Statistical Characteristics of Raindrop Size Distribution in the Meiyu ...

Journal of the Meteorological Society of Japan, Vol. 91, No. 2, pp. 215̶227, 2013 DOI:10.2151/jmsj.2013-208

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Statistical Characteristics of Raindrop Size Distribution in the Meiyu Season Observed in Eastern China Baojun CHEN School of Atmospheric Sciences, Nanjing University, Nanjing, China

Jun YANG School of Atmospheric Physics, Nanjing University of Information Science and Technology, Nanjing, China

and Jiangping PU Institute of Meteorology, PLA University of Science and Technology, Nanjing, China (Manuscript received 7 November 2011, in final form 27 December 2012)

Abstract Characteristics of raindrop size distribution (DSD) during the Meiyu season are studied using ground-based disdrometer measurements carried out in eastern China (Nanjing) from 2009 to 2011. The observational spectra are divided into convective and stratiform types. The results show that the histograms of the logarithm of the generalized intercept parameter (log10 NW ) and mass-weighted mean diameter of raindrops (Dm ) are negatively and positively skewed, respectively, for both convective and stratiform rain. The absolute value of the skewness coefficient is higher for convective rain than for stratiform rain, in particular for the log10NW distribution. The mean log10NW and Dm values are 3.80 and 1.71 mm for convective rain and 3.45 and 1.30 mm for stratiform rain, respectively. The shape (μ)̶slope (Λ) relationship of the gamma distribution and the radar reflectivity (Z)̶rain rate (R) relationship are also derived for 1.21 convective rain. The Z̶R relationship is found to be Z = 368R . The interpretation of the statistical parameters obtained in this study and possible mechanisms that yield difference and similarity in comparison with those in previous studies are discussed. Keywords raindrop size distribution; Meiyu; convective rain; eastern China

1.

Introduction

Precipitation plays a key role in the Earthʼs climate system and is highly variable, both spatially and temporally. Quantifying variability in the global distribution of precipitation is important for better understanding the global climate change. The characCorresponding author: Baojun Chen, School of Atmospheric Sciences, Nanjing University, 22 Hankou Rd., Nanjing 210093, China. E-mail: [email protected] ©2013, Meteorological Society of Japan

teristics of precipitation are determined by a combination of large- and meso-scale meteorological conditions and small-scale microphysical processes (e.g., Bruintjes 1999). Atmospheric aerosols, formed from natural and anthropogenic processes (e.g., Zhang 2010) as cloud condensation nuclei (CCN) or ice nuclei, can also affect cloud microphysics and precipitation processes (e.g., Ramanathan et al. 2001). Such a variety of physical processes are likely to result in significant microphysical variability in time and space. The raindrop size distribution (DSD) is an important aspect of microphysical processes. DSD measure-

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ments carried out around the world show that they vary both spatially and temporally and over a wide range (e.g., Bringi et al. 2003; Uijlenhoet et al. 2003; Ulbrich and Atlas 2007; Lee et al. 2009; Radhakrishna et al. 2009; Marzano et al. 2010; Niu et al. 2010; Thurai et al. 2010; Tokay and Bashor 2010; Jaffrain et al. 2011). The differences in DSD characteristics have been found to be associated with precipitation types, atmospheric conditions, and geographical locations or climatic regimes (Rosenfeld and Ulbrich 2003). The variability of DSDs also has a key influence on radar rainfall estimates. The power-law relationship of the b form Z = AR , where Z and R are the radar reflectivity factor and rain rate, respectively, has been widely used for radar quantitative precipitation estimation (QPE). It has long been recognized that there is a strong connection between the Z̶R relationship and DSD variability (Chandrasekar et al. 2003), differing with rain types, geographical locations, and climatic regimes (Rosenfeld and Ulbrich 2003). Thus, investigating the characteristics of the DSD in various climatic regimes is needed for improving radar rainfall estimation algorithms on a global scale. In this paper, we report the characteristics of the DSDs observed in eastern China during the Asian summer monsoon season. The summer monsoon rainy season from June to July over East Asia is also referred to as Meiyu in China and Baiu in Japan. The MeiyuBaiu rainfalls are characterized by an east-westoriented rainband along a stationary front, the MeiyuBaiu front (e.g., Tao and Chen 1987; Ninomiya and Murakami 1987; Ding 1991). The Meiyu-Baiu front brings heavy rainfall in east China, mainly in the Yangtze-Huaihe River basin, and over the southern part of Japan. In recent years, authors have studied the characteristics of DSDs during the Baiu period in Japan (e.g., Hashimoto and Harimaya 2003, 2005; Shusse et al. 2009; Oue et al. 2010); however, not much is known about the DSDs in the Meiyu season in China, mainly because of the lack of DSD measurements. During the Meiyu season from 2009 to 2011, DSD measurements were carried out at Nanjing with a ground-based optical disdrometer. The objective of this study is to obtain the statistical characteristics of the DSDs in the Meiyu season over eastern China based on the analysis of these disdrometer data. The rest of the paper is organized as follows. The instrumentation and methodology are described in Section 2, followed by the analysis results in Section 3. Section 4 gives a summary and discussion.

2. a.

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Data and methods

PARSIVEL disdrometer and dataset The rain DSD data analyzed in this study were collected with a Particle Size and Velocity (PARSIVEL) disdrometer. Briefly, the instrument is a ground-based optical disdrometer designed to count and to simultaneously measure the fall speeds and sizes of precipitation particles. The core element of the instrument is an optical sensor that produces a 2 horizontal sheet of light of 54 cm . The estimated sizes and fall speeds of the particles are stored in a 32 × 32 matrix that corresponds to 32 nonequidistant classes of diameter (from 0 to 25 mm) and 32 nonequidistant −1 classes of the fall speed (from 0 to 22.4 m s ). All particles in a given class are assigned values that correspond to the center of the size and velocity classes. The first two size classes (0.062 and 0.187 mm) are not used because of their low signal-to-noise ratios. Thus, the smallest size starts at the third class̶ that is, 0.312 mm in diameter. PARSIVEL detects and identifies eight different precipitation types as drizzle, mixed drizzle/rain, rain, mixed rain/snow, snow, snow grains, ice pellets, and hail, according to the WMO, SYNOP, METAR, and NWS weather codes. Yuter et al. (2006) confirmed that PARSIVEL can be employed as a weather sensor because of its capability to distinguish between solid and liquid precipitation. Recently, critical evaluations on PARSIVEL measurements were performed by Battaglia et al. (2010), Jaffrain and Berne (2011), and Thurai et al. (2011). In general, PARSIVEL overestimates the large raindrop diameter owing to the spheroidal assumption (LöfflerMang and Joss 2000; Löffler-Mang and Blahak 2001; Battaglia et al. 2010). To minimize the potential instrument error, the observed data herein are corrected following the method of Battaglia et al. (2010). In this scheme, drops smaller than 1 mm are assumed to be spherical (axis ratio equals 1). For drops between 1 and 5 mm, the axis ratio linearly varies from 1 to 0.7. For drops with a diameter larger than 5 mm, the axis ratio is set to 0.7. This study utilizes three years of disdrometer data collected with PARSIVEL during the Meiyu season in Nanjing (2009̶2011). Nanjing (32° N, 118° E) is located in eastern China and is persistently affected by the Meiyu frontal systems. Continuous measurements were performed at a time resolution of 1 min. By examining the time series of disdrometer data, we determined 23 rain events (Table 1). Herein, we adopted the definition of a rain event proposed by Tokay and Bashor (2010) based on the DSD

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Table 1. Rain events used for the present study and statistical characteristics of rain rate derived from disdrometer data. Event no.

Date

Times (LST)

No. of 1-min spectra

Mean and max rain rate −1 (mm h )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

5̶6 Jul 2009 6 Jul 2009 7 Jul 2009 10 Jul 2009 8̶9 Jun 2010 14 Jun 2010 2̶3 Jul 2010 4 Jul 2010 10 Jul 2010 10 Jul 2010 10 Jul 2010 12 Jul 2010 13 Jul 2010 17 Jun 2011 18 Jun 2011 21 Jun 2011 24̶25 Jun 2011 4 Jul 2011 8 Jul 2011 11 Jul 2011 12 Jul 2011 15 Jul 2011 19 Jul 2011

2326̶0146 1600̶2045 1400̶1531 0552̶0806 1750̶0500 1453̶1624 2206̶0328 1546̶1738 0647̶0749 1427̶1725 2043̶2229 0228̶2332 0109̶0332 1120̶1333 0002̶1501 0555̶1124 1715̶1904 2040̶2317 0540̶0804 1501̶2334 0140̶1320 1417̶1610 0622̶1312

140 267 92 111 655 92 312 86 57 179 107 1150 121 106 897 330 1460 119 131 445 614 114 411

0.7, 1.9 1.3, 4.7 21.2, 137.3 10.9, 50.0 3.3, 21.5 5.7, 34.7 4.7, 70.7 7.2, 43.3 2.4, 7.9 1.0, 2.9 0.9, 3.7 8.0, 83.3 18.7, 73.1 4.9, 32.7 3.7, 46.6 2.5, 9.2 5.3, 63.8 7.5, 51.9 1.8, 7.6 1.3, 27.2 2.7, 22.6 3.3, 7.7 6.6, 44.2

measurements. For each 1-min DSD sample, if the total number of drops is lesser than 10 or a disdrometer-derived rain rate is lesser than 0.1 mm −1 h , then it is disregarded as noise, otherwise it is considered to be a rainy minute. A rain event is subsequently defined on the basis of 1 h or a longer rain-free period between the two consecutive rainy minutes. Moreover, rain events that lasted lesser than 30 min have been discarded for the sake of data processing. Finally, the selected 23 rain events consist of a total of 7996 1-min DSD spectra covering three Meiyu seasons from 2009 to 2011. b.

Raindrop size distribution The number concentration of raindrops per unit volume per unit size interval at the discrete instant has been calculated from the PARSIVEL disdrometer counts by the following equation: 32

N(Di) = ∑ j=1

nij , A·Δt·Vj·ΔDi

(1)

where nij is the number of drops within the size bin i 2 and velocity bin j, A(m ) and Δt(s) are the sampling area and time, respectively, Di(mm) is the raindrop diameter

for the size bin i, and ΔDi is the corresponding −1 diameter interval (mm), Vj(m s ) is the fall speed for −1 −3 the velocity bin j. N(Di ) (mm m ) represents the number concentration of drops with diameters in the interval from Di to Di + ΔDi per unit size interval. Given N(Di ), the integral rainfall parameters of interest can be derived, including the radar reflectivity 6 −3 −1 factor Z (mm m ), rain rate R (mm h ), and rain water −3 content W (g m ), which are given by 32

6

Z = ∑N(Di)Di ΔDi, i=1

(2)

R=

6π 32 32 3 4 ∑ ∑VjN(Di)Di ΔDi, 10 i=1 j=1

(3)

W=

π 32 3 ∑N(Di)Di ΔDi. 6000 i=1

(4)

In this study, we use the well-known gamma function to represent the DSD (Ulbrich 1983) given by μ

N(D) = N0D exp(−ΛD),

(5) −1−μ

where D (mm) is the raindrop diameter, N0 (mm −3 m ) is the intercept parameter, μ is the shape

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−1

parameter, and Λ (mm ) is the slope parameter. The three parameters (N0, μ and Λ) in (5) were estimated from the second, fourth, and sixth moments of the observed distributions using the moment method as described by Ulbrich and Atlas (1998) and Zhang et al. (2003). In addition, the truncated-moment method (Vivekanandan et al. 2004) is also used to test the effects of the fitting method. Detailed descriptions of these two methods have been addressed in previous studies (e.g., Ulbrich and Atlas 1998; Zhang et al. 2003; Vivekanandan et al. 2004) and are not presented herein. For the gamma DSD model, the nth-order moment of the DSDs is expressed as Mn =



∞

0

n

D N(D)dD = N0

Γ(μ + n + 1) , +n+1 Λ

(6)

where Γ(x) is the complete gamma function. Apart from the integral rainfall parameters, two other parameters of interest are the mass-weighted mean diameter Dm(mm), computed as the ratio of the 4th to the 3rd moment of the size distribution, Dm =

M4 , M3

(7) −1

and the generalized intercept parameter NW (mm −3 m ) defined by Bringi et al. (2003) NW =

4

3

4 10 W , πρw D4m





(8)

−3

where ρw (1.0 g cm ) is the density of water. c.

Classification of rain types Precipitation is commonly classified in two main categories: stratiform and convective. Previous studies (e.g., Bringi et al. 2006; Shusse et al. 2009) have shown that Baiu events show stratiform and convective precipitation. In general, intense (weak) rainfall is generated by convective (stratiform) rain. The frequency distribution of the rain rates based on all 23 rain events in Table 1, and their contributions to total rainfall are shown in Fig. 1. Overall, the frequency of occurrence and the corresponding contribution to the total rainfall in the whole datasets are 75% and 24% for −1 rain rates below 5 mm h , 11% and 15% for rain rates −1 in the range 5̶10 mm h , 14% and 61% for rain rates −1 above 10 mm h , respectively. Thus, over 75% of the total rainfall in the Meiyu season is provided by rain −1 rates above 5 mm h , although sample partitioning in the whole dataset is only 25% (1950 samples). Here the shape of the frequency distribution of rain rates is similar to that observed in Baiu over Japan (e.g.,

Fig. 1. Frequency distribution of the rain rates derived from the whole disdrometer datasets (solid line) and cumulative contribution to the total rainfall (dashed line).

Hashimoto and Harimaya 2003). The classification of rain types in this study was mainly based on disdrometer data. Several disdrometer-based classification schemes have been developed to separate convective versus stratiform rain types (e.g., Tokay and Short 1996; Testud et al. 2001; Bringi et al. 2003). Considering that the main goal of this study is to characterize the DSDs in the Meiyu season and to further compare the DSDs with those of other regions reported in Bringi et al. (2003), the classification scheme proposed by Bringi et al. (2003) is adopted here. This scheme is based on the standard deviation (σR) of the rain rate R over five consecutive 2min DSD samples. Based on the analysis of disdrometer data during typical stratiform events, −1 Bringi et al. (2003) used σR = 1.5 mm h as the threshold for the classification of stratiform and convective rain. The classification criteria was based −1 −1 on R ≥ 0.5 mm h and σR ≤ 1.5 mm h for −1 stratiform rain and R ≥ 5.0 mm h and σR > 1.5 mm −1 h for convective rain. Marzano et al. (2010) also adopted a similar concept as Bringi et al. (2003), but −1 they used R = 10 mm h as the threshold for separating convective rain. It is noted that using the −1 threshold of R = 10 mm h is reasonable for delimiting stratiform from convective rain (e.g., Testud et al. 2001; Thurai et al. 2010); however, the early and end stages of convective rain are also excluded from

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Fig. 2. Histogram of Dm (gray shaded) and log10NW (black shaded) from (a) the whole dataset, (b) convective subset, and (c) stratiform subset, respectively. Mean values, standard deviation (SD), and skewness (SK) are also shown in the respective panel. For the whole dataset, data only −1 with R > 0.5 mm h are shown.

the datasets, since rain rates are likely less than 10 mm −1 h . Based on the classification criteria of Bringi et al. (2003), the classification procedure adopted here is similar to that of Marzano et al. (2010). Specifically, for a sample of the rain rate R at the instant ti, R(ti), if the R values from ti − NS to ti + NS are higher than 0.5 −1 mm h , and their standard deviation is less than 1.5 −1 mm h , then it is classified as stratiform; otherwise if the R values from ti − NS to ti + NS are higher than 5 −1 mm h , and the standard deviation is more than 1.5 −1 mm h , then it is classified as convective. Samples R(ti) that belong neither to the stratiform nor convective type are classified as a mixed type and are excluded from the investigation. Herein NS has been set to 5 samples. Such a scheme produced 1562 convective samples and 4184 stratiform samples, accounting for 19.5% and 52.3% of the whole datasets, respectively. −1 Over 80% of samples with rain rates above 5 mm h were classified as convective, and they contribute to 62% of the total rainfall in the whole dataset. The mean rain-rate values for convective and stratiform rains are −1 −1 approximately 17.8 mm h and 2.0 mm h , respecti-

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Fig. 3. Scatter plots of log10 NW vs Dm for convective (solid circles) and stratiform (open circles) rain types. The average value of log10 NW (with ± 1σ standard deviation) and average Dm in Fig. 2 for the whole dataset (black solid diamond), convective subset (gray solid square), and stratiform subset (black solid square) are indicated. The two outlined rectangles correspond to the maritime and continental convective clusters reported by Bringi et al. (2003). The dashed straight line is that of Bringi et al. (2003) for stratiform rain.

vely. 3. a.

Results

Distributions of Dm and NW Figure 2 shows the relative frequency histograms of Dm and log10 NW for the whole dataset and the convective and stratiform subsets as well as key parameters such as mean, standard deviation, and skewness. For the whole dataset (Fig. 2a), the Dm histogram is highly positively skewed, while the log10 NW histogram is slightly negatively skewed. The standard deviation of the histograms is large (0.29 mm for Dm and 0.35 for log10 NW), suggesting a high variability in Dm and NW for the analyzed dataset. The mean Dm and log10 NW values are 1.40 mm and 3.55, −1 −3 respectively (4900 mm m for NW). These values are slightly lower as compared with those obtained in a Baiu front event in Okinawa, Japan (Bringi et al. 2006; −1 −3 values are 1.47 mm for Dm and 6000 mm m for NW). The NW̶Dm pair for the whole dataset (denoted by black diamond in Fig. 3) is very close to the stratiform

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line reported by Bringi et al. (2003, their Fig. 10; also shown as a dashed line in Fig. 3), which further indicates that our data consist mainly of stratiform rain events. Considering the different rain types, it is found that both the convective and stratiform Dm histograms are positively skewed, whereas the log10 NW distributions exhibit negative skewness (Figs. 2b and 2c, respectively). Convective rain histograms show a higher skewness compared with stratiform rain histograms, especially for the log10 NW distribution. Note that convective rain histograms of Dm and log10 NW (including their modal values) tend to shift toward the right (large values) relative to stratiform rain histogram, indicating that convective rains have higher Dm and NW values than stratiform rains. As shown in Figs. 2b and 2c, the histogram means of Dm and log10NW are significantly higher (1.71 mm and 3.80, respectively) for convective rain than for stratiform rain (1.30 mm and 3.45, respectively). To investigate the variability of the two parameters with respect to rain types and rain rates, scatter plots of NW and Dm versus R are shown in Figs. 4 and 5, respectively, where Figs. 4a and 5a correspond to convective rain, while Figs. 4b and 5b correspond to stratiform rain. In addition, the fitted power-law relationships using a least-squares method are also provided in the respective figure panels. For both Dm̶R and NW̶R plots, the exponents in the relationships are positive, suggesting that the Dm and NW values are higher at a higher rain intensity relative to a lower rain intensity, owing to more efficient coalescence and breakup mechanisms. Both the coefficient and exponent of the NW̶R relationship are higher for convective rain than for stratiform rain. For the Dm̶R relation, no significant difference in the relationships could be found between the two types of rain; however, the coefficient and exponent values are slightly higher for stratiform rain compared with convective rain. Hence, for a given rain rate, stratiform rain has higher Dm values compared with convective rain. Comparing Figs. 4 and 5, the exponent values in the NW̶R and Dm̶R relationships indicate the rainfall during convective rain is more sensitive to NW than Dm, especially at higher rain rates. Note that the exponent −1 value in the Dm̶R relationship for R > 90 mm h is only 0.05 (Fig. 5a), in contrast to that value in the NW̶R relationship is 0.73 (Fig. 4a). At high rain rates, an important issue is whether the DSDs have reached an equilibrium state where coalescence and breakup of raindrops are in near balance (e.g., Hu and Srivastava 1995). Under the equilibrium state, Dm is generally a

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Fig. 4. Scatter plots of NW vs R for (a) convective and (b) stratiform rain types. The fitted power-law relationships using a least-squares method are also provided in each panel. The outlined region in panel (a) corresponds to the −1 range of R > 90 mm h .

constant value that is independent of the rain rate, and any increase in rain intensity is mainly due to an increase in NW (e.g., Bringi et al. 2003). As can be seen −1 from Fig. 5a, for rain rates exceeding 90 mm h , Dm tends to a stable value around 2.0 mm. Hence, the DSDs may be considered to have reached an

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concentration of smaller-sized drops. The other is characterized by = 2̶2.75 mm and log10 = 3̶3.5 and referred to as the “continentallike” cluster that reflects DSDs characterized by a lower concentration of larger-sized drops as compared with the maritime-like cluster. From Fig. 3, we can see that most Nw̶Dm data points for convective rain (black solid circles) are centered at the area with log10 = 3.5̶4.2 and = 1.4̶2.0 mm, and only a few data points appear in the rectangles observed for continental convective clusters in Bringi et al. (2003). The overall mean log10NW and Dm (given in Fig. 2b and indicated with the gray square marker in Fig. 3) roughly matches the maritime-like convective cluster. Nevertheless, the NW value reported here is slightly lower than that for the maritime cluster, which indicates that the DSDs of convective rain in the Meiyu season have a lower concentration of raindrops in comparison to maritime convective rain. For stratiform rain, most NW̶Dm data points (gray open circles) appear on the left side of the stratiform line of Bringi et al. (2003). The overall average log10NW and Dm (given in Fig. 2c and denoted as a black solid square in Fig. 3) is also close to the abovementioned stratiform line, but the mean value is lower (i.e., gives a lower NW value for a given Dm). b.

Fig. 5.

As in Fig. 4, but for Dm vs R. −1

equilibrium state at R > 90 mm h . In the NW̶Dm space, Bringi et al. (2003) and Marzano et al. (2010) showed that the DSD parameters were different in various climatic regimes. For convective rain, Bringi et al. (2003) found that the DSDs could be divided into two distinct clusters in their Fig. 11 and also presented in our Fig. 3. One is “maritime-like” cluster that is characterized by = 1.5̶1.75 mm and log10 = 4̶4.5, where angle brackets denote averages, that is, a higher

Composite raindrop spectra To investigate overall DSD characteristics of convective and stratiform rain, Fig. 6 shows the composite drop size spectra for the two rain types that were obtained by averaging all the instant size spectra for each subset, and the integral rain parameters that were derived from the composite spectra are listed in Table 2. Here the maximum raindrop diameter is defined as the maximum bin divided by all drop −3 diameters such that N(D) is greater than 1 × 10 −1 −3 mm m in the composite spectra. In addition, the gamma distribution fitted on each averaged spectrum using the moment method is also plotted, and the parameter values are provided in Table 3. As a reference, the values associated with the whole datasets are also shown in Tables 2 and 3. Despite the two composite spectra exhibiting similar one-peak distributions, distinct differences in the DSDs can be found between the two rain types. Convective spectra have a maximum raindrop diameter of 5.25 mm, and the peak concentration occurs at the diameter of 0.44 mm. In contrast, the stratiform spectra are considerably narrower, where the maximum raindrop diameter is 3.41 mm, and the peak concentration occurs at 0.94 mm. Compared to

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Table 2. Integral rain parameters derived from the composite raindrop spectra for convective (C) and stratiform (S) rains. Parameters NT, Nw, W, R, Dm and Dmax are the total raindrop concentration, generalized raindrop concentration, rain water content, rain rate, mass-weighted mean diameter, and maximum raindrop diameter, respectively. Rain type

Samples

NT (m )

log10 Nw −3 −1 (NW in m mm )

W −3 (g m )

R −1 (mm h )

Dm (mm)

Dmax (mm)

C S All

1562 4184 7996

645.0 185.0 288.7

3.73 3.40 3.42

0.698 0.115 0.250

14.9 2.1 5.1

1.80 1.39 1.66

5.25 3.41 5.25

−3

Table 3. Gamma distribution parameters derived from the composite raindrop spectra using the moment method. The corresponding values estimated from the truncated moment method are presented in parentheses Rain type C S All

−1−μ

N0 (mm

−3

m )

50100 (49523) 105492 (95355) 21051 (20909)

−1

μ

Λ (mm )

4.37 (4.35) 4.94 (4.83) 3.51 (3.50)

4.67 (4.66) 6.43 (6.34) 4.52 (4.52)

c.

Fig. 6. Composite raindrop spectra for convective and stratiform rain types. The gamma functions fitted on each spectrum using the moment method are plotted in gray lines. Since the truncated-moment method produces a similar result, corresponding fitting curves are not presented.

stratiform spectra, the convective spectra has higher concentrations at all size ranges, resulting in a higher number concentration, a higher rain rate and more rain water content. As shown in Table 2, the number concentration, water content, and the rain rate derived from the composite spectra are significantly higher for convective rain than for stratiform rain. From Fig. 6, one can see that the gamma distribution model fits the composite spectra well except for the underestimation of small drops ( 1000. The solid and dashed lines represent the fitting of the μ−Λ relationship and the empirical μ−Λ relationship from Zhang et al. (2003), respectively. The gray lines correspond to the relationship ΛDm = 4 + μ given the value of Dm = 1.0, 1.5, 2.0, and 3.0 mm.

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such as Dm. For a gamma DSD, the μ̶Λ relationship can be expressed as ΛDm = 4 + μ (Ulbrich 1983). Thus, with the given Dm and μ values, the corresponding Λ value can be estimated. As shown in Figs. 7a and 7b, compared to the Florida curve, our fits appears in the higher Dm region, suggesting that the DSDs in Meiyu precipitation have higher Dm values than those observed in Florida. In other words, higher Dm values may be the reason for the higher μ values in this study as compared to the Florida μ values, given the same Λ value. This agrees with the statement of Zhang et al. (2003) and Vivekanandan et al. (2004) that μ̶Λ relationships vary with the geographical location, since each location has different DSD characteristics. d.

Z̶R relationship The empirical power-law Z̶R relationship as Z = b AR has been widely used for radar QPE, but the coefficient A and exponent b were found to vary with geographical locations, atmospheric conditions, and rain types (Rosenfeld and Ulbrich 2003). It has been recognized that there is a strong connection between DSD variability and the A and b values (Chandrasekar et al. 2003). The above analyses have shown that the DSDs in the Meiyu season are different from other regions. Therefore, it is necessary to investigate the Z̶ R relationship in Meiyu precipitation to better understand the variability in Z̶R relationships and to further improve the radar QPE in a specific location. Considering the fact that the convective spectra contribute to approximate two third of the total rainfall for the whole dataset, only the Z̶R relationship for convective rain is studied. Here the filtered data mentioned in Section 3c is used to derive a stable relationship. Figure 8 shows a scatter plot between Z and R for the filtered convective data. The power-law equations are fitted to these scatter plots using the least-squares methods. The coefficient and exponent values of the fitted power-law equations are provided in the figure. For reference, two standard Z̶R relationships that have been widely used in operational weather radar rainfall estimation are also overlaid. The 1.4 first one is Z = 300R (Fulton et al. 1998), the current default equation used in the Next-Generation Weather Radar (NEXRAD) of the United States. The other one 1.2 is Z = 250R , which is generally better for tropical rainfall events (Rosenfeld et al. 1993). Nearly all filtered data points appear on the right side of the standard NEXRAD Z̶R relationship (black dashed line), i.e., gives a lower Z value for a given R, which indicates that the radar would be underestimating the rainfall using this standard Z̶R relationship. In

Fig. 8. Scatter plots of Z−R values for convective rain obtained from the filtered data only for total drop counts > 1000. The fitted power-law relationships in the form of Z = b AR using a least-squares method are shown in the black solid line. The coefficient and exponent values of the fitted power-law equations are provided. The black dashed line represents the standard NEXRAD Z−R relationship (Z = 1.4 300R , Fulton et al. 1998), and the gray solid line is the 1.2 tropical Z−R relationship (Z = 250R , Rosenfeld et al. 1993).

this study, the average underestimation of the rain rate is found to be approximately 32%. In contrast, one can see that most data points appear on the left side of the standard tropical Z̶R relationship (gray solid line), especially those with high rain rates, which indicates that this tropical Z̶R relationship would overestimate rainfall, in particular at high rain rates. On average, the rain rate is overestimated by about 31% by the use of the standard tropical Z̶R relationship. Compared to both standard relationships, our Z̶R relationship (black solid line) fits the measured data relatively well, in particular at the high rain-rate end, although it underestimates the rainfall at low rain rates. The A and b values in the new Z̶R relationship are 368 and 1.21, respectively. The A value is found to be higher in our relationship than in the standard tropical relationship, while the b value is similar in both relationships. Note that the abovementioned tropical Z̶R relationship is derived from the observations of convective precipitation in Darwin, Australia. In comparison with Darwin (refer to Fig. 11 of Bringi et

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al. 2003 and Fig. 9 of Thurai et al. 2010), the convective DSDs in this study have a similar Dm but a lower NW, thereby resulting in a higher A value (A ∝ −0.5 NW , Bringi et al. 2003). 4.

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Summary and discussion

In this study, the statistical characteristics of DSD in the Meiyu season over eastern China have been studied using a three-year (2009̶2011) dataset collected by the PARSIVEL disdrometer. A total of 23 rain events and 7996 1-min DSD spectra were considered for this study. The spectra were divided into convective and stratiform types based on the standard deviation of the rain rate proposed by Bringi et al. (2003). The main conclusions of this study can be summarized as follows. 1) The log10NW(Dm) histograms of both convective and stratiform rain are negatively and positively skewed. The histogram skewness coefficient is higher for convective rain than for stratiform rain, in particular for the log10 NW distribution. The mean log10 NW and Dm are found to be higher for convective rain than for stratiform rain (3.80 versus 3.45 for log10 NW and 1.71 versus 1.30 mm for Dm). The NW̶Dm pair for convective rain roughly matches the maritime-like cluster reported by Bringi et al. (2003), which indicates convective rain in the Meiyu season can be identified as maritimelike. 2) The composite size spectra for each rain type can be well represented by the gamma distribution model. All three parameters of the gamma DSD have lower values for convective spectra than for stratiform spectra. Similar to Brandes et al. (2003) and Zhang et al. (2003), we derived a second-order polynomial-shaped μ̶Λ relationship for convective rain. Given the same Λ value, the μ̶Λ relationship obtained here has higher μ values as compared to Floridaʼs μ̶Λ relationship reported by the two studies. Higher Dm values may be the reason for the higher μ values in this study relative to the Florida cases. 3) The use of the standard NEXRAD Z̶R relationship 1.4 Z = 300R (Fulton et al. 1998) produces an underestimation of rainfall for convective rain, whereas rainfall tends to be overestimated when the standard 1.2 tropical Z̶R relationship Z = 250R (Rosenfeld et al. 1993) is used. Using filtered data, we derived a 1.21 new Z̶R relationship (Z = 368R ) for convective rain. The new Z̶R relationship has a similar exponent and higher coefficient as compared to the standard tropical relationship owing to a lower NW

in this study. This study also analyzed the statistical characteristics of the DSDs in the Meiyu season over eastern China. The results show that DSDs are different from those observed in some other tropical or subtropical locations even though eastern China is situated in a similar latitudinal belt. For instance, compared to Darwin, Florida (e.g., Bringi et al. 2003; Thurai et al. 2010), and Japan (e.g., Bringi et al. 2006; Marzano et al. 2010), the NW value reported here is slightly lower. This is likely associated with local atmospheric aerosols and/or moisture. Recently, May et al. (2011) used polarimetric radar measurements to examine the effects of aerosols on DSDs of thunderstorms in Darwin. Their results showed that high aerosol concentrations could lead to a lower NW and higher Dm compared with low aerosol concentration conditions. In eastern China, especially in the Yangtze River Delta region, aerosol or CCN concentrations are markedly high (Streets et al. 2008; Liu et al. 2011). With increased aerosol loading, warm-rain processes in convective clouds, such as collision-coalescence and break-up of raindrops can be suppressed, resulting in smaller raindrop concentrations. It should be noted that aerosols are one of the factors that could influence clouds and precipitation. Moreover, the aerosol effect on precipitation processes is very complex depending on its concentrations and atmospheric conditions and is not yet well understood (Tao et al. 2012). More research needs to be done to understand the aerosol effects on DSDs. Cloud modeling with spectral bin microphysics would be especially valuable for this purpose. We leave this subject for future research. Acknowledgments The first author thanks Dr. Guifu Zhang at the University of Oklahoma for providing the source code of the truncated-moment method. Two anonymous reviewers provided critical yet valuable comments and suggestions. The authors also thank Dr. Ming Xue at the University of Oklahoma for polishing the manuscript. We also thank Mr. Lei Chen for his assistance in collecting disdrometer data. This study was jointly supported by the National Basic Research Program of China (2010CB428504 and 2013CB 430105), the National Natural Science Foundation of China (41175118), and the R&D Special Fund for Public Welfare Industry in Meteorology (GYHY200906003, GYHY201006004). Baojun Chen was also supported in part by a project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) and the

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