ZDR Backwards Arc: Evidence of Multi‐Directional Size Sorting in the Storm Producing 201.9 mm Hourly Rainfall

In this study, we present radar polarimetric characterizations of the storm producing 201.9 mm hourly rainfall on 20 July 2021 in Zhengzhou, China. We employed the separation signatures of enhanced polarimetric observations to investigate hydrometeor size sorting processes, and developed an algorithm to quantify the size sorting directions. Analysis of coupled polarimetric observations unraveled multi‐directional size sorting (MSS) occurred as a low‐level differential reflectivity ZDR backwards arc signature encompassing the rainfall center during the most intensive rainfall period. The rainfall intensification is in step with the increase of size sorting directions. Model simulations with two‐moment microphysics scheme suggest that the presence of arc‐shaped updrafts is conducive to MSS and increased rain rates around the rainfall center. This work sheds novel insights into the kinematics‐driven microphysics in extreme rainfall storms, warranting the potential of using coupled polarimetric signatures for warning catastrophic extreme rainfall events.


Introduction
Extreme rainfall is a worldwide natural hazard threatening human life, disrupting transport, and causing property damages.Although there is a wide variety of ways for defining extreme rainfall events, the consensus is that the hourly rainfall in such events ranges from several to tens of millimeters (Guerreiro et al., 2018).In the scientific literature, rainfall events characterized by hourly rainfall above 100 mm have been investigated from various perspectives, while there are very limited reports of catastrophic hourly rainfall exceeding 200 mm.Such exceptional extreme rainfall events are particularly conducive to devastating flooding episodes, and may occur more frequently in the future owing to climate change (Seneviratne et al., 2022;X. Zhang et al., 2017).However, the relevant physical processes governing the formation and intensification of exceptional extreme rainfall storms are poorly understood, presenting a challenge for predicting and real-time warning such events (Schumacher & Rasmussen, 2020).
On 20 July 2021, an unprecedented rainfall storm pouring record-breaking hourly rainfall of 201.9 mm hit urban Zhengzhou and caused tremendous losses.This event took place under favorable synoptic conditions (Sun, Fu, et al., 2023;J. Xu et al., 2022;S. Zhang et al., 2022), including the weak Huang-Huai cyclone, the western Pacific subtropical high, the deep Tibetan high, and Typhoons In-Fa and Cempaka (Yin et al., 2022).The meso-β-scale low pressure system developed from southwest of Zhengzhou was conducive to the intensification of the rainstorm (Sun, Li, et al., 2023).Although operational models showed some skills in heavy rainfall prediction, the extremity of rainfall intensity was severely underpredicted (Q.Zhang et al., 2023;Zhu et al., 2022).Some recent studies have investigated the mesoscale dynamics responsible for the exceptional hourly rainfall of 201.9 mm from 16:00 to 17:00 LST.Yin et al. (2022) using Weather Research & Forecasting (WRF)-ARW model simulations reproduced the major synopticscale weather systems and proposed that the arc-shaped updrafts transporting rain water into the same trailing region were the main dynamical driver for the 201.9 mm hourly rainfall.The presence of an arc-shaped convergence zone was also found in another independent simulation study (Wei et al., 2022) and in analyses with real-time radar data assimilation (Sun, Li, et al., 2023).In spite of the consensus on the presence of arc-shaped updrafts, the modeling studies above employed one-moment schemes in which the variations of raindrop size distributions, which were characterized by rather high temporal-spatial variability in this event (Cui et al., 2024) and directly linked to surface rainfall accumulations (Huang et al., 2020;H. Li et al., 2023), was overlooked, suggesting a need to examine the interactions between the storm-scale kinematics and microphysics.
Radars serve as a unique tool for cloud and precipitation observation (D.Li et al., 2024;Protat et al., 2019;C. Zhao & Garrett, 2008).Radar polarimetric observations allow real-time monitoring raindrop size distributions with high temporal and spatial resolutions, demonstrating their unique value in understanding rainfall microphysics (K.Zhao et al., 2019).The underlying link between polarimetric signatures and raindrop size distributions roots from the increasing non-sphericity of raindrops with their diameters.Generally, larger raindrop diameters are characterized by higher differential reflectivity Z DR and increased rainfall water content is correlated with specific differential phase K DP .Presence of updrafts usually leads to storm-relative winds and size sorting, namely larger hydrometeors in rising parcels sediment at the vicinity of updrafts while smaller ones ride with updrafts.Hence, the impact of size sorting on raindrop size distributions is manifested as separation signatures of Z DR and K DP maxima (Loeffler & Kumjian, 2018;Loeffler et al., 2020).
In this study, we employed the separation signatures of enhanced Z DR and K DP to characterize the size sorting signatures in the Zhengzhou event.The paper is organized as follows.Section 2 introduces the used radar data, the approach for quantifying size sorting directions and model settings.Section 3 presents analysis of radar polarimetric observations, followed by model simulations in Section 4. A conceptual model and conclusions are given in Section 5.

Radar Data
In this study, we use observations from China's New Generation Doppler Weather Radars (CINRADs).At the national level, CINRADs are in the progress of upgrading to dual-polarization systems, and this event were observed by S-band dual-polarization radars deployed at Luoyang city (LY radar) and Zhengzhou city (ZZ radar) as marked by black triangles in Figure 1a.The ZZ and LY radars have same configurations, for example, a range resolution of 0.25 km, an azimuth resolution of 1°, and a beam width of 1°.The calibration of Z DR was made during light rainfall periods, and the calibration accuracy is expected to be 0.1-0.2dB (Bringi & Chandrasekar, 2001).K DP was estimated with a least square fitting algorithm, and the uncertainty is expected to be within 0.5°/km in heavy rainfall (H.Li et al., 2023).Both radars work in volume coverage pattern 21 mode consisting nine plan position indicator scans with a volumetric update time of 6 min.
As shown in Figure 1a, the gauge reporting 201.9 mm hourly rainfall is marked by a black solid circle, and the ZZ radar was located at its vicinity.Although the near-surface rainfall can be well detected by the ZZ radar, its observations of this extreme storm were contaminated by surface clutter.To mitigate this, K DP observations filtered with ρ hv = 0.8 from elevations of 0.5, 1.5, 2.4, 3.3, and 4.3°were merged to generate near-surface K DP estimates.The K DP -based rain rates show good consistency (bias of ∼10 mm/hr, standard deviation of 10 ∼ 20 mm/hr) with surface rain gauge observations for hourly rainfall below 100 mm, while the 201.9 mm hourly rainfall was significantly underestimated (H.Li et al., 2023).Here, we use the parameterized K DP as used by H. Li et al. (2023) to estimate rain rates, but the estimated rain rates above 150 mm/hr should be interpreted with caution.
The LY radar was about 120 km away from the rainfall storm, and the mountain between Luoyang and Zhengzhou partially blocked the LY radar beams at 0.5°.K DP is immune to this effect, while Z DR can be affected.Following the method proposed by Giangrande and Ryzhkov (2005), we computed the azimuthal Z DR difference between the elevations at 0.5°and 1.5°within the range of 70-80 km to LY radar during stratiform rainfall on 19th July 2021.
The results suggest severe beam blockages at azimuth angles above 100°(Figure S1 in Supporting Information S1), while the Z DR bias in the region shown in Figure 1b is within the uncertainty of 0.1-0.2dB (Giangrande & Ryzhkov, 2005).Therefore, the radar data quality is assured in this study.Compared with ZZ radar which observed the near-surface structure of this storm, LY radar has a lowest detectable height of about 2.2 km at 0.5°o ver Zhengzhou city.Given the low-level size sorting usually occurs at some distances to the surface, for example, 1 km used by Tam et al. (2022), we employed LY radar observations at 0.5°to characterize the size sorting process in this event.The open-source tool Py-ART (Helmus & Collis, 2016) was used to grid the LY radar data at 0.5°into the spatial resolution of 0.2 km ("Barnes2" method) for quantifying the separation signatures of enhanced Z DR and K DP .Then, the gridded data was used to retrieve the median volume diameter D 0 and total number concentration of raindrops N t (Hu & Ryzhkov, 2022).

Quantification of Size Sorting Directions
The locally enhanced Z DR is indicative of size sorting, as commonly observed in tornadoes (e.g., Kumjian & Ryzhkov, 2008;Ryzhkov et al., 2005).The value of coupled separation signatures between Z DR and K DP enhancement regions has been realized until recent years.Loeffler and Kumjian (2018) retrieved the direction of Z DR -K DP separation relative to nonsupercell tornado motion, and found that the separation direction increasing toward 90°is associated with increased storm-relative helicity.Wilson and Van Den Broeke (2021) developed an automated Python package to quantify the Z DR -K DP separation signatures.Tam et al. (2022) employed the similar rational to quantify the size sorting signatures in convections.These approaches assume the presence of a single inflow, and there is a lack of study addressing the case of multiple directions of size sorting in presence of multidirectional inflows (Sun, Li, et al., 2023;Wei et al., 2022;Yin et al., 2022).Here, we present a seminal approach to quantify the size sorting directions based on coupled Z DR -K DP separation signatures.Firstly, the storm center is identified.Different from using a percentage threshold which is sensitive to the area size (Loeffler & Kumjian, 2018;Tam et al., 2022), we simply define half of the maximum K DP in the region of interest as the K DP threshold.This threshold is used to identify the largest K DP enhancement region whose geometrical center is assigned as the storm center.Note that we do not use point maximum K DP , given that it is sensitive to radar noise (Loeffler & Kumjian, 2018).
Secondly, the threshold used for flagging Z DR enhancement region is estimated.Since the sorting distance mostly does not exceed 10 km (Tam et al., 2022), we define the radial maximum Z DR within 10 km to the rainfall center in each azimuth interval (5°used) at a given time t as Z DR, max (t, i), (i = 1, …, 72).We assume that Z DR monotonously increases from the rainfall center to Z DR enhancement region, and therefore Z DR, max (t, i) is found when the first decrease of Z DR is detected.During the period from t 1 to t 2 , a certain percentile of all Z DR, max values is used to flag enhanced Z DR region.The use of a percentile can be subjective (Loeffler & Kumjian, 2018;Tam et al., 2022;Wilson & Van Den Broeke, 2021), and the impact of different percentiles will be discussed later.
Finally, the sum of size sorting directions is defined as the azimuths of enhanced Z DR relative to each rainfall center.

Model Setup
To assess the impact of storm kinematics on size sorting, this event was simulated with Weather Research & Forecasting Model (WRF)-ARW model with triply nested grids characterized by horizontal resolutions of 9, 3, and 1 km, respectively.The model setup is identical to (Yin et al., 2022) except that we used the National Severe Storms Laboratory (NSSL) two-moment microphysics scheme for facilitating the simulation of size sorting in the storm.The rapid radiative transfer model (Mlawer et al., 1997) and the Dudhia scheme (Dudhia, 1989) were used for long-and short-wave radiative flux calculations.The Mellor-Yamada-Janjic turbulent kinetic energy scheme was used for the planetary boundary layer parameterization, and the Monin-Obukhov scheme for the surface layer (Janjić, 1994).The unified Noah land surface model was implemented (Tewari, 2004).The model was initiated with the operational global analysis data of Global Forecasting System of National Centers for Environmental Prediction.The WRF simulation results were used as input to Cloud-resolving model Radar SIMulator (CR-SIM) (Oue et al., 2020) for generating radar polarimetric products.Then, the model outputs were interpolated into the spatial resolution of 0.2 km for quantifying the size sorting directions.

Overview of the Storm Movement
As shown in Figure 1a, the extreme-rainfall-producing storm as marked by the colored isolines (K DP = 2°/km near-surface) moved eastward before 16:00 LST.Then, it was almost stationary from 16:00 to 17:00 LST after which it moved to the east of Zhengzhou city.From 16:00 to 16:30 LST, the storm was experiencing a slight clockwise rotation, leading to a relatively long-time exposure of the gauge to high rain rates.Interestingly, the gauge observations show two peaks of the rain rate.The first one was at 16:00 LST, and the second one started appearing at around 16:25 LST and peaked at 16:40 LST.It appears that the second surge of rain rate is associated with the clockwise rotation which as a result blocked the storm, leaving 15-20 min exposure of the gauge site to the extreme rainfall.

Z DR backwards arc Signatures
To characterize the rainfall storm during the second rain rate peak, we compared radar polarimetric observations near surface (ZZ radar) and at 2.2 km (LY radar) at 16:30 LST.As shown in Figure 1c, the rainfall maps as observed by ZZ and LY radars were spatially offset owing to the vertically tilted structure of the storm (H.Li et al., 2023;Yin et al., 2022).In addition, there was a prominent Z DR enhancement region at the vicinity of rainfall center at 2.2 km (Figure 1b).One may be reminded of the Z DR arc as commonly observed in convective systems with wind shears, such as, supercells.However, the relative position between Z DR and K DP enhancement regions is essentially different from the Z DR arc at whose outer side the heavy precipitation occurs, for example, in supercells (Kumjian & Ryzhkov, 2008).In this case, the region of enhanced precipitation is located at the arc's inner side and therefore we refer it as Z DR backwards arc.Note that we are aware that the presence of hail may affect the interpretation of Z DR signals (Dawson et al., 2014), but polarimetric signals of hail are insignificant (H.Li et al., 2023).Loeffler and Kumjian (2020) suggested that the vector from Z DR to K DP maxima is aligned with the mean stormrelative wind over the sorting layer.Namely, raindrops are sorted along the wind direction as commonly observed (Tam et al., 2022).In our observations, the Z DR backwards arc coupled with enhanced K DP suggests arc-shaped storm-relative winds blowing toward the rainfall center, leading to multi-directional size sorting (MSS).To the best of our knowledge, this is the first report presenting this distinct feature.The MSS process is in line with underlying arc-shaped updrafts, which take smaller drops toward the rainfall center, leaving an arc-shaped region dominated by large raindrops with a high degree of non-sphericity (Zheng et al., 2023), as indicated in previous model simulations (Sun, Li, et al., 2023;Wei et al., 2022;Yin et al., 2022).
Intensive updrafts can be inferred from distinct Z DR columns, namely elevated enhanced Z DR above the freezing level (Kumjian & Ryzhkov, 2008, 2009).To examine this signature, vertical distributions of rain rates estimated from K DP (H.Li et al., 2023) as well as Z DR at the ranges of 7, 5, and 3 km to the rainfall center at 16:30 LST were analyzed (Figure S2 in Supporting Information S1).The intersected Z DR columns, which are indicative of updrafts, were located at about 50°and 200°, despite that the Z DR values above 0°C level are significantly lower than those in deep convections (Kumjian et al., 2014).The results suggest relatively weak updrafts as well as hail growth above the freezing level in Zhengzhou event (Kumjian et al., 2014;Tam et al., 2022), collaborating with previous studies that the extreme rainfall is more favorable in shallower convection (J.Xu et al., 2022;Yu et al., 2022).
Snapshots of Z DR and coupled K DP observations from 16:06 to 16:48 LST are given in Figures 2a-2h.In general, the observed patterns of high rainfall rates (K DP = 2°/km) near the surface (ZZ radar, black isolines) and at 2.2 km (LY radar, green isolines) are much alike, but are not completely overlapped owing to the vertically titled storm structure (Yin et al., 2022).The region of K DP > 2°/km became increasingly compact from 16:06 to 16:30 LST, after which the storm started weakening.Accordingly, the morphology of high-Z DR area (reddish region) was drastically changing, and the most distinctive Z DR backwards arc occurred at 16:30 LST.Then, the Z DR backwards arc signatures started breaking.Time serials of radial maximum Z DR are given in Figure 2i.We have quantified the directions of size sorting using the percentile of 70% (solid curve) and 80% (dashed curve), respectively.It seems to us that 70% allows a smoother transition of size sorting directions, and therefore 70% was employed.Before 16:00 LST, the storm was maintained by the east inflow and there was no indication of MSS.Then, the size sorting directions expanded and the secondary inflow from south-southwest intensified.At 16:30 LST, the two inflows were merged, leading to the highest Z DR backwards arc length.Comparison to the simulations by Sun, Li, et al. (2023) suggests that the enhanced Z DR is collocated with the arc-shaped convergent line.

Impact of MSS on Rainfall Intensity
The sorting of relatively smaller raindrops can significantly modulate the rain water distribution in the storm (Kumjian & Ryzhkov, 2012).To further assess the effect of MSS on raindrop size distributions, we have retrieved the median volume diameter D 0 and total number concentration of raindrops N t in this event (Figure S3 in Supporting Information S1).Our retrievals show that D 0 around the rainfall center does not significantly change with time, owing to equilibrium-like raindrop size distributions at such high rain rates (Bringi et al., 2003;Cui et al., 2024), and the rainfall rate is mainly correlated with N t .The sorting distance is in step with N t , suggesting that the importance of MSS to the surge of N t during this event.
Directly quantifying the impact of MSS on rainfall intensity seems to be rather challenging, given the radar estimates of rain rates exceeding 150 mm/hr are subject to significant uncertainties (H.Li et al., 2023).Alternatively, we opted to quantify the area of high rain rates.Figure 2j shows the temporal variations of sorting directions (Z DR backwards arc length) as well as the areas of K DP exceeding 2 (light blue), 2.5 (medium blue) and 3 (dark blue) °/km rainfall intensity as observed near surface (dashed curve) and at 2.2 km (solid curve).The areas of K DP at different ranges generally increase with the sorting directions, suggesting the relevance of MSS for increased rain rates near the rainfall center.For a K DP threshold of 2°/km, the corresponding areas are significantly larger near surface than those at 2.2 km, which may attribute to the active warm-cloud processes (Chen et al., 2022) or enhanced horizontal transport of rain water mass below 2.2 km.In contrast, there are no significant differences regarding the areas of K DP > 2.5°/km at both near surface and 2.2 km.Interestingly, the correlation between sorting directions and areas of K DP > 2.5°/km at both near surface and 2.2 km is nearly linear.Although radar observations alone may not be adequate to explain this linear relationship, the strong correlation further suggests the importance of MSS to surged rain rates near the rainfall center.

MSS Signatures in Model Simulations
The model simulations resulted in a rainfall center about 20 km to the southwest of the Zhengzhou city and the simulated maximum rainfall accumulation was 156 mm from 16:00 to 17:00 LST.The decent biases in rainfall location as well as accumulation suggest the defects of model representations which may root from multiple sources as discussed by Y. Zhang et al. (2022).Here, we are not aiming to accurately reproduce this event, but to show how the rain rate can be modulated by MSS which is in principle favorable in arc-shaped convergent zones that can be well identified in simulated updrafts.In contrast, due to the sparse sampling of radars, accurate retrieval of the 3D wind field for diagnosing the arc-shaped updrafts is challenging.Alternatively, model simulation serves as an effective means to disentangle the link between storm dynamics and polarimetric signatures via explicitly resolving the dynamics and microphysics in storms (Kumjian et al., 2014).
As shown in Figures 3d-3f, Z DR backwards arc signatures can be well identified from 16:24-16:48 LST, in spite of the smaller Z DR values and weaker rain rates than radar observations.The rainfall center is located in the vicinity of the inner arc, presenting similar patterns as shown in Figure 2. The Z DR backwards arc is well collocated with arc-shaped updrafts exceeding 4 m/s (dotted isolines), suggesting that the arc-shaped updrafts are conducive to MSS.As shown in Figures 3i and 3j, the expansion of high-rain-rate area is well correlated with the Z DR backwards arc length.From 16:00 to 16:24 LST, the areas of K DP > 1.0°/km and K DP > 1.5°/km show increases in step with the Z DR backwards arc length, collaborating with the dual-polarization radar observations.Given the fact that the size sorting process cannot be emulated in one-moment microphysics schemes, our simulation highlights the importance of using multi-moment schemes for physically simulating such extreme rainfall events.

Discussions and Conclusions
In past 2 years, a vast number of studies have been made to analyze and numerically simulate the catastrophic Zhengzhou event, and some suggest that this event has rather low predictability.Forecasts from major numerical models show large variations in terms of the intensity and distribution of surface rainfall accumulations, and deviate from surface observations (Yin et al., 2022).Although Yin et al. (2022) managed to reproduce the extreme hourly rainfall accumulation, the resultant rainfall center was about 10 km away from observed.The amplification of error growth with the contribution of moist convective process further prevents accurately predicting the location and strength of the Zhengzhou extreme rainfall event (Y.Zhang et al., 2022).Nonetheless, model simulations suggest that the extreme-rainfall-producing storm in the Zhengzhou 20th July 2021 event was characterized by an arc-shaped convergence zone (Sun, Li, et al., 2023;Wei et al., 2022;Yin et al., 2022).This study identified the microphysical fingerprints of the arc-shaped convergence zone using polarimetric radar observations.Furthermore, we found that the increase of sorting directions is well correlated with the amplification of rain rate around the rainfall center.
The effect of multi-directional size sorting is conceptualized in Figure 4.The size sorting process as driven by updrafts effectively redistributes raindrop size distributions in a storm.Large raindrops sediment at the vicinity of updrafts while smaller raindrops are transported to further distances, leading to increased characteristic drop size and enhanced Z DR .The arc-shaped updrafts sort raindrops along the trajectories of stormrelative winds, and smaller raindrops are adverted toward the rainfall center, enhancing rain rates along the sorting path.As the arc length increases, more raindrops will be advected toward the rainfall center where the raindrop size distribution which has already reached equilibrium will be amplified, leading to amplified rain rates around the rainfall center.After briefly comparing the dual-polarimetric observations in recent extreme rainfall events in China, we have also identified such Z DR backwards arc signatures in some cases.Significance of the MSS mechanism in extreme rainfall events will be investigated from a statistical perspective in a separate study.
Our results also warrant the necessity of employing multi-moment cloud microphysics schemes for models attempting to simulate extreme rainfall events.The microphysics parameterization can have substantial impact on extreme rainfall simulation, for example, by modulating latent heating, flows, as well as convergence zones (H.Xu et al., 2023).Our results suggest the importance of parameterizing sorting process, which can be represented in multi-moment schemes instead of single-moment ones, in extreme rainfall simulation.In addition, the observed size sorting distances are on the order of 2-5 km, which are not resolved in most operational weather models.
Besides the major challenges in forecasting extreme rainfall as confronted by numerical models, quantitative remote sensing of such events is highly uncertain.Although radars have been operationally employed to estimate local rainfall accumulation bearing commonly used assumptions (J.Zhang et al., 2016), these estimates do not match with the record-breaking 201.9 mm hourly accumulation (H.Li et al., 2023).Our analysis, albeit on one extreme case, suggests that the rainfall extremity is in general positively correlated with the length of Z DR backwards arc.The presented results show this overlooked mechanism was highly relevant to the amplification of the local rainfall extremity.Hence, the Z DR backwards arc signature may be used to warn that the surface rainfall rates can be much higher than radar estimates.

Data Availability Statement
Due to the radar data management restriction of CMA, the raw radar data is not available.The reprocessed polarimetric data and model outputs can be accessed at H. Li (2024).

Figure 1 .
Figure 1.(a) Topography between Zhengzhou and Luoyang with two weather radars (black triangles) and the gauge (black dot) reporting 201.9 mm hourly rainfall.Minutely (black curve) and hourly (blue bars) rain rates from 12:00 to 18:00 LST as observed by the gauge are shown at the northwest of the figure.Colored isolines indicate K DP = 2°/km near-surface (Zhengzhou radar) at 16:00, 16:30, 17:00 LST, respectively.(b) Z DR and (c) K DP observations at about 2.2 km to surface (0.5°elevation of Luoyang radar) at 16:30 LST.The blue and green isolines indicate K DP = 2°/km observed from Zhengzhou and Luoyang radars, respectively.

Figure 2 .
Figure 2. (a-h) Snapshots of Z DR at about 2.2 km observed by the Luoyang radar during 16:06-16:48 LST.Light gray lines denote the boundaries of Zhengzhou city which is about 120 km to the east of Luoyang radar.Blue and green isolines indicate K DP = 2°/km near-surface (Zhengzhou radar) and at 2.2 km (Luoyang radar), respectively.(i) Maximum radial Z DR within 10 km to each rainfall center as a function of azimuth relative to each rainfall center during 16:00-16:42 LST.Black solid and dashed lines indicate 70% and 80% percentiles of maximum radial Z DR , respectively.(j) Length of Z DR backwards arc (black solid line) as defined by 70% percentiles of maximum radial Z DR versus areas of different ranges of K DP observed nearsurface (Zhengzhou radar, dashed line) and at 2.2 km (Luoyang radar, solid line).

Figure 3 .
Figure 3. (a-h) Model simulations of Z DR at about 2.2 km during 16:06-16:48 LST. Green isolines indicate K DP = 1.5°/km at 2.2 km.Black dashed isolines indicating updrafts exceeding 4 m/s.(i) Maximum radial Z DR within 10 km to each rainfall center as a function of azimuth relative to each rainfall center during 16:00-16:42 LST.Black solid and dashed lines indicate 70% and 80% percentiles of maximum radial Z DR , respectively.(j) Length of Z DR backwards arc (black solid line) as defined by 70% percentile of maximum radial Z DR versus areas of different ranges of K DP observed at 2.2 km.

Figure 4 .
Figure 4.A conceptual model illustrating the low-level multi-directional size sorting manifested as Z DR backwards arc (reddish area) and the associated rain rate enhancement toward the rainfall center (bluish area).The dashed isoline and arrow indicate updrafts in the sorting layer and the inflow from the lower level, respectively.The increase of arc length amplifies raindrop number concentrations toward the rainfall center, thus surging the rainfall extremity.
Figures S1-S3 are available in Supporting Information S1.We appreciate Professor Qinghong Zhang, Professor Yali Luo, Professor Xudong Liang and Dr Rumeng Li for very helpful discussions on the Zhengzhou extreme rainfall event.This study is jointly supported by National Key R&D Program of China (Grant 2022YFC3003903), National Natural Science Foundation of China (Grants 42305087, 42075083), Chinese Academy of Meteorological Sciences Basic Research Fund (Grants 2022Y008, 2023Z008), S&T Development Fund of Chinese Academy of Meteorological Sciences (Grant 2023KJ047) and Alexander von Humboldt Foundation.We thank the information center of China Meteorological Administration for providing us super computing resources and the access to radar data.