and c are the exponent for the horizontal polarization ZH (mm6 m−3) and the differential reflectivity ZDR (dBZ), respectively.The two parameters were calculated from the observed DSDs using the T-matrix scattering technique described by Zhang et al. (2001), as follows:
where λ is the radar wavelength, Kw is the water dielectric factor, and fhh,vv(D) is the backscattering amplitudes of a raindrop for horizontally and vertically polarized waves, respectively. The frequency of the radar’s electromagnetic wave is assumed to be 2.85 GHz (S-band). The raindrop temperature was assumed to be 20°C in this study, and the raindrops were also assumed to follow the axis ratio relation proposed by Beard and Chuang (1987):
In addition, for comparison purposes, we defined two parameters—the normalized mean bias (NB) and normalized standard error (NSE), which can be expressed by:
where RDSD and Rradar are 1-min precipitation values from the DSD data and the calculated radar parameters based on the T-matrix simulation, respectively.
The results are shown in Table 4. As shown in Table 4, the coefficient a in R(ZH, ZDR) decreases from the pre-monsoon to the post-monsoon period, whereas exponents b and c in R(ZH, ZDR) increase from the pre-monsoon to the post-monsoon period. It also clearly shows that both the NB errors and the NES errors are much smaller for precipitation estimated with R(ZH, ZDR) relationships than Z−R relationships, during the same period. The results indicate that the R(ZH, ZDR) estimator has an advantage over the Z−R relation, which reconfirm previous opinion (Cao et al., 2010; Tang et al., 2014; Zhang et al., 2017).
Rainfall estimation methods R(ZH, ZDR) Z−R a b c NB (%) NES (%) A b NB (%) NES (%) PRM 0.009 40 0.730 −1.092 −5.92 34.6 466 1.33 31.4 73.2 MON 0.004 46 0.864 −1.197 −3.16 32.1 346 1.41 12.2 70.5 POM 0.002 39 0.916 −1.245 −3.97 29.9 339 1.46 31.8 67.6 Table 4. Results of the Z −R and R(ZH, ZDR) rainfall estimation methods. ZH denotes the horizontal polarization and ZDR represents the differential reflectivity. NB is short for the normalized mean bias and NSE is short for the normalized standard error.
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Nowadays, the GPM Core Observatory satellite serves as an optimal platform to estimate precipitation globally. However, more ground validation needs to be performed to improve the rainfall retrieval algorithm.
The DPR on board GPM is the key instrument. It estimates the RSD from the attenuation difference between the Ku-band precipitation radar (13.6 GHz) and the Ka-band precipitation radar (35.5 GHz) (Schwaller and Morris, 2011). The normalized gamma distribution described in Eq. (1) is widely used in the GPM DPR rainfall retrieval algorithms (Grecu et al., 2016). Accordingly, the DSD can be reconstructed from Nw and Dm given a μ value. The radar reflectivity at the Ku band or Ka band can be used to derive the parameters Nw and Dm. The DFR (dB) takes the following form:
The effective radar reflectivity factors at Ku-band (ZKu) and Ka-band (ZKa) frequencies can be calculated by
where Ze is the effective radar reflectivity factor at a specific wavelength λ, which can be derived from the onboard disdrometer observations. σb(Di, λ) is the backscattering cross section of a raindrop with diameter Di, which is directly calculated according to Mie theory.
${{k_{\rm{w}}^{2}}} $ is the dielectric factor, which is related to the complex refractive index of region and is conventionally taken to be 0.93.As pointed out by Chen et al. (2017), DFR is commonly used for the retrieval of Dm. As shown by the scatterplots of Dm−ZKu and Dm−ZKa for the three periods in Fig. 7, the values of Dm increase with ZKu or ZKa increasing. There is a high correlation between Dm and ZKu (ZKa). As in Chen et al. (2017), we also derived second-degree polynomial relations between Dm and ZKu (ZKa). The relevant fitting results are presented in Table 5. As shown in Fig. 7, the values of Dm in the monsoon period are the largest for ZKu (ZKa) below 15 dBZ and those in the post-monsoon period are the largest for ZKu (ZKa) above 25 dBZ.
Figure 7. Scatterplots of (a) Dm (units: mm) and the Ku-band effective radar reflectivity factor ZKu (units: dBZ), and (b) Dm (units: mm) and the Ka-band effective radar reflectivity factor ZKa (units: dBZ). The fitted curves of the pre-monsoon, monsoon, and post-monsoon periods are represented by solid, dashed, and dash-dotted lines, respectively.
Relation Data a b c Dm = ${{aZ_{\rm{Ku}}^{2}}} $ + bZKu + c PRM 0.000 417 3 0.0201 0.5178 MON 0.001 232 2 −0.0304 1.1780 POM 0.001 574 1 −0.0288 0.9831 Dm = ${{aZ_{\rm{Ka}}^{2}}} $ + bZKa + c PRM 0.000 309 2 0.0316 0.3581 MON 0.001 161 3 −0.0140 0.9082 POM 0.001 353 1 −0.0073 0.7637 lg(Nw) =${{aD_{\rm{m}}^{2}}} $ + bDm + c PRM 0.0878 −1.1521 4.8647 MON 0.1178 −1.1023 4.9553 POM 0.0652 −0.9211 4.5127 Table 5. Second-degree polynomial relations of Dm−ZKu, Dm−ZKa, and lg(Nw)−Dm for the three monsoon periods.
Figure 8 presents scatterplots of the two parameters lg(Nw) and Dm in a normalized gamma distribution. It clearly shows that the lg(Nw) decreases with the increase of Dm. In order to reduce the parameters in the normalized gamma distribution, we further derived an empirical polynomial relation between lg(Nw) and Dm. The fitting results indicate that the lg(Nw) decreases most obviously with Dm in the monsoon period. Comparing the current results with those for the Tibetan Plateau reported by Chen et al. (2017), the coefficients of the second-degree polynomial relation over the ocean are smaller.
Period | No. samples (min−1) | R (mm h−1) | Z (dBZ) | Da (mm) | Dm (mm) | D0 (mm) | Dmax (mm) | Nt (m−3) | lg(Nw) (mm−1 m−3) | N1 / Nt (%) | R1 / R (%) | Z1 / Z (%) |
PRM | 220 | 5.42 | 32.31 | 0.89 | 1.40 | 0.93 | 2.40 | 904.29 | 3.80 | 81.11 | 7.86 | 1.44 |
MON | 293 | 12.25 | 38.61 | 0.92 | 1.75 | 1.47 | 3.16 | 834.67 | 3.72 | 71.93 | 5.12 | 0.65 |
POM | 282 | 4.86 | 32.27 | 0.84 | 1.45 | 1.07 | 2.54 | 631.02 | 3.66 | 75.65 | 8.53 | 0.94 |
All | 795 | 8.39 | 35.21 | 0.88 | 1.55 | 1.23 | 2.82 | 754.19 | 3.71 | 76.74 | 6.29 | 0.83 |