Identification and Correction of Atypical Extreme Heavy Rainfall over the Guangzhou–Foshan Megacity Cluster Based on Key Circulation Factor Clustering

Abstract

This study investigates the relationship between key circulation factors and ensemble forecast uncertainty during an atypical extreme heavy-rainfall event under weak synoptic forcing that affected the Guangzhou–Foshan megacity cluster in the Pearl River Delta (PRD) on 8 September 2022. Here, “atypical” refers to a localized extreme event occurring over the low-elevation urban river network without strong synoptic-scale drivers. Framed as an event-specific retrospective diagnostic analysis, the study used the China Land Multi-source Precipitation Analysis System version 2.1 (CMPAS-V2.1), ERA5 reanalysis, and 3-km (R3) and 9-km (R9) ensemble forecasts from the CMA Tropical Regional Atmospheric Model Ensemble Prediction System (CMA-TRAMS EPS). Spearman rank correlation and Monte Carlo field-significance tests were first applied to identify environmental variables closely associated with hourly precipitation variations, pinpointing the 700-hPa U-wind, 500-hPa V-wind, and 850-hPa V-wind as the most significant circulation predictors. Spatial anomaly fields of these key predictors were then subjected to hierarchical clustering, with clustering robustness evaluated using the cophenetic correlation coefficient (CCC) and bootstrap resampling. Because the clustering structure of the 925-hPa V-wind was comparatively weak, it was excluded from the final member-selection procedure. Finally, circulation-consistent ensemble members were selected using a multi-predictor consensus criterion (retaining 13 R3 members and 7 R9 members), and their 24 h accumulated precipitation was averaged to obtain a circulation-conditioned subset mean. The results show that persistent high temperatures, abundant moisture in the middle and lower troposphere, and a favorable multilayer circulation configuration provided suitable conditions for convective instability accumulation and localized heavy rainfall development. The precipitation forecasts exhibited substantial member-to-member variability. Under a consistent evaluation threshold, the 9-km configuration demonstrated superior overall ensemble-mean spatial skill compared to the 3-km configuration, indicating that increasing horizontal resolution does not necessarily improve forecast skill for weakly forced extreme rainfall. The resulting circulation-conditioned subset means successfully shifted the predicted heavy-rainfall center toward the observed Guangzhou–Foshan region and reduced the overestimated heavy-rainfall magnitudes over northern Guangzhou. Rather than serving as a purely objective score-maximizing post-processing algorithm, this approach extracts physically indicative spatial scenarios from ensemble spread. These findings provide a practical diagnostic framework for conditional forecast correction of localized heavy rainfall under weak synoptic forcing, though validation across multiple independent cases and consistent quantitative verification are necessary to assess its operational generalizability.

1. Introduction

In meteorological research of South China, heavy rainfall events induced by weak synoptic forcing have become a critical scientific issue demanding urgent breakthroughs, primarily due to their high suddenness and considerable forecasting difficulty. Such heavy rainfall is typically dominated by meso-β-scale convective systems, with a horizontal scale ranging from 2 to 20 km. It is significantly influenced by local factors including orographic lifting and sea-land breeze circulation, while the mechanisms governing convection initiation and maintenance remain complex [1].

Numerical models face multiple challenges when simulating this type of heavy rainfall. On one hand, their limitations in depicting boundary layer parameterization and cloud microphysical processes make it difficult to accurately reflect the real atmospheric conditions in regions with complex underlying surfaces. On the other hand, the insufficient spatiotemporal resolution of observational data leads to biases in initial field information, which further reduces the model’s prediction accuracy regarding the location, intensity, and duration of such heavy rainfall events. For instance, relevant studies conducted by the School of Atmospheric Sciences, Sun Yat-sen University, have indicated through ensemble forecast analysis that the predictability of warm-sector heavy rainfall is lower than that of frontal heavy rainfall [2,3,4]. Additionally, a statistical analysis of weak-forcing heavy rainfall events in South China from 2015 to 2017 showed that the Critical Success Index (CSI) of the 24 h forecast by the European Centre for Medium-Range Weather Forecasts (ECMWF) model was only 0.32, with a missed forecast rate as high as 41%—these results highlight the arduous nature of forecasting such rainfall processes.

Studies have shown that ensemble forecasting plays an irreplaceable role in revealing the unpredictable components of heavy rainfall events induced by weak synoptic forcing and quantifying convective uncertainty. Targeted ensemble forecast experiments for weak-forcing heavy rainfall in South China’s warm sector confirm that by accurately constructing multi-scale perturbations, the system can significantly identify the sensitive areas of convection initiation in low-forcing environments, and greatly improve the warning lead time and probabilistic forecast accuracy for such sudden rainstorms [2,5]. However, in operational practice, model versions at different resolutions have shown clear functional complementarities: coarser-resolution forecasts are adept at capturing large-scale synoptic background evolutions with high computational efficiency, whereas finer-resolution forecasts can detail local meso-β and meso-γ scale processes to better match the refined forecasting needs of short-term localized heavy rainfall. Against this technical background, Lan Zhang et al. [6] employed the Fraction Skill Score (FSS), a method in neighborhood spatial verification, to evaluate precipitation forecasts from two CMA-GD model versions with different resolutions. Their findings indicated that increasing model resolution may be beneficial for precipitation forecasting in southern China, particularly for short-duration heavy rainfall forecasts over longer lead times. Xubin Zhang et al. [7] investigated the impacts of enhanced resolution and shortened forecast lead times on quantitative precipitation forecasts (QPFs) for heavy rainfall events in South China during the rainy seasons from 2013 to 2020. They observed that improving model resolution significantly enhanced pre-flood season precipitation forecasts, with more pronounced improvements under conditions of strong large-scale forcing. However, relevant verification studies on atypical heavy rainfall under weak synoptic forcing remain unconducted.

In South China meteorology, extreme heavy rainfall under weak synoptic forcing is often considered “atypical” when it lacks dominant synoptic-scale drivers (such as cold fronts or typhoons), occurs over low-elevation urban plain terrain (such as the Guangzhou–Foshan megacity cluster) rather than traditional windward mountain slopes, and exhibits abrupt, highly concentrated short-duration convective intensity. It should be emphasized that this study is designed as an event-specific retrospective diagnostic analysis. The primary goal is not to develop an objective post-processing algorithm that optimizes quantitative verification scores (such as ETS or TS) for a single deterministic forecast product. Instead, the focus is on extracting physically indicative scenario information from the ensemble spread based on circulation consistency. Therefore, this study selects an atypical heavy rainfall event under weak synoptic forcing that occurred in the PRD on 8 September 2022, and applies clustering analysis to investigate its key circulation factors, aiming to provide a diagnostic framework for interpreting ensemble uncertainty.

As a crucial method for ensemble forecast post-processing, clustering analysis exhibits significant advantages in extracting key circulation features and quantifying forecast uncertainties. Its core value lies in classifying similar circulation modes through statistical methods, revealing the corresponding relationship between different modes and precipitation distribution, thereby reducing the complexity of high-dimensional meteorological data [8]. For instance, using the K-means clustering algorithm, a study took the 500 hPa geopotential height and 850 hPa meridional wind within the range of 20° N–35° N, 105° E–120° E at 08:00 BT (Beijing Time) on 222 heavy rainfall days during the flood season in Hunan Province from 2006 to 2014 as parameters for clustering. This resulted in 6 objective synoptic patterns for heavy rainfall days. The study found that some of these patterns were consistent with the characteristics of heavy rainfall processes such as typhoon-type and low-vortex cold-trough-type, and the classification results could serve as a reference for the objective classification of flood-season heavy rainfall forecasts in Hunan [9]. From the 50 members of the ECMWF (European Centre for Medium-Range Weather Forecasts) global ensemble numerical prediction model, a clustering method was used to select 16 representative members, which provided initial and boundary condition perturbations for the limited-area ensemble forecast system in Central Europe. The study revealed that the members selected by clustering could well represent the uncertainties of the large-scale background; the ensemble mean corrected the precipitation magnitude and false alarm issues, and the forecast results of the clustered ensemble system were superior to operational forecasts [10].

Although previous studies have demonstrated the value of clustering for circulation classification and ensemble-member selection, most previous applications have focused on synoptic-pattern classification or representative-member selection from large-scale ensemble systems. It remains unclear whether independently clustered, event-specific circulation predictors can be combined to identify a circulation-consistent subset of regional ensemble members for a localized heavy-rainfall event under weak synoptic forcing. In particular, the relationship between circulation-conditioned member selection and the spatial displacement of predicted heavy-rainfall centers has received limited attention for the Pearl River Delta. The methodological contribution of this study is not a statistical regression correction or a distance-weighted post-processing scheme. Instead, it combines hourly predictor identification, independent hierarchical clustering of circulation-anomaly fields, and a strict multi-predictor consensus rule. The selected members are mapped back to the precipitation field through an equal-weight arithmetic mean, here termed the circulation-conditioned subset mean. This approach is evaluated as case-specific conditional guidance for the spatial organization of heavy rainfall.

2. Data and Methods

This study develops a circulation-conditioned ensemble-member selection framework for an atypical extreme heavy-rainfall event under weak synoptic forcing. First, hourly CMPAS precipitation and ERA5 environmental fields are used to calculate Spearman rank correlations and identify candidate circulation predictors. The spatial anomaly fields of the CMA-TRAMS ensemble members are then calculated relative to the 30-member ensemble mean, normalized using Min-Max scaling, and clustered independently for the R3 and R9 configurations using Euclidean distance and Ward linkage. The optimal number of clusters is determined using the mean silhouette coefficient, while the cophenetic correlation coefficient and bootstrap resampling are used to assess clustering robustness. The 925-hPa V-wind is excluded from the final selection because of its relatively weak clustering structure. Members belonging to the target clusters of the 700-hPa U-wind, 500-hPa V-wind, and 850-hPa V-wind are then selected using a strict three-predictor consensus criterion. Finally, the 24 h precipitation forecasts from the selected members are averaged with equal weights to obtain the circulation-conditioned subset mean, which is compared with the remaining-member mean and evaluated against the observations.

2.1. Observation Data

In this study, the China Land Multi-source Precipitation Analysis System (CMPAS-V2.1), developed by the National Meteorological Information Center (NMIC) of the China Meteorological Administration (CMA), was employed as the observational ‘truth’ for verifying and analyzing forecast performance. This product integrates data from over 30,000 automatic weather stations across China, FY-series satellite estimates, and Doppler radar quantitative precipitation estimation (QPE) through advanced fusion techniques, including probability density function (PDF) matching and optimal interpolation (OI). Hourly precipitation data on 8 September 2022 were retrieved for analysis. To align with the study’s focus on daily totals, the hourly data were aggregated into 24 h accumulated precipitation. Featuring a spatial resolution of 0.05° × 0.05° (approximately 5 km) and benefiting from rigorous quality control and bias correction, CMPAS-V2.1 accurately captures localized heavy rainfall characteristics over the complex terrain of the Pearl River Delta (PRD). Consequently, it serves as a reliable benchmark for evaluating the precipitation forecast skills of the CMA-TRAMS (EPS).

2.2. Reanalysis Data

To analyze the environmental background and its statistical association with hourly precipitation, hourly ERA5 data with a horizontal resolution of 0.25° × 0.25° were used. The analyzed variables included CAPE; geopotential height; relative humidity; U-wind, V-wind, vertical velocity, and relative vorticity at 500, 700, 850, and 925 hPa; and pressure vertical velocity integrated over the 1000–200 hPa layer. The hourly data were used for the correlation analysis, while the 08:00 BT fields were used to illustrate the environmental conditions during the key stage of the event.

2.3. Forecasting Data

The CMA-TRAMS (EPS) model is based on CMA-TRAMS version 3.0 (TRAMS-V3.0) [11], with perturbed initial conditions and lateral boundary conditions for each ensemble member derived through downscaling the analysis and forecast fields of ECMWF-EPS. CMA-TRAMS employs a height-based terrain-following coordinate in the vertical direction, with the Charney-Philips leapfrog layer. The cumulus convection parameterization scheme adopts SAS [12], the microphysical process uses the WSM6 scheme [13], the boundary layer physics scheme applies MRF [14], the longwave radiation process utilizes the RRTM scheme, and the shortwave radiation process employs the Dudhia scheme.

The archived CMA-TRAMS (EPS) dataset available for this study contains 30 perturbed ensemble members (member IDs 01–30) at each of the 3-km (R3) and 9-km (R9) resolutions. The corresponding control forecast was not retained in the available archive and could therefore not be included. Accordingly, all ensemble, clustering, and subset-mean analyses in this study are based on 30 perturbed members.

The available 30-member datasets provide forecasts of accumulated precipitation, geopotential height, relative humidity, U-wind, V-wind, vertical velocity, and relative vorticity at 500, 700, 850, and 925 hPa. The analysis domain is 22–24° N and 112–115° E, and the 24 h forecasts are used to examine the predictability of the selected extreme rainfall event. The 24 h accumulation was selected because it is the consistently archived precipitation product available for all members and both resolutions, and because the circulation-conditioned subset mean is designed to evaluate the spatial placement and areal organization of the event-scale heavy-rainfall forecast. The observed hourly precipitation is retained to characterize the short-duration evolution of the event, but member-level 1 h and 3 h precipitation verification is beyond the scope of the available archived forecast dataset.

Because the control forecast was unavailable, the perturbation field of member ii was defined relative to the 30-member ensemble mean:

$$X_{iens}^{\prime }=X_{iens}-{\overline{X}}_{30}$$

(1)

where $X_i(s)$ denotes the forecast from member iens, and ${\overline{X}}_{30}(s)$ is the average of the 30 archived members. This formulation identifies members with circulation structures that differ from the available-ensemble mean.

2.4. Rank Correlation and Field-Significance Test Between Precipitation and Environmental Variables

To quantify the relationship between hourly precipitation and thermodynamic, moisture, and dynamical environments, Spearman rank correlations were calculated between regional-mean hourly precipitation and gridded environmental variables. The precipitation series was defined as the area-mean hourly precipitation over the core study region (22–23° N, 112.5–114° E), yielding 24 hourly samples. The environmental variables included convective available potential energy (CAPE), pressure vertical velocity integrated between 1000 and 200 hPa, and relative humidity, zonal wind, meridional wind, vertical velocity, and relative vorticity at 500, 700, 850, and 925 hPa. Correlations were calculated independently at each grid point, thereby characterizing the spatial correspondence between the temporal evolution of precipitation and environmental conditions.

For each grid point, the precipitation series $P_t$ and environmental-variable series $X_t$ were converted to ranks, $R(P_t)$ and $R(X_t)$, respectively. The Spearman rank correlation coefficient was calculated as:

$$r_s=1-{\displaystyle \frac{6{{\displaystyle {\sum }_{t=1}^N{d}_t}}^2}{N(N^2-1)}}$$

(2)

where N = 24 is the sample size and $d_t=R(P_t)-R(X_t)$ is the rank difference at time t. As a nonparametric statistic, Spearman correlation does not require normally distributed variables and is therefore appropriate for hourly precipitation and atmospheric variables that may exhibit skewed distributions or nonlinear covariability.

The column-integrated vertical velocity was calculated using trapezoidal integration:

$$I_{\omega }={\displaystyle \frac{1}{g}}{\displaystyle {\int }_{P_t}^{P_b}\omega (p)dp}\approx {\displaystyle \frac{1}{g}}{\displaystyle {\displaystyle \sum _{k=1}^{K-1}}\frac{{\omega }_k+{\omega }_{k+1}}{2}}\left|p_{k+1}-p_k\right|$$

(3)

where $\omega$ denotes pressure vertical velocity, g = 9.80665 m/s², pt = 200 hPa, and pb = 1000 hPa. This quantity serves as an integrated indicator of column vertical motion; negative and positive $\omega$ generally represent ascent and subsidence, respectively.

A Monte Carlo permutation test was used to assess field significance and account for the multiple-comparison problem inherent in gridded correlation maps. Specifically, the precipitation time series was randomly permuted while the environmental-variable series was retained. A correlation map was recalculated for each of M = 2000 permutations. For the m-th permutation, the maximum absolute correlation over the domain was defined as:

$$T^{(m)}=\underset{i,j}{{\displaystyle \max }}\left|r_s^{(m)}(i,j)\right|$$

(4)

The 99th percentile of the ordered ${\left\{T(m)\right\}}_{m=1}^M$ distribution, denoted by T_0.99, was used as the field-significance threshold. A grid point was regarded as field significant at α = 0.01 when:

$$\left|r_s(i,j)\right|\ge T_{0.99}$$

(5)

In the figures, color shading denotes the Spearman rank correlation coefficient and black stippling denotes regions passing the Monte Carlo field-significance test.

Spearman rank correlation was selected because the hourly precipitation series may be non-normal, zero-inflated, and nonlinearly related to environmental variables. The analysis is intended to identify monotonic event-specific associations rather than to construct a multivariate predictive model or infer causality. Candidate predictors were first screened according to the magnitude and spatial coherence of their rank correlations, together with the field-significance results. Because the candidate circulation fields are physically related and may exhibit multicollinearity, they were not combined into a single regression model. Instead, they were clustered independently, and the final three-predictor consensus criterion required simultaneous membership in the target cluster for the 700-hPa U-wind, 500-hPa V-wind, and 850-hPa V-wind. This design reduces reliance on any single correlated circulation field.

2.5. Hierarchical Clustering Method

Agglomerative hierarchical clustering [15] was applied to identify differences in the key circulation structures represented by ensemble members. The analysis was conducted separately for the R3 and R9 configurations and independently for four circulation predictors selected from the correlation analysis: 700-hPa U-wind, 500-hPa V-wind, 850-hPa V-wind, and 925-hPa V-wind.

(1)

Preprocessing and Spatial Anomaly Fields

Because the control run was unavailable, the spatial anomaly field of each ensemble member was calculated relative to the mean of the 30 archived members. For a given circulation variable, the anomaly field of member i at grid point s was defined as Formula (1).

Subsequently, to suppress disparities in absolute spatial magnitudes and project the vectors onto a homogeneous scale, global Min-Max normalization (scaling range: [0, 1]) is applied to the spatial anomaly subset:

$$X_{iens}^{\ast }={\displaystyle \frac{X_{iens}^{\prime }-X_{\min }^{\prime }}{X_{\max }^{\prime }-X_{\min }^{\prime }}}$$

(6)

where $X_{\max }^{\prime }$ and $X_{\min }^{\prime }$ represent the overall maximum and minimum bounds of the anomaly subset for the given variable and resolution. The normalized vectors were then used as the input for hierarchical clustering.

(2)

Distance Metric and Linkage Criterion

Based on the normalized multidimensional feature vector $X^{\ast }$, the Euclidean distance is employed as the similarity metric to quantify spatial dissimilarity between ensemble members $X_i^{\ast }$ and $X_j^{\ast }$:

$$d(i,j)={‖X_i^{\ast }-X_j^{\ast }‖}_2=\sqrt{{\displaystyle {\sum }_{p=1}^M{(x_{i,p}^{\ast }-x_{j,p}^{\ast })}^2}}$$

(7)

where M represents the flattened spatial-grid dimension.

Agglomerative clustering was performed using Ward’s minimum-variance linkage criterion. At each level, the two candidate clusters that produced the smallest increase in within-cluster sum of squares were merged, thereby preserving within-cluster similarity in spatial anomaly structure as far as possible.

(3)

Objective Determination of the Number of Clusters

The optimal number of clusters, k, was determined objectively using the mean silhouette coefficient. Candidate values of k ranged from 2 to 12. For each candidate partition, the silhouette coefficient of member i was calculated as:

$$S(k)={\displaystyle \frac{1}{N}}{\displaystyle {\sum }_{i=1}^N\frac{b(i)-a(i)}{\max (a(i),b(i))},k\in [2,12]}$$

(8)

where $a(i)$ represents the mean intra-cluster distance of member i to all other members within its own cluster, and $b(i)$ is the mean nearest-cluster distance from member i to all points in the closest neighboring cluster.

For all eight resolution-variable combinations, the silhouette maximum occurred at k = 2; therefore, the subsequent analyses used two-cluster partitions. The numerical labels generated by hierarchical clustering have no intrinsic physical order or quality ranking. Thus, the term “1st cluster” is no longer used. Instead, the target cluster was defined as the cluster with the largest membership in the silhouette-selected partition. This definition was made solely from the circulation-member distribution, before precipitation verification was considered.

The complete cluster-size distribution, including the number and percentage of members in each cluster, was recorded during the partitioning process. This procedure prevents a small-member cluster from being interpreted directly as a representative ensemble subset.

(4)

Initial Four-Predictor Screening and Final Three-Predictor Consensus Selection

The four candidate circulation predictors, namely the 700-hPa U-wind, 500-hPa V-wind, 850-hPa V-wind, and 925-hPa V-wind, were initially clustered independently for each model resolution. For each resolution-predictor combination, the candidate number of clusters ranged from k = 2 to 12, and the optimal value was selected according to the maximum mean silhouette coefficient.

The four candidate predictors were further screened using their cophenetic correlation coefficients. The CCC values for the 925-hPa V-wind were 0.5053 for R3 and 0.4987 for R9, indicating a relatively weak dendrogram representation compared with the other predictors. Therefore, the 925-hPa V-wind was excluded from the final member-selection procedure. The final clustering-based selection used only the 700-hPa U-wind, 500-hPa V-wind, and 850-hPa V-wind.

For each final predictor, the cluster with the largest membership was defined as the target cluster. A member was retained in the final circulation-conditioned subset only when it belonged to the target cluster for all three predictors. This strict consensus criterion retained 13 members for R3 and 7 members for R9.

The conditional mean of 24 h accumulated precipitation was calculated as:

$$P_{sub}(x,y)={\displaystyle \frac{1}{n_{sub}}}{\displaystyle \sum _{i\in C_{sub}}{P}_i(x,y)}$$

(9)

where $P_i(x,y)$ is the 24 h accumulated precipitation forecast of member i, $C_{sub}$ represents the selected circulation-conditioned subset, and $n_{sub}$ is the number of selected members. The mean is an equal-weight arithmetic mean and does not use cluster-distance weighting. Because the R9 subset contains only seven members, the corresponding result is interpreted as case-specific conditional guidance and not as a replacement for the full probabilistic ensemble.

The procedure is illustrated in Figure 1. For each resolution, the four candidate predictors were initially clustered independently; no joint distance matrix containing variables with different physical units was constructed. The 925-hPa V-wind was excluded from the final selection because its CCC was relatively weak. For each of the remaining three predictors, the target cluster was defined as the larger cluster in the silhouette-selected two-cluster partition. A member was retained only if it belonged to the target cluster for all three predictors.

(5)

Robustness Assessment of the Hierarchical Clustering Structure

Because each analysis contains only 30 members, clustering robustness was assessed jointly using the CCC and non-parametric bootstrap resampling.

The CCC measures how faithfully the dendrogram represents the original pairwise distance structure. It is calculated as the correlation between the original Euclidean distances and the cophenetic distances represented by the hierarchical dendrogram. A higher CCC indicates better preservation of the original member-distance structure.

In addition, 5000 bootstrap resamples with replacement were generated from the normalized member-feature matrix for every resolution-variable combination. Ward hierarchical clustering was repeated for each resample, and the dendrogram was cut using the silhouette-selected optimal k from the original analysis. The adjusted Rand index (ARI) was used to quantify agreement between the original and bootstrap partitions, while the Jaccard similarity coefficient was used to quantify overlap between the original target-cluster membership and bootstrap target-cluster membership. Pairwise co-assignment probabilities were also calculated to quantify the probability that two members were assigned to the same cluster across bootstrap resamples.

Cluster robustness was therefore evaluated from the silhouette coefficient, CCC, bootstrap ARI, target-cluster Jaccard similarity, pairwise co-assignment probability, and cluster-size distribution rather than from a single diagnostic. The corresponding diagnostic metrics (including the bootstrap ARI, target-cluster Jaccard distributions, and silhouette curves for candidate values of k) are detailed in Section 3.3.

All preprocessing, hierarchical clustering, silhouette analysis, cophenetic-correlation calculation, bootstrap resampling, and precipitation-composite calculations were implemented using Python (version 3.12.0). Hierarchical clustering was performed with the scipy.cluster.hierarchy module using Euclidean distance and Ward linkage. Silhouette coefficients, adjusted Rand indices, and Jaccard similarities were calculated using scikit-learn. Data handling and numerical calculations were conducted with xarray, numpy, and pandas. Figures were produced using NCL and Python plotting routines. The analysis settings were fixed for both resolutions: 30 archived perturbed members, candidate cluster numbers from 2 to 12, and 5000 bootstrap resamples.

2.6. Testing Method

Before verification, the R3, R9, and CMPAS-V2.1 precipitation fields were remapped to a common verification grid. The same spatial domain, 24 h accumulation period, spatial mask, precipitation threshold, and categorical verification procedure were then applied to both model resolutions. The verification of deterministic precipitation forecasts was conducted using a binary contingency table on a common verification grid. All R3, R9, and CMPAS-V2.1 precipitation fields were remapped to the same verification grid and evaluated over the identical domain, 24 h accumulation period, and spatial mask. The threshold of 25 mm/day was selected because it corresponds to the operational heavy-rainfall category used in this case study and allows direct comparison with the spatial distribution of the observed heavy-rainfall area. The results at this threshold should be interpreted as threshold-specific. Frequency Bias Index (FBI) and Equitable Threat Score (ETS) were calculated together to evaluate categorical overlap, frequency bias, and chance-corrected skill, respectively. In addition, FSS was calculated across multiple neighborhood scales to assess spatial consistency while reducing sensitivity to small displacement errors.

To fully guarantee a rigorous, unbiased evaluation of the model’s skill and systematic forecasting tendency based on the contingency table (

Table 1. Precipitation testing classification table.

	Observation	Precipitation	No Precipitation
Forecast
Precipitation		NA	NB
No Precipitation		NC	ND

), three essential metropolitan verification indices are adopted: the Frequency Bias Index (FBI), and the Equitable Threat Score (ETS).

The TS is highly sensitive to the frequency of events (base rate) and lacks correction for random forecast hits. To address these limitations, we introduce the Frequency Bias Index (FBI) and the Equitable Threat Score (ETS).

The FBI reflects the ratio of the total forecast rain area to the total observed rain area, helping to diagnose global systematic wet or dry biases of the model:

$$FBI={\displaystyle \raisebox{1ex}{$(N_A+N_B)$}\!\left/ \!\raisebox{-1ex}{$(N_A+N_C)$}\right.}$$

(10)

An FBI = 1.0 represents an unbiased frequency. FBI > 1.0 indicates that the model tends to over-forecast rainfall (wet bias), whereas FBI < 1.0 suggests under-forecasting (dry bias).

The ETS measures the fraction of observed rain events that were correctly predicted, adjusted for hits expected purely by random chance:

$$ETS={\displaystyle \raisebox{1ex}{$(N_A-N_{AR})$}\!\left/ \!\raisebox{-1ex}{$(N_A+N_B+N_C-N_{AR})$}\right.}$$

(11)

where NAr represents the expected number of correct forecasts based solely on random chance, calculated as:

$$N_{AR}={\displaystyle \raisebox{1ex}{$(N_A+N_B)(N_A+N_C)$}\!\left/ \!\raisebox{-1ex}{$(N_A+N_B+N_C+N_D)$}\right.}$$

(12)

The range of ETS is from −1/3 to 1.0. An ETS ≤ 0 indicates that the forecast possesses no practical skill (comparable to or worse than random guessing), while an ETS closer to 1.0 stands for superior forecasting capability, with random chance hits thoroughly penalized and removed.

3. Results

3.1. Analysis of Observations and Comparison with Model Precipitation Forecasts

An extreme heavy-rainfall event affected the Pearl River Delta (PRD) on 8 September 2022. Based on the hourly CMPAS-V2.1 precipitation product, the 24 h accumulated precipitation maxima were mainly distributed over central-southern Guangzhou, with the maximum accumulated-precipitation grid point marked by the five-pointed star in Figure 2a. Accumulated precipitation at this location exceeded 100 mm, indicating the pronounced local character of this event. It should be noted that CMPAS-V2.1 is a gridded multi-source merged precipitation product, and its grid-cell values may differ from observations at an individual rain gauge. Thus, Figure 2 is used to characterize the regional precipitation distribution and its hourly evolution, whereas station-based extremes represent rainfall intensity at a smaller spatial scale.

Figure 2c presents the hourly rainfall evolution at the maximum accumulated-precipitation grid point. Rainfall intensified rapidly around 10:00 BT and peaked during 11:00–12:00 BT, with hourly precipitation of approximately 56 and 62 mm/h, respectively, followed by rapid weakening after 13:00 BT. This evolution indicates that the event was not characterized by persistent rainfall throughout the day; instead, a short-lived and highly concentrated convective rainfall burst contributed most of the accumulated precipitation. As shown in Figure 2b, the rainfall center was located in the relatively low-elevation area near the PRD river network and estuary, while higher terrain is found to the north and northwest. This topographic setting may modulate low-level moisture transport and local convergence.

The event was characterized by localized and short-duration heavy rainfall in the absence of an obvious frontal passage, tropical cyclone, strong low-level vortex, or other dominant large-scale lifting system over the Pearl River Delta. The ERA5 fields instead indicate a favorable convective environment with instability, moisture, multilayer flow, and localized ascent. Therefore, the term describes the relative absence of a clearly dominant synoptic-scale forcing mechanism in this case; it does not represent a universal operational classification criterion.

Figure 3 provides a combined view of the convective environment and circulation conditions over the study area and its surroundings at 08:00 BT on 8 September 2022. In Figure 3a, relatively high CAPE values are distributed over the study area and adjacent regions, indicating that substantial convective instability had accumulated and that the thermodynamic environment was favorable for the development of deep convection. Figure 3b further shows relatively high relative humidity at 500, 700, and 850 hPa. The middle- and lower-tropospheric moist layers are vertically connected near the study area, indicating sufficient moisture for the initiation and maintenance of deep convective clouds. Figure 3d–f present the wind speed and wind direction at 500, 700, and 850 hPa, respectively. The differences among the wind fields at these levels indicate a vertically varying environmental circulation. The lower-level winds describe the background moisture-transport conditions, while the middle-level flow characterizes the environmental airflow in which the convective system developed. The spatial co-occurrence of enhanced CAPE, high relative humidity, and the multilayer wind fields therefore indicates a favorable environment for intense convective rainfall.

Figure 3c presents the pressure vertical velocity integrated from 1000 to 200 hPa, providing a tropospheric-column perspective of the vertical motion. Negative values indicate enhanced column-integrated ascent, whereas positive values indicate relatively stronger subsidence or weaker ascent. The spatial correspondence between the column-integrated ascent and the regions of high CAPE and relative humidity provides additional dynamical support for the development and maintenance of deep convection. However, CAPE and moisture primarily describe favorable thermodynamic preconditioning rather than a sufficient trigger for convection. For this case, the lower-tropospheric wind configuration, together with the spatial correspondence between moist air and column-integrated ascent, suggests that low-level moisture transport and localized convergence may have contributed to convective initiation and subsequent maintenance. Because the present analysis does not include a full moisture-budget or convergence diagnosis, this interpretation is limited to a physically plausible environmental association rather than a uniquely demonstrated triggering mechanism.

The 3-km ensemble members exhibit substantial differences in the spatial distribution, location of heavy-rainfall centers, and areal coverage of precipitation. Members with relatively higher ETS values for precipitation ≥25 mm/day are outlined in red for visual reference only (The highlighting criterion is not used in predictor identification, clustering, or final member selection). Members 3, 10, 17, and 26 exceed the unified ETS threshold of 0.10. Since ETS accounts for hits expected by random chance, these members show genuinely higher skill than the remaining members in predicting heavy rainfall (>25 mm/d). Nevertheless, their absolute ETS values remain modest, indicating considerable uncertainty in accurately forecasting the location of this weakly forced extreme-rainfall event. Although these members reproduce localized heavy-rainfall centers to varying degrees, the position, structure, and extent of the heavy-rainfall band differ markedly among members.

The FBI values further show that members with relatively high ETS do not necessarily have a realistic event frequency (Figure 4). Member 3 has an FBI of 0.84, which is comparatively close to the unbiased value of 1.0, suggesting that its ETS is associated with a relatively reasonable heavy-rainfall coverage. In contrast, members 10, 17, and 26 have FBI values of only 0.45, 0.38, and 0.43, respectively, indicating pronounced underforecasting. Their limited skill mainly results from capturing parts of the heavy-rainfall cores rather than accurately reproducing the full heavy-rainfall area. Therefore, a member with a relatively high ETS but an FBI far below 1 still substantially underestimates the spatial coverage of heavy rainfall.

In the 9-km configuration, as shown in the figure, members with an ETS exceeding the unified threshold of 0.10 are highlighted with red boxes for consistent visual comparison. By applying the identical highlighting threshold (ETS > 0.10) across both resolutions, a consistent visual reference is maintained. These members retain more effective heavy-rainfall prediction skill than the other members after random hits are removed. Member 25 has the highest ETS (0.26), indicating a relatively good ability to capture the heavy-rainfall region. Compared with the 3-km members, the best 9-km members attain higher ETS values.

FBI provides further insight into the forecast bias associated with these higher ETS values(Figure 5). The highest ETS of member 25 is accompanied by an FBI close to unity, indicating that its performance was not obtained primarily by enlarging the forecast rain area and increasing false alarms; it therefore provides more credible overall forecast skill. In contrast, members 28 and 30 have FBI values of 0.72 and 0.41, respectively, indicating underforecasting of the heavy-rainfall area. Although they capture parts of the rainfall core and achieve relatively high ETS, they do not adequately reproduce the full spatial coverage. The joint use of ETS and FBI thus prevents a one-sided assessment based only on TS or ETS.

Both model configurations show pronounced member-to-member differences in precipitation forecast performance. These differences are evident not only in ETS, which measures forecast skill after accounting for random hits, but also in FBI, which diagnoses systematic overforecasting or underforecasting. For this weakly forced extreme-rainfall event, some members can capture localized heavy-rainfall cores but may still fail to represent the overall coverage realistically; members with higher ETS and FBI close to 1 provide more robust operational guidance. However, because precipitation forecast accuracy differs substantially among ensemble members for such extreme events, real-time manual selection of members is difficult to implement in operational practice. We therefore argue that, if the key circulation features controlling such weakly forced events can be identified, ensemble members can be objectively classified and fitted according to these features. This approach can exclude members with poor precipitation forecast skill and thereby improve the overall forecast accuracy of the model ensemble. The following section further investigates this classification and optimization framework.

To reduce the double-penalty effect caused by small spatial displacement errors in strict gridpoint verification, a multi-scale Fraction Skill Score (FSS) analysis was conducted for heavy rainfall exceeding 25 mm/day (Figure 6). The FSS values of both R3 and R9 increase consistently as the neighborhood scale expands from 5 to 125 km, indicating that both configurations contain some displacement and scale-mismatch errors in the predicted heavy-rainfall structures. Their spatial skill improves when increasing positional tolerance is allowed. The ensemble-mean FSS of R9 increases from approximately 0.38 at 5 km to 0.81 at 125 km, while its median increases from approximately 0.40 to 0.83. In comparison, the ensemble-mean and median FSS values of R3 increase from approximately 0.22 and 0.23 to approximately 0.51 and 0.53, respectively.

At all neighborhood scales, the ensemble-mean and median FSS values of R9 are higher than those of R3, suggesting that R9 retains more stable overall spatial skill for this weakly forced extreme-rainfall case even after spatial tolerance is introduced. Thus, the better performance of R9 in the strict gridpoint ETS evaluation cannot be attributed entirely to the double-penalty effect. Nevertheless, the member ranges of the two configurations overlap substantially at most scales, and some R3 members attain relatively high FSS values at larger neighborhood scales, demonstrating considerable member-dependent uncertainty. Therefore, the results indicate higher ensemble-level spatial consistency of R9 for this particular event, rather than supporting a general conclusion that the 9-km configuration is universally superior to the 3-km configuration.

The strict gridpoint and neighborhood verification results provide complementary information. The ETS and FBI values quantify categorical skill and frequency bias at the verification-grid scale, whereas FSS quantifies spatial agreement after progressively increasing positional tolerance. For the present case, R9 has higher ensemble-mean and median FSS values than R3 at all examined neighborhood scales. These quantitative differences indicate higher spatial consistency of the R9 ensemble for this event; however, the overlapping member ranges indicate substantial member-dependent uncertainty and do not support a general resolution-ranking conclusion.

The clustering and member-selection procedures were implemented separately but identically for R3 and R9. Therefore, differences between the two circulation-conditioned subset means may reflect not only resolution-dependent circulation representation but also differences in the size and composition of the selected subsets. The R3-R9 comparison is consequently interpreted as event-dependent and conditional on the respective ensemble structures.

3.2. Extraction of Key Circulation Factors Influencing Precipitation

Figure 7 presents the spatial distributions of the Spearman rank correlations between area-mean hourly precipitation and the environmental variables over the study region on 8 September 2022. Each gridpoint correlation was calculated from N = 24 paired hourly samples. Statistical significance was evaluated at the field level, rather than by interpreting pointwise confidence intervals independently: the 99th percentile of the maximum absolute correlations from 2000 precipitation-series permutations was used as the domain-wide threshold (α = 0.01). The correlation patterns exhibit pronounced spatial and vertical variations, indicating that the rainfall event was not controlled by a single thermodynamic or dynamical factor. Instead, the precipitation evolution was associated with the combined variations in convective instability, lower-tropospheric moisture availability, and horizontal circulation at different levels.

CAPE is positively correlated with precipitation over most of the northern and western portions of the domain, with relatively extensive areas passing the field-significance test. This indicates that increases in convective instability generally occurred simultaneously with enhanced precipitation. However, weak negative or nonsignificant correlations are present over parts of the southeastern domain, demonstrating that the relationship between CAPE and precipitation was spatially heterogeneous. For heavy rainfall over Guangdong, high CAPE is generally a favorable thermodynamic background condition, but it does not necessarily provide a unique indication of the rainfall location, intensity, or hourly evolution. The column-integrated vertical velocity exhibits generally weak correlations, with alternating positive and negative areas and only limited significant regions. This suggests that the vertically integrated vertical-motion index alone cannot fully characterize this short-duration and highly localized convective rainfall event.

Relative humidity is predominantly positively correlated with precipitation, particularly at 700 and 850 hPa, where the positive correlation areas are more coherent and include extensive significant regions. This result highlights the importance of middle- and lower-tropospheric moisture in regulating precipitation variability. The 500 hPa relative humidity pattern is comparatively weaker, suggesting that the rainfall event was more directly associated with moisture variations in the middle and lower troposphere.

The wind-related correlation patterns show a distinct vertical structure. At 500 and 700 hPa, both the U- and V-winds are predominantly negatively correlated with precipitation across broad portions of the domain. The negative correlation associated with the 700 hPa U-wind is particularly extensive and spatially coherent. In contrast, the 850 and 925 hPa V-winds exhibit more pronounced positive correlations over the southern part of the domain and its surrounding area, with extensive significant regions. This vertical contrast suggests that variations in the mid-level zonal and meridional flow, together with changes in the low-level southerly flow, may jointly regulate moisture transport, horizontal convergence, and the organization of the convective system.

Relative vorticity displays strong spatial heterogeneity and dipole-like positive and negative structures at several levels. Relatively extensive significant areas appear at 500, 700, and 925 hPa, indicating that local rotational flow and dynamical disturbances in the middle and lower troposphere were closely associated with precipitation evolution. However, the coexistence of positive and negative correlation regions implies that the role of relative vorticity was strongly dependent on location. Its contribution to the regional precipitation signal therefore cannot be inferred solely from an isolated local maximum.

Figure 8 summarizes the spatial correlation fields in Figure 7 by calculating regional-mean correlation coefficients over 22–24° N and 112–115° E. The resulting bar chart demonstrates substantial differences among the environmental variables. The 700 hPa U-wind has the largest absolute correlation coefficient and therefore exhibits the strongest regional association with precipitation among all the examined variables. The negative sign indicates that, during the analyzed period, changes toward weaker or more negative 700 hPa U-wind anomalies were generally accompanied by enhanced regional precipitation. This result is consistent with Figure 7, where the 700 hPa U-wind shows broad negative correlations and extensive significant areas. It identifies the 700 hPa zonal flow as the most prominent middle-tropospheric dynamical indicator of this weakly forced heavy-rainfall event.

The 850 and 925 hPa V-winds both have correlation coefficients of +0.58, representing the second-largest absolute correlations in Figure 8. Their positive correlations indicate that enhanced low-level southerly flow was closely associated with increased precipitation. Together with the spatial patterns in Figure 7, these results suggest that the two low-level V-wind variables may reflect the variability of warm-moist airflow from the south, as well as its contribution to moisture transport and low-level convergence. The 500 hPa V-wind has a relatively strong negative correlation, indicating that meridional circulation changes in the middle troposphere also contributed to the organization or maintenance of the rainfall system.

CAPE has a regional-mean correlation coefficient of +0.33, which is lower than those of the most strongly correlated circulation factors but still represents a moderate positive relationship. The correlation coefficients of relative humidity at 500 hPa, 700 hPa, and 850 hPa confirm the supportive role of moisture conditions, although their regional-mean correlations are weaker than those of the key wind factors. The correlation coefficients of vertical velocity are −0.33 at 500 hPa, +0.06 at 700 hPa, and +0.17 at 850 hPa, while the column-integrated vertical velocity has a value of −0.14. This inconsistency indicates that vertical-motion correlations depend strongly on pressure level and are not sufficiently stable when represented by a single regional-mean index. The regional-mean correlations of relative vorticity are +0.07, +0.16, +0.23, and +0.07 at 500, 700, 850, and 925 hPa, respectively. Although relative vorticity shows extensive significant regions in parts of Figure 7, the cancellation between positive and negative correlation areas leads to relatively small regional-mean coefficients in Figure 8.

Considering both the spatial significance patterns in Figure 7 and the regional-mean correlation coefficients in Figure 8, the 700-hPa U-wind, 500-hPa V-wind, 850-hPa V-wind, and 925-hPa V-wind were selected as the primary circulation predictors for the subsequent clustering analysis. The 700-hPa U-wind exhibited the largest absolute regional correlation coefficient, while the 850-hPa and 925-hPa V-winds highlighted the importance of low-level warm-moist airflow and moisture transport. The 500-hPa V-wind provided an additional indicator of middle-tropospheric meridional circulation.

CAPE was not included in the clustering analysis because the purpose of the clustering procedure was to identify circulation-related predictors that could distinguish circulation-dependent ensemble differences. Although CAPE is an important thermodynamic prerequisite for deep convection, its positive correlation does not necessarily distinguish the rainfall center or the precipitation differences among ensemble members. Accordingly, the clustering analysis focused on the four circulation predictors listed above.

3.3. Clustering Analysis of Key Circulation Factors in the Model

Figure 9a presents the bootstrap distributions of the ARI and target-cluster Jaccard similarity for the eight resolution–predictor combinations. Both metrics show considerable variation across resamples and combinations, indicating that the reproducibility of the complete cluster partition and the target-cluster membership is not uniform. Nevertheless, the distributions cover a broad range of similarity values rather than being concentrated exclusively near zero, suggesting that the clustering results retain a detectable degree of robustness under perturbation of the 30-member sample. The differences among combinations also indicate that clustering stability depends on both model resolution and circulation predictor.

Figure 9b shows that the mean silhouette coefficients are generally highest at, or close to, k = 2, while they tend to decrease or fluctuate at relatively low levels as the number of clusters increases to k = 12. This indicates that increasing the number of clusters does not produce a clearer overall separation of the circulation patterns and may instead lead to weaker or less distinct groupings. Accordingly, k = 2, marked in the figure, provides the most appropriate and relatively parsimonious clustering solution among the candidate values examined.

Agglomerative hierarchical clustering using Ward’s minimum-variance linkage and Euclidean distance was applied independently to the four key circulation predictors for both the R3 and R9 configurations. As shown in

Table 2. Cluster-size distributions and diagnostic statistics for hierarchical clustering of the key circulation predictors at the two model resolutions.

Resolution	Predictor	Silhouette	CCC	Cluster Sizes	Target Cluster
R3	700 hPa Uwind	0.2885	0.5796	8 (26.7%), 22 (73.3%)	22
R3	500 hPa Vwind	0.2639	0.5866	6 (20.0%), 24 (80.0%)	24
R3	850 hPa Vwind	0.3251	0.6193	5 (16.7%), 25 (83.3%)	25
R3	925 hPa Vwind	0.1868	0.5053	18 (60.0%), 12 (40.0%)	18
R9	700 hPa Uwind	0.3790	0.6440	12 (40.0%), 18 (60.0%)	18
R9	500 hPa Vwind	0.3258	0.6427	10 (33.3%), 20 (66.7%)	20
R9	850 hPa Vwind	0.4059	0.6836	8 (26.7%), 22 (73.3%)	22
R9	925 hPa Vwind	0.2497	0.4987	17 (56.7%), 13 (43.3%)	17

Note: CCC denotes the cophenetic correlation coefficient. The target cluster is defined as the largest cluster in the optimal two-cluster partition selected using the silhouette coefficient.

, Silhouette analysis selected two clusters for all eight resolution–predictor combinations, although the degree of separation varied among predictors and resolutions, with mean silhouette coefficients ranging from 0.1868 to 0.4059. The CCC values ranged from 0.4987 to 0.6836. In particular, the CCC values for the 925-hPa V-wind were relatively low for both R3 and R9 (0.5053 and 0.4987, respectively), approaching or falling below the empirical reference threshold of 0.5. This indicates that the hierarchical clustering structure of the 925-hPa V-wind was relatively weak; therefore, this predictor was not used independently as a decisive criterion for member selection.

Instead, the target cluster was defined using a three-predictor consensus criterion. Members were selected only when they belonged to the target clusters identified from all three more reliable predictors: 850-hPa V-wind, 700-hPa U-wind, and 500-hPa V-wind. This procedure retained 13 members for the R3 configuration and 7 members for the R9 configuration. The selected subsets were therefore based on cross-predictor agreement rather than on any single clustering result, providing a more conservative and physically consistent basis for subsequent analysis.

Figure 10 compares the composite spatial anomaly fields of the target-cluster members and the remaining members for the 500-hPa V-wind, 700-hPa U-wind, and 850-hPa V-wind under the R3 and R9 configurations. The differences between the target-cluster members and the remaining members are mainly reflected in the spatial extent, gradient strength, and location of the anomaly centers rather than in a complete reversal of the circulation signs across the entire domain. The 500-hPa V-wind exhibits relatively coherent middle-tropospheric anomaly structures in both configurations. The 700-hPa U-wind shows a southwest-negative and northeast-positive pattern, whereas the 850-hPa V-wind shows relatively positive anomalies over the western and central parts of the domain and weaker or negative anomalies toward the east. These differences indicate that the spatial organization of the lower- and middle-tropospheric anomalies provides information for distinguishing different ensemble forecast scenarios.

The broad spatial configurations are similar between R3 and R9, but the anomaly centers and gradient strengths are not identical, indicating that model resolution affects the representation of local lower- and middle-tropospheric circulation among ensemble members. Because the target clusters were independently determined for the three selected predictors, Figure 10 represents case-specific relative circulation characteristics rather than universally applicable weather regimes. Under the strict consensus criterion requiring a member to belong to the target cluster for all three predictors, 13 R3 members and 7 R9 members were retained. The precipitation composites in Figure 11 were therefore calculated as equal-weight means of these two circulation-conditioned subsets.

Figure 11 presents the 24 h accumulated precipitation composites for the circulation-conditioned subsets selected using the three-predictor consensus criterion and for the remaining members. In the R3 configuration, the subset mean concentrates the heavier precipitation over the central and southern parts of the study domain and provides better spatial coverage of the observed heavy-rainfall region near Guangzhou-Foshan. In contrast, the remaining-member mean is more spatially diffuse and exhibits a less concentrated heavy-rainfall center. In the R9 configuration, the subset mean also shows a more organized heavy-rainfall band than the mean of the remaining members. Overall, the members that belonged to the target clusters for all three predictors produced a precipitation pattern with spatial organization closer to the observed rainfall distribution.

The circulation-conditioned subset mean is defined as the equal-weight arithmetic mean of the 24 h accumulated precipitation forecasts of the selected members. No distance-based weighting, additional spatial smoothing, or posterior fitting of the precipitation field was applied. The R3 and R9 subsets contain 13 and 7 members, respectively. It is worth reiterating that the subset mean presented in Figure 11 is evaluated primarily as a visual and spatial diagnostic scenario. The intention is not to claim an optimized deterministic post-processing product that unconditionally maximizes quantitative scores, but rather to demonstrate how circulation-consistency selection extracts physically meaningful spatial indications from ensemble spread. Consequently, the comparison in Figure 11 is therefore intended to assess differences in the spatial organization of the subset mean relative to the remaining-member mean, rather than to claim statistically significant forecast improvement from a single case. The subset means show a more concentrated heavy-rainfall pattern and a precipitation region closer to the observed Guangzhou-Foshan area. However, because only one event is available, these differences should be interpreted as case-specific conditional guidance. A robust quantitative assessment of improvement relative to the full ensemble mean, remaining-member mean, and alternative selection strategies requires additional independent events.

3.4. Discussion and Limitations

This study focuses on the localized extreme heavy-rainfall event that occurred on 8 September 2022, for which the circulation predictors were identified from the statistical associations between hourly precipitation and ERA5 environmental fields. These predictors were subsequently used to classify the 30 CMA-TRAMS ensemble members. Accordingly, the circulation predictors and target-member subsets identified in this study characterize the ensemble uncertainty associated with this particular event. They should not be regarded as universal predictors or circulation regimes applicable to all weakly forced heavy-rainfall events, nor as evidence that one model resolution is generally superior to another. Nevertheless, localized and abrupt heavy-rainfall events, although less frequent than ordinary precipitation systems, can pose substantial risks because of their rapid development, strong spatial intermittency, and potential for simultaneous misses by both subjective human forecasting and objective numerical-model prediction. The present case study therefore provides an initial assessment of the circulation associations of such an event and examines the feasibility of a circulation-conditioned ensemble-member selection approach.

The CCC diagnostics further indicate that the clustering structure associated with the 925-hPa V-wind was relatively weak. This predictor was therefore excluded from the final member-selection procedure. The final selection was based on the 700-hPa U-wind, 500-hPa V-wind, and 850-hPa V-wind, with a strict criterion requiring each retained member to belong to the target cluster for all three predictors. This criterion helps limit the influence of the less reliable predictor and ensures greater consistency among the selected members; however, it also reduces the size of the conditional subset. This reduction is particularly notable for R9, for which only seven members were retained. The mean of the R9 conditional subset should therefore be interpreted with appropriate caution, as it may be more sensitive to sampling variability.

The circulation-conditioned subset mean is calculated as the equal-weight arithmetic mean of the 24 h accumulated precipitation forecasts from the selected members. It represents a conditional deterministic scenario constrained by circulation consistency, rather than a replacement for the full 30-member ensemble. The full ensemble remains necessary for representing forecast spread and probabilistic uncertainty. Figure 11 suggests that the circulation-conditioned subset provides a more organized spatial representation of heavy precipitation for this particular event. However, this result should be viewed as event-specific evidence and should not yet be interpreted as demonstrating stable correction skill or general superiority across different cases or model resolutions.

Because this study relies on predictors identified retrospectively using observed precipitation and reanalysis data from the same event, it serves primarily as a proof-of-concept diagnostic study. For potential operational application in future real-time forecasting, these key circulation predictors would need to be pre-established beforehand by constructing climatological predictor libraries or weather-pattern look-up tables from extensive historical case archives. Consequently, a larger and independent sample of events is needed to evaluate the transferability of the identified predictors and the stability of the clustering-based precipitation guidance. Future work will use the numerical-model archive to identify additional representative localized extreme-rainfall events and construct a broader event database. Multi-event ensemble verification and comparative analyses will then be conducted to examine forecast biases, circulation associations, and possible formation mechanisms more systematically.

4. Conclusions

This study investigated an atypical extreme heavy-rainfall event over the Pearl River Delta under weak synoptic forcing on 8 September 2022. Ensemble forecasts from the same CMA-TRAMS (EPS) model at the R3 and R9 resolutions were used to analyze key circulation predictors and circulation-conditioned member selection. The main conclusions are as follows:

(1)

Environmental background. The rainfall event was short-lived, localized, and highly concentrated. The spatial configuration of relatively high CAPE, enhanced middle- and lower-tropospheric humidity, multilayer circulation, and column-integrated vertical motion provided favorable environmental conditions for deep convection. Because the analysis used specific-time environmental fields and statistical associations, these results describe favorable background conditions rather than proving a unique causal trigger.

(2)

Key circulation predictors. The 700-hPa U-wind, 500-hPa V-wind, 850-hPa V-wind, and 925-hPa V-wind were initially considered as candidate clustering predictors. Because the CCC values for the 925-hPa V-wind were 0.5053 for R3 and 0.4987 for R9, indicating a relatively weak clustering structure, this predictor was excluded from the final selection. The final member-selection procedure used the 700-hPa U-wind, 500-hPa V-wind, and 850-hPa V-wind.

(3)

Ensemble-member selection. After independent clustering of the three final predictors, a member was retained only when it belonged to the target cluster for all three predictors. This strict consensus criterion retained 13 R3 members and 7 R9 members. The corresponding precipitation fields were calculated as equal-weight means of the 24 h accumulated precipitation forecasts of the selected members.

(4)

Precipitation response. For the analyzed event, the three-predictor consensus subset means produced more concentrated heavy-rainfall structures and placed the precipitation region closer to the observed Guangzhou-Foshan area than the corresponding remaining-member means. This result provides case-specific evidence that circulation-consistency selection may extract a conditional precipitation scenario. However, because the analysis is based on one event and the selected subsets contain different numbers of members, the result should not be interpreted as proof of statistically significant or generally transferable correction skill.

(5)

Limitations and future work. In conclusion, under weak synoptic forcing, clustering-based analysis of key circulation predictors provides a robust diagnostic framework for extracting extreme scenario information from ensemble datasets. However, users should interpret these results within the context of an event-specific retrospective analysis. Because this study examined only one atypical heavy-rainfall event—with the final R3 and R9 subsets containing 13 and 7 members, respectively—the statistical representativeness of the clustering partitions and circulation-conditioned subset means is inherently limited. Future studies using independent multi-case datasets and standardized quantitative verification are required to validate the operational transferability and generalizability of this approach. Specifically, future work should extend this method across multiple independent weakly forced heavy-rainfall events to compare the full ensemble mean, the circulation-conditioned subset mean, the remaining-member mean, and alternative member-selection strategies. Sensitivity tests should also examine alternative precipitation thresholds, neighborhood scales, predictor combinations, clustering algorithms or linkage settings, and verification metrics such as ETS, FBI, FSS, POD, and FAR. Furthermore, bootstrap or event-based resampling should be used, where appropriate, to quantify uncertainty in the reported improvements.