Analysis of a Hail Process in Foshan, Guangdong Province Using an Advanced Phased-Array Radar System and Development of a New Early Warning Index

1.   Introduction

Hail is a type of severe convective weather known for its severe local impact, brief duration, and potential for causing extensive damage. Hail detection and prediction have been extensively studied by using traditional weather radar systems (Browning, 1964; Weisman and Klemp, 1984; Witt et al., 1998; Zhang et al., 2014). Foote (1984) postulated that hail formation is linked to an inclined updraft, allowing precipitation particles to separate from the updraft without causing it to weaken notably because of particle fallout. In supercells, interaction between storm-scale rotation and ambient wind shear creates an additional upward pressure gradient force, thereby reinforcing the updraft. This relationship indicates that hail is closely related to updrafts and vertical wind shear (Johns and Doswell III, 1992).

A traditional single weather radar can only detect radial velocity, which limits its ability to accurately estimate updrafts and vertical wind shear. To address this issue, Potvin et al. (2012) proposed a multiradar wind-field retrieval method based on a three-dimensional variational (3D-Var) technique. This approach provides more consistent estimates of updrafts near the storm top compared with those produced by traditional methods based on the continuity equation (Protat and Zawadzki, 1999). North et al. (2017) evaluated these methods using WSD-88D and concluded that the 3D-Var approach satisfies both the mass continuity equation and the observational constraints, making it more robust than traditional methods.

To retrieve a three-dimensional wind field, it is essential to acquire radial velocity data for the same spatial point from the perspective of at least two different radars. Networked weather radar systems can fulfill this requirement through collaboration of multiple radars that provide comprehensive data from various directions. However, because of the time required for volume scans in networked radar systems (typically 1‒2 min, even at the most rapid rate), data acquisition times at the same spatial point can differ substantially. This time lag can have negative impact on the accuracy of wind-field retrieval (Chandrasekar et al., 2008; Bharadwaj et al., 2010). The advanced X-band phased-array weather radar system developed by the China Meteorological Administration Meteorological Observation Centre and related manufacturers differs from traditional networked weather radar. This system uses multiple phased-array radar front-ends (PARFs) synchronized in azimuth to complete a full-volume scan in 30 s. This configuration can achieve a maximum data time difference of only 5 s within the common detection area of multiple radar front-ends (Ma et al., 2019; Zhen et al., 2022). Li et al. (2020) experimentally validated the accuracy of wind retrieval using an X-band phased-array weather radar and examined the effect of data time differences on wind retrieval errors. Their results showed that greater data time differences lead to larger wind-field errors, and that convective precipitation systems are more sensitive to data time differences than non-convective precipitation systems. Xiao et al. (2022) used the Foshan X-band phased-array weather radar to study changes in the horizontal wind field during a short-term heavy precipitation event. Zhen et al. (2022) deployed seven front-end array weather radars for synchronized azimuth scanning, completing a rapid volume scan within 12 s with a front-end data time difference of < 2 s. This equipment was applied successfully to observation of convective weather at Huanghua International Airport (Hunan Province, China).

Despite these advancements, investigations on the dynamic structure of hail based on wind fields derived by using data with small time differences remain limited. The present study utilizes high-accuracy three-dimensional flow-field structure information obtained from an advanced X-band phased-array radar system in Foshan City, China to analyze the dynamic characteristics of supercell hail processes. Based on this analysis, a new hail early warning index is developed.

2.   Methods

2.1   Three-dimensional wind-field retrieval method

To describe the three-dimensional wind field, each grid point in a Cartesian coordinate system was defined with wind components (u, v, and w), where u represents the east–west direction, v represents the north‒south direction, and w represents the vertical direction. The wind field at any spatial point with coordinates (x, y, z) can be derived by interpolating these three components within the gridded field.

A 3D-Var method was employed for wind-field retrieval. This method involves defining an appropriate cost function and then minimizing it using an iterative approach, thereby achieving optimal wind-field retrieval.

The formulation of the cost function ensures that the retrieved three-dimensional wind field is consistent with physical principles and mathematical conditions; therefore, cost function $J$ can be calculated as follows:

where ${J}_{\rm O}$ is the observation constraint that is the integration of radial velocity data from multiple radars. For details regarding the other three constraints (${J}_{\rm M}$ for mass continuity, ${J}_{\rm P}$ for the ground boundary layer, and ${J}_{\rm S}$ for spatial smoothing), please refer to the literature (Potvin et al., 2012; North et al., 2017). This section focuses on the observation constraint ${J}_{\rm O}$, which is calculated as follows:

where N represents the number of radars used in the calculation and ${\lambda }_{\rm O}$ is a constant weight. The coordinates of the ith radar are denoted by ${x}_{i}$, ${y}_{i}$, and ${z}_{i}$, and ${V}_{\rm ri}^{\rm ob}$ is the radial velocity detected by the ith radar at the observation point (x, y, z). Parameter ${V}_{\rm ri}$ represents the projection of the retrieved wind vector (u, v, w) of the ith radar in the radial direction at the observation point (x, y, z), which is calculated by using Eq. (3):

where ${r}_{i}$ is the distance between the ith radar and point (x, y, z), which is calculated as follows:

and ${V}_{\rm Z}$ represents the upward velocity of the particle:

where $w$ is the updraft velocity and ${V}_{\rm T}$ is the terminal velocity of the particle. The value of ${V}_{\rm T}$ can be derived from the empirical R‒${V}_{\rm T}$ relationship proposed by Potvin et al. (2012). The formula for calculating ${V}_{\rm T}$ is expressed as follows:

where ${\rho }_{0}$ is the air density under standard atmospheric conditions (at sea level), $\rho$ is the air density at a specific altitude, R represents the reflectivity factor of radar echoes, α is the empirical value of 0.4 (Beard, 1976), and A and B are coefficients, the specific values of which are presented in Table 1.

Table  1.  R‒${V}_{\rm T}$ relationship parameters

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Coefficient	Reflectivity factor (dBZ) (below the bright band)				Reflectivity factor (dBZ) (above the bright band)
	R < 55	55 ≤ R < 60	R ≥ 60		R < 33	33 ≤ R < 49	R ≥ 49
A	−2.600	−2.500	−3.950		−0.817	−2.500	−3.950
B	0.0107	0.0130	0.0148		0.0063	0.0130	0.0148

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There is potential risk of error propagation owing to the constraints imposed by the 3D-Var analysis and empirical values of the particle terminal velocity, together with difficulty in verifying the updraft velocity (w). In such cases, using Eqs. (5) and (6) to calculate the particle rising velocity (${V}_{\rm Z}$) might increase the error. To reduce the risk of error propagation, in this study, the rising velocity of a particle was computed directly from the relationship between the retrieved wind field and the radar radial velocity using Eqs. (3) and (4) without adding extra constraint errors. To calculate w, we used empirical values for ${V}_{\rm T}$ and applied the 3D-Var method under several constraints. In this case, the errors stem mainly from the empirical values of ${V}_{\rm T}$ and those introduced during the variational analysis owing to the constraints.

2.2   Feature quantity construction method

Several key factors that contribute to hail formation can be used to predict hail events. These factors include the reflectivity factor, updraft velocity, vertical wind shear, and horizontal wind speed.

2.2.1   Reflectivity factor

Wu and Yu (2009) found correlation between the altitude of strong reflectivity and hail size, whereby higher altitudes correspond to larger hail diameters. In the present study, reflectivity factors observed at each front-end of the advanced X-band phased-array weather radar system were transferred onto three-dimensional grid points in the Cartesian coordinate system using interpolation techniques. In cases where multiple front-end observations converged on the same grid point, the maximum value was selected, facilitating improved analysis of hail processes.

2.2.2   Updraft velocity

Updraft velocity represents the speed at which air rises during a storm and provides the lift necessary for hailstone growth. Strong updrafts can keep hailstones aloft for longer, allowing them more time to increase in size. The 3D-Var method was used in this study to calculate the updraft velocity based on radar-detected radial velocities.

2.2.3   Vertical wind shear

Vertical wind shear measures the change in wind velocity with altitude. Strong vertical wind shear in hail-producing storms can enhance the rotation and structure of supercells, contributing to formation of larger hailstones. Vertical wind shear can be calculated as follows:

2.2.4   Horizontal wind speed

Horizontal wind speed represents the overall wind strength at different altitudes in a storm. Strong horizontal wind speeds can influence storm organization and development of supercell structures. In the present study, horizontal wind speed was calculated from the wind fields obtained through 3D-Var analysis by using the following formula:

Consideration of the reflectivity factor, updraft velocity, vertical wind shear, and horizontal wind speed can provide comprehensive understanding of the conditions that promote hailstone formation and growth.

3.   Hail case study and observations

3.1   Weather overview

On 26 March 2022, Foshan experienced severe weather activities that brought about heavy rainfall and localized hailstorms. At approximately 1455 local time (LT), the Dali Observatory (near the South China Sea) observed and recorded hail, as shown in Fig. 1. Approximately 20 min later, at 1515 LT, the Dashi Observatory (also close to the South China Sea) reported hailfall for a duration of approximately 20 min.

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Fig  1.  Size and shape of hail that occurred in Foshan on 26 March 2022.

3.2   Equipment and data overview

As shown in Fig. 2, this study used an S-band weather radar (abbreviated to S-band radar) and an advanced X-band phased-array weather radar system. The X-band phased-array weather radar system consists of multiple PARFs, each of which is responsible for transmitting and receiving radar signals. Table 2 outlines the differences in the indicators between the two radar systems. Compared with the S-band radar, the X-band PARFs have higher grid resolution, shorter range gate length, quicker scanning speed, and more scanning levels, thereby providing notable advantages for accurately tracking and analyzing small-scale convective weather processes such as hail.

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Fig  2.  Schematic of radar station layout and evolution of the strong echo region of hail clouds (black dots: X-band PARF radar station locations, with the dashed circle representing their maximum detection range; red star: Guangzhou S-band radar station; Radar_N: the Nth X-band PARF radar station).

Table  2.  Differences in radar parameters

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Parameter		S-band radar	X-band PARF
Range gate length (km)		0.25	0.03
Volume scan period (s)		360	30
Range of elevation (°)		0.5‒14.9 (12 levels)	0.75‒71.25 (48 levels)
Grid resolution (km)		1 × 1 × 1	0.2 × 0.2 × 0.2
Observation altitude range (km)		1‒15	0.1‒14.9

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The layout of the X-band PARFs and the position of the S-band radar used in this study are illustrated in Fig. 2. During the studied event, as the hailstorm clouds traversed from west to east, only X-band PARFs 3–7 captured data. At 1430 and 1442 LT, the hailstorm cloud was within the overlapping areas of detection of PARFs 3, 4, and 6. By 1448 LT, it had moved into the common area of detection of PARFs 3, 4, 6, and 7. Subsequently, at 1454 LT, the hailstorm cloud was located within the common area of detection of PARFs 4, 6, and 7. By 1512 LT, it had entered the common area of detection of PARFs 5–7. After 1530 LT, the hailstorm cloud exited the detection range of all PARFs.

3.3   Data quality verification

3.3.1   Radial velocity consistency verification

Radial velocity consistency indicates the level of agreement between the radial velocities detected by two adjacent X-band PARFs [as illustrated in Fig. 2, derived from Zhen et al. (2022)]. During verification, the midpoint between two adjacent X-band PARFs was selected, and the radial velocities at the lowest elevation angle from both PARFs were compared to assess whether they were equal in magnitude and opposite in direction. This verification method effectively reduced the influence of the vertical velocity components, allowing for more precise evaluation of radial velocity consistency.

Figure 3 illustrates the consistency of the radial velocities measured at the lowest elevation angle by two adjacent X-band PARFs (Radar_03 and Radar_07) at their midpoint from 1439 to 1449 LT during the weather event. The left-hand y-axis in Fig. 3 represents the difference in radial velocity between the two radars and the right-hand y-axis represents the magnitude of the radial velocity. For comparison, the velocities observed by Radar_07 are reversed. The red and blue lines in Fig. 3 indicate the velocities recorded by Radar_03 and Radar_07, respectively, during the same period. The radial velocity trends detected by Radar_03 and Radar_07 generally show the expected consistency. The histogram reveals a maximum deviation of 2 m s⁻¹ and a minimum deviation of 0 m s⁻¹, satisfying the radial velocity consistency verification criteria proposed by Li et al. (2020). This consistency provided a solid foundation for accurate wind-field verification and enhanced the reliability of subsequent meteorological analyses.

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Fig  3.  Velocity differences at midpoints between two adjacent X-band PARFs. Bar graph illustrates the error in velocity detection between two adjacent X-band PARFs, with values corresponding to the scale on the left. Line graph represents the actual X-band PARF speed, aligned with the scale on the right.

3.3.2   Evaluation of reflectivity factor and wind-field retrieval

The time delay for the radar to obtain data at higher elevation angles increased relative to that of obtaining data at the lowest elevation angle. This delay led to timing discrepancies between data from different altitude levels when converting the data from polar coordinates to Cartesian coordinates. These discrepancies became more pronounced with longer radar scanning times. For the S-band radar, the maximum time difference could approach 6 min, whereas it was approximately 30 s for the X-band PARFs.

Figure 4 shows radar data from the X-band PARFs and S-band radar at altitudes of approximately 1 and 3 km. Figures 4a and 4b show the reflectivity factors and horizontal wind field detected by the X-band PARFs at these altitudes, Figs. 4c and 4d illustrate the reflectivity factors, and Figs. 4e and 4f depict radial velocities at the corresponding altitudes for the S-band radar. Both radars captured similar echo shapes and intensities with hook-shaped structures at the altitude of approximately 3 km, as shown in Figs. 4b, d. However, the reflectivity recorded by the X-band PARFs was notably lower in areas where the reflectivity factor of the S-band radar exceeded 65 dBZ. This discrepancy can be attributed to the fact that the one-way attenuation rate for X-band electromagnetic waves is more than 10-times higher than that for S-band electromagnetic waves (Park et al., 2005).

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Fig  4.  Joint observation data from X-band PARFs 5–7 and observations from the S-band radar at 1512 LT. Reflectivity factor and horizontal wind field from the X-band PARFs at altitudes of (a) 1.1 and (b) 3.1 km. Reflectivity factor from the S-band radar at altitudes of (c) 1 and (d) 3 km. Radial velocity from the S-band radar at altitudes of (e) 1 and (f) 3 km [note: at this time, the S-band radar was to the southeast of the echo structure (refer to Fig. 2)]. Arrows within the ovals in (e) and (f) match the streamlines in (a) and (b), respectively. CAPPI: Constant Altitude Plan Position Indicator.

The wind vectors within the blue oval in Fig. 4a formed a cyclonic structure with counterclockwise rotation. In contrast, the wind direction in Fig. 4b shifted from westerly to southwesterly as the altitude increased, eventually returning to a westerly direction through clockwise rotation. Comparison of the wind-field streamline patterns observed by the X-band PARF in the blue oval in Fig. 4a with the radial velocities measured by the S-band radar at the same altitude, as shown in Figs. 4e, f, revealed that the S-band radar was positioned to the southeast of the echo structure. This comparative analysis indicated clear correspondence between the wind-field structure obtained from the X-band PARFs and the radial velocity patterns observed by the S-band radar. This alignment provided a reliable basis for interpreting the wind-field behavior and the radial velocity trends.

4.   Radar echoes and flow-field structure analysis

Hailstorm development was examined effectively by analyzing the reflectivity factor captured by the S-band radar, whereas the broader flow-field structure during hailstorm development was analyzed using the X-band PARF data.

4.1   Analyzing reflectivity factor evolution in hailstorm clouds observed by the S-band radar

Figure 5 presents the Constant Altitude Plan Position Indicator (CAPPI) reflectivity factor detected by the S-band radar at altitudes of 1, 3, 5, 7, and 9 km from 1430 to 1500 LT at 6-min intervals.

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Fig  5.  CAPPI reflectivity factors obtained from S-band weather radar observations at altitudes of 1, 3, 5, 7, 9, and 11 km from 1430 to 1500 LT.

During the initial period from 1430 to 1442 LT (Figs. 5a, b), the peak reflectivity factor at altitudes of 1‒7 km remained relatively consistent, varying by ≤ 5 dBZ. However, at altitudes of 9‒11 km, where temperatures were < −20°C, notable changes occurred in the area and shape of the intense echoes (defined as regions with reflectivity factors of > 45 dBZ). The peak reflectivity factor increased to 56.4 dBZ, indicating hailstorm development.

During 1442‒1454 LT (Figs. 5c, d), a noticeable inverted V-shaped gap emerged within the echoes at the altitude of 5 km (Figs. 5c3‒d3), indicating infiltration of a southerly airflow in the updraft region (Qin et al., 2017). At higher altitudes of 7 and 11 km, the intensity and extent of the strong echoes increased, with a peak reflectivity factor of 72.4 dBZ. Specifically, at the altitude of 11 km, the reflectivity factor increased from 52.2 to 65.5 dBZ (i.e., an increase of 13.3 dBZ) and the echo exhibited a southward tilt in the vertical structure, suggesting that hailstorm development was approaching maturity. In the final period from 1454 to 1500 LT (Fig. 5e), the peak reflectivity factor at the altitude of 3 km increased from 67.7 to 75.8 dBZ. Furthermore, the gap in the echoes at the altitude of 5 km began to diminish, and the peak reflectivity factors at the altitudes of 9 and 11 km decreased from 67.9 to 57.2 dBZ and from 65.5 to 53.7 dBZ, respectively. This inverse relationship between echo altitude and intensity suggested that the hail began to descend. This observation aligns with the expected behavior of hailstorms during their mature stage, indicating that the hailstone development process was nearing completion. After 1500 LT, the proximity of the hailstorm cloud to the S-band radar caused scanning of blind spots at higher altitudes; consequently, further analysis beyond 1500 LT was not performed.

4.2   Analysis of hailstorm cloud flow-field structure with X-band PARFs

This section examines the critical timeframe in hailstorm cloud development using X-band PARF data to understand the reflectivity factors, horizontal wind fields, and updrafts at altitudes of 1, 5, and 9 km. Comparative analysis was conducted to align the time-synchronized observations of the reflectivity factors, updrafts, and particle vertical velocities from the radar echo profiles.

4.2.1   Initial stage at 1442 LT

Figures 6a1–a3 and 6b1–b3 present the distributions of reflectivity factors and updrafts at altitudes of 1, 5, and 9 km, respectively, superimposed on the corresponding horizontal wind fields at 1442 LT. The reflectivity factors at different altitudes indicated progressive concentration of stronger echo regions in the southwest of the area as altitude increased, with weaker echo regions spreading eastward. The 30-s volume scan cycle of the X-band PARFs ensured high temporal consistency in data acquisition, minimizing the time lag between observations. However, discrepancies in data obtained at high-elevation scanning angles were possible owing to the 6-min volume scan cycle of the S-band radar.

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Fig  6.  Reflectivity and updraft superimposed wind fields derived from the joint observation data of X-band PARFs 3, 4, and 6 at 1442 LT. Reflectivity factor at altitudes of (a1) 1.1, (a2) 5.1, and (a3) 9.1 km. Updraft at altitudes of (b1) 1.1, (b2) 5.1, and (b3) 9.1 km (thick black lines indicate positions of longitudinal and latitudinal profiles).

Comparison of the reflectivity factor at the altitude of 9 km (Fig. 6a3) with the concurrent measurement from the S-band radar (Fig. 5c5) revealed inconsistencies due to these time lags, whereas comparison of the reflectivity factor at the altitude of 9 km (Fig. 6a3) with the S-band radar data at the same altitude but delayed by 6 min (Fig. 5b5) resulted in more accurate alignment of the echo structures.

As shown in Fig. 6b, the horizontal wind fields at different altitudes exhibited varying patterns. At the altitude of 1 km, wind speeds were relatively low, with a small cyclonic vortex in the southern part of the strong-echo region (red box in Fig. 6b1). The westerly wind speed increased in intensity as the altitude increased. At the altitude of 5 km, the vortex structure dissipated, and the wind direction became more uniform. At 9-km altitude, the speed of the wind with an overall westerly tendency decreased compared with that at 5-km altitude.

Analysis of the updrafts shown in Fig. 6b revealed a consistent distribution on the western side across the various altitudes. The updraft strength initially increased with altitude, but began to weaken at higher altitudes. From a dynamic perspective this indicated that updraft intensity played a crucial role in hailstorm system evolution.

Figures 7a‒c and 7d‒f offer detailed insights into the structure and dynamics of the storm system along the black lines shown at 23.09°N, 112.87°E in Fig. 6. These cross sections reveal key aspects of hailstorm behavior.

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Fig  7.  Vertical profiles obtained from the joint observation data of X-band PARFs 3, 4, and 6 at 1442 LT. Vertical sections of the (a) reflectivity factor, (b) updraft, and (c) particle rising velocity along longitude 112.87°E. Vertical sections of the (d) reflectivity factor, (e) updraft, and (f) particle rising velocity along latitude 23.09°N (note: the reflectivity factor was additionally superimposed on the same spatiotemporal wind-field information).

It is evident from Figs. 7a, d that the reflectivity factors exceeded 50 dBZ at the altitude of approximately 9 km and also exhibited a distinct north‒south tilt, indicating directional bias in storm development. As shown in Figs. 7b, e, updrafts were concentrated primarily at altitudes of 4‒8 km, with the strongest updrafts reaching speeds of approximately 20 m s⁻¹, peaking near the altitude of 6 km. Figures 7c and 7f further reveal that the particle velocities arose primarily in the lower and middle parts of the echo region with a clear pathway of ascent. However, this pathway appeared relatively short, extending only below the core region of the reflectivity factor. This limited pathway of ascent indicating constrained vertical motion within the storm might have affected the precipitation pattern. Additionally, in the meridional cross sections (Figs. 7d‒f), the updraft areas were mainly on the left-hand side of the strong-echo region, creating asymmetry in updraft formation. This uneven distribution led to a pendant-like structure in the echo pattern, indicating differential lift within the storm system, with one side exhibiting notably stronger dynamics than the other.

4.2.2   Development stage at 1448 LT

The observations captured at 1448 LT, shown in Fig. 8, revealed marked changes in the structure and dynamics of the hailstorm system compared with the situation at 1442 LT, as shown in Fig. 6. The most notable change in the reflectivity factor was the appearance of a south-facing echo gap at the altitude of approximately 5 km (Fig. 8a2). This echo gap might have been due to strong updrafts transporting hail embryos to higher altitudes, which increased the reflectivity intensity at higher altitudes and created a gap at the altitude of 5 km that reflected the particle uplift path. Additionally, compared with that at 1442 LT, the peak reflectivity factor at the altitude of approximately 9 km increased, indicating intensified storm activity at higher altitudes. There was minimal change in the wind-field characteristics; however, horizontal wind shear in the strong echo region persisted, contributing to the organization and severity of the storm. The maximum updraft weakened at intermediate altitudes, particularly near the altitude of 5 km, whereas it strengthened at the altitude of approximately 9 km. This shift in updraft intensity suggested that the vertical structure and dynamics of the storm were changing, with potentially important impacts on storm development and precipitation processes.

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Fig  8.  As in Fig. 6, but for joint observation data of X-band PARFs 3, 4, and 7 at 1448 LT.

Figures 9a and 9d reveal the structure and dynamics of the storm system, showing the maximum altitude of strong reflectivity factors (> 50 dBZ) near the altitude of 10 km, with a distinct pendant-like structure with a southward tilt. This tilt might have been caused by internal airflow or other storm dynamics. As shown in Figs. 9b, e, the altitude of the updraft area increased, aligning with the area of the storm that exhibited the highest intensity. Figures 9c and 9f show that the length of the pathway of particle ascent within the updraft area indicated robust vertical transport. This extension could explain both the pendant-like structure and the upward shift of the strong reflectivity factors. The increasing tilt of the echoes in the north‒south cross sections (Figs. 9d‒f) indicated that the intensity and directional focus of the storm evolved over time.

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Fig  9.  As in Fig. 7, but for joint observation data of X-band PARFs 3, 4, and 7 at 1448 LT. Panels (a–c) are along longitude 112.91°E. Panels (d–f) are along latitude 23.10°N.

4.2.3   Hailfall stage at 1454 LT

As shown in Fig. 10, the analysis at 1454 LT revealed a consistent horizontal wind-field structure with distinctive downdraft and updraft features.

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Fig  10.  As in Fig. 6, but for joint observation data of X-band PARFs 4, 6, and 7 at 1454 LT.

Figure 10b1 shows a concentrated area of downdrafts at the altitude of approximately 1.1 km, suggesting a change in storm dynamics. The reflectivity factor and updrafts at the altitude of 9.1 km, shown in Fig. 10b3, indicated increasing storm intensity at higher altitudes, characteristic of growing storm systems.

As shown in Fig. 11, regions with strong reflectivity factors (Figs. 11a, d) continued to move upward, indicating ongoing storm development. Updraft velocities (Figs. 11b, e) increased proportionally with altitude, indicating strengthening of the vertical motion within the storm. The pathways of particle ascent (Figs. 11c, f) exhibited an upward shift, demonstrating a trend toward stronger convection. Along the meridional cross section (Figs. 11d‒f), strong echoes persisted within the subsiding region, indicating a shift toward downdraft activity, which might have correlated with cooling or precipitation during the storm lifecycle.

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Fig  11.  As in Fig. 7, but for joint observation data of X-band PARFs 4, 6, and 7 at 1454 LT. Panels (a–c) are along longitude 112.98°E. Panels (d–f) are along latitude 23.10°N.

These observations indicated an evolving hailstorm system with clear indications of intense convection and dynamic changes in updraft and downdraft patterns, characteristic of complex weather systems with potential for severe weather phenomena such as hail and heavy precipitation.

4.3   Time-series analysis of primary characteristic quantities of hailstorms

This section analyzes the evolution and dynamics of the hailstorm by tracking the temporal variation of four key parameters: the maximum reflectivity factor, maximum updraft velocity, maximum vertical wind shear, and maximum horizontal wind speed. To reduce noise and potential outliers in the data, the latter three parameters were smoothed by using a 3 × 3 × 3 mean filter.

4.3.1   Evolution of reflectivity factors

Examining the temporal evolution of reflectivity factors across different altitudes provided valuable insights into hailstorm development. Owing to substantial attenuation of reflectivity factors with the X-band radar, the altitude‒time graph presented in Fig. 12a tracked the maximum reflectivity factors at various altitudes over time, as observed by the S-band radar, revealing the key stages in the hailstorm life cycle. During 1436‒1442 LT, rapid increase in the maximum reflectivity factors at higher altitudes suggested substantial intensification of updrafts. As the storm progressed during 1442‒1448 LT, there was notable increase in the maximum reflectivity factors at lower altitudes, indicating that particles with strong reflectivity, such as hailstones, descended toward the ground. This shift in reflectivity from high to lower altitudes was consistent with hailstone movement through the storm structure, eventually leading to hailfall. The final observation at 1455 LT confirmed descent of the hailstones, consistent with the increased reflectivity factors at lower altitudes.

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Fig  12.  Time–altitude variation of (a) maximum reflectivity of S-band radar, (b) maximum updraft velocity, (c) maximum vertical wind shear, and (d) maximum horizontal wind speed. Profiles shown in (b‒d) were obtained from the joint observation data of the X-band PARFs.

4.3.2   Evolution of updraft velocity

Figure 12b provides further understanding of the flow-field characteristics of the maximum updraft velocity observed by the X-band PARFs during the same time intervals, as depicted in Fig. 12a. Substantial increases in both the maximum reflectivity factors and the maximum updraft velocities were observed at altitudes of > 8 km, starting at approximately 1442 LT. By 1454 LT, updraft velocities exceeded 50 m s⁻¹ at altitudes of 10‒14 km, indicating strong and rapid uplift of particles within the storm system. This intense uplift is critical for hail development because it allows particles to grow as they ascend to higher altitudes. In contrast, Fig. 12b shows reduction in the maximum updraft velocities at mid‒low altitudes by 1454 LT. This reduction in updraft intensity at lower altitudes, corresponding to the previously noted enhancement of the maximum reflectivity factors at lower altitudes, caused the particles to begin descending and led to the hailfall observed at ground level at 1455 LT.

4.3.3   Evolution of vertical wind shear

Figure 12c shows the maximum vertical wind shear observed by the X-band PARFs. The maximum vertical wind shear at a specific altitude was calculated as the maximum wind vector difference between two adjacent levels that were 200-m apart. The maximum vertical wind shear at altitudes of 4‒10 km began to increase after 1436 LT, preceding the peak maximum updraft velocities. This earlier increase in vertical wind shear might have been a precursor to the peak maximum updraft velocities, indicating its role in storm evolution. Vertical wind shear caused updrafts to tilt, reducing the effects of particle drag and allowing the updraft to develop without notable obstruction from descending particles. This contributed to a more organized storm structure that was conducive to hail formation and other severe weather events.

4.3.4   Evolution of horizontal wind speed

Figure 12d shows the maximum horizontal wind speeds observed by the X-band PARFs. Maximum horizontal wind speeds were observed before the maximum updraft velocities peaked, providing an additional context for storm evolution. Horizontal wind speed can influence the organization and structure of storm systems (Fang et al., 2023). When these speeds preceded the peak in the maximum updraft velocities, they might have contributed to shaping the storm structure, allowing the system to grow and organize effectively. High wind speeds helped maintain the storm structure, supported development of tilted updrafts, and enhanced hail production conditions.

Overall, the earlier onset of vertical wind shear and the occurrence of maximum horizontal wind speeds before the peak in maximum updraft velocities reflected the critical dynamics within hailstorm development. These factors can lead to stronger and more sustained updrafts, supporting growth and organization of the storm system, and ultimately contributing to conditions conducive to hail formation and other severe weather events.

5.   Early warning indicators

5.1   Common early warning indicators

Vertically integrated liquid water content (VILWC) is a key indicator for identification and early warning of hail (Xiao et al., 2022). It represents the total amount of liquid water in a vertical column of air within a storm system and integrates the reflectivity factor over a given altitude range.

The formula for calculation of VILWC is expressed as follows:

where R is the reflectivity factor, H₀ is the echo bottom altitude (where precipitation begins), and H_max is the echo top altitude, which indicates the upper boundary of the storm system.

Figure 13 shows the relationship between the maximum VILWC and the maximum updraft velocities in the altitude range of 10–12 km, providing insight into the dynamics of severe weather conditions, particularly hailstorm development. The red lines in Fig. 13 represent the variations in the maximum updraft at the three different altitudes, showing a synchronized temporal trend. The maximum updraft began to increase from 1448 LT, peaked at 50 m s⁻¹ at approximately 1454 LT, and then gradually diminished until 1500 LT. The VILWC (green line in Fig. 13) followed a similar trend but peaked slightly later, reaching a maximum value of 70 kg m⁻² at approximately 1457 LT before beginning to diminish toward 1500 LT. However, the rate of decline in VILWC was more gradual than the reduction in updraft velocity.

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Fig  13.  Maximum VILWC and maximum updraft velocity at altitudes of 10, 11, and 12 km over time.

Hu et al. (2015) and Yu and Zheng (2020) identified vertical wind shear within the deep troposphere, particularly within the altitude range of 0‒6 km, as a critical environmental factor influencing the occurrence and intensity of severe hail events.

Figure 12c shows that the maximum vertical wind shear below the altitude of 6 km exhibited marked temporal variability. For further analysis, Fig. 14 provides a detailed examination of how the maximum vertical wind shear evolved temporally at altitudes of 4, 5, and 6 km, and across the entire altitude range of 0‒6 km. The patterns of the maximum vertical wind shear fluctuations at these specific altitudes were similar, peaking at approximately 1440 LT, whereas the maximum vertical wind shear for the entire altitude range of 0‒6 km reached its peak after 1500 LT. This suggested that storm evolution can be observed at different times, depending on the altitude level analyzed.

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Fig  14.  Maximum vertical wind shear (MVWS) at altitudes of 4, 5, and 6 km, and over the altitude range of 0‒6 km.

Additionally, analyzing the maximum vertical wind shear at specific altitudes, rather than across broader layers, can reveal subtle shifts and trends in the vertical wind shear. This allows for earlier detection of key atmospheric changes, thereby providing warnings of severe weather events such as hailstorms.

5.2   Preliminary construction of new early warning indices based on flow-field characteristics

The challenge in developing effective warning metrics for severe weather lies in predicting where critical data might manifest in dynamic weather environments.

According to Section 5.1, the peak values of the maximum vertical wind shear at specific altitudes indicated the onset of severe weather conditions. These peaks often occurred earlier than the peaks of the maximum updraft velocity and VILWC, suggesting that they could be valuable early warning indicators. Analysis of the overall vertical wind shear across the altitude range of 0‒6 km provides a general overview, but might lack the specificity required to detect early signs of severe weather. Because critical data points might emerge at specific altitudes, integrating data from multiple layers, particularly where critical patterns tend to emerge earlier, can offer a more robust and reliable warning index.

Developing a novel early warning index based on vertical integration and flow-field features is essential for addressing the need for a flexible and comprehensive warning system. For comparison, the maximum updraft velocity and vertical wind shear were integrated vertically, as described in Sections 5.2.1 and 5.2.2.

5.2.1   Vertically integrated maximum updraft (VIMU)

Updraft intensity within strong echo areas, such as the 50-dBZ area, is commonly associated with severe weather conditions (de la Torre et al., 2015). The VIMU index, used to quantify updraft intensity across the echo vertical extent, is calculated by integrating the maximum updraft velocities and dividing by the altitude difference between the bottom and top of the echo. The formula for calculating VIMU is expressed as follows:

where ${w}_{\rm max}$ is the maximum updraft velocity at each altitude, and ${H}_{0}$ and ${H}_{\rm max}$ represent the altitude of the bottom and top of the echo, respectively.

5.2.2   Vertically integrated maximum wind shear (VIMWS)

VIMWS is an index that quantifies the variability in the maximum vertical wind shear between the 0°C isotherm and the −20°C isotherm within a 50-dBZ echo area, commonly found in severe weather events. The formula for calculation of VIMWS is as follows:

where ${\left|{\Delta {{\boldsymbol{\nu}} }_{{{\rm{H}}}}}\right|}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum magnitude of the vertical wind shear at each altitude, indicating the change in wind speed or direction between two layers; ${H}_{0^{\circ }{\mathrm{C}}}$ is the altitude of the 0°C isotherm (i.e., the level at which freezing generally begins); and ${H}_{-20^{\circ }{\mathrm{C}}}$ represents the altitude of the −20°C isotherm, indicating common reference points for examining severe weather characteristics.

Figure 15 presents detailed observations of these early warning metrics for severe weather events, focusing on VILWC, VIMU, and VIMWS. Each metric is presented on a separate y-axis for clarity with color coding: green for VILWC, red for VIMU, and blue for VIMWS. The red VIMU curve showed strong correlation with the green VILWC curve, suggesting that updraft velocities tended to rise in tandem with increase in liquid water content, which is a key factor in severe weather events. The peak of the VILWC curve occurred at approximately 1455 LT, indicating intense precipitation and serving as a marker for identifying severe weather. The blue VIMWS curve followed a trend similar to that of the other two curves but achieved its maximum value approximately 12 min earlier, i.e., at approximately 1442 LT. This observation suggested that changes in VIMWS might serve as early indicators of severe weather.

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Fig  15.  Vertical integration of liquid water, updraft, and wind shear (y-axes from left to right are associated with VILWC, VIMU, and VIMWS).

6.   Conclusions and discussion

In this study, we explored the use of X-band PARFs in analyzing a substantial hailstorm. Compared with an S-band weather radar, the X-band PARFs provided data with higher spatiotemporal resolution that allowed more accurate retrieval of the three-dimensional wind field. This enabled detailed exploration of the flow-field structures within the studied hailstorm, such as the updraft velocity, vertical wind shear, and horizontal wind speed. This technological advancement supported comprehensive analysis of the rapid development and evolution of the hailstorm, and led to construction of a novel early warning index.

Analysis of the flow-field revealed that in the early stages of hail growth, gradually rising strong echoes typically corresponded to increase in the maximum updraft intensity, accompanied by broader and higher updraft regions and longer pathways of particle ascent. In the mid-development phase of the hailstones, reflectivity intensified at mid‒high altitudes and the updraft region at lower altitudes contracted. During the hailfall phase, the downdraft area at lower altitudes expanded, exhibiting a more distinct downward airflow.

This study also found that different maximum updraft velocities, horizontal wind speeds, and vertical wind shears occurred at different altitudes. At higher altitudes, changes in updrafts became more pronounced with increasing reflectivity factors. At mid‒high altitudes, the vertical wind shear demonstrated noticeable variation, typically peaking before the maximum updraft velocities.

Furthermore, the updrafts at altitudes of 10, 11, and 12 km followed a similar trajectory to the VILWC trend but with a less pronounced lead time. In contrast, the peak times of the vertical wind shear at altitudes of 4, 5, and 6 km often occurred earlier than the peaks of the updraft velocity and VILWC, demonstrating some early warning capability.

Based on these observations and considering a broader atmospheric context, a vertical integration approach was utilized to integrate the updrafts and vertical wind shear across the entire altitude range. This led to development of two indices: VIMU and VIMWS. The time of peak VIMWS occurred approximately 12 min earlier than the time of peak VIMU and VILWC, demonstrating its superior predictive capability and potential as a novel hail-warning index.

Owing to the limited number of statistical samples, the conclusions of this study have certain limitations. Future research should focus on increasing the size of the dataset to improve the generalizability of the conclusions, and to support further analysis of the quantitative relationship between the characteristic parameters and hail growth. Overall, this study emphasized the importance of radar data with high spatiotemporal resolution in understanding hailstorm dynamics and contributing to the development of effective early warning indices.