Raindrop Size Distributions in the Zhengzhou Extreme Rainfall Event on 20 July 2021: Temporal–Spatial Variability and Implications for Radar QPE

1.   Introduction

Extreme rainfall events usually lead to catastrophic socioeconomic damages, but the major mechanisms governing the formation and development of extreme rainfall are poorly understood (Sun et al., 2012; Sun, 2017). One of the key knowledge gaps on extreme rainfall is cloud/precipitation microphysics, that is, how individual hydrometeors are formed and grown (Lu et al., 2016, 2023) and how a population of hydrometeors result in a heavy rainfall. Limited by current means of observations, it is challenging to unambiguously observe microphysical processes in extreme rainstorms, which are usually driven by entangled dynamics and thermodynamics of the precipitation system. Alternatively, fingerprints of dominant microphysical processes taking place aloft are detectable in rain microphysics (Dolan et al., 2018; Li and Moisseev, 2020; Li et al., 2020). Therefore, analysis of hydrometeors, such as the drop size distributions (DSDs) observed by surface disdrometers, may provide unique insights into the precipitation microphysics (Wang et al., 2016; Wang et al., 2019).

In presence of extreme rainfall, the falling raindrops are influenced by various microphysical processes. The observed DSDs are dependent on precipitation type and local climatology (Maki et al., 2001; Chakravarty and Raj, 2013). Bringi et al. (2003) used disdrometer observations to analyze the DSD characteristics in different climatic regimes and identified “maritime-like” and “continental-like” clusters in convective rain in the mass-weighted mean diameter (D_m) and generalized intercept parameter (N_w) space. Tang et al. (2014) and Ma et al. (2019) respectively analyzed DSD observations in Yangjiang and Beijing, China and found great differences in convective cloud precipitation between North China and South China. Specifically, the DSDs of convective cloud precipitation show a larger D_m in Beijing (in North China) and a higher N_w in Yangjiang (in South China), and they are neither “continental” nor “oceanic” in both regions.

On 20 July 2021, an unprecedented extreme rainfall event took place over Zhengzhou, the capital city of Henan Province, China. From 0800 LST (local standard time) 20 July to 0800 LST 21 July, the maximum 24-h rainfall at Zhengzhou Station was as high as 624.1 mm. The maximum hourly rainfall within 1600–1700 LST reached up to 201.9 mm, a new meteorological record in the Chinese mainland. A vast number of studies have investigated the cause of this unprecedented event. Su et al. (2021) found that the top height of 55 dBZ echo was higher than 10 km before the rainstorms hit urban Zhengzhou, while the regional convective systems around Zhengzhou Station developed relatively weakly. Yin et al. (2022) found that Zhengzhou was influenced by a well-organized meso-γ-scale convective system during the extraordinary rainstorm event, and there was a strong arc-shaped convergence zone around the convective system.

It has been suggested that microphysical processes may play a vital role in forming the unprecedented rainfall. Chen et al. (2022) investigated the significant rainfall microphysical variability for the extremely heavy rainfall event over Henan Province in the July 2021 rainstorms using data from 50 Parsivel OTT disdrometer stations and weather radars, and attributed the formation of extreme rain rate exceeding 100 mm h⁻¹ to vigorous ice-phase and efficient warm cloud microphysical processes in the deep convection over the plain regions. On a smaller scale, however, there is a lack of analysis on the regional variability of rainfall microphysics on 20 July when the record-breaking hourly rainfall (201.9 mm) was observed. This is not only important for ascertaining the major responsible microphysical processes, but also relevant for radar-based quantitative precipitation estimation (QPE) in which the parameterized radar estimators are dependent on the regional DSDs. Li et al. (2023) showed that the extreme rainstorms were formed in the southwest of Zhengzhou City and moved northeastwards with violently increasing intensity during 1400–1700 LST.

As expected, such rapid and drastic evolution of rainstorms was associated with various precipitation microphysics, and thus the QPE estimators may need to be tuned in real-time applications. Although radar polarimetric observations are less sensitive to the changes of DSD shapes compared with radar reflectivity factor (Z) observations, Z is the most widely-used variable in many operational services. In addition, Zhang et al. (2022) studied the DSD characteristics at Zhengzhou Station and found that the radar QPE performance is sensitive to the radar estimators. Therefore, there is a need to analyze the temporal–spatial variability of the rainfall on 20 July 2021. Significant progress has been achieved to address radar QPE over recent years by diverse dynamic Z–R relationships (Gou et al., 2018; Chen et al., 2019). Nonetheless, effective utilization of the changing precipitation microphysics in real-time radar QPE is challenging (Gou et al., 2020; Zhang et al., 2022). In light of the inadequacy of using a fixed QPE parameterization, this study proposes the use of reflectivity-grouped fitting approach by radar reflectivity intensity to improve radar QPE in Zhengzhou area by using the parameterization method obtained from the nearest disdrometer station.

The remainder of this paper is organized as follows. Section 2 introduces the data and associated quality control methods, followed by the analysis of DSDs observed by disdrometers in Section 3. Section 4 analyzes the linkage between surface DSDs and radar observations. In Section 5, the radar QPE is conducted with different Z–R parameterizations, and the results are validated by using rain gauge observations. The summary and conclusions are presented in Section 6.

2.   Data and methods

2.1   Observation instruments and stations

In this study, the data obtained from six Parsivel OTT (PS32/DSG4) laser raindrop disdrometers at Zhengzhou, Songshan, Xinzheng, Xingyang, Xinmi, and Zhongmou stations are analyzed. In addition, the data from 139 rain gauge stations are used. The disdrometer data and rain gauge data are from 0800 LST 20 to 0800 LST 21 July 2021. The Parsivel OTT disdrometer observes raindrops falling through a sampling area of 54 mm² with a time resolution of 1 min (Tokay et al., 2014).

An overview of the deployment of Parsivel OTT disdrometers and rain gauges is shown in Fig. 1a. Compared with rain gauges, much less Parsivel disdrometers are in operation. The 24-h rainfall accumulation recorded by the Parsivel disdrometers ranges from 198.3 to 624.1 mm. The remarkable spatial difference of rainfall may be, at least partly, associated with the orographic effects (Chen et al., 2022). Figure 1b shows the hourly rainfall recorded at each Parsivel disdrometer station. The 201.9 mm hourly rainfall sampled at Zhengzhou Station is profound, while the majority of hourly rainfall records are below 50 mm.

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Fig  1.  (a) Distribution of the Parsivel OTT laser raindrop spectrometers (red cross) and rain gauges (blue dot), the rain gauge 24-h accumulated rainfall (mm), and topographic altitude (shaded area; m), and (b) the hourly rainfall intensity evolution (color line; mm h⁻¹) in the Zhengzhou region from 0800 LST 20 to 0800 LST 21 July 2021. “ZZ” indicates Zhengzhou Station, “SS” Songshan Station, “XZ” Xinzheng Station, “XY” Xingyang Station, “XM” Xinmi Station, and “ZM” Zhongmou Station.

2.2   Quality control of raindrop size distributions and parameter calculation

We follow the method of Tokay et al. (2013) to perform the quality control of the Parsivel data. Specifically, we first analyzed the minute-by-minute DSD observations. If the total number of particles observed in 1 min is less than 10 or the estimated rainfall intensity is less than 0.1 mm h⁻¹, the data in the whole minute are excluded as non-precipitation observations. Then, particles in any diameter class are analyzed. If the fall velocity of a particle exceeds ±50% of its theoretical fall velocity (average values of fall velocity–diameter), the particles in that diameter class are excluded. In addition, the data with particle diameter at the first two classes or larger than 6 mm are excluded (Wu et al., 2016).

A total of 7796 samples passed the above criteria of quality control from 0800 LST 20 to 0800 LST 21 July 2021. Figure 2 shows the comparison of the minute-by-minute rainfall intensity retrieved by the rain gauge and Parsivel observations between Zhengzhou (Fig. 2a) and Xinmi (Fig. 2b) stations. The results suggest that the evolution trends of rain intensities over time observed by both instruments are basically consistent, and the other four stations also have the same characteristics. The maximum deviation value of all samples is −10.7%. Du et al. (2018) calibrated and tested the domestic raindrop spectrometers (Parsivel OTT laser raindrop disdrometers) and concluded that the rainfall intensity retrieved from the observations is within the error range of ±20%, which is in line with the basic requirements for general applications. Therefore, the data measured by the raindrop spectrometers are of reliable quality and can reflect the actual precipitation characteristics.

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Fig  2.  Minute-by-minute rainfall intensity retrieved from the rain gauge (green line; mm h⁻¹) and Parsivel observations (red line; mm h⁻¹) at (a) Zhengzhou Station and (b) Xinmi Station.

The Parsivel data represent the number of particles falling into the diameter channel D_i (1 ≤ i ≤ 32). The rainfall intensity R (mm h⁻¹) and liquid water content W (g m⁻³) can be calculated by Eqs. (1)–(2).

where D_i denotes the diameter (mm) in the ith channel, V_i (m s⁻¹) represents the fall speed of raindrops calculated with the fall velocity–diameter relationship from Brandes et al. (2002), N(D_i) (mm⁻¹ m⁻³) the corresponding number concentration of raindrops in each bin i, ΔD_i the corresponding diameter interval (mm), and ρ_w (1.0 g m⁻³) the density of liquid water.

In this study, gamma distribution (Ulbrich, 1983) with three parameters (N₀, µ, Λ) has been used to represent the variation of DSDs,

where N(D) indicates the normalized number concentration of particles (mm⁻¹ m⁻³), D the particle diameter (mm), N₀ the intercept parameter (mm^−1−μ m⁻³), μ the distribution shape parameter, Λ the slope parameter (mm⁻¹), M_n the nth order moment of the raindrop spectrum, D_m the mass-weighted mean diameter (mm), N_w the generalized intercept parameter (mm⁻¹ m⁻³) reflecting the particle number concentration and precipitation types (Bringi et al., 2003), and W the liquid water content (g m⁻³).

2.3   Classification of rainfall intensity

The terrain height of Henan Province is high in the west and low in the east, with complex terrain in the Taihang and Funiu Mountains in the west, which are the most affected areas by heavy rainfall. Hourly rain intensity equal to or greater than 20.0 mm h⁻¹ can cause severe disasters such as flash floods and debris flows. Therefore, in this study, based on the classification criteria of rainstorms and short-term heavy precipitation in Henan (GB/T 28592-2012 and GB/T 27966-2011) and considering the extremes of the “7·20” heavy rainfall event in Zhengzhou, six rainfall intensity (R; mm h⁻¹) classes, i.e., 0.1 ≤ R < 10.0, 10.0 ≤ R < 20.0, 20.0 ≤ R < 50.0, 50.0 ≤ R < 80.0, 80.0 ≤ R < 150.0, 150.0 ≤ R < 250.0, are divided for comparative analysis of the DSDs.

Table 1 shows the numbers of samples at different rainfall intensity classes, as well as the average values and standard deviations of their rainfall intensity. The results suggest that the sample number of the non-short duration heavy precipitation (0.1 ≤ R < 20.0) is the largest, accounting for 82% of all the samples. The number of samples with the rainfall intensity larger than 20.0 mm h⁻¹ is relatively small. In terms of the rainfall intensity below 80.0 mm h⁻¹, the mean values and standard deviations of the rain intensities of samples with the same class show relatively small differences, indicating that the distributions of precipitation samples are basically the same, which is conducive to the comparison of the differences in the DSD characteristics at different stations in the Zhengzhou region. Therefore, we analyze the differences in the DSDs based on the comparison of heavy rainfall samples at six stations in this research.

Table  1.  Statistics of rainfall intensity at different classes based on the Parsivel observations from 0800 LST 20 to 0800 LST 21 July 2021. “Mean” and “SD” denote the average values (mm h⁻¹) and standard deviations (mm h⁻¹) at the corresponding rainfall intensity class; “R” denotes rain intensity

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Rain intensity (mm h−1)	Zhengzhou				Xingyang				Xinmi				Xinzheng				Zhongmou				Songshan
	Sample number	Mean	SD		Sample number	Mean	SD		Sample number	Mean	SD		Sample number	Mean	SD		Sample number	Mean	SD		Sample number	Mean	SD
0.1 ≤ R < 10.0	594	5.2	2.6		879	4.2	2.7		996	4.0	2.7		987	3.7	2.5		1191	3.3	2.3		750	2.6	2.7
10.0 ≤ R < 20.0	221	14.1	2.7		272	14.0	2.7		208	14.6	2.8		183	14.2	3.0		111	13.6	2.9		166	14.7	2.9
20.0 ≤ R < 50.0	160	30.9	7.7		223	30.8	8.6		124	32.2	8.7		136	26.1	6.5		96	24.1	4.2		131	26.4	5.2
50.0 ≤ R < 80.0	60	62.7	8.5		20	58.9	6.4		76	61.2	7.9		20	59.8	7.5		26	58.1	8.3		30	62.4	7.6
80.0 ≤ R < 150.0	45	109.0	20.1		—	—	—		29	102.8	17.7		3	102.6	7.2		8	90.3	8.9		1	84.9	0
150.0 ≤ R < 250.0	50	209.8	31.1		—	—	—		—	—	—		—	—	—		—	—	—		—	—	—

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3.   Comparative analysis of raindrop size distributions

3.1   Case analysis at Zhengzhou and Xinmi stations

The rainfall amounts at Zhengzhou and Xinmi are larger than at other stations during this event, but the rainfall intensity at Zhengzhou station is more extreme. Figure 3 shows the scatter distributions of lgN_w versus D_m at Zhengzhou Station during 1200–1800 LST (Fig. 3a) and at Xinmi Station during 1000–1600 LST (Fig. 3b) on 20 July 2021. Since the DSDs of convective and stratiform precipitation are different, we refer to the methods of Bringi et al. (2003) and Chen et al. (2013) to classify stratiform and convective precipitation samples according to the temporal variation and standard deviation of the rainfall intensity.

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Fig  3.  Scatter distributions, mean values, and standard deviations of lgN_w (mm⁻¹ m⁻³) versus D_m (mm) at (a) Zhengzhou Station during 1200–1800 LST and at (b) Xinmi Station during 1000–1600 LST 20 July 2021. Color dots denote the 1-h convective precipitation samples, and yellow triangles indicate all stratiform precipitation samples. The color dots and yellow triangles with black edge respectively represent the average values of lgN_w versus D_m for 1-h convective and stratiform precipitation samples. Black straight lines denote the lgN_w–D_m relationship for stratiform precipitation as in Bringi et al. (2003). Gray rectangles show the distribution areas of lgN_w versus D_m for marine and continental convective precipitation samples as in Bringi et al. (2003).

At Zhengzhou and Xinmi stations (yellow triangles), the average state of the lgN_w–D_m relationship reflecting stratiform precipitation is located on the stratiform line (black line) shown by Bringi et al. (2003), and the DSD characteristics of convective precipitation are significantly different. However, the D_m and lgN_w values of stratiform precipitation at Zhengzhou Station are relatively larger. The majority of convective cloud precipitation samples at Zhengzhou and Xinmi stations are in the continental–oceanic transition zone, which is directly related to the fact that this precipitation process is influenced by both continental weather systems and the water vapor transport from oceans. At Zhengzhou Station, the average values of D_m and lgN_w for the convective precipitation are about 1.9 mm and 3.6–3.9 mm⁻¹ m⁻³ over 1200–1500 LST, respectively. In addition, the average D_m increases from 1.9 to 2.5 mm during 1400–1600 LST, and the average D_m and lgN_w respectively reach the peaks of 2.7 mm and 4.2 mm⁻¹ m⁻³ during 1600–1700 LST, when the sample standard deviation is the smallest and the characteristics are similar. At Xinmi Station, the average D_m of convective precipitation increases from 1.8 to 2.0 mm during 1000–1200 LST, and the average lgN_w is about 3.8 mm⁻¹ m⁻³. Besides, the average values of D_m and lgN_w over 1200–1400 LST are quite close, about 2.2 mm and 4.0 mm⁻¹ m⁻³, respectively, which is related to the similar hourly rainfall intensity during this period. The average D_m and lgN_w values reach their peaks at Zhengzhou and Xinmi stations during the period with the strongest rainfall intensity, suggesting that the occurrence of this extreme rainfall event is closely related to the increase of D_m and lgN_w. Before the heavy rainfall, the average D_m increases by 0.6 and 0.2 mm at Zhengzhou and Xinmi stations, respectively, indicating that D_m increases before the heavy rainfall event. Note that the increase of D_m is more noticeable at Zhengzhou Station.

3.2   Temporal–spatial variations

Figure 4 presents the DSDs and hourly rainfall from rain gauges at six stations of Zhengzhou area from 0800 LST 20 to 0800 LST 21 July 2021. As can be seen, the precipitation particles diameter (D) is concentrated in 0.5–3.0 mm, the lgN(D) peak value reaches 3.0–4.0 mm⁻¹ m⁻³, and the D value is more than 5 mm during the extreme rainfall at Zhengzhou Station within 1600–1700 LST 20 July 2021 (Fig. 4a). During the strongest precipitation period of Xinmi Station (Fig. 4e), there are two peaks of lgN(D) with D values of 0.5–2.5 mm, which are 3.0–4.0 mm⁻¹ m⁻³ during 1200–1400 LST 20 July 2021. The lgN(D) values are mostly smaller than 2.0 mm⁻¹ m⁻³ when D is above 3 mm, and are larger than 2.0 mm⁻¹ m⁻³ when D is 0.5–2.0 mm at Zhengzhou and Xinmi. There are similar characteristics at the other four stations. The peak of lgN(D) values appears when D values are 0.5–1.5 mm (Figs. 4b–f). The maximum lgN(D) values are mostly 2.5–4.0 mm⁻¹ m⁻³ and the corresponding D values are basically less than 1.5 mm. For those four stations, the large raindrops are relatively few, and the peak lgN(D) of small raindrops is concentrated at 2.5–3.5 mm⁻¹ m⁻³, mostly. The precipitation particles are mainly small raindrops with relatively low concentrations, and this is one main reason for the weak rainfall for those four stations. Those results indicate that the heavy precipitation in Zhengzhou is affected by both large precipitation particles and abundant small precipitation particles, and the heavy rainfall is caused by high concentration raindrops of different sizes.

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Fig  4.  Raindrop size distribution (shaded area; mm⁻¹ m⁻³) and hourly rainfall from rain gauges (black line; mm h⁻¹) at (a) Zhengzhou Station, (b) Songshan Station, (c) Xinzheng Station, (d) Xingyang Station, (e) Xinmi Station, and (f) Zhongmou Station from 0800 LST 20 to 0800 LST 21 July 2021. “R” denotes hourly rainfall.

Figure 5 shows DSD parameters observed at these stations from 0800 LST 20 to 0800 LST 21 July 2021. As expected, Z_h, D_m, and lgN_w in general increase with R, while significant site-to-site variations can be found. Specifically, the most intensive rainfall recorded at Zhengzhou Station is characterized by rather high D_m and Z_h, while D_m does not show significantly increase when R exceeds 50 mm h⁻¹. As will be discussed later, this may be attributed to the equilibrium state of raindrop size distributions. At around 1530 LST, D_m recorded at Zhengzhou Station reaches the peak value of about 3 mm and decreases to about 2.5 mm as the rain rate surges (Fig. 5a). Ahead of the record-breaking 201.9 mm hourly rainfall observed at Zhengzhou, the 64 mm rainfall accumulation was recorded between 1200 and 1300 LST at Xinmi. Interestingly, the increase of D_m ahead of the rainfall surging was observed at both Zhengzhou and Xinmi stations, suggesting the effect of size sorting driven by updrafts on rain microphysics.

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Fig  5.  Time series of the raindrop lgN_w (green line; mm⁻¹ m⁻³), D_m (blue line; mm), Z_h (red line; dBZ), and R (black line; mm h⁻¹) at (a) Zhengzhou Station, (b) Songshan Station, (c) Xinzheng Station, (d) Xingyang Station, (e) Xinmi Station, and (f) Zhongmou Station from 0800 LST 20 to 0800 LST 21 July 2021.

3.3   Variation of DSDs in different rainfall intensities

Chen et al. (2022) have shown that the rainfall microphysics are associated with rainfall intensity in this event. We further investigate the observed DSDs in different rainfall intensities. The statistics of DSDs from different sites are more scattered in light rainfall (Fig. 6a), while the shapes of DSDs are getting more similar as the rainfall intensity increases (Figs. 6b, c), suggesting that the DSDs are approaching the equilibrium state as rainfall intensity increases. Majority samples of low rain rates are attributed to stratiform rainfall and the DSDs which are affected by melting, vapor deposition, aggregation, and riming processes (Dolan et al., 2018).

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Fig  6.  Raindrop size distributions at different rainfall intensity classes from 0800 LST 20 to 0800 LST 21 July 2021. “N(D)” indicates the number concentration, “D” the raindrop diameter, and “R” the rainfall intensity.

Another evidence of the equilibrium DSDs at heavy rainfall may be from the rainfall intensity dependence of D_m. We have classified the DSDs observed at Zhengzhou, Xinmi, and the other stations into three groups. As shown in Fig. 7, D_m values increase rapidly with rainfall intensity when it is less than 50 mm h⁻¹. After that, the fits between D_m and R are similar for Zhengzhou, Xinmi, and other stations, despite slightly higher D_m at higher rain rates as potentially due to the overestimation of large drops at high rainfall conditions (Tokay et al., 2013). This is expected, since the raindrop size distributions in heavy rainfall are mainly dependent on drop concentrations while the characteristic drop sizes do not significantly change (Uijlenhoet et al., 2003). Therefore, the continuous increase of number concentration is a critical factor leading to extreme rainfall intensity after D_m at Zhengzhou Station reaches an equilibrium state (Uijlenhoet et al., 2003; Chen et al., 2016).

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Fig  7.  Observations (scatter) of rainfall intensity (R; mm h⁻¹) and mass-weighted mean diameter (D_m; mm) and their fitting relationships (solid and dashed lines) at Zhengzhou Station (red line), Xinmi Station (blue line), and the other four stations (green line) from 0800 LST 20 to 0800 LST 21 July 2021. Note that the fitted curves are obtained by the least squares method, “> 50.0 mm h⁻¹” indicates the samples with the rainfall intensity larger than 50 mm h⁻¹, and “> 0.1 mm h⁻¹” denotes all samples.

4.   Linkage between surface DSDs and radar observations

4.1   Raindrop size distributions for different radar reflectivity ranges

Figure 8 shows the scatter distributions of lgN_w versus D_m at six stations for different radar reflectivity values in Zhengzhou area from 0800 LST 20 to 0800 LST 21 July 2021. Six radar reflectivity intensity (Z_h; dBZ) categories are defined for comparative analysis, namely 0.0 ≤ Z_h < 10.0, 10.0 ≤ Z_h < 20.0, 20.0 ≤ Z_h < 30.0, 30.0 ≤ Z_h < 40.0, 40.0 ≤ Z_h < 50.0, and 50.0 ≤ Z_h < 60.0. The majority of precipitation samples at the six stations are located in the continental–oceanic transition zone. For 0–20 dBZ, the scatter distributions of D_m and lgN_w are different at six stations. The highest value of lgN_w appears at Xingyang Station (Fig. 8d) and the lowest value is at Zhengzhou Station (Fig. 8a). The lowest D_m occurs at Xingyang Station (Fig. 8d). The scattered points are more concentrated at Xinmi Station (Fig. 8e), and the values of lgN_w and D_m are about 0.7–1.5 mm and 3.0–4.5 mm⁻¹ m⁻³, respectively. For 20–50 dBZ, D_m and lgN_w are respectively about 1.3–2.5 mm and 3.0–4.5 mm⁻¹ m⁻³ at the six stations. Especially, for 40–50 dBZ, the value of D_m reaches up to 2.7 mm at Zhengzhou Station, which is higher than other stations. Figure 8 presents that the increase of lgN_w is slower than D_m at the six stations and the precipitation particle diameter increases more significantly with the increase of radar reflectivity. When extreme heavy precipitation occurred at Zhengzhou Station, the highest radar reflectivity was above 50 dBZ; lgN_w and D_m also reached their peak values. The DSD characteristics of each station are quite different, which may be caused by the difference of precipitating cloud location (Gou et al., 2020; Li et al., 2023). The above analysis shows that lgN_w and D_m are less scattered as the rainfall intensity increases while the DSDs exhibit significant variations during this event.

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Fig  8.  Scatter distributions of lgN_w (mm⁻¹ m⁻³) versus D_m (mm) for different radar reflectivity categories at (a) Zhengzhou Station, (b) Songshan Station, (c) Xinzheng Station, (d) Xingyang Station, (e) Xinmi Station, and (f) Zhongmou Station from 0800 LST 20 to 0800 LST 21 July 2021. Black rectangles show the distribution areas of lgN_w versus D_m for marine and continental convective precipitation samples as in Bringi et al. (2003).

4.2   Vertical profiles of radar polarimetric observations

From 0800 LST 20 to 0800 LST 21 July 2021, the scatter distribution of lgN_w with D_m, the vertical profiles of radar reflectivity (Z_h), differential phase shift (K_dp), and differential reflectivity (Z_dr) for rainfall intensity larger than 50 mm h⁻¹ at different stations are used to further analyze the effects of DSDs on dual-polarization radar parameters of heavy rainfall.

From the scatter distribution of lgN_w with D_m (Fig. 9a), it can be found that lgN_w and D_m both increase markedly with increasing rainfall intensity. At the rainfall intensity (R; mm h⁻¹) class of 50.0 ≤ R < 80.0, the dense areas of the scatter are located in the range with D_m of 1.8–2.5 mm and lgN_w of 3.5–4.2 mm⁻¹ m⁻³. At the class of 80.0 ≤ R < 150.0, the dense areas of the scatter are located in the region with D_m of 2.1–2.6 mm and lgN_w of 3.7–4.3 mm⁻¹ m⁻³. At the class of 150.0 ≤ R < 250.0, the dense areas of the scatter are located in the range with D_m of 2.4–2.7 mm and lgN_w of 4.0–4.4 mm⁻¹ m⁻³.

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Fig  9.  (a) Scatter distribution of lgN_w (mm⁻¹ m⁻³) versus D_m (mm) and average profiles of (b) Z_h (dBZ), (c) K_dp (° km⁻¹), and (d) Z_dr (dB) at different rainfall intensity classes. Color squares and (1) denote the samples with 50.0 ≤ R < 80.0, color triangles and (2) denote the samples with 80.0 ≤ R < 150.0, and color stars and (3) denote the samples with 150.0 ≤ R < 250.0.

Figure 9b shows the average vertical profile of Z_h (three-dimensional radar mosaics in Henan Province) in the range of 2 km × 2 km with the raindrop spectrometer as the center, and Figs. 9c, d present the average vertical profiles of K_dp and Z_dr at Luoyang Radar Station in the range of 2 km × 2 km with the raindrop spectrometer as the center, respectively. Although the vertical profiles of Z_h, K_dp, and Z_dr obtained by the above method do not exactly match with the actual observations, they can reflect the vertical distribution characteristics of the radar parameters over the raindrop spectrometer at each station to the greatest extent. From Figs. 9b–d, we find that Z_h, K_dp, and Z_dr at all stations generally increase with decreasing height and increasing rainfall intensity. For rainfall intensity greater than 50 mm h⁻¹, the average profiles of Z_h, K_dp, and Z_dr at Zhengzhou Station are different from those at the other stations.

The average height of 30-dBZ echo at Zhengzhou Station (Fig. 9b) exceeds 9 km (−20°C layer). In terms of rainfall intensity above 80 mm h⁻¹, the average height of the 30-dBZ echo reaches 11 km at Zhengzhou Station, while the average height of the 30-dBZ echo at other stations is only 7.5 km. This indicates that the upward motion of the convective system at Zhengzhou Station is more intense during this extraordinary rainstorm event (DeMott and Rutledge, 1998; Chen et al., 2022). The average height of the 30-dBZ echo reaches 11 km when rainfall intensity is larger than 80 mm h⁻¹ at Zhengzhou Station, which is dramatically different from the conclusion that the intensity of extreme convective precipitation is weakly correlated with the height of convection development during the Meiyu period in the Jianghuai River basin (Yang et al., 2019). At Zhengzhou Station, the Z_h value below the 0°C layer is higher than that at the other stations by about 5–10 dBZ, indicating that the precipitation intensity over Zhengzhou is higher than other stations.

The observed K_dp generally increases as the height approaches surface (Fig. 9c). Zhengzhou, Songshan, and Xinmi are characterized by the most significant increase of K_dp close to the surface. At the rainfall intensity class of 80.0 ≤ R < 150.0, the K_dp values at Zhengzhou and Xinmi stations are relatively close, i.e., 0.8° km⁻¹ at the 0°C layer and 1.4° km⁻¹ near the surface. When rainfall intensity is larger than 150 mm h⁻¹ at Zhengzhou Station, the K_dp values are 1.2° km⁻¹ at the 0°C layer and 2.8° km⁻¹ near the surface, corresponding to the observed 201.9 mm hourly rainfall recorded at the surface (Li et al., 2023).

As shown in Fig. 9d, Z_dr decreases with the descending of radar sampling height until the height of about 7 km, potentially owing to decreased snow density during aggregation process (Li et al., 2018, 2020). From 7 km to the environmental 0°C height, the increases of Z_dr may be associated with updrafts lofting rain water above the melting layer. The most extensive rainfall period (red sterns) is characterized by the highest Z_dr above the melting layer, suggesting the essential link between updrafts and extreme rainfall formation. Below the 0°C height, Z_dr of the most intensive rainfall further increases towards the surface, which collaborates with observations of enhanced K_dp.

5.   Radar QPE applications

In China’s operational weather radar QPE system, fixed parameters (Z = aR^b; a = 300.00, b = 1.40) are implemented. As discussed above, this extreme rainfall event is characterized by rather significant temporal–spatial variations of DSDs, and therefore the prescribed parameters may need to be adapted. Given radar reflectivity is still the most used radar measurement in operational service and the dependence of DSDs characteristics on reflectivity ranges (Fig. 8), the coefficients used for Z = aR^b are fitted in different reflectivity groups (Table 2) by using DSD data of the six stations from 0800 LST 20 to 0800 LST 21 July 2021. For a given radar reflectivity, the QPE can be made by employing the parameters in corresponding ranges, which is referred to as reflectivity-grouped fitting. This method was implemented on Zhengzhou Radar, and the QPE results were validated against 139 rain gauges in the Zhengzhou area (Fig. 1a). Note that due to the sparsity of DSD samples, fixed Z–R relation parameters were used for the reflectivity group of 0–20 and 50–60 dBZ. For a comparison, the results were compared to the operational QPE products (Z = 300.00R^1.40) as well as Z = 232.87R^1.40 in which the coefficients were fitted using all OTT observations.

Table  2.  Parameters (a and b) of the Z–R relationship of DSDs at the six stations by using the reflectivity-grouped fitting algorithm for different radar reflectivity ranges

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Radar reflectivity (dBZ)	ZZ			SS			XZ			XY			XM			ZM
	a	b		a	b		a	b		a	b		a	b		a	b
20.0 ≤ Zh < 30.0	338.93	0.90		144.73	1.54		309.81	0.83		203.5	0.97		241.2	0.99		276.25	1.03
30.0 ≤ Zh < 40.0	603.89	0.99		422.85	1.07		521.61	1.05		311.73	1.14		458.37	0.99		564.48	0.97
40.0 ≤ Zh < 50.0	473.17	1.25		446.11	1.22		360.84	1.29		156.43	1.46		382.66	1.28		526.02	1.17

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We use mean bias ratio (MBR) and the root-mean-square error (RMSE) to evaluate the performance of different approaches:

where G and R denote the hourly rainfall from rain gauge and radar estimates, respectively.

Figure 10 compares the hourly rainfall between rain gauge observations and radar estimates. As can be seen, although some scatters are above the 1 : 1 line, majority of the scatters are distributed below the 1 : 1 line in Figs. 10a–c, indicating an overall underestimation. The majority of the scatters are distributed above the 1 : 1 line for gauge rainfall less than 20 mm h⁻¹ in Fig. 10a, representing an overestimation for light rainfall. The MBR and RMSE are 0.78 and 14.31 for the operational algorithm. For the fixed parameter algorithm and the reflectivity-grouped fitting algorithm, the MBRs (RMSEs) are 0.65 (10.77) and 0.88 (8.70), respectively. The scores of the reflectivity-grouped fitting algorithm are the best among all algorithms. Scrutinizing the evaluation results in Fig. 10, the underestimation of the heavy rainfall is found for all three algorithms. Nevertheless, the reflectivity-grouped fitting algorithm has superior performance to both the operational algorithm and fixed parameter algorithm in terms of MBR and RMSE. As shown in Fig. 10c, the QPE results agree fairly well with gauge observations. Especially, the rainfall accumulations estimated by the operational algorithm, the fixed parameter algorithm, and the reflectivity-grouped fitting algorithm are 77.4, 73.3, and 97.2 mm h⁻¹ during 1600–1700 LST 20 July 2021 at Zhengzhou Station.

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Fig  10.  Comparison of hourly rainfall between rain gauge and (a) the operational algorithm, (b) the fixed parameter algorithm, and (c) the reflectivity-grouped fitting algorithm from 0800 LST 20 to 0800 LST 21 July 2021.

Table 3 compares the performance of different algorithms. For the R below 20.0 mm h⁻¹, significant overestimation can be found for operational algorithms and the values of MBR and RMSE are 1.16 and 7.81. The MBR values are 0.68 and 0.93 and the RMSE values are 4.88 and 4.78 for fixed parameter algorithm and reflectivity-grouped fitting algorithm, which shows that the two algorithms have overall underestimation and the reflectivity-grouped fitting algorithm has better performance. For the R equal to or greater than 20.0 mm h⁻¹, the MBR values are 0.55, 0.57, and 0.79 and the RMSE values are 28.46, 23.69, and 18.36 for the operational algorithm, the fixed parameter algorithm, and the reflectivity-grouped fitting algorithm, respectively. As can be seen, the use of Z–R parameterization of the operational algorithms and the fixed parameter algorithm more significantly underestimate the rain rate, while the obviously better performance is found using the reflectivity-grouped fitting algorithm. As mentioned, the reflectivity-grouped fitting algorithm yields the smallest RMSE for all rain rate, suggesting the reflectivity-grouped fitted Z–R relationship can substantially improve the radar QPE performance.

Table  3.  Mean bias ratio (MBR) and root-mean-square error (RMSE) of the operational algorithm, the fixed parameter algorithm, and the reflectivity-grouped fitting algorithm from 0800 LST 20 to 0800 LST 21 July 2021

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Rainfall intensity (mm h−1)	Operational			Fixed parameter			Reflectivity-grouped fitting
	MBR	RMSE		MBR	RMSE		MBR	RMSE
R < 20.0	1.16	7.81		0.68	4.88		0.93	4.78
R ≥ 20.0	0.55	28.46		0.57	23.69		0.79	18.36

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6.   Conclusions

Based on the data from operational observations of Parsivel OTT laser raindrop disdrometers, rain gauges, and weather radars during the extraordinary rainstorm in Zhengzhou on 20 July 2021, we investigated the DSDs at different stations in this event and assessed the radar-based QPE during this event. The main conclusions are as follows.

This event is characterized by rather significant temporal–spatial variability in rainfall and hydrometeors distributions. Observations of six Parsivel OTT disdrometers show remarkable site-to-site variations of 24-h accumulated rainfall, which ranges from 198.3 to 624.1 mm. The observed DSDs are more scattered at low rain rates and are increasingly approaching the equilibrium state as the rainfall intensity increases. Specifically, the most intensive rainfall recorded at Zhengzhou Station is characterized by rather high D_m and Z_h, while D_m does not show significantly increase when R exceeds 50 mm h⁻¹.

Given the observed prevalence of DSDs with an equilibrium state in extreme rainfall, it would be interesting to assess the general applicability of assuming an equilibrium state in future studies. The most extreme rainfall as recorded by the Parsivel OTT disdrometers network is characterized by highest Z_dr between −10 and 0°C, suggesting the essential link between updrafts and extreme rainfall formation. Below the melting layer, the most intensive rainfall as recorded by OTT increases towards the surface, collaborating with continuingly enhanced Z_dr and K_dp.

A reflectivity-grouped fitting Z–R parameterization algorithm for radar QPE is developed, and rain gauge observations are used for evaluation. This approach yields the smallest RMSE compared with the methods using fixed Z–R parameterization and the operational algorithm. Since the Z–R relationship is strongly influenced by DSDs characteristics, the precipitation retrieval abilities of the stations in the Zhengzhou area are quite different from using the same Z–R fitting relationship. Although the R(Z) is operationally used for QPE, dual-polarization observations, which are becoming more available, are expected to yield more accurate QPE (Cifelli et al., 2011; Chen and Chandrasekar, 2015; Li et al., 2023).

However, we are aware that the microphysics of raindrops, e.g., the standard deviation of raindrop canting angles, aspect ratios, oscillations, and so on, are prone to environmental conditions, and the use of traditional assumptions may introduce significant biases (Li et al., 2023; Zheng et al., 2023). We advocate that more efforts be made to examine extreme rain microphysics for better monitoring of extreme rainfall.