Seasonal Characteristics of Disdrometer-Observed Raindrop

remote sensing

Article Seasonal Characteristics of Disdrometer-Observed Raindrop Size Distributions and Their Applications on Radar Calibration and Erosion Mechanism in a Semi-Arid Area of China

Zongxu Xie 1,2, Hanbo Yang 1,2,* , Huafang Lv 1,2 and Qingfang Hu 3

1 Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China; [email protected] (Z.X.); [email protected] (H.L.) 2 State Key Laboratory of Hydro-Science and Engineering, Tsinghua University, Beijing 100084, China 3 State Key Laboratory of Hydro-Water Resources and Hydraulic Engineering, Nanjing Hydraulic Research Institute, Nanjing 210029, China; [email protected] * Correspondence: [email protected]

Received: 28 November 2019; Accepted: 10 January 2020; Published: 12 January 2020

Abstract: Raindrop size distributions (DSDs) are the microphysical characteristics of raindrop spectra. Rainfall characterization is important to: (1) provide information on extreme rate, thus, it has an impact on rainfall related hazard; (2) provide data for indirect observation, model and forecast; (3) calibrate and validate the parameters in radar reflectivity-rainfall intensity (Z-R) relationships (quantitative estimate precipitation, QPE) and the mechanism of precipitation erosivity. In this study, the one-year datasets of raindrop spectra were measured by an OTT Parsivel-2 Disdrometer placed in Yulin, Shaanxi Province, China. At the same time, four TE525MM Gauges were also used in the same location to check the disdrometer-measured rainfall data. The theoretical formula of raindrop kinetic energy-rainfall intensity (KE-R) relationships was derived based on the DSDs to characterize the impact of precipitation characteristics and environmental conditions on KE-R relationships in semi-arid areas. In addition, seasonal rainfall intensity curves observed by the disdrometer of the area with application to erosion were characterized and estimated. The results showed that after quality control (QC), the frequencies of raindrop spectra data in different seasons varied, and rainfalls with R within 0.5–5 mm/h accounted for the largest proportion of rainfalls in each season. The parameters in Z-R relationships (Z = aRb) were different for rainfall events of different seasons (a varies from 78.3–119.0, and b from 1.8–2.1), and the calculated KE-R relationships satisfied the form of power function KE = ARm, in which A and m are parameters derived from rainfall shape factor µ. The sensitivity analysis of parameter A with µ demonstrated the applicability of the KE-R formula to different precipitation processes in the Yulin area.

Keywords: raindrop size distribution; radar reﬂectivity; raindrop spectrometer; semi-arid area

1. Introduction Characteristics of precipitation show the impact of meteorological conditions [1], and the measurement of quantitative distribution of precipitation is important for studying the mechanism of global climate and environmental change [2]. Raindrop size distributions (DSDs) show the microphysical properties of a rainfall event and vary with precipitation both in time and space. The DSDs are of importance to enhance the accuracy of quantitative precipitation estimation (QPE) by weather radar, and raindrop spectra have been used to calculate radar reﬂectivity factors in many studies [3–6]. Thus, investigating the raindrop spectra is essential for providing information on the

Remote Sens. 2020, 12, 262; doi:10.3390/rs12020262 www.mdpi.com/journal/remotesensing Remote Sens. 2020, 12, 262 2 of 23 microphysical characteristics of different precipitation types, and improving the parameterizations of different rainfall processes. Raindrop spectra can be measured by many methods, e.g., as done by Das et al., Waldvogel et al., Schönhuber et al. and Liu et al. [3,7–9], and these different methods vary in measurement principles and precision of data. In recent years, the raindrop disdrometer has been widely used to measure raindrop spectra because of its high measurement accuracy and small-time interval for data acquisition. Liu et al. [9] measured the precipitation in Nanjing, China and compared four different methods of rainfall to conclude that the disdrometer and other methods are consistent within the range of medium particle size. However, Zhang et al. [10] used three different methods to analyze the DSD characteristics in Zhuhai, China and found that the disdrometer had limitations in measuring small raindrops when compared to other methods. Raupach et al. [11] used a 2DVD device to correct the DSDs measured by three disdrometers and the correction showed its general applicability under different climate types. However, the study on the seasonal variation of rainfall characteristics in semi-arid areas of China using a raindrop disdrometer is very limited. The measured raindrop spectra can be used to calibrate and validate the parameters in radar reflectivity-rainfall intensity (Z-R) relationships (quantitative estimate precipitation, QPE). Variability of DSDs in different forms of precipitation impact the radar reflectivity-rainfall intensity relationships (Z-R relationships, normally in the form of power function Z = aRb, in which a and b are parameters derived from data fitting) [12,13], and the quantitative estimation of rainfall intensity (R) by Z-R relationships can be further modified. Sulochana et al. [14] investigated the Z-R relationships over a tropical station and concluded that the prefactor of Z-R relationships is larger for stratiform rain than for convective rain, which was in agreement with the results reported from two other tropical stations. Sulochana et al. also found that there were large variations in Z-R relationships in different seasons. Das et al. [3] analyzed the impact of different precipitation types on Z-R relationships in a hill station with a pronounced monsoon climate, and the results showed that the Z values of the shallow-convective system are the lowest, compared to other precipitation types. Das et al. concluded that the coefficient a is larger for stratiform rain than for convective and shallow-convective rain. However, there remains very limited research on using disdrometers to investigate raindrop spectra in semi-arid areas [15], and further research on the parameters in Z-R relationships is needed. In addition, the measured raindrop spectra can be used to explore the mechanism of precipitation erosivity. The relationship between rainfall kinetic energy (KE) and intensity (R) is a significant approach to study the impact of precipitation on soil erosion [16], and a disdrometer can be deployed to measure the rainfall kinetic energy and intensity [17]. Angulo-Martínez et al. [18] measured and analyzed the uncertainty in KE-R relationships with five Parsivel disdrometers among three locations, and found that the types, accuracy and location of the disdrometers and precipitation types influence the estimation results of KE. Overestimation of the midsize raindrops led to a high estimation result of KE. Moreover, Carollo et al. [19] concluded that KE/R depends on the median volume diameter of precipitation events strictly, and this relationship does not rely on the locations of disdrometers. There have also been studies investigating the KE-R relationships in arid and semi-arid areas, e.g., Meshesha et al. and Abd Elbasit et al. [20,21], and many KE-R relationships were derived with this approach [22]. Nevertheless, many of the relationships vary greatly because of the different climate conditions, and a general formula for KE-R relationships needs to be derived to be suitably utilized in arid and semi-arid areas. Yulin (in the northern region of Shaanxi Province, China) has a semi-arid climate, and the precipitation in this area is not evenly distributed throughout different seasons of the year [23]. The analysis of DSDs in different seasons is helpful to understand the variability of precipitation in this semi-arid area. The objectives of this paper are: (1) to analyze the detailed statistical data of DSDs based on the observation of a raindrop disdrometer located in Yulin, and collect data on the variability of microphysical characteristics of precipitation in different seasons; (2) to investigate the Z-R relationships in different seasons, and analyze the variability of the parameters in the Z-R relationships across Remote Sens. 2020, 12, 262 3 of 23 different precipitation types; (3) to derive a theoretical formula for KE-R relationships and further analyze the calculated results. The following sections are organized below. Section2 describes the research method, the datasets of the research area, and the derivation processes of theoretical formula. Section3 analyzes the observed results statistically and presents the comparison of different precipitation periods in different seasons. Section4 presents a further discussion of the comparison of disdrometer- and gauges-measured rainfall data, the comparison of different Z-R relationships and the theoretical formula of KE-R relationships through sensitivity analysis. Section5 gives the conclusion.

2. Materials and Methods

2.1. Observation Station and Disdrometer Datasets Microphysical characteristics of different precipitation types were measured at Yulin Ecohydrological Station (109◦2802.700E, 38◦26043.600N, 1236 m above sea level (a.s.l.), located in Mu Us Sandy Land) in Shaanxi Province, China. Mu Us Sandy Land has a semi-arid climate type with a low amount of precipitation [24]. The average annual precipitation in this area is 413 mm (from the year 1951 to 2018, measured by Yulin Meteorological Station (109◦2801200E, 38◦903600N, 936 m a.s.l.)). Figure1a shows the location of Yulin Ecohydrological Station and Yulin Meteorological Station. One OTT Parsivel-2 Disdrometer was placed in Yulin Ecohydrological Station, and continuously recorded data during a 1-year period between 10 August 2018 and 10 August 2019. There are also four TE525MM rainfall gauges placed at the same location (shown in Figure1b), and the specific placement of the disdrometer and the four gauges is proposed by Xie et al. [25], providing a reference for the measurement data by the disdrometer. Data were recorded every 30 min during the researching period, with the four gauges recording data simultaneously and individually. The disdrometer conducted a 54 cm2 laser beam to record the rainfall spectrum every 1 min. The record of the disdrometer includes two parts: raindrop diameters (D) and raindrop terminal velocity (v). When precipitation particles pass the laser beam of the sensor, the beam is blocked off by the particles equal to the diameters, and the output voltage will be reduced. If there is no particle passing through, the voltage will then be recorded as maximum. The duration of the reducing signal will be used to determine the terminal speed of a particle. Through the observation by the disdrometer, radar reflectivity (Z), rainfall intensity (R) and kinetic energy (KE) are derived from D and v. Figure2 summarizes how the materials and methods and results are managed via a schematic.

2.2. Processing Microphysical Datasets from Disdrometer In order to process the calculation of the characteristic variables of precipitation, the formulas are derived as follows: 32 32 X nij X nij N(Di) = = (1) Vj ∆Di A ∆t vj ∆Di j=1 · j=1 · · · where N(D ) (mm 1 m 3) is the number concentration of raindrops per unit diameter interval for i − · − raindrops per unit volume with the diameter equal to Di (the ith-bin of diameters of the spectra); A = 5.4 10 4 m2 is the sampling area scanned by the laser beam; ∆t = 60 s is the sampling time × − interval; vj is the raindrop terminal velocity of the jth-bin of velocities of the spectra; ∆Di is the class spread of the ith-bin of diameters of the spectra. Remote Sens. 2019, 11, x FOR PEER REVIEW 3 of 24

95 relationships across different precipitation types; (3) to derive a theoretical formula for KE-R 96 relationships and further analyze the calculated results. 97 The following sections are organized below. Section 2 describes the research method, the 98 datasets of the research area, and the derivation processes of theoretical formula. Section 3 analyzes 99 the observed results statistically and presents the comparison of different precipitation periods in 100 different seasons. Section 4 presents a further discussion of the comparison of disdrometer- and 101 gauges-measured rainfall data, the comparison of different Z-R relationships and the theoretical 102 formula of KE-R relationships through sensitivity analysis. Section 5 gives the conclusion.

103 2. Materials and Methods

104 2.1. Observation Station and Disdrometer Datasets 105 Microphysical characteristics of different precipitation types were measured at Yulin 106 Ecohydrological Station (109°28′2.7″E, 38°26′43.6″N, 1236m above sea level (a.s.l.), located in Mu Us 107 Sandy Land) in Shaanxi Province, China. Mu Us Sandy Land has a semi-arid climate type with a low 108 amount of precipitation [24]. The average annual precipitation in this area is 413 mm (from the year 109 1951 to 2018, measured by Yulin Meteorological Station (109°28′12″E, 38°9'36"N, 936m a.s.l.)). 110 Figure 1 (a) shows the location of Yulin Ecohydrological Station and Yulin Meteorological 111 Station. One OTT Parsivel-2 Disdrometer was placed in Yulin Ecohydrological Station, and 112 continuously recorded data during a 1-year period between 10 August 2018 and 10 August 2019. 113 There are also four TE525MM rainfall gauges placed at the same location (shown in Figure 1 (b)), and 114 the specific placement of the disdrometer and the four gauges is proposed by Xie et al. [25], providing 115 a reference for the measurement data by the disdrometer. Data were recorded every 30 mins during 116 the researching period, with the four gauges recording data simultaneously and individually. The 117 disdrometer conducted a 54 cm2 laser beam to record the rainfall spectrum every 1 minute. The record 118 of the disdrometer includes two parts: raindrop diameters (D) and raindrop terminal velocity (v). 119 When precipitation particles pass the laser beam of the sensor, the beam is blocked off by the particles 120 equal to the diameters, and the output voltage will be reduced. If there is no particle passing through, 121 the voltage will then be recorded as maximum. The duration of the reducing signal will be used to 122 determine the terminal speed of a particle. Through the observation by the disdrometer, radar 123 reflectivity (Z), rainfall intensity (R) and kinetic energy (KE) are derived from D and v. Figure 2 Remote Sens. 2020, 12, 262 4 of 23 124 summarizes how the materials and methods and results are managed via a schematic.

125 Figure 1. (a) The location of Yulin Ecohydrological Station (green point) and the location of Yulin 126 RemoteFigure Sens. 1. 2019 (a), T11he, x FORlocation PEER of REVIEW Yulin Ecohydrological Station (green point) and the location of Yulin4 of 24 Meteorological Station (blue point) and the DEM (Digital Elevation Model) characteristics around the 127 Meteorological Station (blue point) and the DEM (Digital Elevation Model) characteristics around the 128 sites.sites The. The red red rectangle rectangle in in the the ChinaChina mapmap highlights the the location location of of Mu Mu Us Us Sandy Sandy Land Land;; (b) ( bthe) the OTT OTT

129 Parsivel-2Parsivel- disdrometer2 disdrometer and and the the surroundingsurrounding 4 TE525MM rain rain gauges gauges in in Yulin Yulin Ecohydrological Ecohydrological Station; Station; 130 (c)(c) vegetation vegetation cover cover situation situation in in Yulin Yulin EcohydrologicalEcohydrological Station.

131 132 FigureFigure 2.2. SchematicSchematic of the research research technical technical route route in in this this study study..

133 2.2.The Processingnth-moment Microphysical of the DSDDatasets can from be calculated Disdrometer as: Z 134 In order to process the calculation of the characteristic∞ variables of precipitation, the formulas M = DnN(D)dD 135 are derived as follows: n (2) 0 32 푛푖푗 32 푛푖푗 N(퐷푖) = ∑푗=1 = ∑푗=1 6 3 (1) Moreover the 6th-moment of the DSD is equal푉푗·훥퐷푖 to the radar퐴·훥푡·푣푗· reﬂectivity훥퐷푖 Z (mm m ): · − −1 −3 136 where N(퐷푖)(mm · m ) is the number concentration of raindrops per unit diameter interval for Z X32 ∞ 6 6 137 raindrops per unit volume with the diameter equal to 퐷푖 (the ith-bin of diameters of the spectra); Z = M6 = D N(D)dD = Di N(Di)∆Di (3) 138 퐴 = 5.4 × 10−4m2 is the sampling area0 scanned by the laseri=3 beam; 훥푡 = 60s is the sampling time

139 interval; 푣푗 is the raindrop terminal velocity of the jth-bin of velocities of the spectra; 훥퐷푖 is the class 140 spread of the ith-bin of diameters of the spectra. 141 The nth-moment of the DSD can be calculated as:

∞ 푛 ( ) 푀푛 = ∫0 퐷 푁 퐷 푑퐷 (2) 142 Moreover the 6th-moment of the DSD is equal to the radar reflectivity Z (mm6 · m−3):

∞ 6 ( ) ∑32 6 ( ) 푍 = 푀6 = ∫0 퐷 푁 퐷 푑퐷 = 푖=3 퐷푖 푁 퐷푖 훥퐷푖 (3) 143 where the 1st-bin and the 2nd-bin of diameters are not evaluated in the measurements of the OTT 144 Parsivel-2 because these two bins are out of the measurement range of the disdrometer, thus i starts 145 from 3 to 32. −1 146 The 푅total(i,j)(mm · h ) is the total rainfall per unit time in the 푛푖푗 grid: 1 3휋 푅 = 푣 · 푁(퐷 ) · 훥퐷 · 휋퐷3 · 3600 · 10−6 = 푣 퐷3푁(퐷 )훥퐷 (4) total(i,j) 푗 푖 푖 6 푖 5000 푗 푖 푖 푖 −1 147 The rainfall intensity R(mm · h ) is the summation of 푅total(i,j), and thus, can be calculated as: 32 32 3휋 3 푅 = ∑ (∑ 푣푗퐷푖 푁(퐷푖)훥퐷푖) (5) 5000 푖=3 푗=1

Remote Sens. 2020, 12, 262 5 of 23 where the 1st-bin and the 2nd-bin of diameters are not evaluated in the measurements of the OTT Parsivel-2 because these two bins are out of the measurement range of the disdrometer, thus i starts from 3 to 32. 1 The R (mm h− ) is the total rainfall per unit time in the n grid: total(i,j) · ij

1 3 6 3π 3 R = v N(D ) ∆D πD 3600 10− = v D N(D )∆D (4) total(i,j) j· i · i·6 i · · 5000 j i i i

1 The rainfall intensity R (mm h− ) is the summation of R , and thus, can be calculated as: · total(i,j)

32 32 3π X X R = ( v D3N(D )∆D ) (5) 5000 j i i i i=3 j=1

The content of liquid raindrop W (g m 3) is the mass of liquid raindrops per unit volume: · − Z X32 π 3 ∞ 3 π 3 3 W = 10− D N(D)dD = 10− D N(D )∆D (6) 6 · · 6 · · i i i 0 i=3

The gamma distribution of raindrop spectra is derived as:

N(D) = N Dµ exp ( ΛD) (7) 0 − where N (mm 1 µ m 3) is the intercept parameter and varies in dozens of orders of magnitudes [26]. 0 − − · − Thus, the normalized intercept parameter Nw (mm 1 m 3) is used by Testud et al. [27] to represent N , − · − 0 in order for the characteristics of the parameter of distribution of raindrop spectra can be calculated without any assumption about the DSD shapes:

44M5 N = 3 (8) w 4 6ρwM4

Nw is better than N0 for representing the raindrop concentration with certain raindrop sizes, as is not dependent on parameter µ. The mass-weighted mean diameter Dm(mm), and the rainfall shape parameter µ (dimensionless, related to rainfall types [28]), can be expressed as [29,30]:

4 + µ Dm = (9) Λ

 1   3  3  3  2  1  M  M  M   µ = 11 4 +  4  4 + 8 8 (10) M3  2  2  2   4  M M6 M M6 M M6 −  2 1 2 3 3 3 − M3M6 1 The slope parameter of gamma distribution Λ (mm − ) is dependent on parameter µ, and Seela et al. [31] concluded that µ-Λ relationships vary with diﬀerent precipitation types in diﬀerent areas. In this study, the Λ is expressed as a function of the 2nd and 4th-moment of the DSD and parameter µ [32]: " # 1 M2Γ(µ + 5) 2 Λ = (11) M4Γ(µ + 3)

2.3. Precipitation Types and Quality Control (QC) In this study, in order to analyze the characteristics of raindrop spectra in diﬀerent precipitation types, the precipitation data is classiﬁed into convective and stratiform rain based on the rainfall intensity [14]. Quality control is carried out in this study because there are errors in the measurement Remote Sens. 2020, 12, 262 6 of 23

of large diameters of raindrops using the disdrometer. In this study, raindrops larger than 6 mm in diameter were considered to have crushed during falling [33]. Therefore, raindrops larger than 6 mm in diameter are excluded in this study Figure3 illustrates the principle of classifying stratiform, convective, mixed-cloud rain and non-rainfall events. In this study, the eﬀective observation range of raindrop diameter is 0.25–6 mm. Raindrop spectrum data with the total number of raindrops less than 10 or rain intensity less than

Remote0.5 Sens. mm 2019/h,is 11 regarded, x FOR PEER as REVIEW noise [34,35]. 6 of 24

No Yes Raindrop spectrum data σ<1.5mm/h Stratiform rain

No No Σnij 10 Yes Non-rainfall event and R 5mm/h Mixed-cloud rain R 0.5mm/h No

σ>1.5mm/h Convective rain Yes Yes 171 172 Figure 3. Classifying stratiform, convective rain and non-rainfall events. This classification method is Figure 3. Classifying stratiform, convective rain and non-rainfall events. This classification method is 173 derived by Li et al. [36] and used in Mt. Huangshan (118°10′E, 30°07′N, 1351m a.s.l.), and is considered derived by Li et al. [36] and used in Mt. Huangshan (118 10 E, 30 07 N, 1351 m a.s.l.), and is considered 174 valid in this study to classify stratiform/convective rain. ◦ 0 ◦ 0 valid in this study to classify stratiform/convective rain. 175 The quality control principle is similar to the method used by Li et al. [36]. For an instantaneous The quality control principle is similar to the method used by Li et al. [36]. For an instantaneous 176 moment 푡푛 during a rainfall event, if the rain intensity R within the time range [푡푛 − 푁푠, 푡푛 + 푁푠] is > moment tn during a rainfall event, if the rain intensity R within the time range [tn Ns, tn + Ns] is > 177 5 mm/h and the standard deviation is >1.5 mm/h, the event is classified as a convective rainfall− event; 5 mm/h and the standard deviation is >1.5 mm/h, the event is classified as a convective rainfall event; if 178 if the rain intensity R within the time range [푡푛 − 푁푠, 푡푛 + 푁푠 ] satisfies 0.5 < R < 5 mm/h and the the rain intensity R within the time range [tn Ns, tn + Ns] satisfies 0.5 < R < 5 mm/h and the standard 179 standard deviation is <1.5 mm/h, then the event− is classified as a stratiform rainfall event. Other deviation is <1.5 mm/h, then the event is classified as a stratiform rainfall event. Other rainfall events 180 rainfall events are classified as mixed-cloud rain [37]. are classified as mixed-cloud rain [37]. 181 2.4. Derivation of KE-R Relationships 2.4. Derivation of KE-R Relationships 182 Rainfall kinetic energy (KE) can be calculated from the raindrop disdrometer, rainfall terminal Rainfall kinetic energy (KE) can be calculated from the raindrop disdrometer, rainfall terminal 183 velocity and raindrop size distribution. The total kinetic energy KE (J/(m3 · s)) can be derived as velocity and raindrop size distribution. The total kinetic energy KE (J/(m3 s)) can be derived as [25,38]: 184 [25,38]: ·

1 3 ∞ 휇Z+3+3푏 −훬퐷 KE = 휌휋1푎 푁0 ∫3 퐷 ∞ 푒µ+3+푑퐷3b ΛD (12) KE12= ρπa0N0 D e− dD (12) 12 0 185 where a = 3.78 and b = 0.67 are constant parameters [39]. In arid or semi-arid areas, most of the where a = 3.78 and b = 0.67 are constant parameters [39]. In arid or semi-arid areas, most of the 186 precipitation is of weak or moderate levels and Marshall et al. [40] concluded that 푁0 in the N 187 expressionprecipitation of 푁(퐷 is) ofisweak almost or fixed moderate to 0.08 levels cm −4 and. The Marshall parameter et al.x is [40 defined] concluded as: that 0 in the expression 4 of N(D) is almost ﬁxed to 0.08 cm− . The parameter x is deﬁned as: 푥 = 휇 + 4 + 3푏 = 휇 + 6.01 (13) x = µ + 4 + 3b = µ + 6.01 (13) 188 From Equations (12) and (13), the KE can be further expressed as: 3 ∞ 3 From Equations (12) and (13),휌휋푎 the푁0 KE can푥−1 be−푡 further휌휋푎 expressed푁0Γ(푥) as: KE = 푥 ∫ 푡 푒 푑푡 = 푥 (14) 12훬 0 12훬 3 Z 3 ρπa N0 ∞ x 1 t ρπa N0Γ(x) 189 The expression of Λ is: KE = x t − e− dt = x (14) 12Λ 0 12Λ Λ = 4.1푅−0.21 (15) The expression of Λ is: 0.21 190 which is commonly used in the calculation of KEΛ-R =relationships4.1R− in many studies[41–43], and: (15) 3 휌휋푎 푁0Γ(푥) KE = · 푅0.21푥 (16) 12 · 4.1푥 191 The parameter 휂 is defined as:

휌휋푎3푁 휂 = 0 (17) 12 192 and is constant. Then: 휂Γ(푥) KE = · 푅0.21푥 (18) 4.1푥

Remote Sens. 2020, 12, 262 7 of 23

which is commonly used in the calculation of KE-R relationships in many studies [41–43], and:

3 ρπa N0Γ(x) KE = R0.21x (16) 12 4.1x · · The parameter η is deﬁned as: 3 ρπa N0 η = (17) 12 and is constant. Then: Remote Sens. 2019, 11, x FOR PEER REVIEW ηΓ(x) 7 of 24 KE = R0.21x (18) 4.1x · 193 Therefore, the empirical formula of the relationship between KE and R with the variable Therefore, the empirical formula of the relationship between KE and R with the variable parameter 194 parameter x for the semi-arid area is derived. x for the semi-arid area is derived.

195 3. Results

196 3.1. Data after Quality Control 197 InIn this this study,study, 8184 8184 recordsrecords areare selected selected as as rainfall rainfall events, events, including including 7388 7388 stratiform stratiform and 796 198 convective data. The amou amountnt of observed mix mixed-clouded-cloud rain is zero. Figure 44 showsshows thethe frequencyfrequency 199 accumulation curvecurve ofof rainfall rainfall intensity intensity recorded. recorded. The The average averageR of푅̅ theof the recorded recorded data data is 2.3 is mm2.3 /mm/hh (the 200 calculated(the calculated average averageR includes 푅̅ includes only rainy only hours,rainy hours as shown, as shown in Section in Section 2.3), and 2.3 the), and data the with data rainfall with 201 intensityrainfall intensity less than less 5 mm than/h 5 is mm/h more thanis more 90% than of the 90% total of the time total of rainfalltime of data.rainfall data.

1400 100

90 1200 80

1000 70

Frequency/% 60 800 50

Counts 600 40

400 30

20 200 10

0 0 0 5 10 15 20 25 30 35 R/(mm·h-1) 202 203 Figure 4. 4. FrequencyFrequency distribution distribution of rain of rates rain calculated rates calculated from the fromwhole theOTT whole Parsivel OTT-2 disdrometer Parsivel-2 204 disdrometerdatasets. datasets. A division of the rainfall data into different seasons (spring from March to May, Summer from 205 A division of the rainfall data into different seasons (spring from March to May, Summer from June to August, Autumn from September to November and Winter from December to February) and 206 June to August, Autumn from September to November and Winter from December to February) and rainfall types (stratiform and convective rain) acquired by the OTT Parsivel-2 is reported in Table1. 207 rainfall types (stratiform and convective rain) acquired by the OTT Parsivel-2 is reported in Table 1. The results shown in Table1 reflect the trend of precipitation change in this region with di fferent 208 The results shown in Table 1 reflect the trend of precipitation change in this region with different seasons. The frequency of raindrop spectra data recorded in summer is the highest (with 7019 records), 209 seasons. The frequency of raindrop spectra data recorded in summer is the highest (with 7019 followed by autumn (4230 records), spring (3387 records) and winter (only 116 records). In spring, 210 records), followed by autumn (4230 records), spring (3387 records) and winter (only 116 records). In summer and autumn, the total time of stratiform rainfall events Ts is higher than the total time of 211 spring, summer and autumn, the total time of stratiform rainfall events 푇푠 is higher than the total convective rainfall events Tc, which reflects the precipitation characteristics of semi-arid areas [44]. 212 time of convective rainfall events 푇푐, which reflects the precipitation characteristics of semi-arid areas 213 [44]. The percentage of stratiform rain is from small to large summer (85.9%), spring (93.5%) and 214 autumn (95.5%). Winter is not considered when comparing the characteristics of different seasons 215 due to too few liquid precipitation data recorded. The percentage of convective rain, ordered from 216 small to large, is spring (4.5%), autumn (6.5%) and summer (14.1%). In summer the R varies most and 217 has the highest standard deviation of 2.8 mm/h. However, the percentage of rainfall time over the 218 seasons is ordered from small to large, are spring (1.4%), autumn (1.7%) and summer (3.0%).

219 Table 1. Disdrometer-measured data of different seasons: total time with recorded data, the 220 percentage of stratiform and convective rain and percentage of different ranges of rainfall intensity; 221 maximum and average rainfall intensity, and standard deviation of rainfall intensity. 222

Remote Sens. 2020, 12, 262 8 of 23

The percentage of stratiform rain is from small to large summer (85.9%), spring (93.5%) and autumn (95.5%). Winter is not considered when comparing the characteristics of diﬀerent seasons due to too few liquid precipitation data recorded. The percentage of convective rain, ordered from small to large, is spring (4.5%), autumn (6.5%) and summer (14.1%). In summer the R varies most and has the highest standard deviation of 2.8 mm/h. However, the percentage of rainfall time over the seasons is ordered from small to large, are spring (1.4%), autumn (1.7%) and summer (3.0%).

Table 1. Disdrometer-measured data of diﬀerent seasons: total time with recorded data, the percentage of stratiform and convective rain and percentage of diﬀerent ranges of rainfall intensity; maximum and average rainfall intensity, and standard deviation of rainfall intensity.

Autumn Winter Spring Summer Rainfall Characteristics (September– (December– (March–May) (June–August) November) February) Total time with data recorded T total 3387 7019 4230 116 (min) Total time of stratiform rain Ts (min) 1813 3431 2126 18 Total time of convective rain T c 86 563 147 - (min) Percentage of stratiform rain 95.5 85.9 93.5 100 Ts/(Ts + TC) (%) Percentage of convective rain 4.5 14.1 6.5 - Tc/(Ts + Tc) (%) Percentage of rainfall time over the 1.4 3.0 1.7 0 season (%) ≈ Maximum rainfall intensity 1 12.6 33.7 21.2 1.1 Rmax (mm h− ) · 1 Average R (mm h− ) 2.0 2.6 2.0 0.7 · 1 Median Rm (mm h− ) 1.9 1.9 1.6 0.7 · Precipitation Accumulation P total 76.7 236.9 105.9 - * (mm) Standard deviation of rainfall 1 1.6 2.8 1.8 0.15 intensity R (mm h− ) · T 1 /(T + T )(%) 60.3 58.8 66.4 100 0.5–2 mm h− s C · T 1 /(T + T )(%) 35.1 27.1 27.1 - 2–5 mm h− s C · T 1 /(T + T )(%) 4.2 11.3 6.0 - 5–10 mm h− s C · T 1 /(T + T )(%) 0.4 2.8 0.5 - >10 mm h− s C · * The rainfall accumulation is not calculated in winter because of the inclusion of solid precipitation (e.g., snow).

Weak and moderate rainfalls (with rainfall intensity satisfying 0.5 < R < 5 mm/h) account for the largest proportion of rainfalls in each season, and data satisfying R > 5 mm/h in summer is of the highest percentage of total rainfall time in the season (11.3%). The Rmax is 33.7 mm/h in summer, 21.2 mm/h in autumn and 12.6 mm/h in spring. The R and Ptotal in summer are also the highest (2.6 mm/h and 236.9 mm, respectively), while the difference in R between spring (2.0 mm/h) and autumn (2.0 mm/h) is not significant. The difference in Rm between spring (1.9 mm/h) and summer (1.9 mm/h) is not significant.

3.2. Microphysical Characteristics of Precipitation in Different Seasons Figure5 is the distribution of di fferent diameters with varying velocities obtained in different seasons. In spring, summer and autumn, the majority of raindrop particles are in an area close to the theoretical curve proposed by Beard [45]; in winter, the data is accumulated in low levels of both v and D. Data are overall lying over the theoretical curve in spring, summer and autumn; in winter, however, the velocities are underestimated compared to the theoretical curve in winter. This is because the type of rainfalls during winter was mainly snow (regarded as solid rainfalls) and could cause deviation in call speed, and the raindrop data with D > 6 mm are excluded as shown in Section 2.3. Remote Sens. 2020, 12, 262 9 of 23 Remote Sens. 2019, 11, x FOR PEER REVIEW 9 of 24

12 7.0% 12

) ) 7.0%

-1 -1 Spring Beard Summer Beard 6.0% 6.0%

(m·s (m·s 10 10

5.0% 5.0% 8 8

4.0% 4.0% 6 6 3.0% 3.0% 4 4 2.0% 2.0%

2 1.0% 2 1.0%

0.0% 0.0% 0 2 4 6 0 2 4 6 (a) D (mm) (b) D (mm) 12 7.0% 12 7.0%

)

-1 Autumn Beard -1 Winter Beard 10 6.0% 10 6.0%

(m·s

v 5.0% 5.0% 8 8

4.0% 4.0% 6 6 3.0% 3.0% 4 4 2.0% 2.0%

2 1.0% 2 1.0%

0.0% 0.0% 0 2 4 6 0 2 4 6 240 (c) D (mm) (d) D (mm) 241 FigureFigure 5. Plots 5. Plotsof measured of measured raindrop raindrop terminal velocity-diameter velocity-diameter relationships relationships in diﬀerent in different seasons. The seasons. red curve is derived by Beard [45] in 1976, giving the relationships between v and D, and used as the 242 The red curve is derived by Beard [45] in 1976, giving the relationships between v and D, and used as reference line for the v-D distribution in each season (a) spring; (b) summer; (c) autumn; (d) winter. 243 the reference line for the v-D distribution in each season (a) spring; (b) summer; (c) autumn; (d) winter.

Figure6 shows the histogram of Dm and log10Nw in different seasons and precipitation types. 244 FigureThe yearly 6 show averages theDm histogramand log10Nw of areDm 1.41 and and log 3.9110Nw mm, in respectively. different seasons The average andDm precipitationof stratiform types. 245 The yea(convective)rly average rain Dm from and small log10 toNw large are is 1.41 1.38 and mm 3.91 (1.46 mm mm), respectively. in summer, 1.46 The mm average (1.52 mm) Dm in of spring stratiform 246 (convective)and 1.51 rain mm from (1.57 mm)small in to autumn. large is However, 1.38 mm there (1.46 is lessmm) variation in summer, in average 1.46 logmm10Nw (1.52data mm) among in spring the three seasons. The average log10Nw of stratiform rain from small to large is 3.88 mm in summer, 247 and 1.51 mm (1.57 mm) in autumn. However, there is less variation in average log10Nw data among 3.89 mm in autumn and 3.92 in spring. However, the maximum of the average log10Nw of convective 248 the threerain seasons is 4.28 in. summer.The average This reflects log10Nw the micro-physicalof stratiform characteristicsrain from small of rainfall to large in Yulin is 3.88 area: mm according in summer, 249 3.89 mmto thein autumn results shown and in3.92 Section in spring 3.1, the. However, average rainfall the intensitymaximum is larger of the in average summer thanlog10 inNw spring of convective and 250 rain isautumn. 4.28 in According summer. to This Equation reflects (5), the the rain micro intensity-physical is related characteristics to raindrop diameter of rainfall and DSD. in Yulin The area: 251 accordingaverage to theDm resultsof different shown precipitation in Section types 3.1, inthe di ffaverageerent seasons rainfall shows intensity that for is stratiform larger in rain, summerR is than 252 in springaffected and moreautumn. by the According raindrop diameter; to Equation for convective (5), the rain,rain Rintensityis affected is more related by DSD. to raindrop The average diameter 253 and DSD.value The of Dm averageis slightly Dm less of than different that of in southernprecipitation China (1.46types mm) in [ different10]. seasons shows that for Besides the average value, standard deviation and skewness of different Dm and log Nw were 254 stratiform rain, R is affected more by the raindrop diameter; for convective rain, R is10 affected more also calculated. The standard deviation of Dm in stratiform and convective rain among different 255 by DSDseasons. The average varies from value 0.19 of mm Dm to 0.26is slightly mm. The less skewness than that of Dmof inand southernNw in stratiform China ( and1.46 convective mm) [10]. 256 Besiderain ares the less average than 0 in value, spring standard and autumn, deviation illustrating and the skewness frequency of of different the data below Dm and the Dmlogmean10Nw were 257 also calculated.(Nw mean)is The less standardthan data above deviation the Dm ofmean Dm(Nw in meanstratiform). However, and the convective skewness ofrainDm amongand Nw differentin 258 seasonsstratiform varies from and convective 0.19 mm rain to 0.26 in summer mm. The are larger skewness than 0, of illustrating Dm and the Nw frequency in stratiform of the data and below convective the Dm (Nw ) is more than data above the Dm (Nw ). 259 rain are less thanmean 0 in springmean and autumn, illustrating themean frequencymean of the data below the Dm mean (Nw 260 mean) is less than data above the Dm mean (Nw mean). However, the skewness of Dm and Nw in stratiform 261 and convective rain in summer are larger than 0, illustrating the frequency of the data below the Dm 262 mean (Nw mean) is more than data above the Dm mean (Nw mean). 263

Remote Sens. 2020, 12, 262 10 of 23 Remote Sens. 2019, 11, x FOR PEER REVIEW 10 of 24

50.0 50.0 45.0 Stratiform 45.0 Convective 40.0 Mean = 1.46 40.0 35.0 35.0 Mean = 1.52 Stdev = 0.21 30.0 Mean = 3.92 30.0 Stdev = 0.22 Mean = 4.16 Skew = -0.32

25.0 Stdev = 0.30 25.0 Skew = -0.16 Stdev = 0.22 20.0 Skew = -0.39 20.0 Frequency/% Skew = -0.16

15.0 Frequency/% 15.0 10.0 10.0 5.0 5.0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 D/mm log N /mm D/mm log N /mm (a) 10 w (b) 10 w 50.0 50.0 45.0 Stratiform 45.0 Convective 40.0 40.0 35.0 Mean = 1.38 35.0 Mean = 1.46 30.0 Stdev = 0.23 Mean = 3.88 30.0

Stdev = 0.26 25.0 Skew = 0.11 Stdev = 0.32 25.0 Mean = 4.28

Frequency/% 20.0 20.0 Skew = 0.05 Stdev = 0.21

Skew = 0.27 Frequency/% 15.0 15.0 Skew = 0.03 10.0 10.0 5.0 5.0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 D/mm log N /mm log N /mm (c) 10 w D/mm (d) 10 w 50.0 50.0 45.0 Stratiform 45.0 Convective 40.0 40.0 Mean = 1.51 35.0 35.0 Mean = 1.57 Stdev = 0.19 Mean = 3.89 30.0 30.0 Stdev = 0.21 Mean = 4.27

Skew = -0.45 25.0 Stdev = 0.28 25.0 Stdev = 0.18

Frequency/% Skew = -0.10 Frequency/% 20.0 Skew = -0.23 20.0 Skew = -0.17 15.0 15.0 10.0 10.0 5.0 5.0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 D/mm (e) log10Nw/mm D/mm (f) log10Nw/mm

264 Figure 6. Frequency histogram of mass-weighted median diameter Dm and the denary logarithm of 265 NwFigurein diff 6.erent Frequency precipitation histogram types of and mass di-ffweightederent seasons median calculated diameter from Dmthe and data the measureddenary logarithm by OTT of 266 Parsivel-2.Nw in different (a) Histogram precipitation in stratiform types and rain different in spring; seasons (b) calculated Histogram from in convective the data measured rain in spring; by OTT 267 (c)Par Histogramsivel-2. ( ina) stratiformHistogram rain in stratiform in summer; rain (d) in Histogram spring; (b in) convectiveHistogram rainin convective in summer; rain (e) Histogramin spring; (c) 268 inHistogram stratiform rainin stratiform in autumn; rain (f) in Histogram summer; in(d convective) Histogram rain in convective in autumn. rain The in average summer; value, (e) standardHistogram 269 deviationin stratiform and skewness rain in autumn; are also (f given) Histogram for Dm inand convectiveNw in each rain plot. in autumn. The average value, standard 270 deviation and skewness are also given for Dm and Nw in each plot. Figure7 shows the Nw-R relationships in different seasons and precipitation types. The base-10 d 271 logarithmFigure of Nw 7 showis useds the to Nw fit the-R relationships relationship curvesin different log10 Nwseasons= cR and, in precipitation which c and dtypes. are parameters The base-10 272 fittedlogarithm by measured of Nw is data. used For to fit the the error relationship bars in each curves panel, logR10Nwin the = cR ranged, in which (0.5, 5) c (forand stratiformd are parameters rain) 273 arefitted divided by measured into nine data intervals. For evenly,the error and bars in in the each range panel, (5, 35) R in (for the convective range (0.5, rain) 5) (for are stratiform divided into rain) 1 274 fiveare intervals divided (5into< Rnine< 10, intervals 10 < R evenly,< 15, 15 and< R in< the20, range 20 < R (5,< 35)25 and(for Rconvective>25 mm hrain)− ), andare divided error bars into · 275 arefive used intervals for each (5 interval.< R < 10, 10 The < R error < 15, bars 15 < for R < each 20, 20 interval < R < are25 and based R >25 on themm·h mean−1), and value error of Rbarsand are 276 log10usedNw for, with each the interval.1 Stdev The (standard error bars deviation), for each interval respectively. are based A significance on the mean analysis value of of R fitting and log10 resultsNw, ± 277 iswith also proposedthe ±1 Stdev [46 ].(standard The p-values deviation), in each res panelpectively. of Figure A significance7 are derived analysis from the of fitting fitting results tests of is the also 278 powerproposed function. [46]. TheThe p-valuesp-values show in each that panel thefits of Figure for stratiform 7 are derived rain are from statistically the fitting relevant tests of and the sound power 279 (shownfunction in. Figure The p7-a,c,e).values When show comparing that the fits the for disparity stratiform in precipitation rain are statistically types, parameters relevant and c and sound d 280 have(shown a smaller in Figure range 7 in(a), variability (c), (e)). When in diff erentcomparing seasons. the Figure disparity7a,c,e inindicate precipitation that for types, stratiform parameter rain,s c 281 theand di ffderence have a of smaller parameter range c in among variability different in different seasons seasons. ranges inFigure 3.73–3.79 7 (a), ((c)p < and0.05). (e) indicate However, that the for 282 parameterstratiform c rain for convective, the difference rain of varies parameter in a larger c among range different of 3.86–4.14 seasons (p < ranges0.1). Forin 3.73 each–3.7 season,9 (p < the0.05). 283 parameterHowever, a ofthe stratiform parameter rain c for is smallerconvective than rain that varies of convective in a larger rain. range The of di ff3.86erence-4.14 in (p parameter < 0.1). For d each is 284 smallseason, among the diparameterfferent seasons, a of stratiform and the d rain of stratiform is smaller rain than is that larger of thanconvective that of convectiverain. The difference rain. in 285 parameter d is small among different seasons, and the d of stratiform rain is larger than that of 286 convective rain.

Remote Sens. 2019, 11, x FOR PEER REVIEW 11 of 24 Remote Sens. 2020, 12, 262 11 of 23

5.5 5.5 Stratiform (Spring) Convective (Spring) Error bar Error bar 5.0 5.0

4.5 4.5

N 4.0 N 4.0

10 0.04

log 3.5 log 3.5 log10Nw=3.86R 0.07 p < 0.1 3.0 log10Nw=3.78R 3.0 p < 0.05 2.5 2.5

0 1 2 3 4 5 6 0 10 20 30 -1 (a) R/(mm·h-1) (b) R/(mm·h ) 5.5 5.5 Stratiform (Summer) Convective (Summer) Error bar 5.0 5.0 Error bar

4.5 4.5

N 4.0 N 4.0

10 10 0.02 log10Nw=4.14R

log 3.5 log 3.5 p < 0.05 3.0 0.08 3.0 log10Nw=3.73R 2.5 p < 0.05 2.5

0 1 2 3 4 5 6 0 10 20 30 -1 -1 (c) R/(mm·h ) (d) R/(mm·h ) 5.5 5.5 Stratiform (Autumn) Convective (Autumn) Error bar 5.0 5.0 Error bar

4.5 4.5

N 4.0 N 4.0

log 3.5 log 3.5

3.0 0.07 log N =4.04R0.03 log10Nw=3.79R 3.0 10 w p < 0.05 2.5 p < 0.05 2.5

0 1 2 3 4 5 6 0 10 20 30 -1 -1 287 (e) R/(mm·h ) (f) R/(mm·h ) 288 FigureFigure 7. 7.Nw Nw-R-Rrelationships relationships for for di differentfferent precipitation precipitation types types in in di differentfferent seasons. seasons The. The fitted fitted power power 289 formulaformula based based on on the theleast-squares least-squares methodmethod is also shown shown in in each each plot plot:: (a ()a stratiform) stratiform rain rain in inspring; spring; (b) 290 (bconvective) convective rain rain in in spring; spring; (c (c) )stratiform stratiform rain rain in in summer; summer; (d) convectiveconvective rainrain in in summer; summer; ( e()e) stratiform stratiform 291 rainrain in in autumn autumn (f ()f convective) convective rain rain in in autumn. autumn.

292 3.3.3.3. Z-R Z-R Relationships relationships inin DiDifferentfferent RainfallRainfall EventsEvents 293 ThreeThree rainfall rainfall events events were were selected selected to illustrateto illustrate the ditheff erencesdifferences between between the data the measureddata measured by OTT by 294 Parsivel-2OTT Parsivel Disdrometer-2 Disdrometer and four and TE525MM four TE525MM Rainfall Rainfall Gauges. Gauges. The three The events three are, events respectively, are, respectively chosen , 295 fromchosen each from season, each regarding season, regarding their representation their representation of different of levels different of rainfall levels of intensity rainfall (all intensity of the three(all of 296 eventsthe three last events for > 4h last and for include > 4h and stratiform include stratiform and convective and convective records). records).

Remote Sens. 2020, 12, 262 12 of 23

Table2 shows the precipitation characteristics of these rainfall events. S /C records show the relative rates of amounts of the stratiform and the convective records during the selected rainfall events, for which Event 1, 2 and 3 are 662%, 888% and 753%, respectively. The results correspond to the average rainfall intensity R of each rainfall event. Event 2 is with the least R (2.42 mm h 1), while · − Event 1 is with the highest R (3.07 mm h 1). · − Table 2. Precipitation characteristics of selected three rainfall events.

Rainfall 1 1 Rainfall Time Season R /(mm h− ) * Rg/(mm h− ) ** Duration S/C Records Number d · · Event 1 19–20 April 2019 Spring 3.36 3.51 4 h 30 min 225/34 Event 2 3 August 2019 Summer 1.65 1.78 12 h 30 min 897/101 1 September Event 3 Autumn 3.09 3.22 4 h 241/32 2018 * Derived from disdrometer-measured raindrop spectra. See in Equation (5). ** Obtained by the four rainfall gauges and averaged.

Figure8 shows the di fference in Z-R relationships of the three rainfall events of spring, summer and autumn, and the results are Z = 109.6R2.1 (Event 1), Z = 119.0R1.8 (Event 2) and Z = 78.3R1.9 (Event 3). The parameter a of each of the three rainfall events is less than the parameter a of the default Z-R relationship [47](Z = 300R1.4, where parameter a is equal to 300). Parameter b in Z = aRb has only slight difference among different rainfall events, and ranges in 1.8–2.1 (p < 0.05). This is consistent with previous studies [48–51], that parameter b in Z = aRb varies in the range of 1–2.87 (p < 0.05). The raindrop spectra have obvious changes for different precipitation types, causing the parameters of Z-R relationships to vary. It is clear that the Z-R relationships of rainfall events vary depending on the season and the precipitation types. The rainfall events with a higher S/C rate tend to have a higher average rainfall intensity. Therefore, precipitation estimates for different types should be treated as such. The results indicate that there is a need to utilize modified Z-R relationships in different seasons when calculating the rainfall intensity by the QPE method.

3.4. KE-R Relationships The rainfall kinetic energy KE and rainfall intensity R are calculated based on Equations (5) and (18), respectively. The KE-R relationships of stratiform rain in different seasons are derived in the form of a power function. The fitting results show the KE-R relationships satisfy the form of power function KE = ARm, in which A and m are parameters. Figure9 shows that the stronger the rainfall intensity is, the faster the rainfall kinetic energy tends to increase. The exponent of different power functions m varies from 1.45 to 1.82, in order from small to large, spring < autumn < summer. Parameter A has similar values in spring (equal to 8.56) and in summer (equal to 8.10), but in autumn the parameter A is 5.56. The value of the parameter A is closely related to the raindrop spectra [52]. The parameter A is also related to the median rainfall intensity Rm, which results in the decrease of A in autumn compared to spring and summer. Remote Sens. 2019, 11, x FOR PEER REVIEW 12 of 24

297 Table 2 shows the precipitation characteristics of these rainfall events. S/C records show the 298 relative rates of amounts of the stratiform and the convective records during the selected rainfall 299 events, for which Event 1, 2 and 3 are 662%, 888% and 753%, respectively. The results correspond to 300 the average rainfall intensity 푅̅ of each rainfall event. Event 2 is with the least 푅̅ (2.42 mm·h−1), while 301 Event 1 is with the highest 푅̅ (3.07 mm·h−1).

302 Table 2. Precipitation characteristics of selected three rainfall events.

Rainfall Rainfall time Season 푅̅̅̅d̅/(mm · 푅̅̅g̅/(mm · Duration S/C −1 Number h )* h−1)** records Event 1 19 Apr. – 20 Spring 3.36 3.51 4h30min 225/34 Apr. 2019 Event 2 3 Aug. 2019 Summer 1.65 1.78 12h30min 897/101 Event 3 1 Sep. 2018 Autumn 3.09 3.22 4h 241/32 303 * Derived from disdrometer-measured raindrop spectra. See in Equation (5). 304 ** Obtained by the four rainfall gauges and averaged. 305 306 Figure 8 shows the difference in Z-R relationships of the three rainfall events of spring, summer 307 and autumn, and the results are 푍 = 109.6푅2.1 (Event 1), 푍 = 119.0푅1.8 (Event 2) and 푍 = 78.3푅1.9 308 (Event 3). The parameter a of each of the three rainfall events is less than the parameter a of the default 309 Z-R relationship [47] (푍 = 300푅1.4, where parameter a is equal to 300). Parameter b in 푍 = a푅b has 310 only slight difference among different rainfall events, and ranges in 1.8-2.1 (p < 0.05). This is consistent 311 with previous studies [48–51], that parameter b in 푍 = a푅b varies in the range of 1–2.87 (p < 0.05). 312 The raindrop spectra have obvious changes for different precipitation types, causing the parameters 313 of Z-R relationships to vary. It is clear that the Z-R relationships of rainfall events vary depending on 314 the season and the precipitation types. The rainfall events with a higher S/C rate tend to have a higher 315 average rainfall intensity. Therefore, precipitation estimates for different types should be treated as 316 such. The results indicate that there is a need to utilize modified Z-R relationships in different seasons Remote Sens. 2020 12 317 when calculating the, ,rainfall 262 intensity by the QPE method. 13 of 23

60000

50000 19 Apr. - 20 Apr. 2019

)

-3 40000

·m

6 30000 z = 109.6R2.1 / (mm 20000 2 z R = 0.63 10000 p < 0.05 0

0 2 4 6 8 10 12 14 16 18 (a) R /(mm·h-1) 60000

50000 3 Aug. 2019

)

-3 40000

·m 6 30000 z = 119.0R1.8

Remote Sens. 2019, 11/ (mm 20000, x FOR PEER REVIEW R2 = 0.64 13 of 24

z 10000 p < 0.05

321 19 April to 20 April0 2019; (b) Z-R relationship of a rainfall event in summer, on 3 August 2019; (c) Z-

322 R relationship of 0a rainfall2 event 4in autumn,6 on 18 September10 2018;12 the fitted14 curves16 are18 derived based (b) R /(mm·h-1) 323 on the power60000 function, which are solid red curves in (a)–(c).

50000 1 Sep, 2018

)

324 3.4. KE-R Relationships-3 40000

·m 1.9 6 30000 z = 78.3R 325 The rainfall kinetic energy KE and rainfall intensity R areR2 = calculated 0.74 based on Equation (5) and

/ (mm 20000 p < 0.05 326 (18), respectively.z The KE-R relationships of stratiform rain in different seasons are derived in the 327 form of a power10000 function. The fitting results show the KE-R relationships satisfy the form of power 0 328 function KE = ARm, in which A and m are parameters. 0 2 4 6 8 10 12 14 16 18 318 329 Figure 9 shows that the stronger the rainfall(c) intensity is, the faster Rthe /(mm·h rainfall-1) kinetic energy 330 tends to increase. The exponent of different power functions m varies from 1.45 to 1.82, in order from Figure 8. Z-R relationships (Z = abRb) in three rainfall events. Each rainfall event is selected from 319 331Figure small 8. toZ- Rlarge relationships, spring < autumn (푍 = a<푅 summer.) in three Parameter rainfall A events. has similar Each value rainfalls in spring event (equal is selected to 8.56) from diﬀerent seasons (spring, summer and autumn). (a) Z-R relationship of a rainfall event in spring, from 320 332different and in seasons summer (spring, (equal tosummer 8.10), but and in autumn). autumn the (a )parameter Z-R relationship A is 5.56. of The a rainfall value ofevent the parameterin spring, Afrom 19 April to 20 April 2019; (b) Z-R relationship of a rainfall event in summer, on 3 August 2019; (c) Z-R 333 is closely related to the raindrop spectra [52]. The parameter A is also related to the median rainfall relationship of a rainfall event in autumn, on 1 September 2018; the ﬁtted curves are derived based on 334 intensitythe power Rm, function, which results which arein the solid decrease red curves of inA (ian– autumnc). compared to spring and summer.

400 Stratiform (Spring) Stratiform (Summer) Stratiform (Autumn) 600 Error bar 1000 Error bar Error bar

KE/J

KE/J KE/J 1.51 KE = 8.56R1.43 800 KE = 8.10R1.82 KE = 5.56R p < 0.05 p < 0.05 p < 0.05 400 600 200

400 200

200

0 0 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 0 1 2 3 4 5 6 (a) R/(mm·h-1) R/(mm·h-1) -1 335 (b) (c) R/(mm·h ) 336 FigureFigure 9. 9.KE- KER -curvesR curves ﬁtted fitted in di inﬀerent different seasons. seasons. Data of Data stratiform of stratiform rain in spring, rain in summer, spring, and summer, autumn and 337 areautumn analyzed. are (a analyzed.) KE-R relationship (a) KE-R inrelationship spring; (b) in KE- spring;R relationship (b) KE-R in relationship summer; (c) KE-in summer;R relationship (c) KE in-R 338 autumn.relationship For the in errorautumn. bars For in eachthe error panel, barsR in in the each range panel, (0.5, R 5)in arethe divided range (0.5, into 5) nine are intervalsdivided into evenly, nine 339 andintervals error bars evenly, are used and forerror each bars interval. are used The for error each bars interval. for each The interval error bars are for based each on interval the mean are value based of R and KE, with the 1 Stdev (standard deviation), respectively. 340 on the mean value of± R and KE, with the ±1 Stdev (standard deviation), respectively.

341 4. Discussion

342 4.1. Uncertainty Analysis of Disdrometer-Measured Data 343 Figure 10 shows the relationship between two different measurements on a daily scale. Each 344 point represents the total rainfall of a given day during the 1-year observation period. The abscissa is 345 the total measured rainfall of Parsivel-2, and the ordinate is the averaged total rainfall measured by 346 four TE525MM Gauges (data with both daily total rainfall greater than 1mm are taken for analysis). 347 The results show that the disdrometer-measured data demonstrates a good correlation with the 348 average rainfall gauge-measured data, and the deviation is mainly caused by the instrument 349 theoretical error in measurement of disdrometer and gauges (e.g., sampling error), which was 350 concluded by Tokay et al. [29]. The measured rainfall data of the disdrometer is suitable for this semi- 351 arid area.

Remote Sens. 2020, 12, 262 14 of 23

4. Discussion

4.1. Uncertainty Analysis of Disdrometer-Measured Data Figure 10 shows the relationship between two diﬀerent measurements on a daily scale. Each point represents the total rainfall of a given day during the 1-year observation period. The abscissa is the total measured rainfall of Parsivel-2, and the ordinate is the averaged total rainfall measured by four TE525MM Gauges (data with both daily total rainfall greater than 1mm are taken for analysis). The results show that the disdrometer-measured data demonstrates a good correlation with the average rainfall gauge-measured data, and the deviation is mainly caused by the instrument theoretical error in measurement of disdrometer and gauges (e.g., sampling error), which was concluded by TokayRemote Sens. et al. 2019 [29, ].11, The x FOR measured PEER REVIEW rainfall data of the disdrometer is suitable for this semi-arid area.14 of 24

100

y=1.14x-0.06 2 60 R =0.95

20 Gauge-measured total rainfall/(mm)

0 0 20 40 60 80 100 Disdrometer-measured total rainfall/(mm) 352 353 FigureFigure 10.10. Scatter plot of gauge-gauge- and disdrometer-measureddisdrometer-measured totaltotal rainfallrainfall onon aa dailydaily scale.scale. TheThe resultsresults 354 obtainedobtained byby thethe twotwo measurementmeasurement methods methods are are compared compared with with the the scatter scatter plot. plot. The The solid solid green green line line is 355 theis the fitted fitted result. result. Figure 11 shows the precipitation process of three rainfall events, with the calculated average 356 Figure 11 shows the precipitation process of three rainfall events, with the calculated average of of the data measured by four rainfall gauges. The determinate coefficient R2 of a linear relationship 357 the data measured by four rainfall gauges. The determinate coefficient R2 of a linear relationship between Parsivel Disdrometer and TE525MM Gauges is 0.68 for (a), 0.83 for (b) and 0.96 for (c). The 358 between Parsivel Disdrometer and TE525MM Gauges is 0.68 for (a), 0.83 for (b) and 0.96 for (c). The standard deviations of disdrometer-measured (gauge-measured) rainfall intensity in (a), (b) and (c) are 359 standard deviations of disdrometer-measured (gauge-measured) rainfall intensity in (a), (b) and (c) 1.37 mm/h (2.90 mm/h), 1.02 mm/h (1.43 mm/h) and 1.43 mm/h (2.46 mm/h), respectively. The standard 360 are 1.37 mm/h (2.90 mm/h), 1.02 mm/h (1.43 mm/h) and 1.43 mm/h (2.46 mm/h), respectively. The deviation of the disdrometer-measured data in each season is less than the gauge-measured data in the 361 standard deviation of the disdrometer-measured data in each season is less than the gauge-measured corresponding season. In order to further compare the difference between disdrometer-measured and 362 data in the corresponding season. In order to further compare the difference between disdrometer- gauges-measured data, the mean absolute error(MAE) and the root mean square error(RMSE) of the 363 measured and gauges-measured data, the mean absolute error(MAE) and the root mean square events are also given. Event 3 has the smallest MAE (0.69 mm h 1) and smallest RMSE (0.99 mm h 1) 364 error(RMSE) of the events are also given. Event 3 has the smallest· − MAE (0.69 mm·h−1) and smallest· − among the three events. This indicates that the disdrometer can potentially estimate the precipitation 365 RMSE (0.99 mm·h−1) among the three events. This indicates that the disdrometer can potentially with better performance during Event 3, according to the comparison with gauge-measured data. 366 estimate the precipitation with better performance during Event 3, according to the comparison with 367 gauge-measured data. 368

Remote Sens. 2020, 12, 262 15 of 23 Remote Sens. 2019, 11, x FOR PEER REVIEW 15 of 24

)

-1 10 OTT Parsivel-2 19 Apr. - 20 Apr. 2019 8 TE525MM Gauges (Average) / (mm·h 2 R R = 0.68 6 MAE=1.43 mm·h-1 -1 4 RMSE=1.88 mm·h

0 21:30 22:00 22:30 23:00 23:30 00:00 00:30 01:00 01:30 02:00 Time (a)

)

-1 10 OTT Parsivel-2 3 Aug. 2019 8 TE525MM Gauges (Average)

/ (mm·h 2 R R = 0.83 6 MAE=1.24 mm·h-1 -1 4 RMSE=1.05 mm·h

0 07:30 08:30 09:30 10:30 11:30 12:30 13:30 14:30 15:30 16:30 17:30 18:30 19:30Time

) (b)

-1 10 OTT Parsivel-2 1 Sep, 2018 8 TE525MM Gauges (Average)

/ (mm·h 2 R R = 0.96 6 MAE=0.69 mm·h-1 -1 4 RMSE=0.99 mm·h

0 15:00 15:30 16:00 16:30 17:00 17:30 18:00 18:30 19:00 Time (c) 369 Figure 11. The comparison of measurement results of OTT Parsivel-2 (orange solid lines) and four 370 Figure 11. The comparison of measurement results of OTT Parsivel-2 (orange solid lines) and four TE525MM gauges (green dotted lines, averaged) in 3 rainfall events. (a) a rainfall event in spring, from 371 TE525MM19–20 gauges April 2019; (green (b) adotted rainfall lines event, averaged) in summer, in on 3 3 rainfall August 2019;events. (c) ( aa rainfall)a rainfall event event in autumn, in spring, on from 372 19 April1 Septemberto 20 April 2018. 2019; (b)a rainfall event in summer, on 3 August 2019; (c)a rainfall event in autumn, 373 on 1 September 2018. The measuring range of Parsivel-2 is 0.25–6 mm, and it has been proved that the disdrometer has 374 Theerrors measuring in measuring range both of smallerParsivel and-2 largeris 0.25 diameters–6 mm, and of raindrops it has been in many proved studies that [53 the,54], disdrometer which have more accuracy in measuring mid-level raindrops in the spectra. Liu et al. [54] further explained 375 has errors in measuring both smaller and larger diameters of raindrops in many studies [53,54], which the algorithm of the disdrometer and concluded that the diﬀerences can be attributed to a certain error 376 have moreof rainfall accuracy amount in accumulation.measuring mid In all-level three raindrops measured events, in the whenspectra. the TE525MMLiu et al. Gauges-measured[54] further explained 377 the algorithmdata reaches of the itspeak disdrometer (at 0:30 in (a),and 19:00 concluded in (b), and that 18:30 the in (c)),differences the data measuredcan be attributed by gauges areto a all certain 378 error ofmore rainfall than theamount disdrometer-measured accumulation. data; In all and three when measured the TE525MM events, Gauges-measured when the dataTE525MM reaches itsGauges- 379 measuredminimum data reaches of the event its (atpeak 23:30 (at in 0:30 (a), atin 11:30 (a), in19:00 (b) andin (b), 15:00 and in (c)),18:30 the in data (c)), measured the data by measured gauges by 380 gaugesare are all all no more more than than the disdrometer-measureddisdrometer-measured data. data; As raindrop and when spectra the TE525MM data larger than Gauges 6 mm-measured are 381 data reachestreated as its solid minimum rainfall and of eliminated, the event the (at peak 23:30 value in of (a), the at disdrometer 11:30 in is (b) lessened. and 15:00 This is in consistent (c)), the data with the results in Section 3.3 that in Event 1 the disdrometer- and gauge-measured R data indicates a 382 measured by gauges are all no more than the disdrometer-measured data. As raindrop spectra data signiﬁcant gap (2.94 and 3.51 mm h 1, respectively). Since the measured raindrop spectra data larger · − 383 larger than 66 mm mm have are beentreated removed, as solid and rainfall raindrops and of eliminated, large diameter the are peak often value accompanied of the disdrometer by heavy is 384 lessened.rain This [25], is it consistent is speculated with that the this results is the reasonin Section why 3.3 the that peak in of Event rainfall 1 intensitythe disdrometer obtained- by and the gauge- 385 measuredraindrop 푅̅ data disdrometer indicates is smallera significant than the gap value (2.94 measured and 3.51 by mm rain· gauges.h−1, respectively). Since the measured 386 raindrop spectra data larger than 6 mm have been removed, and raindrops of large diameter are often 387 accompanied by heavy rain [25], it is speculated that this is the reason why the peak of rainfall 388 intensity obtained by the raindrop disdrometer is smaller than the value measured by rain gauges.

389 4.2. Comparison of Different Z-R Relationships 390 In this section, the Z-R relationships of different experiment areas are compared, as shown in 391 Table 3. The Z-R relationships calculated in different studies vary with different measurement 392 methods, different study areas and rainfall time and types. Previous studies have shown that 393 parameter a has a very wide range of values. This is consistent with Kang [55] that the range of 394 parameter a is 10–1200. The parameters a and b vary with different seasons and locations, as well as 395 with the measurement methods. It can be concluded that there is a great variation in the parameters 396 a and b at different places, and Z-R relationships should be determined according to different regions. 397 The above analysis also shows that it is of great significance to further improve the accuracy of radar 398 rain measurement inversion and to further study the microphysical characteristics of rainfall [56].

Remote Sens. 2020, 12, 262 16 of 23

4.2. Comparison of Different Z-R Relationships In this section, the Z-R relationships of different experiment areas are compared, as shown in Table3. The Z-R relationships calculated in different studies vary with different measurement methods, different study areas and rainfall time and types. Previous studies have shown that parameter a has a very wide range of values. This is consistent with Kang [55] that the range of parameter a is 10–1200. The parameters a and b vary with different seasons and locations, as well as with the measurement methods. It can be concluded that there is a great variation in the parameters a and b at different places, and Z-R relationships should be determined according to different regions. The above analysis also shows that it is of great significance to further improve the accuracy of radar rain measurement inversion and to further study the microphysical characteristics of rainfall [56].

Table 3. Results of Z-R relationships in diﬀerent study areas.

Precipitation Measurement Z-R Reference [57–62] Location Rainfall Type Time/Season Method relationships Jiangsu, Eastern Zhang et al., 1992 July in 1981 Digital Radar Z = 60R2.3 Heavy rain China Marshall et al., Summer in 1946 Canada MHF Radar Z = 190R1.72 Thunderstorm 1947 15 July–7 August Leizhou Peninsula, Parsivel Z = 269R1.54 Convective rain Chen et al., 2008 in 2007 China Disdrometer Z = 178R1.58 Mixed-cloud rain Kototabang, West 2D-Video Marzuki et al., 2013 2006–2007 Z = 136R1.26 Stratiform rain Sumatra, Indonesia Disdrometer Hazenberg et al., Cévennes-Vivarais OTT/Parsivel 14 September 2006 Z = 79R1.52 Stratiform rain 2011 region, France Disdrometer October in 1951– Blanchard, 1953 Hawaii, USA Filter-paper Z = 31R1.71 Thunderstorm August in 1952 Sivaramakrishnan, November in 1958 India Filter-paper Z = 67.6R1.94 Thunderstorm 1961

4.3. Sensitive Analysis of the Formula of KE-R Relationships Many previous studies [22,52,63] have shown that parameters of the KE-R relationship are highly sensitive to DSD, and for parameters closely related to DSD characteristics, such as µ, the change in µ represents the difference in rainfall characteristics, which can affect the value of the parameters. Equation (18) indicates the KE-R relationships under the impact of parameter x. The parameter A and m are used to simplify the KE-R formula (expressed as Equation (18)) and are defined as:

ηΓ(x) A = (19) 4.1x m = 0.21x (20) in which A and m are functions of parameter x, thus, A and m are affected by raindrop microphysical characteristics and the environmental conditions. The parameter x (known as a linear variation with the parameter µ according to the Equation (13)) varies differently due to the different regions, different time periods. Therefore, sensitivity analysis is conducted on the parameters A and m with the change of parameter x, in order to indicate the applicability of the KE-R relationships formula (derived as Equation (18)) under different rainfall conditions. S1 and S2 were defined as the parameters to analyze the sensitivity of A and m with the change of x, and the influence of change on parameter x on the KE-R relationships is further shown. The definition of sensitive parameters S1 and S2 are derived in Equations (21) and (22): ∆A/A dA x S1 = lim ( ) = (21) ∆x 0 ∆x/x dx ·A → ∆m/m dm x S2 = lim ( ) = = 1 (22) ∆x 0 ∆x/x dx ·m → Remote Sens. 2020, 12, 262 17 of 23

in which S1 (S2) is the ratio of the change rate of parameter A (parameter m) to the change rate of parameter x. It is obvious from Equation (20) that the parameter m is proportional to parameter x, thus, S2 is a constant, as shown in Equation (22). The sensitive parameter S1 is further calculated of stratiform and convective rain obtained via disdrometer in diﬀerent seasons, and the results are summarized in Table4.

Table 4. Sensitive analysis results for parameter A with x of diﬀerent precipitation types in diﬀerent seasons and the total year.

Spring Summer Autumn Total Year

S1(Stratiform) 4.10 4.68 3.83 4.29 S1(Convective) 3.88 3.79 3.97 3.88

Table4 shows the results of the sensitivity analysis for A with x of different precipitation types in different seasons. The sensitivity of parameter A varies with different precipitation types and seasons. In the whole-year scale, the S1 is 4.29 of stratiform rain and 3.88 of convective rain, which indicates the parameter A of stratiform rain is more sensitive to the change of parameter x in the total year. The S1 of stratiform rain in spring and summer is also more than that of convective rain in corresponding seasons. However, the S1 of stratiform rain (3.83) is less than that of convective rain (3.97) in autumn, and the S1 reaches its lowest in autumn among three seasons. The parameter x is affected by changes in environmental factors and rainfall types [64], and in autumn, the sensitivity of parameter A with the change of x is lower than in spring or summer. This explains the obvious decrease of parameter A in autumn compared with the other two seasons calculated in Section 3.4. For convective rain in different seasons, the S1 from small to large is summer (3.79) < spring (3.88) < autumn (3.97). According to Teng [65], the values of µ for raindrop spectra are between 1 and 4, and different µ − values correspond to different rainfall characteristics. The larger the µ, the more likely it is to cause convective rain. In order to analyze the KE-R relationship when the rainfall shape parameter µ takes different values, the KE-R relationship curve of different values of µ was therefore made based on Equation (18), as shown in Figure 12a–f. The rule of this study is that both parameter A and m increase with the increase of µ. Figure 12g further shows the relationship among KE-R-µ. At a certain R, KE increases as µ increases. At the same rainfall intensity, the rainfall kinetic energy is also related to the rainfall type: the more the rainfall type is inclined to convective rain, the greater the rainfall kinetic energy will be, which can be explained by the Equation (18) and corresponds to the conclusions in other studies [66,67]. KE-R relationship changes with the change of the parameter x, according to Equation (18). From Equation (13), the parameter x can be calculated with a linear function from parameter µ. As discussed in Section 2.2, the parameter µ is correlated with the rainfall types; thus, the KE can be interpreted by the rainfall types according to Equation (18). In addition, different fitted formulas obtained in previous studies can be approximated with Equation (18) by changing the parameter µ (see Table A1), and the specific results can be approximated by Figure A1. This shows that the derived theoretical formula (Equation (18)) in this study is universal in various regions; however, whether the formula can be directly used to further analyze the KE-R relationship in other semi-arid areas should be further discussed in the future. Remote Sens. 2020, 12, 262 18 of 23 Remote Sens. 2019, 11, x FOR PEER REVIEW 18 of 24

100 2500

·s))

3 80 μ = -1 2000 μ = 2

3 60 1500 40 1000

KE / (J/(m 20 KE=2.35x1.05 KE / (J/(m 500 KE=7.18x1.68 0 0

0 5 10 15 20 25 30 0 5 10 15 20 25 30 -1 -1 (a) R / (mm·h ) (d) R / (mm·h ) 250 10000

·s)) 200 μ = 0 ·s)) μ = 3 3 8000

3 150 6000 100 4000

KE / (J/(m 1.26 50 KE=2.87x KE / (J/(m 2000 KE=14.0x1.89 0 0

0 5 10 15 20 25 30 0 5 10 15 20 25 30 -1 (b) R / (mm·h ) (e) R / (mm·h-1)

700 600 40000

·s)) μ = 1 ·s)) μ = 4

3 500 3 30000 400 300 20000 200

KE / (J/(m 1.47 KE=4.20x KE / (J/(m 10000 100 KE=30.8x2.10 0 0

0 5 10 15 20 25 30 0 5 10 15 20 25 30 R / (mm·h-1) -1 453 (c) (g) (f) R / (mm·h ) 454 FigureFigure 12. The 12. RThe-KE Rrelationships-KE relationships under under different diﬀ erentvalues values of shape of shape factors factors μ. Theµ .curves The curves are derived are derived 455 basedbased on Equation on Equation (18). (a) (18). KE (a-R) KE-relationshipR relationship for μ for= -1;µ =(b) 1;KE (b-R) KE-relationshipR relationship for μ for= 0;µ (c)= 0;KE (c-R) KE-R − 456 relationshiprelationship for μ for= 1;µ (d)= 1; KE (d-R) KE-relationshipR relationship for μ for= 2;µ (e)= 2; KE (e-)R KE-relationshipR relationship for μ for= 3;µ (f)= 3; KE (f-)R KE-R 457 relationshiprelationship for μ for= 4; µ(g)= KE4; (g)-R- KE-μ relationship.R-µ relationship.

458 5. Conclusions5. Conclusions 459 CharacteristicsCharacteristics of raindrop of raindrop size distributions size distributions (DSDs) (DSDs) are important are important for improving for improving the accuracy the accuracy 460 of radarof radar reflectivity reflectivity-rainfall-rainfall intensity intensity (Z-R) ( Z-Rrelationships) relationships in remote in remote sensing sensing (QPE) (QPE) and the and estimation the estimation 461 of soilof erosivity. soil erosivity. In this In study, this study, an OTT an OTTParsivel Parsivel-2-2 Disdrometer Disdrometer is used is usedto measured to measured raindrop raindrop spectra spectra 462 from from10 August 10 August 2018 2018to 10 toAugust 10 August 2019 2019in Yulin in Yulin Ecohydrological Ecohydrological Station, Station, Shaanxi Shaanxi Province, Province, China. China. 463 The precipitationThe precipitation events events obtained obtained are classified are classified as stratiform as stratiform and convective and convective rain based rain based on the on rain thefall rainfall 464 intensityintensity classifying classifying processes. processes. The conclusions The conclusions are summarized are summarized as follows. as follows. 465 (1) The(1) Thecharacteristics characteristics of of microphysical microphysical variables variables (the (the mass mass median median diameter diameterDm Dmand and the raindropthe 466 raindropsize distributionsize distributionNw) Nw were) were analyzed. analyzed. The The average averageDm Dmof di offferent different precipitation precipitation types types in di infferent 467 differentseasons seasons shows show thats that forstratiform for stratiform rain, rain rainfall, rainfall intensity intensityR is R aff isected affected more more by the byaverage the average raindrop 468 raindropdiameter diameterDm; forDm convective; for convective rain, Rrainis a, ffRected is affected more bymore DSD. by TheDSD. yearly The averageyearly averageDm and Dm log 10andNw are 469 log10Nw1.41 are and 1.41 3.91 and mm, 3.91 respectively. mm, respectively. The average The averageDm of Dm stratiform of stratiform (convective) (convective) rain from rain smallfrom small to large is 470 to large1.38 is mm 1.38 (1.46 mm mm) (1.46 in mm) summer, in summer, 1.46 mm 1.46 (1.52 mm mm) (1.52 in mm) spring in and spring 1.51 and mm 1.51 (1.57 mm mm) (1.57 in autumn. mm) in This 471 autumn.reflects This the reflects semi-arid the semi climate-arid rainfall climate characteristics rainfall characteristics in Yulin Station. in Yulin Station. 472 (2) The(2) variance The variancess of rainfall of rainfall microphysical microphysical characteristics characteristics in different in different precipitation precipitation types types and and 473 seasonsseasons are related. are related. The distribution The distribution of rainfall of rainfall terminal terminal velocity velocity-diameter-diameter (v-D) (spectrav-D) spectra of spring, of spring, 474 summersummer and autumn and autumn is concentrated is concentrated near nearthe theoretical the theoretical curve curve derived derived by Beard by Beard [45]. [The45]. ba These- base-1010 d 475 logarithmlogarithm of Nw of isNw usedis usedto fit tothe fit relationship the relationship curves curves log10 logNw10 =Nw cRd=, incR which, in which c and c d and are dparameters are parameters 476 fittedfitted by measured by measured data. data. The Thedifference difference in parameter in parameter d is d small is small among among different different seasons seasons (0.07 (0.07–0.08–0.08 for 477 for stratiformstratiform rain rain and and 0.02 0.02–0.04–0.04 for for convective convective rain rain),), and and the the d of d ofstratiform stratiform rain rain is islarger larger than than that that of 478 of convectiveconvective rain rain.. 479 (3) The(3) Z The-R relationshipsZ-R relationships of different of di ffrainfallerent rainfallevents in events spring, in summer spring, and summer autumn and in autumn this semi inthis 480 arid areasemi-arid are derived area are in derivedthis study. inthis The study. parameter The parametera is larger in a is stratiform larger in stratiformrain than in rain convective than in convective rain, 481 whilerain, the parameter while the parameter b is larger bin is convective larger in convective rain, showing rain, the showing impact the of impactdifferent of rainfall different types rainfall on a types 482 and b.on The a and results b. The show results that showthe estimation that the estimation of different of seasons different should seasons be should treated be, respectivel treated, respectively.y. 483 (4) The(4) theoretical The theoretical formula formula of KE of-R KE- relationshipsR relationships for stratiform for stratiform precipitation precipitation in semi in semi-arid-arid areas areas is ( ) 휂Γ(푥)ηΓ x 0.210.21푥 x 484 is derivedderived (KE (KE= = · 푅x R , where, where the the parameter parameter 휂 ηis isconstant constant and and 푥x==휇µ++6.6.0101),) ,which which indicates indicates the 4.1푥 4.1 · 485 the characteristicscharacteristics of of precipitation andand environmentalenvironmental conditions conditions represented represented by by parameter parameterµ. Thisμ. This formula 486 formulagives gives a general a general expression expression of the KE- of R therelationships KE-R relationships and is simple and to is use simple because to use the parameters because the are all 487 parametersderived are from all the derived parameter fromµ . the The parameter sensitivity μ analysis. The sensitivity results show analysis that the results parameter showA for that stratiform the 488 parameterrain is A more for stratiform sensitive to rain the is change more ofsensitive different to precipitation the change of types different and environmental precipitation types conditions and in a 489 environmental conditions in a total year. The closer the precipitation types are to convective rain, the

Remote Sens. 2020, 12, 262 19 of 23 total year. The closer the precipitation types are to convective rain, the larger the KE is at the same level of R. By changing the parameter µ, different empirical formulas obtained in previous studies can be approximated with the derived theoretical formula (Equation (18)). In summary, the DSD characteristics of Yulin Station were obtained and the results can help to understand the microphysical characteristics of precipitation and have a strong impact on the mechanism of soil erosivity in the semi-arid area. Additionally, the formula of KE-R relationships provides a convenient way to fit with different rainfall events in semi-arid areas by adjusting its parameters. But the results are not conclusive because of the limited sample records of different rainfall types. In this study, data in winter is not deeply investigated, e.g., the solid precipitation processes should be further considered and analyzed. Moreover, the impact of environmental conditions on the parameter A and m is still not well understood. In the future, the influence of environmental factors on the parameters in Z-R relationships should be further discussed.

Author Contributions: Conceptualization, Z.X.; Data curation, Z.X. and H.L.; Formal analysis, Z.X.; Funding acquisition, H.Y.; Methodology, Z.X. and H.Y.; Project administration, H.Y. and H.L.; Resources, H.L. and Q.H.; Supervision, H.Y.; Writing—original draft, Z.X.; Writing—review & editing, H.Y. All authors have read and agreed to the published version of the manuscript. Funding: This research was partially supported by funding from the National Natural Science Foundation of China (Grant Nos. 51622903, 51979140 and 51809147), the National Program for Support of Top-notch Young Professionals, and the Program from the State Key Laboratory of Hydro-Science and Engineering of China (Grant No. 2017-KY-01). APC was funding by the National Natural Science Foundation of China (Grant No. 51622903). Conﬂicts of Interest: The authors declare no conﬂict of interest.

Appendix A Table A1 shows different fitting formulas of KE-R relationships in different research areas. KE- R formulas obtained in different regions vary, including polynomial, exponential, logarithm and other forms. In order to reflect the universality of the theoretical formulas introduced in this paper, KE-R relationships are obtained by changing equations based on Equation (18) to approximate the formulas given in different studies. The deterministic coefficient is used as the index to evaluate the approximation results, and the fitting results ensure that the deterministic coefficient of the two is greater than 0.99 for each reference listed in Table A1. The scatter points obtained by the KE-R relationship obtained by Equation (18) are described, and then, the linear fitting is performed with the points traced based on the original equation; results are shown in Figure A1. The abscissa is the KE obtained by changing different equations in this paper, and the ordinate is the relation obtained by different researchers. The red line is the fitting result. The rainfall intensity corresponding to the horizontal and vertical coordinates of each point on the line is the same. Figure A1 shows that the deterministic coefficients of different results are all above 0.99, indicating that Formula (18) can approximate the KE-R results obtained in different studies by changing the parameter values. Since the equation can be fixed only by determining the parameters, it has the value of further generalization.

Table A1. Diﬀerent formulas of KE-R relationships.

KE-R Relationships References KE-R Relationships (Originally Derived) Form µ (Based on Equation (18)) KE = 11.32R + 0.5546R2 0.5009 Carter et al., 1974 [68] Polynomial KE = 4.38R1.49 1.09 10 2R3 + 0.126 10−4R4 × − × − McGregor et al., 1976 [69] KE = R(27.3 + 21.68e 0.048R 41.26e 0.072R) Index KE = 4.86R1.53 1.30 − − − Wischmeier et al, 1978 [70] KE = R(11.9 + 8.73logR) Logarithm KE = 4.62R1.51 1.20 Bollinne et al., 1984 [71] KE = 12.32 R + 0.56 R2 Polynomial KE = 4.79R1.53 1.27 · · Steiner et al., 2000 [67] KE = 11R1.25 Power KE = 4.86R1.53 1.30 Sanchez-Moreno et al., KE = (10.09 + 12 logR) R Logarithm KE = 4.83R1.53 1.29 2012 [72] · Remote Sens. 2019, 11, x FOR PEER REVIEW 20 of 24

McGregor et al， KE = 푅(27.3 + 21.68푒−0.048푅 Index KE = 4.86푅1.53 −0.072푅 1.30 1976 [69] − 41.26푒 )

Wischmeier et al, KE = 푅(11.9 + 8.73log푅) Logarithm KE = 4.62푅1.51 1.20 1978 [70]

Bollinne et al., KE = 12.32 · 푅 + 0.56 · 푅2 Polynomial KE = 4.79푅1.53 1.27 1984 [71]

Steiner et al， KE = 11푅1.25 Power KE = 4.86푅1.53 1.30 2000 [67]

Sanchez-Moreno KE = (10.09+12logR)·R Logarithm KE = 4.83푅1.53 1.29 et al., 2012 [72]

530 Remote Sens. 2020, 12, 262 20 of 23

1000 (a) Carter et al, 1974 (b) McGregor et al, 1976 (c) Wischmeier et al., 1978 800 800 800

600 600 600

400 400 400

) y=0.94x y=0.98x y=0.97x -1 R2=0.998 R2=0.994 R2=0.991 200 200 200

·s)

10000 0 0 200 400 600 800 200 400 600 800 200 400 600 800 (d) Bollinne et al., 1984 (e) Steiner et al 2000 KE/(J·(m 800 800 ， 800 (f) Sanchez- Moreno et al., 2012 600 600 600

400 400 400 y=1.08x y=0.99x y=0.97x R2=0.994 R2=0.999 R2=0.993 200 200 200

0 0 0 0 200 400 600 800 1000 200 400 600 800 1000 200 400 600 800 1000 3 -1 531 KE/(J·(m ·s) ) 方程 y = a + b*x 方程 y = a + b*x 方程 y = a + b*x 绘图 B 绘图 B 绘图 B 532 Figure A1. The approximated results of KE-R relationships derived by different权重不加权 studies are as follows: 不加权 Figure A1. The权重 approximated results of KE-权重R relationships不加权 derived by截距 diﬀerent0 ± -- studies are as follows: 533 (a)–((af–) f) are are the the linear linear relationships relationships betweenbetween KE- KER-Robtained obtained by by this this paper paper and and KE- R KEobtained-R obtained by di ﬀ byerent 534 differentstudies studies shown shown in Table in A1Table, respectively. A1, respectively.

535 ReferencesReferences

536 1. 1.Ding,Ding, B.; Yang, B.; Yang, K.; K.;Qin, Qin, J.; Wang, J.; Wang, L.; L.;Chen, Chen, Y.; Y.;He, He, X. The X. The dependence dependence of precipitation of precipitation types types on surface on surface 537 elevationelevation and and meteorological meteorological conconditionsditions and and its its parameterization. parameterization.J. Hydrol. J. Hydrol.2014 , 5132014, 154–163., 513, 154 [CrossRef–163, ] 538 2.doi:10.1016/j.jhydrol.2014.03.038.Chen, B.J.; Yang, J.; Pu, J.P. Statistical Characteristics of Raindrop Size Distribution in the Meiyu Season 539 2. Chen,Observed B.J.; Yang, in Eastern J.; Pu, China.J.P. StatisticalJ. Meteorol. Characteristics Soc. Jpn. 2013 of ,Raindrop91, 215–227. Size [CrossRef Distribution] in the Meiyu Season 540 3.ObservedDas, S.K.; in Eastern Konwar, China. M.; Chakravarty, J. Meteorol. Soc. K.; Deshpande, Jpn. 2013, 91 S.M., 215 Raindrop–227, doi:10.2151/jmsj.2013 size distribution of-208. diff erent cloud types 541 3. Das,over S.K.; the Konwar, Western M.; Ghats Chakravarty, using simultaneous K.; Deshpande, measurements S.M. Raindrop from Micro-Rain size distribution Radar and of disdrometer. different cloudAtmos. 542 typesRes. over2017 the, 186 Western, 72–82. Ghats [CrossRef using] simultaneous measurements from Micro-Rain Radar and disdrometer. 543 4.AtmosHazenberg,. Res. 2017 P.;, 186 Leijnse,, 72–82, H.; doi:10.1016/j.atmosres.2016.11.003. Uijlenhoet, R. The impact of reflectivity correction and accounting for raindrop 544 4. Hazenberg,size distribution P.; Leijnse, variability H.; Uijlenhoet, to improve R. The precipitation impact of reflectivity estimation correction by weather and radar accounting for an extreme for raindrop low-land 545 sizemesoscale distribution convective variability system. to improveJ. Hydrol. precipitation2014, 519 ,estimation 3410–3425. by [CrossRef weather] radar for an extreme low-land 546 5.mesoscaleJanapati, convective J.; Seela, B.K.;system. Reddy, J. Hydrol. M.V.; 2014 Reddy,, 519 K.K.;, 3410 Lin,–3425, P.-L.; doi:10.1016/j.jhydrol.2014.09.057. Rao, T.N.; Liu, C.-Y. A study on raindrop size distribution variability in before and after landfall precipitations of tropical cyclones observed over southern India. J. Atmos. Sol.-Terr. Phys. 2017, 159, 23–40. [CrossRef] 6. Hazenberg, P.; Yu, N.; Boudevillain, B.; Delrieu, G.; Uijlenhoet, R. Scaling of raindrop size distributions and classification of radar reflectivity–rain rate relations in intense Mediterranean precipitation. J. Hydrol. 2011, 402, 179–192. [CrossRef] 7. Waldvogel, A. TheN0Jump of Raindrop Spectra. J. Atmos. Sci. 1974, 31, 1067–1078. [CrossRef] 8. Schönhuber, M.; Randeu, W.L.; Baptista, J.P.V.P. Application of the 2D-video-distrometer for weather radar data inversion. Phys. Chem. Earth Part B 2000, 25, 1037–1042. [CrossRef] 9. Liu, X.; He, B.; Zhao, S.; Hu, S.; Liu, L. Comparative measurement of rainfall with a precipitation micro-physical characteristics sensor, a 2D video disdrometer, an OTT PARSIVEL disdrometer, and a rain gauge. Atmos. Res. 2019, 229, 100–114. [CrossRef] 10. Zhang, A.; Hu, J.; Chen, S.; Hu, D.; Liang, Z.; Huang, C.; Xiao, L.; Min, C.; Li, H. Statistical Characteristics of Raindrop Size Distribution in the Monsoon Season Observed in Southern China. Remote Sens. 2019, 11, 432. [CrossRef] 11. Raupach, T.H.; Berne, A. Correction of raindrop size distributions measured by Parsivel disdrometers, using a two-dimensional video disdrometer as a reference. Atmos. Meas. Tech. 2015, 8, 343–365. [CrossRef] 12. Bringi, V.N.; Chandrasekar, V.; Hubbert, J.; Gorgucci, E.; Randeu, W.L.; Schoenhuber, M. Raindrop size distribution in different climatic regimes from disdrometer and dual-polarized radar analysis. J. Atmos. Sci. 2003, 60, 354–365. [CrossRef] Remote Sens. 2020, 12, 262 21 of 23

13. Seliga, T.A.; Bringi, V.N. Potential use of the radar differential reflectivity measurements at orthogonal polarizations for measuring precipitation. J. Appl. Meteorol. 1976, 15, 69–76. [CrossRef] 14. Sulochana, Y.; Rao, T.N.; Sunilkumar, K.; Chandrika, P.; Raman, M.R.; Rao, S.V.B. On the seasonal variability of raindrop size distribution and associated variations in reflectivity—Rainrate relations at Tirupati, a tropical station. J. Atmos. Sol.-Terr. Phys. 2016, 147, 98–105. [CrossRef] 15. Wen, G.; Xiao, H.; Yang, H.L.; Bi, Y.H.; Xu, W.J. Characteristics of summer and winter precipitation over northern China. Atmos. Res. 2017, 197, 390–406. [CrossRef] 16. Carollo, F.G.; Ferro, V.; Serio, M.A. Predicting rainfall erosivity by momentum and kinetic energy in Mediterranean environment. J. Hydrol. 2018, 560, 173–183. [CrossRef] 17. Ji, L.; Chen, H.N.; Li, L.; Chen, B.J.; Xiao, X.; Chen, M.; Zhang, G.F. Raindrop Size Distributions and Rain Characteristics Observed by a PARSIVEL Disdrometer in Beijing, Northern China. Remote Sens. 2019, 11, 1479. [CrossRef] 18. Angulo-Martínez, M.; Barros, A.P. Measurement uncertainty in rainfall kinetic energy and intensity relationships for soil erosion studies: An evaluation using PARSIVEL disdrometers in the Southern Appalachian Mountains. Geomorphology 2015, 228, 28–40. [CrossRef] 19. Carollo, F.G.; Serio, M.A.; Ferro, V.; Cerdà, A. Characterizing rainfall erosivity by kinetic power - Median volume diameter relationship. Catena 2018, 165, 12–21. [CrossRef] 20. Meshesha, D.T.; Tsunekawa, A.; Tsubo, M.; Haregeweyn, N.; Tegegne, F. Evaluation of kinetic energy and erosivity potential of simulated rainfall using Laser Precipitation Monitor. Catena 2016, 137, 237–243. [CrossRef] 21. Abd Elbasit, M.A.M.; Yasuda, H.; Salmi, A.; Anyoji, H. Characterization of rainfall generated by dripper-type rainfall simulator using piezoelectric transducers and its impact on splash soil erosion. Earth Surf. Process. Landf. 2010, 35, 466–475. [CrossRef] 22. Serio, M.A.; Carollo, F.G.; Ferro, V. Raindrop size distribution and terminal velocity for rainfall erosivity studies. A review. J. Hydrol. 2019, 576, 210–228. [CrossRef] 23. Fan, Y.; Chen, Y.; Wei, J. An Analysis of Drought Features in Shaanxi Province. J. Xi’an Univ. Technol. 1996, 12, 200–206. 24. Li, Y.; Cao, Z.; Long, H.; Liu, Y.; Li, W. Dynamic analysis of ecological environment combined with land cover and NDVI changes and implications for sustainable urban–rural development: The case of Mu Us Sandy Land, China. J. Clean. Prod. 2017, 142, 697–715. [CrossRef] 25. Xie, Z.; Yang, H.; Lv, H. Study on the relationship between rainfall kinetic energy and rainfall intensity based on raindrop spectrum observations. Water Resour. Hydropower Eng. 2019. under review. 26. Ulbrich, C.W. Natural Variations in the Analytical Form of the Raindrop Size Distribution. J. Clim. Appl. Meteorol. 1983, 22, 1764–1775. [CrossRef] 27. Testud, J.; Oury, S.; Black, R.A.; Amayenc, P.; Dou, X.K. The concept of “normalized” distribution to describe raindrop spectra: A tool for cloud physics and cloud remote sensing. J. Appl. Meteorol. 2001, 40, 1118–1140. [CrossRef] 28. Ulbrich, C.W.; Atlas, D. Rainfall microphysics and radar properties: Analysis methods for drop size spectra. J. Appl. Meteorol. 1998, 37, 912–923. [CrossRef] 29. Tokay, A.; Wolff, D.B.; Petersen, W.A. Evaluation of the New Version of the Laser-Optical Disdrometer, OTT Parsivel2. J. Atmos. Ocean. Technol. 2014, 31, 1276–1288. [CrossRef] 30. Zhang, H.; HE, H.; Zhang, Y.; Zeng, Q.; Bai, S. Parameter Characteristics Analysis of Raindrop Spectrum Fitting Models in Nanjing. Meteorol. Environ. Sci. 2017, 40, 77–84. 31. Seela, B.K.; Janapati, J.; Lin, P.L.; Wang, P.K.; Lee, M.T. Raindrop Size Distribution Characteristics of Summer and Winter Season Rainfall Over North Taiwan. J. Geophys. Res.-Atmos. 2018, 123, 11602–11624. [CrossRef] 32. Zhang, G.; Vivekanandan, J.; Brandes, E.A. The Shape–Slope Relation in Observed Gamma Raindrop Size Distributions: Statistical Error or Useful Information? J. Atmos. Ocean. Technol. 2003, 20, 1106–1119. [CrossRef] 33. Low, T.B.; List, R. Collision, Coalescence and Breakup of Raindrops. Part I: Experimentally Established Coalescence Efficiencies and Fragment Size Distributions in Breakup. J. Atmos. Sci. 1982, 39, 1591–1606. [CrossRef] 34. Tokay, A.; Bashor, P.G. An Experimental Study of Small-Scale Variability of Raindrop Size Distribution. J. Appl. Meteorol. Clim. 2010, 49, 2348–2365. [CrossRef] Remote Sens. 2020, 12, 262 22 of 23

35. Zhou, L.M.; Zhang, H.S.; Wang, J.; Wang, Q.; Chen, X.L. Raindrop Spectral Charcteristics of Mixed-cloud Precipitation in Shandong Province. Meteorol. Sci. Technol. 2010, 38, 73–77. 36. Li, H.; Yin, Y.; Shan, Y.; Jin, Q. Statistical Characteristics of Raindrop Size Distribution for Stratiform and Convective Precipitation at Different Altitudes in Mt. Huangshan. Chin. J. Atmos. Sci. 2018, 42, 268–280. 37. Chen, C.; Yin, Y.; Chen, B.J. Raindrop Size Distribution at Different Altitudes in Mt. Huang. Trans. Atmos. Sci. 2015, 38, 388–395. [CrossRef] 38. Kinnell, P. Rainfall Intensity-Kinetic Energy Relationships for Soil Loss Prediction 1. Soil Sci. Soc. Am. J. 1981, 45, 153–155. [CrossRef] 39. Atlas, D.; Ulbrich, C.W. Path-and area-integrated rainfall measurement by microwave attenuation in the 1–3 cm band. J. Appl. Meteorol. 1977, 16, 1322–1331. [CrossRef] 40. Marshall, J.S.; Palmer, W.M.K. The Distribution of Raindrops with Size. J. Meteorol. 1948, 5, 165–166. [CrossRef] 41. Uijlenhoet, R.; Stricker, J. A consistent rainfall parameterization based on the exponential raindrop size distribution. J. Hydrol. 1999, 218, 101–127. [CrossRef] 42. Lane, J.; Hackathorn, M.; Kewley, J.; Madore, M.; May, M.; Briggs, C.; DeLeon Springs, F. A method for estimating 3-D spatial variations of rainfall drop size distributions over remote ocean areas. Presented at the Fifth International Conference on Remote Sensing for Marine and Coastal Environments, San Diego, CA, USA, 5–7 October 1998; p. 7. 43. Ochou, A.D.; Nzeukou, A.; Sauvageot, H. Parametrization of drop size distribution with rain rate. Atmos. Res. 2007, 84, 58–66. [CrossRef] 44. Li, P.; Sun, X.; Zhao, X. Analysis of precipitation and potential evapotranspiration in arid and semi-arid area of China in recent 50 years. J. Arid Land Res. Environ. 2012, 7, 57–63. 45. Beard, K.V. Terminal Velocity and Shape of Cloud and Precipitation Drops Aloft. J. Atmos. Sci. 1976, 33, 851–864. [CrossRef] 46. Hunt, W.F.; Jarrett, A.R.; Smith, J.T.; Sharkey, L.J. Evaluating bioretention hydrology and nutrient removal at three field sites in North Carolina. J. Irrig. Drain. Eng. 2006, 132, 600–608. [CrossRef] 47. Hunter, S.M. WSR-88D radar rainfall estimation: Capabilities, limitations and potential improvements. Natl. Weather Dig. 1996, 20, 26–38. 48. Austin, P.M. Relation between Measured Radar Reflectivity and Surface Rainfall. Mon. Weather Rev. 1987, 115, 1053–1071. [CrossRef] 49. Sauvageot, H. Rainfall Measurement by Radar—A Review. Atmos. Res. 1994, 35, 27–54. [CrossRef] 50. Wilson, J.W.; Brandes, E.A. Radar measurement of rainfall—A summary. Bull. Am. Meteorol. Soc. 1979, 60, 1048–1060. [CrossRef] 51. Zhang, P.; Du, B.; Dai, T.P. Radar Meteorology; China Meteorological Press: Beijing, China, 2001. 52. Petan, S.; Rusjan, S.; Vidmar, A.; Mikos, M. The rainfall kinetic energy-intensity relationship for rainfall erosivity estimation in the mediterranean part of Slovenia. J. Hydrol. 2010, 391, 314–321. [CrossRef] 53. Battaglia, A.; Rustemeier, E.; Tokay, A.; Blahak, U.; Simmer, C. PARSIVEL Snow Observations: A Critical Assessment. J. Atmos. Ocean. Technol. 2010, 27, 333–344. [CrossRef] 54. Liu, X.C.; Gao, T.C.; Liu, L. A comparison of rainfall measurements from multiple instruments. Atmos. Meas. Tech. 2013, 6, 1585–1595. [CrossRef] 55. Kang, L. A Study on Dynamic Correction for Radar-Derived Quantitation Precipitation Estimation Based on the Optimal Z-I Relationship; Lanzhou University: Lanzhou, China, 2014. 56. Yuan, X.; Ni, G.; Pan, A.; Wei, L. NEXRAD Z-R Power Relationship in Beijing Based on Optimization Algorithm. J. Chin. Hydrol. 2010, 30, 1–6. 57. Zhang, P.; Dai, T.; WANG, D.; Lin, B. Derivation of The Z-I Relationship by Optimization and The Accuracy in The Quantitative Rainfall Measurement. Sci. Meteorol. Sin. 1992, 12, 333–338. 58. Marshall, J.S.; Langille, R.C.; Palmer, W.M.K. Measurement of Rainfall by Radar. J. Meteorol. 1947, 4, 186–192. [CrossRef] 59. Chen, Q.; Niu, S.; Zhang, Y.; Xu, F. Z-R Relationship from the Particle Size and Velocity (Parsivel) optical disdrometer and its Application in Estimating Areal Rainfall. In Proceedings of the 2008 2nd International Conference on Bioinformatics and Biomedical Engineering, Shanghai, China, 16–18 May 2008. Remote Sens. 2020, 12, 262 23 of 23

60. Marzuki; Randeu, W.L.; Kozu, T.; Shimomai, T.; Hashiguchi, H.; Schönhuber, M. Raindrop axis ratios, fall velocities and size distribution over Sumatra from 2D-Video Disdrometer measurement. Atmos. Res. 2013, 119, 23–37. [CrossRef] 61. Blanchard, D.C. Raindrop Size-Distribution in Hawaiian Rains. J. Meteorol. 1953, 10, 457–473. [CrossRef] 62. Sivaramakrishnan, M.V. Studies of raindrop size characteristics in different types of tropical rain using a simple recorder. Indian J. Meteorol. Geophys. 1961, 12, 189–217. 63. Yakubu, M.L.; Yusop, Z.; Fulazzaky, M.A. The influence of rain intensity on raindrop diameter and the kinetics of tropical rainfall: Case study of Skudai, Malaysia. Hydrolog. Sci. J. 2016, 61, 944–951. [CrossRef] 64. Takeuchi, D. Characterization of raindrop size distributions. In Proceedings of the Conference on Cloud Physics and Atmospheric Electricity, Issaquah, WA, USA, 31 July–4 August 1978; pp. 154–161. 65. Teng, X. Sensitivity of the W Band Airborne Cloud Radar Reflectivity Factor Z to Cloud Parameters; Nanjing University of Information Science and Technology: Nanjing, China, 2011. 66. Park, S.W.; Mitchell, J.K.; Bubenzer, G.D. An analysis of splash erosion mechanics. In Proceedings of the ASAE 1980 Winter Meeting, Chicago, IL, USA, 4 December 1980; p. 27. 67. Steiner, M.; Smith, J.A. Reflectivity, rain rate, and kinetic energy flux relationships based on raindrop spectra. J. Appl. Meteorol. 2000, 39, 1923–1940. [CrossRef] 68. Carter, C.E.; Greer, J.D.; Braud, H.J.; Floyd, J.M. Raindrop Characteristics in South Central United-States. Trans. ASAE 1974, 17, 1033–1037. [CrossRef] 69. McGregor, K.C.; Mutchler, C.K. Status of the R factor in northern Mississippi. In Soil Erosion: Prediction and Control, Soil Conservation Soc. Amer.; Nature: UK, 1976; pp. 135–142. 70. Wischmeier, W.H.; Smith, D.D. Predicting Rainfall Erosion Losses: A Guide to Conservation Planning; Science and Education Administration, US Department of Agriculture: Washington, WA, USA, 1978; Volume 537. 71. Bollinne, A.; Florins, P.; Hecq, P.; Homerin, D.; Renard, V. Etude de l’énergie des pluies en climat tempéré océanique d’Europe Atlantique. Zeitschrift für Geomorphologie 1984, 49, 27–35. 72. Sanchez-Moreno, J.F.; Mannaerts, C.M.; Jetten, V.; Loffler-Mang, M. Rainfall kinetic energy-intensity and rainfall momentum-intensity relationships for Cape Verde. J. Hydrol. 2012, 454, 131–140. [CrossRef]

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).