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  • View in gallery

    Diagram of 2DVD measurement (Joanneum Research 2016). The illumination unit directs light toward each camera, causing a raindrop shadow that is captured by the camera. The height difference between the two cameras is 6.2 mm.

  • View in gallery

    (a) Map of East Asia showing Daegu and Boseong (red circles). (b) Map of North America showing Oklahoma (blue circle; National Severe Storms Laboratory site, NSSL). (c) Photograph of 2DVD installed at Daegu and Boseong. (d) Photograph of 2DVD (old version) installed at the NSSL site (Schuur et al. 2001).

  • View in gallery

    Comparison of the RSD shape for KOR and OKL. (a) N(D)–D graph. Solid (dashed) lines are KOR (OKL). (b) ΔN(D) as a function of Z. The Δ means N(D) of OKL subtracted by N(D) of KOR.

  • View in gallery

    Comparison of normalized RSD (NRSD) for KOR and OKL. (a) h(x)–x graph for KOR. (b) h(x)–x graph for OKL. The solid line is the average h(x) [⟨h(x)⟩] with Δx = 0.2 and the dot–dash line is least squares fit (hgg). The vertical bar is the standard deviation at each Δx. (c) Average h(x) [⟨h(x)⟩] and (d) fitted h(x) (hgg). Red (blue) is KOR (OKL).

  • View in gallery

    Normalized frequency distributions (NFDs) of RSD variables. (a) NFD of R (KOR). (b) NFD of R (OKL). The N is the data number and ⟨⟩ indicates the average value. (c) NFD of log N0. MP indicates the N0 of the Marshall and Palmer (1948) distribution. Red (blue) is KOR (OKL) and the dashed line is the average value. (d) NFD of Dm.

  • View in gallery

    Comparison of generalized parameters for KOR and OKL as a function of ZZ = 2 dBZ). The N0Z scatterplot for (a) KOR and (b) OKL. (c) The DmZ scatterplot for (c) KOR and (d) OKL. Solid (dashed) lines indicate the median values of KOR (OKL). Note high N0 values (oval) at Z ~20 dBZ in (a) and high Dm values (circle) at Z ~ 50 dBZ in (d).

  • View in gallery

    Average RSDs at different Z intervals with Dm>2.0 mm for KOR (solid line) and OKL (dashed line).

  • View in gallery

    Comparison of generalized parameters between KOR, OKL, the maritime convective cluster (MT), continental convective cluster (CT), and Nanjing, East China (ECN). (a) The N0Dm scatterplot with ΔZ = 2 dBZ. The diamond (square) symbol is KOR (OKL). (b) The N0Dm scatterplot with statistical values in convective rainfall. The vertical bar is SDlog(N0), the horizontal bar is SDlog(Dm), and the cross point of the bars is the average value.

  • View in gallery

    RZH scatterplots. (a) KOR, S band. (b) OKL, S band. (c) KOR, C band. (d) OKL, C band. (e) KOR, X band. (f) OKL, X band. The black solid line is RZH relationship of the MP distribution. The dash–dot line is the derived relationship.

  • View in gallery

    Direct comparison of the RZH relationships between KOR (red) and OKL (blue). The solid, dash–dot, and dashed lines are the relationships at the S-, C-, and X-band wavelengths, respectively.

  • View in gallery

    RKDP scatterplots. (a) KOR, S band. (b) OKL, S band. (c) KOR, C band. (d) OKL, C band. (e) KOR, X band. (f) OKL, X band. The dash–dot line is the derived relationship.

  • View in gallery

    RKDP/f graph for direct comparison of the RKDP relationships in KOR (red) and OKL (blue). The solid, dash–dot, and dashed lines are the relationships at the S-, C-, and X-band wavelengths, respectively. The f indicates the radar frequency (GHz).

  • View in gallery

    RAH scatterplots. (a) KOR, S band. (b) OKL, S band. (c) KOR, C band. (d) OKL, C band. (e) KOR, X band. (f) OKL, X band. The dash–dot line is the derived relationship.

  • View in gallery

    RAH graph for direct comparison of RAH relationships in KOR (red) and OKL (blue). The solid, dash–dot, and dashed lines are the relationships at the S-, C-, and X-band wavelengths, respectively.

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Comparison of Microphysical Characteristics between the Southern Korean Peninsula and Oklahoma Using Two-Dimensional Video Disdrometer Data

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  • 1 Center for Atmospheric Remote Sensing, Department of Astronomy and Atmospheric Sciences, Kyungpook National University, South Korea
  • | 2 Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, Oklahoma
  • | 3 NOAA/OAR/National Severe Storms Laboratory, Norman, Oklahoma
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Abstract

Differences in atmospheric environments can have a significant impact on microphysical processes of precipitation. Dominant warm (cold) rain processes in East Asia (southern Great Plains of the United States) are implied by a large (small or constant) gradient of reflectivity at low levels in vertical reflectivity profiles. Long-term ground observations using two-dimensional video disdrometers were conducted in the southern Korean Peninsula (KOR) and Norman, Oklahoma, United States (OKL). Raindrop size distributions (RSD) and their moments in the two regions were analyzed in the framework of scaling normalized RSDs. Results show that the concentrations of small (big) raindrops were higher (smaller) in KOR than in OKL. KOR RSDs were also found to be characterized by relatively high characteristic number concentrations N0 and small characteristic diameters Dm when compared to OKL RSDs. The N0 increases with increasing Dm in both KOR and OKL at lower Z with the opposite trend at higher Z. In addition, OKL RSDs with Dm>2.5mm indicate the existence of an equilibrium between coalescence and breakup processes. Rainfall estimation relationships between the rain rate R and radar variables were retrieved from scattering simulations at S-, C-, and X-band wavelengths. KOR RSDs showed relatively small horizontal reflectivity and specific differential phase shift at the same R and same wavelength when compared to OKL RSDs. The regional dependency was significant due to the different microphysical process in KOR and OKL. The specific attenuation of KOR was, however, similar to that of OKL only at S band, indicating an advantage of using specific attenuation in S band in rainfall estimation.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: GyuWon Lee, gyuwon@knu.ac.kr

Abstract

Differences in atmospheric environments can have a significant impact on microphysical processes of precipitation. Dominant warm (cold) rain processes in East Asia (southern Great Plains of the United States) are implied by a large (small or constant) gradient of reflectivity at low levels in vertical reflectivity profiles. Long-term ground observations using two-dimensional video disdrometers were conducted in the southern Korean Peninsula (KOR) and Norman, Oklahoma, United States (OKL). Raindrop size distributions (RSD) and their moments in the two regions were analyzed in the framework of scaling normalized RSDs. Results show that the concentrations of small (big) raindrops were higher (smaller) in KOR than in OKL. KOR RSDs were also found to be characterized by relatively high characteristic number concentrations N0 and small characteristic diameters Dm when compared to OKL RSDs. The N0 increases with increasing Dm in both KOR and OKL at lower Z with the opposite trend at higher Z. In addition, OKL RSDs with Dm>2.5mm indicate the existence of an equilibrium between coalescence and breakup processes. Rainfall estimation relationships between the rain rate R and radar variables were retrieved from scattering simulations at S-, C-, and X-band wavelengths. KOR RSDs showed relatively small horizontal reflectivity and specific differential phase shift at the same R and same wavelength when compared to OKL RSDs. The regional dependency was significant due to the different microphysical process in KOR and OKL. The specific attenuation of KOR was, however, similar to that of OKL only at S band, indicating an advantage of using specific attenuation in S band in rainfall estimation.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: GyuWon Lee, gyuwon@knu.ac.kr

1. Introduction

Different climatology and regional differences of the atmospheric environment can significantly affect the microphysical characteristics of precipitation (Bringi et al. 2003). When compared with Oklahoma (OKL), United States, the atmospheric environment of the southern Korean Peninsula (KOR) is characterized by abundant lower-level moisture caused by an ample supply of water vapor from the sea during the summer, which leads to deficient ice crystals at upper levels (Sohn et al. 2013). The relatively abundant ice crystals in OKL are attributed to strong updrafts and relative dry air at the lower layers in the region. The strong updrafts produce graupel by mostly efficient riming of snow within convection. In particular, many of the larger raindrops comprising the OKL raindrop size distributions (RSDs) also comes from melted hail with a relatively small number concentration (Ryzhkov and Zrnić 2019). The abundant moisture in KOR is likely to cause the growth of raindrops at lower levels and thus efficient warm rain process (Sohn et al. 2013). Other studies have also suggested that the growth of lower-level raindrops in East Asian coastal regions can be attributed to water vapor supplied from the ocean (Fu and Liu 2003; Fu et al. 2003; Cao and Qi 2014).

Several studies have analyzed the characteristics of RSD in different regions by using generalized characteristic number concentrations N0 (m−3 mm−1) and generalized characteristic diameters Dm (mm) that is derived from the scaling normalization of RSD without any assumption on the functional form of RSD (Lee et al. 2004). Bringi et al. (2003) used two-dimensional video disdrometer (2DVD) data to show that convective RSDs of Colorado, United States, in June 2000 were characterized by logN01.52.5, Dm2.4mm (the symbol ⟨⟩ indicates a simple average value, and the values are hereafter converted from the original definition into N0 and Dm). Chen et al. (2013) showed that convective RSDs of Nanjing in East China (ECN) were characterized by logN01.952.39, Dm1.471.95mm using Particle Size and Velocity (PARSIVEL) data collected in July from 2009 to 2011. Furthermore, Wen et al. (2016) showed that convective RSDs of ECN were characterized by logN02.363.12, Dm1.171.65mm with using 2DVD data collected from June to August in 2014 and 2015. These studies illustrated that the convective RSDs in the continental air mass tended to have larger raindrops and a smaller total number concentration and vice versa for those in the tropical/maritime air mass. When compared with Bringi et al. (2003), RSDs of OKL during April to June 2011 in the Midlatitude Continental Convective Clouds Experiment (MC3E) showed slightly higher N0 and smaller Dm [logN01.95, logSD(N0)2.250, and Dm1.051.93mm] for both stratiform and convective rain (Tokay et al. 2017). However, RSDs for stratiform rain in Wallops Island in Virginia (WIV) during December 2013–March 2014 had relatively larger N0 and smaller Dm [logN02.184, logSD(N0)2.338, and Dm0.811.41mm] than those of MC3E (Tokay et al. 2016). Here, the SD stands for the standard deviation.

RSD variability, raindrop shape–size relation, type of disdrometers, drop axis ratio, measurement uncertainty, sampling volume, and way of the fitting can influence rainfall estimation relationships (Chandrasekar et al. 1990; Smith et al. 1993; Lee and Zawadzki 2005a,b; Ryzhkov et al. 2005; Lee 2006; Lee and Zawadzki 2006; Gorgucci and Baldini 2009; Adirosi et al. 2018). Many studies have compared rainfall estimation relationships of two distinctive RSDs: one with a large N0 and small Dm, and the other with a small N0 and large Dm (Ulbrich and Atlas 1978; Tokay and Short 1996; Ulbrich and Atlas 1998; Illingworth and Blackman 2002; Martner et al. 2008; Schönhuber et al. 2015). The radar reflectivity factor at horizontal polarization ZH (dBZ or mm6 m−3) of the former RSD is smaller when compared to the ZH of the latter at the same rain rate R (mm h−1; Ulbrich and Atlas 1978; Tokay and Short 1996; Ulbrich and Atlas 1998; Martner et al. 2008). Furthermore, the specific differential phase KDP (° km−1) of the former is smaller when compared to the KDP of the latter at the same R (Illingworth and Blackman 2002). The specific attenuation at horizontal polarization AH (dB km−1) of the former is also smaller at shorter wavelength when compared to the AH of the latter at the same R (Schönhuber et al. 2015). In addition, the three parameters (ZH, KDP, AH) have different dependency on the diameter and thus on raindrop concentration. The KDP is more sensitive to the raindrop concentration than ZH due to the dependency of ZH on the 6th power of the particle diameter (Zrnić and Ryzhkov 1996; Straka et al. 2000; Lee 2006; Kumjian and Ryzhkov 2009). Similarly, the AH has the highest sensitivity to raindrop concentration among these three parameters. The R depends on the 3.67th power of the raindrop diameter. These dependency suggest that R(ZH), R(KDP), and R(AH) reflect different microphysical processes and subsequent different characteristics of RSDs.

This study focuses on two objectives. First, we compare RSD characteristics between KOR and OKL. Second, we examine the impact of RSD differences through a comparison of rainfall estimation relationships between the two regions. To achieve this, we use long-term 2DVD observations from KOR and OKL. RSDs, their moments, characteristic parameters derived from scaling RSD, and dual-polarization variables obtained from each dataset are also analyzed.

2. Two-dimensional video disdrometer data

The 2DVD is an optical disdrometer that observes the shadow of precipitation particles using two orthogonal cameras and illumination units (Fig. 1). The nominal measurement area is 100 cm2 and the height difference between the two cameras is 6.2 mm. Equivalent diameter D (mm), measured fall velocity Vf (m s−1), and the axis ratio of raindrop can be obtained from the observation data (Kruger and Krajewski 2002).

Fig. 1.
Fig. 1.

Diagram of 2DVD measurement (Joanneum Research 2016). The illumination unit directs light toward each camera, causing a raindrop shadow that is captured by the camera. The height difference between the two cameras is 6.2 mm.

Citation: Journal of Hydrometeorology 21, 11; 10.1175/JHM-D-20-0087.1

The 2DVD observed data are used only for the warm season (May–September) from 1998 to 2006 in Norman of OKL and from 2011 to 2015 in the southern part [combined dataset from two regions; Daegu (2011–12) and Boseong (2013–15)] of KOR. The solid and mixed precipitation were excluded by selecting data during the warm season and by checking the hail events. Measurement locations and the instruments used are shown in Fig. 2. Figure 2a shows a map of East Asia with the KOR observation sites (red circles), Fig. 2b shows a map of North America with the OKL observation site (blue circle), and Figs. 2c and 2d show photographs of the 2DVD instruments used in KOR and OKL, respectively. The monthly average relative humidity in Daegu (Norman) was in the range of 60%–68% (50%–60%).

Fig. 2.
Fig. 2.

(a) Map of East Asia showing Daegu and Boseong (red circles). (b) Map of North America showing Oklahoma (blue circle; National Severe Storms Laboratory site, NSSL). (c) Photograph of 2DVD installed at Daegu and Boseong. (d) Photograph of 2DVD (old version) installed at the NSSL site (Schuur et al. 2001).

Citation: Journal of Hydrometeorology 21, 11; 10.1175/JHM-D-20-0087.1

The 2DVD manufactured three versions from 1991 to now: tall unit (1991–2001; first generation), low-profile unit (2002–08; second generation), and compact unit (2009–present; third generation). Although different versions of 2DVD instruments were used in OKL (tall unit; first generation) and KOR (compact unit; third generation), the main processing software was identical. The hardware was similar, with the exception of the scan frequency and number of pixels of line scan camera. The number of pixels and scan frequencies were 500–512 and 34.1 kHz for the tall unit and 632 and 55.3 kHz for the compact unit, respectively (Schuur et al. 2001; Kruger and Krajewski 2002; Schönhuber et al. 2008). This change should improve the size resolution and the accuracy in fall velocity. The internal temperature of the tall unit is not stabilized. Thus, it requires frequent recalibration due to temperature change and can create the disturbance of airflow around the measuring area. In addition, the first generation had a design issue that tiny droplets can hang or land on the mirrors or slits (Larsen and Schönhuber 2018).

There are few studies about the intercomparison of RSD measurement between different 2DVDs. Brandes et al. (2005) showed that the difference of 1-min drop size distribution and its characteristics parameters (total number concentration, rainfall rate, median volume diameter, and drop maximum diameter) between tall and low-profile units was quite small regardless of different wind fences. A similar comparison of the low-profile and compact units showed that the measured fall velocity, rainfall intensity, mass-weighted mean diameter, and width of the mass spectrum were in agreement and, furthermore, the fall velocity, shape, and axis ratio were close to the expected or reference values (Thurai et al. 2010).

The KOR dataset were from the two regions (Daegu and Boseong). These two regions were about 180 km apart. Boseong is close to the ocean and is directly affected by the abundant moisture and land/sea breeze. However, Daegu is located in inland and downstream location of mountains during the dominant westerly, and is significantly affected by the dry air and summertime heating. This discrepancy may cause some difference in microphysics. Detailed analysis of N0 and Dm indicated the difference of their average is within about 7%–9%, which is much less than that between KOR and OKL (not shown). That is, Daegu is slightly close to OKL with slightly smaller (larger) N0 (Dm). Hereafter, the comparison of KOR and OKL is only shown.

The RSD N(D) (m−3 mm−1) is defined as follows:
N(Di)=j=1n1AVf(Dj)ΔtΔD,
where i is the diameter bin number. A total of 41 bins were used, ranging from 0 to 10.25 mm; ∆D is 0.25 mm, ∆t is 1 min, n indicates the total number of raindrops at the ith bin during 1 min, and A is the measurement area of the 2DVD.
Processing of the 2DVD data is done in two steps. First, outliers were eliminated using fall velocity according to Kruger and Krajewski (2002):
|Va(D)Vf(D)|<0.4Va(D),
where Va(D) = 9.65–10.3 exp(−0.6D) (Atlas et al. 1973). Data that satisfied Eq. (2) were retained. Second, the data were inspected and RSDs that had one or more contiguous zero-concentration bins between nonzero concentration bins were eliminated by assuming RSD as a continuous function (Marshall and Palmer 1948; Ulbrich 1983; Auf der Maur 2001). This second data processing is to use continuous RSDs with no missing data between diameter channels. This is quite reasonable since the RSD should be considered as a continuous distribution. A total of 34 780 (22 066) RSDs for KOR (OKL) were acquired from 116 (120) rainfall events. In this study, we assume that one day of rainfall represents a single rainfall event.

3. Analysis method

a. Derivation of rain microphysical characteristics

RSD diversity can be attributed to cloud and precipitation microphysical processes such as coalescence, breakup, evaporation, accretion, aggregation, and so on (Rosenfeld and Ulbrich 2003; Lee et al. 2004; Tapiador et al. 2014; Testik and Pei 2017). These microphysical processes can lead to variety of different RSDs. We compared the RSD shape of the two regions as a first step in our analysis to reveal the difference in dominant microphysical processes. To reveal these differences, the RSDs were averaged for 5-dB intervals from 0 to 55 dBZ. The relative difference ΔN(D) [NOKL(D) − NKOR(D)] of averaged RSD between two regions was then compared at each 5-dB interval.

RSDs can be normalized using generalized characteristic parameters (generalized characteristic number concentration N0 and generalized characteristic diameter Dm) with an assumption of the scaling law (Lee et al. 2004):
N(D)=N0h(D/Dm)=N0h(x),
where h is the nondimensional normalized generic function and x is the nondimensional normalized diameter. Here, we defined N0=Mi(j+1)/(j1)Mj(i+1)/(ij) and Dm=(Mj/Mi)1/(ji), and the index i and j are the order of the moment. We examined the normalized function and characteristic parameters of the KOR and OKL RSD data. In this study, RSDs are assumed to be a generalized gamma distribution, as suggested by Auf der Maur (2001). The normalized form of the generalized gamma distribution hgg is expressed using the following equation:
hgg(x,c,μ)=cΓi(i+cμ)/(ij)Γj(icμ)/(ij)xcμ1exp[(ΓjΓi)c/(ij)xc],
where Γi = Γ(μ + i/c), Γj = Γ(μ + j/c) (Lee et al. 2004). The normalization of Testud et al. (2001) is a special case of (3) when i = 3, and j = 4. The nondimensional parameters (c and μ) are shape parameters of the generalized gamma distribution and were estimated using least squares method. The 1-min RSDs are used in the scaling normalization and the negative μ is allowed in the fitting. These shape parameters were compared between the two regions.
The characteristic variables of RSD can be helpful to explain characteristics of RSD quantitatively. Therefore, we calculated R, radar reflectivity Z (mm6 m−3 or dBZ), N0, and Dm used in many previous studies. The N0 and Dm are derived by using i = 3 and j = 4:
N0(M3,M4)=M35M44,
Dm(M3,M4)=M4M31,
where Mn (m−3 mmn) means nth moment of RSD. The magnitude of N0 (Dm) depends on the intercept parameter of RSD (mean diameter). We compared normalized frequency distributions (NFDs) of R, N0, and Dm in the two regions and analyzed the relationship of N0Z and DmZ.

RSD characteristics between the convective and stratiform rainfall significantly differ (Tokay and Short 1996; Thurai et al. 2016). Herein, convective (stratiform) rainfall is classified as a precipitation system without (with) a bright band in cold rain. Methodologies to classify between convective and stratiform rainfall using disdrometer data have been suggested in previous studies, for example, Bringi et al. (2003), Chen et al. (2013), and Wen et al. (2016). In this study, we classify precipitation using the Chen et al. (2013) method to in order to compare our datasets with the ECN data. Chen et al. (2013) classified the convective rainfall with the thresholds of Rmin ≥ 5 mm h−1 and SD(R) ≥ 1.5 mm h−1. Here, the Rmin and SD(R) are the minimum R value and standard deviation within a window of 10 min. An N0Dm scatterplot was analyzed to compare our results with previous studies such as the maritime convective cluster, continental convective cluster (Bringi et al. 2003), and ECN (Chen et al. 2013; Wen et al. 2016).

b. Derivation of rainfall estimation relationships

Several studies have shown that R(ZH), R(KDP), and R(AH) can be influenced by RSD characteristics (Ulbrich and Atlas 1978; Tokay and Short 1996; Ulbrich and Atlas 1998; Illingworth and Blackman 2002; Schönhuber et al. 2015). For example, using the fall velocity data of Gunn and Kinzer (1949), R can be approximated to D3.67. Parameter ZH is proportional to D6. Furthermore, KDP depends on concentration and shape of the raindrop (Kumjian and Ryzhkov 2008), and AH is proportional to D3 (D3D6) when Rayleigh (Mie) approximation can be adopted (Sauvageot 1992). Consequently, we compared the rainfall estimation relationships between KOR and OKL to examine the impacts of microphysical differences. Radar variables were derived using a T matrix and rainfall relationships were assumed to have a power law (Y = aXb). The multiplicative factor a and exponent b were estimated using the weighted total least squares (WTLS) method following Amemiya (1997). The R threshold (>0.5 mm h−1) was adopted to improve the fitness of the relationships. After adopting the threshold, the RSD sample number for KOR was 17 849 (51.3% of data) and for OKL was 13 070 (59.2%).

The T-matrix method can be performed under control conditions such as temperature, radar wavelength, radar elevation angle, and raindrop shape model (Mishchenko et al. 1996). The control conditions and the values used in this study are shown in Table 1. The elevation angle of the radar was set at 0°. Three radar wavelengths were considered: 11.01 cm (S band), 5.61 cm (C band), and 3.23 cm (X band). The raindrop shape model of Thurai et al. (2007) was used. The environment temperature was fixed to be 23°C based on Table 2, which shows the monthly mean temperatures of KOR and OKL during the summer. Temperature data for Daegu and Jangheung (adjacent to Boseong) were obtained from the automatic weather station (AWS) during 1981–2010 (KMA 2011). Temperature for OKL was obtained from climate data during 1982–2012 (Climate-data.org 2016). Climatological temperatures are important because AH can be influenced by temperature variation (Ryzhkov et al. 2014). The canting angle of raindrops was assumed to be a Gaussian distribution with a width of 10°.

Table 1.

Control conditions for the T-matrix method. The μ indicates mean, and σ indicates standard deviation.

Table 1.
Table 2.

Monthly mean temperatures for KOR and OKL during summer.

Table 2.

Parameters ZH, KDP, and AH were calculated as follows:
ZH,V=4λ4π4|K2|DminDmax|sH,V(π,D)|2N(D)dD,
KDP=180λπDminDmaxRe[fH(0,D)fV(0,D)]N(D)dD,
AH=8.686λDminDmaxIm[f(0,D)]N(D)dD,
where λ is the radar wavelength (cm), |K2| is the dielectric term of water, and f(π, D) is the complex forward scattering amplitude and s(π, D) is complex backscattering amplitude at horizontal H or vertical V polarization (Mishchenko et al. 1996).
Statistical values, such as SD [Eq. (10)], average fractional error [AFE, Eq. (11)], and standard deviation of the fractional error [SDFE, Eq. (12)] were calculated as follows:
SD(mmh1)=[1k1(RobsRest)2]0.5,
AFE(%)=1k1|RobsRest|Robs,
SDFE(%)=[1k1(RobsRestRobs)2]0.5,
where k is the data number, obs is the observed value, and est is the value estimated from the empirical rainfall estimation relationship.

4. Analysis result

a. Difference in rain microphysical characteristics

A comparison of the average RSD for each ΔZ = 5-dB interval (⟨N(D)⟩) between the two regions is shown in Fig. 3 (KOR in solid line and OKL in dashed line). The different colors represent the intervals of Z in which RSDs are averaged. It is apparent that RSDs become broad (high number concentration at larger sizes) as Z increases. In addition, the number concentration in the size of 0.5–1 mm increases with higher Z. The RSDs in the two regions differ in that NKOR(D) has a relatively high (low) concentration at small (large) D. This difference [∆N(D) = NOKL(D) − NKOR(D)] is highlighted in Fig. 3b. Warm colors [higher N(D) in OKL than in KOR] dominates the larger sizes and cold colors [lower N(D) in OKL than in KOR] are shown in smaller sizes. Therefore, NKOR(D) is characterized by higher number concentration of small raindrops and lower concentration of large raindrops when compared with NOKL(D).

Fig. 3.
Fig. 3.

Comparison of the RSD shape for KOR and OKL. (a) N(D)–D graph. Solid (dashed) lines are KOR (OKL). (b) ΔN(D) as a function of Z. The Δ means N(D) of OKL subtracted by N(D) of KOR.

Citation: Journal of Hydrometeorology 21, 11; 10.1175/JHM-D-20-0087.1

Figure 4 shows the results of the normalized RSD for KOR and OKL. All RSDs are normalized and average h(x) (⟨h(x)⟩) with Δx = 0.2 is shown as the black solid line in Fig. 4a for KOR and 4b for OKL. The vertical bar is the standard deviation at each Δx. The dash–dot line represents the best-fit line [hgg(x, c, μ)] estimated from ⟨h(x)⟩ using the least squares method. The normalized RSD collapses into a single line at the size range of 0.5–1.5. The large scatter in the smaller and larger sizes may be attributed to the disdrometer measurement uncertainty (Lee et al. 2004). The average h(x) and fitted h(x) are nearly identical for the two regions [hgg,KOR(x, 2.46, 0.39) and hgg,OKL(x, 2.79, 0.12)] in Figs. 4c and 4d. These results indicate that the different microphysical processes in the two regions do not significantly affect the change of average h(x) and most of the microphysical variation is contained in the two normalization parameters, characteristic number concentration and characteristic diameter.

Fig. 4.
Fig. 4.

Comparison of normalized RSD (NRSD) for KOR and OKL. (a) h(x)–x graph for KOR. (b) h(x)–x graph for OKL. The solid line is the average h(x) [⟨h(x)⟩] with Δx = 0.2 and the dot–dash line is least squares fit (hgg). The vertical bar is the standard deviation at each Δx. (c) Average h(x) [⟨h(x)⟩] and (d) fitted h(x) (hgg). Red (blue) is KOR (OKL).

Citation: Journal of Hydrometeorology 21, 11; 10.1175/JHM-D-20-0087.1

The NFDs of RSD variables are shown in Fig. 5. The OKL NFD shows a wide R distribution and large ⟨R⟩ as compared to KOR. These differences indicate that light rainfall (<2.5 mm h−1) is more frequent in KOR, whereas extreme heavy rainfall (>100 mm h−1) is more frequent in OKL with a long tail. The NFD of logN0 of KOR (Fig. 5c) shows a large average value (2.47) and shifts to larger values as compared to logN0 of OKL (2.10). We attribute this result to frequent light rainfall from a moisture rich environment in KOR (Fu and Liu 2003; Fu et al. 2003; Sohn et al. 2013; Cao and Qi 2014). A second peak with logN02.85 is evident in both regions, with higher and distinctive frequency in KOR. This larger values of N0 suggest frequent development of shallow systems and drizzle-like precipitation (Joss and Waldvogel 1969; Wen et al. 2016) whereas evaporation in the relatively dry environment in OKL causes depletion of smaller drops, leading to lower N0 values. In particular, the low R (<2.5 mm h−1 with low N0) in OKL is dominated from trailing stratiform of mesoscale convective systems. The NFD of Dm of OKL (Fig. 5d) shows a large average value (1.28 mm) as compared to the Dm of KOR (0.99 mm). We attribute this result to OKL experiencing frequent extreme heavy rainfall from deep convective systems, such as a supercell storm (Schuur et al. 2005). Deep convective systems allow more time for the growth of large particles through ice microphysical processes and, in particular, heavy riming to produce graupel by strong updraft, resulting in a large Dm. In addition, RSDs from melted hail in deep convective systems tend to produce larger raindrops but a relatively small number concentration (Ryzhkov and Zrnić 2019).

Fig. 5.
Fig. 5.

Normalized frequency distributions (NFDs) of RSD variables. (a) NFD of R (KOR). (b) NFD of R (OKL). The N is the data number and ⟨⟩ indicates the average value. (c) NFD of log N0. MP indicates the N0 of the Marshall and Palmer (1948) distribution. Red (blue) is KOR (OKL) and the dashed line is the average value. (d) NFD of Dm.

Citation: Journal of Hydrometeorology 21, 11; 10.1175/JHM-D-20-0087.1

Relationships between N0Z and DmZ in KOR (right panels) and OKL (left panels) are analyzed to examine microphysical differences in detail (Fig. 6). The black solid (dashed) line indicates the median value in KOR (OKL) at each interval of ZZ = 2 dBZ). The N0 (Dm) of KOR shows a relatively large (smaller) median value for given Z values. This indicates that the concentration of small raindrops in KOR is generally higher as compared to OKL regardless of Z. In addition, this trend persists over the entire range of Z with the difference between the two median values becoming larger in the range Z = 30–45 dBZ, implying the precipitation growth is controlled more by the number concentration in KOR. Furthermore, the N0 of KOR shows higher frequency at 15 dBZ < Z < 25 dBZ and N0>102.85m3mm1 as compared to OKL (see the circle in Fig. 6a). This second peak of high N0 is less distinctive in OKL. As explained earlier, this indicates the frequent development of shallow precipitation systems at KOR, which provide heavier R for a given Z.

Fig. 6.
Fig. 6.

Comparison of generalized parameters for KOR and OKL as a function of ZZ = 2 dBZ). The N0Z scatterplot for (a) KOR and (b) OKL. (c) The DmZ scatterplot for (c) KOR and (d) OKL. Solid (dashed) lines indicate the median values of KOR (OKL). Note high N0 values (oval) at Z ~20 dBZ in (a) and high Dm values (circle) at Z ~ 50 dBZ in (d).

Citation: Journal of Hydrometeorology 21, 11; 10.1175/JHM-D-20-0087.1

Compared with OKL, Dm of KOR shows a relatively small median value for the entire range of Z, indicating the smaller raindrop sizes for given Z. The difference of Dm is rather small in the range of 10 dBZ < Z < 25 dBZ and becomes more distinctive for Z > 30 dBZ. The Dm is typically derived from the differential reflectivity and/or reflectivity. The noisy differential reflectivity in Z < 25 dBZ alludes to use the reflectivity only. However, the smaller slope of DmZ suggests large retrieval uncertainty. Thus, other parameters such as attenuation may require to improve the accuracy.

The growth of drops is more prominent with increasing Z in OKL. The frequency of Dm>3mm in OKL is higher as compared to KOR at Z > 40 dBZ (see the circle on Fig. 6d), indicating that the microphysical characteristics of heavy precipitation systems differ in the two regions. Studies indicate that heavy precipitation systems in KOR are dominantly driven by cloud clusters (Lee and Kim 2007) whereas supercell storms are the source of heavy precipitation in OKL (Hocker and Basara 2008). The leading edge of a supercell storm produces an RSD with D0 > 3 mm (Schuur et al. 2005). Here, D0 is the median volume diameter (mm) and the value is very similar to Dm (Ulbrich 1983).

Figure 7 shows the average RSDs for four different intervals of Z when Dm>2.0mm in KOR (solid line) and OKL (dashed line). As Z increases, the number concentration systematically increases, that is, a parallel shift of RSDs toward increasing number concentration, in particular, for OKL. This trend indicates the constant Dm and continuous increase of N0 with increasing Z and, furthermore, is evidence of the equilibrium RSD as noted by Zawadzki and Antonio (1988), Uijlenhoet et al. (2003), and Lee et al. (2004). In addition, the shape of RSDs, the so-called “S” shape, shows high number concentrations for small (D < 1.0 mm) and big (D = 2.0–4.0 mm) raindrops and a relative small number concentration for medium-size (D = 1.0–2.0 mm) drops. The average N(D) for KOR shows higher number concentration than OKL at D < 2 mm and significant increase of the number concentration at D = 2.0–2.5 mm. It is noted that the sudden drop of N(D) at D < 0.4 mm, in general, significant underestimation of small drop is due to the instrumental limitation (Thurai et al. 2017; Chang et al. 2020). In particular, the first channel of the observed RSD by 2DVD is significantly low (Thurai et al. 2017). This shape is similar to the simulated shape from the equilibrium of coalescence and breakup processes in the quasi-stochastic growth equation (Valdez and Young 1985; List 1988; Hu and Srivastava 1995; Straub et al. 2010) and the N(D) with − 1 = −2 in Fig. 9 of Lee et al. (2004). The simulated shape of the equilibrium RSD changes with breakup parameterization (Straub et al. 2010).

Fig. 7.
Fig. 7.

Average RSDs at different Z intervals with Dm>2.0 mm for KOR (solid line) and OKL (dashed line).

Citation: Journal of Hydrometeorology 21, 11; 10.1175/JHM-D-20-0087.1

Figure 8 shows a comparison of N0Dm in the two regions. Both N0 and Dm are derived from the average RSDs shown in Fig. 3a. The diamond and square symbols represent KOR and OKL, respectively. The colors indicated different reflectivity intervals and the typical values of the maritime convective cluster (MT) and continental convective cluster (CT) from Bringi et al. (2003) are shown as the boxes in Fig. 8a. It is apparent that the value N0 of KOR is close to that of MT while that of OKL is close to CT. For further comparison, we classified the convective rainfall by the method of Chen et al. (2013) and calculated typical N0 and Dm values (Fig. 8b). The ranges of R (or Z) and standard deviation of log N0 and Dm are shown in Table 3 for the different regions. The minimum rainfall intensity is 5 mm h−1 and the maximum one varies from 109.3 to 185 mm h−1 with the maximum in the maritime convective cluster (MT) of Bringi et al. (2003). The values from ECN (Wen et al. 2016) are shown as an additional box in Fig. 8b. The values of KOR overlaps with MT and ECN while those of OKL is in between MT and CT with N0 close to MP value and Dm smaller than CT.

Fig. 8.
Fig. 8.

Comparison of generalized parameters between KOR, OKL, the maritime convective cluster (MT), continental convective cluster (CT), and Nanjing, East China (ECN). (a) The N0Dm scatterplot with ΔZ = 2 dBZ. The diamond (square) symbol is KOR (OKL). (b) The N0Dm scatterplot with statistical values in convective rainfall. The vertical bar is SDlog(N0), the horizontal bar is SDlog(Dm), and the cross point of the bars is the average value.

Citation: Journal of Hydrometeorology 21, 11; 10.1175/JHM-D-20-0087.1

Table 3.

Ranges of R (or Z) and standard deviation of logN0 and Dm for the four different regions used in Fig. 8b.

Table 3.

The N0Dm shows different dependence on reflectivity values (Fig. 8a). The N0 value increases as Dm increases for Z < 16 dBZ in KOR and OKL, indicating the growth and new generation of drops are significant. However, it decreases with increasing Dm for Z > 16 dBZ in KOR and for 16 dBZ < Z < 32 dBZ in OKL. This indicates that the precipitation processes are dominated by drop growth by coalescence as well as possible aggregation in light/moderate stratiform system. The N0 value increases with increasing Dm for Z > 32 dBZ in OKL. This may be attributed to further generation of smaller drops due to strong convection. This is somehow linked with the traditional classification of convection with Z > 35 dBZ. Furthermore, the collision–coalescence process increases with further increasing Z and there finally exists an equilibrium between coalescence and breakup processes with extreme Z values (see Fig. 7). In addition, the strong convection produces graupel and possible hail as Z further increases, resulting into large Dm.

b. Difference in rainfall estimation relationships

Figure 9 shows a comparison of RZH relationships at different radar wavelengths for the two regions, KOR and OKL, to examine the impacts of the differences in RSD characteristics. The black solid line is the Marshall and Palmer (1948) relationship, RMP(Z) (Z = 296R1.47), and the dashed line is the best fit relationship, R(ZH), derived using the WTLS method. The Marshall and Palmer RSDs were obtained from Ottawa, Canada, and were affected by the continental environment. The left (right) panels are for KOR (OKL). The RKOR is larger than RMP at the same Z for each radar wavelength whereas ROKL is similar to RMP. This is an outcome of higher number concentration of smaller drops in KOR and of larger drops in OKL. It is worthwhile to recall the RMP(Z) is derived for stratiform rain in summer from Ottawa, Canada. In addition, the OKL RSDs at 35 dBZ are dominant as shown in the shade in Fig. 9b or Fig. 9d. Thus, the ROKL is close to RMP. Furthermore, ROKL is well fit data at Z > 35 dBZ. In addition, the exponent of R(Z) ranges from 1.42 to 1.52 [similar to that of RMP(Z)] except for X band in OKL. This similar exponent is valid only when the N0 is independent to R.

Fig. 9.
Fig. 9.

RZH scatterplots. (a) KOR, S band. (b) OKL, S band. (c) KOR, C band. (d) OKL, C band. (e) KOR, X band. (f) OKL, X band. The black solid line is RZH relationship of the MP distribution. The dash–dot line is the derived relationship.

Citation: Journal of Hydrometeorology 21, 11; 10.1175/JHM-D-20-0087.1

The error (AFE and SDFE) in R estimation with reflectivity only is smaller in KOR and is the largest at X band, in particular, in OKL. Larger the error, higher the variability of RSDs that cannot explain by a single parameter, Z. This is thus partially attributed to the significant variation of RSD at high Z as shown in the large scatter at Z > 45 dBZ in OKL (Fig. 9f). The best fit relationships are overlapped in Fig. 10 and the coefficient and exponent are summarized in Table 4. In general, no significant variation is shown in the different wavelengths and the RSD difference is the dominant factor to deviate the relationships from the two regions.

Fig. 10.
Fig. 10.

Direct comparison of the RZH relationships between KOR (red) and OKL (blue). The solid, dash–dot, and dashed lines are the relationships at the S-, C-, and X-band wavelengths, respectively.

Citation: Journal of Hydrometeorology 21, 11; 10.1175/JHM-D-20-0087.1

Table 4.

The R–ZH relationships derived from the RSD for KOR and OKL.

Table 4.

Figure 11 shows the RKDP scatterplots for KOR and OKL at each radar wavelength. The dashed line is the best fit relationship, R(KDP), derived using the WTLS method for R > 0.5 mm h−1and KDP > 0.1° km−1. The KDP is normalized with the radar frequency (in GHz). The error in R estimation did not show the significant dependency to the radar wavelengths and regions when the best fit relationships are used. Similar to R(ZH), the best fit relationships, R(KDP), show the slight dependency to different RSDs in the two regions. For a given KDP, R in KOR is higher than in OKL (shown in Fig. 11 and Table 5). The dependency to the radar wavelengths is eliminated by normalizing KDP with the radar frequency (Fig. 12). The exponents (0.79–0.86) of R(KDP) slightly vary with wavelengths and regions and the coefficients vary with the wavelengths and regions. The exponent of 0.83 is corresponding to the moment order of KDP as 4.6. When the lower threshold of KDP (>0.001° km−1) is used (i.e., light rain is included), the exponent (0.75–0.76) is nearly constant, showing no dependency on wavelengths and regions. The exponent of 0.75 implies that the moment order of KDP is close to 5.2, that is, to radar reflectivity (Illingworth 2003). This value is related to the mean axis ratio versus diameter relation for small sized drops (Thurai et al. 2007).

Fig. 11.
Fig. 11.

RKDP scatterplots. (a) KOR, S band. (b) OKL, S band. (c) KOR, C band. (d) OKL, C band. (e) KOR, X band. (f) OKL, X band. The dash–dot line is the derived relationship.

Citation: Journal of Hydrometeorology 21, 11; 10.1175/JHM-D-20-0087.1

Table 5.

The RKDP relationships derived from RSD for KOR and OKL. RSDs with R > 0.5 mm h−1 and KDP > 0.1° km−1 are used.

Table 5.
Fig. 12.
Fig. 12.

RKDP/f graph for direct comparison of the RKDP relationships in KOR (red) and OKL (blue). The solid, dash–dot, and dashed lines are the relationships at the S-, C-, and X-band wavelengths, respectively. The f indicates the radar frequency (GHz).

Citation: Journal of Hydrometeorology 21, 11; 10.1175/JHM-D-20-0087.1

The RAH scatterplots for KOR and OKL are shown in Fig. 13. It is apparent that the SD, AFE, and SDFE of RKOR(AH) vary significantly with the wavelengths and regions. In particular, the SD at C band is the largest. The best fit RAH relationships show different characteristics compared with RZH and RKDP (Fig. 14 and Table 6). Significant variation is shown in different wavelengths due to the dependency of attenuation to the wavelength. However, the regional variation of R(AH) is small at S band, indicating that this relationship is immune to different RSDs and is less sensitive to microphysical variation. In addition, the exponent is close to unity at S band and decreases with shorter wavelengths. The exponent of 1 implies the moment order of AH is close to 3.67. As the radar wavelength decreases, the regional difference becomes significant, particularly at higher values of AH. The exponent in the same wavelength is smaller in OKL due to higher number concentration in larger size drops in OKL. The smaller exponent at shorter wavelength suggests that the moment order of AH is higher (4.4–5.1), likely due to strong Mie effect and higher dependency of attenuation into diameter.

Fig. 13.
Fig. 13.

RAH scatterplots. (a) KOR, S band. (b) OKL, S band. (c) KOR, C band. (d) OKL, C band. (e) KOR, X band. (f) OKL, X band. The dash–dot line is the derived relationship.

Citation: Journal of Hydrometeorology 21, 11; 10.1175/JHM-D-20-0087.1

Fig. 14.
Fig. 14.

RAH graph for direct comparison of RAH relationships in KOR (red) and OKL (blue). The solid, dash–dot, and dashed lines are the relationships at the S-, C-, and X-band wavelengths, respectively.

Citation: Journal of Hydrometeorology 21, 11; 10.1175/JHM-D-20-0087.1

Table 6.

The RAH relationships derived from RSD for KOR and OKL.

Table 6.

5. Summary and conclusion

Rainfall characteristics in OKL and KOR were compared using a 2DVD dataset. First, we compared microphysical characteristics through the scaling normalization of RSDs. Second, we examined the impact of different RSD characteristics on the two regions through the comparison of rainfall estimation relationships.

Comparison of RSD characteristics highlighted the different systems driving precipitation in the two regions. Rainfall in the southern Korean peninsula tended to be light and derived from shallow systems. The NFD of N0 of KOR showed a relatively large NF for large N0 (≥102.85 m−3 mm−1) as compared to the NFD of N0 of OKL. The N0Z scatterplots showed that RSDs with large N0 have a small Z (15 dBZ < Z < 25 dBZ). Hence, NKOR(D) has a relatively narrow distribution when rainfall is light. Rainfall in OKL is typically heavy and from supercell systems; producing large raindrops relative to KOR. The NFD of Dm of OKL displayed a relatively large NF for large Dm (≥2 mm) as compared to the NFD of Dm of KOR. The DmZ scatterplots showed that the RSDs with large Dm also had a large Z (>40 dBZ). Hence, NOKL(D) has a relatively wide distribution when rainfall is heavy. Our results were compared with previous studies (Marshall and Palmer 1948; Bringi et al. 2003; Chen et al. 2013; Wen et al. 2016). Typical values for KOR generalized parameters were found to be similar to ECN and MT groups. Conversely, typical values for OKL show relatively large Dm and small N0 as compared to the MT group.

In summary, the KOR RSD showed large N0 and small Dm and vice versa in OKL. This was persistent throughout different range of Z. Thus, we can conclude the KOR RSD is controlled by the new generation of drops and less cold microphysics, in particular, riming process, while the OKL RSD is controlled by the drop growth by the collision–coalescence process and by significant production of graupel and heavily rimed particles due to strong updraft in the deep layer. In particular, the OKL RSD with larger characteristic diameter shows the typical behavior of the equilibrium between coalescence and breakup processes. The shape of DSD was close to the so-called “S” shape that is predicted by the quasi-stochastic growth equation in this equilibrium (Valdez and Young 1985; List 1988; Hu and Srivastava 1995). The RSD moved toward higher number concentration with increasing Z while maintaining the shape and the characteristic diameter. The RSD was dominantly controlled by the number concentration. In addition, the larger N0 in lower Z (so-called second peak in this work) was prominent in the KOR RSD. This was an indication of drizzle-like precipitation driven by the shallow systems.

The two regions showed similar dominant microphysical processes up to moderate rain (<32 dBZ). The drop growth and new generation of drops were dominant in light rain (<16 dBZ), indicated by increasing trend in both N0 and Dm with increasing Z. However, the drop growth becomes dominant in the moderate rain (<32 dBZ) since the N0 value decreases with increasing Dm. The N0 value becomes nearly constant with higher Z in KOR RSD but again increases with increasing Z over 32 dBZ in OKL RSD. Finally, the OKL RSD showed the clear signature of the equilibrium RSD in extreme Z values by the balance between collision–coalescence and breakup processes.

Rainfall estimation relationships such as R(ZH), R(KDP), and R(AH) were compared at S, C, and X bands. Dual-polarization radar variables were retrieved from the RSD dataset using the T-matrix method. KOR displayed smaller ZH and KDP as compared to OKL at the same R and radar wavelength. The result was attributed to the relatively wide distribution of NOKL(D). The RAH relationships with S-band wavelength showed a negligible dependence on microphysical processes because R(AH,KOR) was similar to R(AH,OKL). Conversely, C- and X-band AH,KOR showed relatively large differences as compared to AH,OKL.

This study compared the different RSD characteristics of KOR and OKL. The impacts of these differences were determined by comparing the rainfall estimation relationships of the two regions. These results will be useful for improving the results of global precipitation estimation projects, such as the Global Precipitation Measurement (GPM) or TRMM. We also anticipate that the results of this study will aid in the understanding of cloud and precipitation microphysics during the East Asian monsoon.

Acknowledgments

This study was funded by the Korea Environmental Industry & Technology Institute (KEITI) of the Korea Ministry of Environment (MOE) as “Advanced Water Management Research Program” (79615) and by the Korea Meteorological Administration Research and Development Program “Enhancement of Convergence Technology of Analysis and Forecast on Severe Weather” under Grant (KMA2018-00121). Funding for T. Schuur and A. Ryzhkov was provided by NOAA/Office of Oceanic and Atmospheric Research under NOAA–University of Oklahoma Cooperative Agreement NA16OAR4320115, U.S. Department of Commerce.

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