Evaluation Method of Severe Convective Precipitation Based on Dual-Polarization Radar Data

Abstract

With global warming and intensified human activities, extreme convective precipitation has become one of the most frequent natural disasters. An accurate and reliable assessment of severe convective precipitation events can support social stability and economic development. In order to investigate the accuracy enhancement methods and data fusion strategies for the assessment of severe convective precipitation events, this study is driven by the horizontal reflectance factor (Z_H) and differential reflectance (Z_DR) of the dual-polarization radar. This research work utilizes microphysical information of convective storms provided by radar variables to construct the precipitation event assessment model. Considering the problems of high dimensionality of variable data and low computational efficiency, this study proposes a dual-polarization radar echo-data-layering strategy. Combined with the results of mutual information (MI), this study constructs Bayes–Kalman filter (KF) models (RF, SVR, GRU, LSTM) for the assessment of severe convective precipitation events. Finally, this study comparatively analyzes the evaluation effectiveness and computational efficiency of different models. The results show that the data-layering strategy is able to reduce the data dimensions of 256 × 256 × 34,978 to 5 × 2213, which greatly improves the computational efficiency. In addition, the correlation coefficient of interval III–V calibration period is increased to 0.9, and the overall assessment accuracy of the model is good. Among them, the Bayes–KF-LSTM model has the best assessment effect, and the Bayes–KF-RF has the highest computational efficiency. Further, five typical precipitation events are selected for validation in this study. The stratified precipitation dataset agrees well with the near-surface precipitation, and the model’s assessment values are close to the observed values. This study completely utilizes the microphysical information offered by dual-polarized radar Z_H and Z_DR in precipitation event assessment, which provides a wide range of application possibilities for the assessment of severe convective precipitation events.

1. Introduction

In recent years, with global warming and intensified human activities, extreme precipitation weather often occurs in many regions of the world [1,2,3,4]. This type of weather causes serious urban disasters annually, leads to large-scale power outages, and seriously threatens both lives and social stability [5,6]. Heavy precipitation is highly heterogeneous in time and space, making accurate and reliable prediction challenging. Therefore, developing high-precision and high-resolution assessments of the timing and intensity of precipitation has become an urgent problem for meteorological departments [7,8,9].

Precipitation forecasting is an important issue in the field of meteorology, and the two mainstream methods are numerical model forecasting and radar echo extrapolation [10]. Numerical models forecast future atmospheric conditions by solving equations for atmospheric dynamics and thermodynamics, predicting further into the future than radar methods [11]. Compared with the radar echo extrapolation method, the numerical model can obtain the forecast results for a longer period of time in the future, but it also has some drawbacks. First, there are numerous uncertainties in the process of numerical simulation, such as inaccurate initial conditions and parameterization of physical processes [12]. The effect of the above factors can lead to a decrease in the reliability of the numerical model results [13]. Second, measurement errors in the input data make the solution process error magnified. Based on real-time radar images acquired, the radar echo extrapolation method realizes the prediction and assessment of precipitation events by analyzing the moving trend, shape and intensity changes of strong storms [14,15]. Capecchi et al. [16] investigated the impact of assimilated radar and automated weather station data on precipitation forecasts to improve the accuracy of early forecasting systems. The study by Ansh Srivastava et al. [17] demonstrated the important role played by radar echo data in extreme rainfall forecasting. Further, numerous scholars have conducted in-depth studies on the assessment of extreme rainfall forecasting based on radar echoes. However, these methods use only a small number of historical radar echo images to predict the next radar echo image. This results in low model data utilization, while the effective forecast time usually cannot exceed one hour [18].

In recent years, with the accumulation of big data and the development of computer arithmetic power, artificial intelligence and deep learning techniques have developed rapidly [19]. Deep learning methods are data-driven with strong nonlinear mapping capabilities and theoretically improve as the volume of training data increases. These methods are particularly well-suited for short-range forecasting, where extensive radar observation data are available [20]. Based on the scale-invariant feature transform (SIFT) and UNet convolutional neural network methods, Yao et al. [21,22] performed 0–2 h proximity forecasting of strong convective weather. Yu et al. [23] used a recurrent convolutional neural network in the UNet framework for 0–2 h proximity forecasting and achieved good results in some weather conditions. While the integration of deep learning has enhanced severe convective weather now-casting, challenges persist in managing massive radar raster datasets; these include overfitting, slow training speeds, and limited applicability [24].

The technology of combining dual linearly polarized weather radars and phased array antenna scanning modes has become increasingly mature over the past few years [25]. At the same time, Doppler radars with dual-polarization capability have been progressively upgraded in recent years [26,27]. Compared with the single-polarization weather radar, the bilinear polarization radar can simultaneously transmit polarized electromagnetic waves in the horizontal and vertical directions. It can obtain more accurate hydrometeorological estimation, which plays an important role in the prediction and monitoring of extreme precipitation events [28,29]. In addition, polarized radar variables such as differential reflectivity (Z_DR) and specific differential phase (K_DP) can provide richer convective storm microphysical information than radar reflectivity [30]. Meanwhile, Z_DR and K_DP contain the unique properties of raindrop size and distribution. These attributes may change greatly in different stages of storm evolution, thus helping to provide information on storm evolution [31]. Therefore, dual-polarization radar variables have great potential to improve the nowcasting of convective precipitation [32].

This study advances beyond traditional numerical simulations based on radar echoes by introducing a stratification strategy for radar echo data and developing a precipitation event evaluation model utilizing intelligent learning techniques. Compared with the current mainstream convolutional neural network method, this study greatly reduces the data dimension, improves the model’s computing efficiency, and enhances the model’s generalization performance. The findings demonstrate that the radar echo data stratification strategy and the intelligent learning-based precipitation evaluation method offer high computational reliability and efficiency, showcasing substantial practical value.

The rest of this paper is organized as follows. Section 2 introduces the data sources and quality control methods in detail. Meanwhile, the precipitation event assessment system based on radar echo data is presented in Section 3. Then, the result analysis and application cases are given in Section 4. Finally, and analysis and discussion are presented in Section 5. The general framework of this study is shown in Figure 1.

2. Dataset and Experimental Design

2.1. NJU-CPOL Dataset

Dual-polarization radar (DPR) is a radar system that uses two different polarizations, usually horizontal (H) and vertical (V) polarization. It transmits horizontal or vertical polarized microwave pulse signals through the antenna system, and obtains the following three microphysical variables for precipitation assessment. The horizontal reflectivity factor (Z_H) is the echo intensity in the horizontal direction, which mainly reflects the strength of precipitation. Differential reflectivity (Z_DR) is the difference in echo intensity between the horizontal and vertical directions, which mainly reflects the size of the precipitation particles in the observation area. The specific differential phase shift (K_DP) is the phase difference between the horizontal and vertical echoes caused by precipitation particles per unit distance, which mainly reflects the liquid water content. Wen et al. [33,34] deeply studied the performance of K_DP in simulating near-surface precipitation and proved its excellent performance. In addition, the radar system can also obtain reflected signals at different altitudes by adjusting the elevation angle of the antenna to cover the vertical height range of interest.

This study uses data from the NJU C-band dual-polarization weather radar, partially derived from Pan et al. [32]. The dataset (called NJU-CPOL) covers a total of 268 precipitation events from 2014 to 2019, including 35,133 data files. However, Pan et al. [32] only provided a dataset of dual-polarization radar at 3 km. This study collected and supplemented 1 km, 7 km Z_H and Z_DR datasets and near-surface precipitation (R_t) datasets. Referring to the work of Huang et al. [34,35], the near-surface precipitation calculation method used in this study is $R_t\left(K_{DP}\right)=58.01K_{DP}^{0.785}$. At the same time, the radar data have been subjected to quality control and interpolated to Cartesian coordinates. All the data in this study have a spatial resolution of 1 km in the horizontal direction, and contain CAPPI (Constant altitude Plan Projection Indicator) data at altitudes of 1 km, 3 km, and 7 km in a 256 × 256 km area around the radar center, and the overall dataset has a temporal resolution of 6–7 min.

2.2. Experimental Design

In this study, the Z_H and Z_DR datasets under 1 km, 3 km and 7 km are used as the assessment factor sets for the rainfall event R_t. Firstly, we screen the evaluation factors at different time steps. These factors will be used as input data for the rainfall event assessment model. Equation (1) is the formula for evaluating rainfall events using Z_H, Z_DR factors under different time steps.

$${\widehat{R}}_t=M\left(\begin{array}{l}(\mathrm{Optional})Z_{H,t-K}^{1\mathrm{k}\mathrm{m}},\dots ,Z_{H,t}^{1\mathrm{k}\mathrm{m}},Z_{DR,t-K}^{1\mathrm{k}\mathrm{m}},\dots ,Z_{DR,t}^{1\mathrm{k}\mathrm{m}}\\ (\mathrm{Optional})Z_{H,t-K}^{3\mathrm{k}\mathrm{m}},\dots ,Z_{H,t}^{3\mathrm{k}\mathrm{m}},Z_{DR,t-K}^{3\mathrm{k}\mathrm{m}},\dots ,Z_{DR,t}^{3\mathrm{k}\mathrm{m}}\\ (\mathrm{Optional})Z_{H,t-K}^{7\mathrm{k}\mathrm{m}},\dots ,Z_{H,t}^{7\mathrm{k}\mathrm{m}},Z_{DR,t-K}^{7\mathrm{k}\mathrm{m}},\dots ,Z_{DR,t}^{7\mathrm{k}\mathrm{m}}\end{array}\right)$$

(1)

where ${\widehat{R}}_i$ is the near-surface precipitation event at moment t; M is the assessment model; Optional is the factor selection mechanism; $Z_{H,t}^{1\mathrm{k}\mathrm{m}}$ is the Z_H value at moment t at a height of 1 km, and $Z_{H,t}^{3\mathrm{k}\mathrm{m}}$ and $Z_{H,t}^{7\mathrm{k}\mathrm{m}}$ are similar; $Z_{DR,t}^{1\mathrm{k}\mathrm{m}}$ is the Z_DR value at moment t at a height of 1 km, and $Z_{DR,t}^{3\mathrm{k}\mathrm{m}}$ and $Z_{DR,t}^{7\mathrm{k}\mathrm{m}}$ are similar; and K is the time step. We set the time step to be 5 when we performed the factor selection.

2.3. Evaluating Indicator

In this study, three evaluation metrics, namely correlation coefficient (r), root mean square error (RMSE) and mean absolute error (MAE), were used to assess the performance of the evaluation model. The calculation formula is as follows:

$$r=\frac{\mathit{cov}(\widehat{R},R)}{\sqrt{\mathit{var}(\widehat{R})\cdot \mathit{var}(R)}}$$

(2)

$$RMSE=\sqrt{\frac{1}{\mathrm{n}}{\displaystyle \sum _{i=1}^n{(R_i-{\widehat{R}}_i)}^2}}$$

(3)

$$MAE=\frac{1}{n}{\displaystyle \sum _{i=1}^n|{\widehat{R}}_{\mathrm{i}}-R_i|}$$

(4)

where cov(X, Y) is the covariance; var(X) is the variance; R_i is the observed value of the precipitation event; ${\widehat{R}}_i$ is the assessed value of the precipitation event; and n is the data length.

3. Methodology

3.1. Data-Layering Strategy

Considering that the weak precipitation scenario has limited reference significance for this study, this study set the minimum threshold of precipitation data coverage in the data-processing stage. Specifically, when the proportion of rainfall data exceeded 10% of the study area (256 × 256 km), we retained the data of the precipitation event. Meanwhile, the Z_H and Z_DR data under 1 km, 3 km and 7 km corresponding to the precipitation events that did not satisfy the threshold were excluded. We also removed redundant data (radar stations, building reflections) and anomalies, and replaced those exceeding the range of values with the mean of the surrounding values. Through this screening method, a total of 2213 valid precipitation event data files were collected and organized to provide data support for this study.

Eventually, the processed Z_H values were restricted to the interval [0, 65] while the Z_DR values were restricted to the interval [−1, 5]. Since there is an exponential relationship between radar reflectivity and precipitation intensity, the larger the reflectivity, the stronger the rainfall intensity. Therefore, in this study, the Z_H of 1 km, 3 km and 7 km were all divided into five layers according to the target interval (0, 65]. At the same time, the raster positions after stratification according to Z_H were mapped into Z_DR and R, which, in turn, yielded the five-layer stratified data of Z_DR and R under the heights of 1 km, 3 km and 7 km. In stratification, the non-zero values of each layer are summed up and averaged as the value of the layer, and different layers correspond to different intensities of precipitation, and the intensity of precipitation increases in the order of Ⅰ–Ⅴ layers.

The stratified frame-by-frame Z_H and Z_DR value factor sets are used as the factor set to be selected for the precipitation data R_t.

$$\left[Z_{H1}^{\mathit{height}}~Z_{H5}^{\mathit{height}},Z_{\mathit{DR}1}^{\mathit{height}}~Z_{\mathit{D}\mathit{R}5}^{height}\right]$$

(5)

where height is the dual-polarization radar scanning height, which is 1 km, 3 km and 7 km, respectively.

3.2. Factor Screening Method

In this study, mutual information (MI) was used to assess the degree of correlation between Z_H, Z_DR and the rainfall event R_t at different heights and time steps. MI is a useful information metric in information theory that can be considered as the amount of information a random variable contains about another random variable. It is used to represent the degree of interdependence between variables [36,37]. Unlike the correlation coefficient, mutual information is not restricted to real-valued random variables; it is more general and determines the degree of similarity between the product of the joint and marginal distributions p(X), p(Y).

In general, the mutual information of two discrete random variables X and Y can be defined as follows:

$$I\left(X;Y\right)={\displaystyle \sum _{y\in Y}{\displaystyle \sum _{x\in X}p\left(x,y\right)\mathit{log}\left(\frac{p\left(x,y\right)}{p\left(x\right)p\left(y\right)}\right)}}$$

(6)

where p(x, y) is the joint density function of X and Y, and p(x) and p(y) are the edge density functions of X and Y, respectively.

3.3. Data Noise Reduction Method

To reduce the effect of systematic errors in dual- polarization radar observation data, this work uses the Kalman filtering (KF) approach for smoothing and noise reduction in hierarchically processed radar data [38]. KF is renowned for its ability to estimate the state of dynamic systems accurately, making it particularly suited for sensor data plagued by noise. This technique not only forecasts system state variables effectively and optimizes future state predictions but also adeptly handles measurement errors and uncertainties inherent in system dynamics [39]. KF has been widely used as an extremely effective estimation tool in a variety of fields such as aerospace, navigation, robotics, finance, and signal processing. Its core idea is to characterize the system state in terms of a probability distribution and to continuously update this distribution to integrate new dynamic and measurement information in order to improve the accuracy of estimating the state of a dynamic system.

3.4. Rainfall Assessment Model

3.4.1. Random Forest

Random Forest (RF) is an integrated learning algorithm especially for classification and regression tasks. RF employs Bootstrap resampling to create multiple subsets from the original training set, each of which is used to build a decision tree [40,41]. It improves the accuracy and robustness of the model by constructing multiple decision trees and merging their results to obtain the final prediction. The Random Forest algorithm excels at coping with multidimensional inputs, determining the relevance of variables, and maintaining high classification accuracy. The effectiveness of the RF model hinges on various hyperparameters, including the number of trees, the branching complexity of these trees, and the data volume in their leaf nodes. To identify optimal hyperparameter settings, this paper employs Bayesian optimization, a method that effectively adapts to diverse data characteristics and enhances the model’s generalization capability.

3.4.2. Support Vector Regression

Support Vector Regression (SVR) is a regression method based on Support Vector Machine (SVM). The core idea of SVR lies in determining a hyperplane that approximates all training datasets as closely as possible [42,43]. Different from the goal of SVM to find the maximum interval between classifications, the goal of SVR is to make the hyperplane contain as many data points as possible while ensuring that the error is within an acceptable range. In many practical applications, SVR has become a widely used regression method because of its robustness and high efficiency. In this study, the Bayesian method is used to optimize the key hyperparameters in SVR to improve the performance of the model, such as kernel function type, kernel function parameters, error penalty coefficient and so on.

3.4.3. Gate Recurrent Unit

Gated Recurrent Unit (GRU) is an upgraded form of Recurrent Neural Networks (RNN) that addresses the issues of gradient vanishing and explosion in long-sequence situations. GRU introduces a gating mechanism that is better able to capture long-term dependencies in sequences while reducing the number of parameters [44]. GRU mainly includes two key gating units: Update Gate and Reset Gate. These gating mechanisms allow the GRU network to selectively update the state when processing sequential data while controlling the transmission of information. This method can help the model to identify the key features in the sequence more accurately. In order to improve the evaluation effect of GRU, this paper uses the Bayesian method to optimize some hyperparameters. These hyperparameters include the number of hidden layer nodes, initial learning rate, learning rate decay period, and factor.

3.4.4. Long Short-Term Memory

Since the introduction of the Artificial Neural Network (ANN) in the 1980s, its excellent nonlinear mapping ability has made it the focus of research in many fields. Long Short-Term Memory (LSTM) solves the problem of disappearing or exploding RNN gradients and insufficient long-term memory capacity. It greatly improves the performance of RNN in temporal prediction [45,46]. LSTM is mainly composed of an input gate, output gate and forgetting gate. It has the recursive attribute of RNN and can effectively use long-sequence data information, as shown in Figure 2. The unique memory structure and gating mechanism of LSTM make it well-adapted and reliable in feature learning. Therefore, it is widely used in time series model training. To improve the prediction performance of LSTM, this paper strategically adjusts hyperparameters, including the number of nodes in the hidden layer, the initial learning rate, and the rate of learning decay. Concurrently, it employs optimized L2 regularization to mitigate the risk of overfitting, ensuring a more reliable model performance.

3.4.5. Bayesian Hyperparameter Optimization

In order to improve the evaluation performance of the model, the optimization of model-sensitive hyperparameters is crucial. The traditional exhaustive method is prone to a “dimensional disaster”. In order to avoid this problem, this study uses the Bayesian method to optimize the model’s hyperparameters [47,48]. Compared with other optimization methods, the Bayesian method uses the information of the probability model to find the optimal hyperparameter value faster. The Bayesian optimization method takes the surrogate model as the core. Based on the acquisition function (AF), the Bayesian optimization method selects a hyperparameter that is most promising to improve the performance of the model and updates the surrogate model. It will repeat this process until the optimal hyperparameter value is found.

In conclusion, Bayesian optimization is a powerful global optimization method that is particularly suitable for black-box objective functions that are computationally expensive and have high uncertainty. Therefore, this study uses Bayesian optimization to optimize the hyperparameters of RF, SVR, GRU and LSTM models, as shown in

Table 1. The optimized hyperparameters of different models.

Model	Hyperparameters to Be Optimized	Number of Hyperparameters
RF	numTrees; MaxNumSplits; MinLeafSize	3
SVR	BoxConstraint; KernelScale	2
GRU	hiddenSize; InitialLearnRate; LearnRateDropFactor; LearnRateDropPeriod	4
LSTM	hiddenSize; InitialLearnRate; L2Regularization; LearnRateDropFactor; LearnRateDropPeriod	5

. In this study, the evaluation model and the Bayesian optimization algorithm are implemented using functions or tools in Matlab.

4. Results Analysis

4.1. Data Stratification Results

This study explores the correlation between dual-polarization radar data and rainfall data from two dimensions of time and space. In the time dimension, this paper takes the sequence of frames in 258 rainfall processes as the timing standard. In the spatial dimension, this paper takes the 256 × 256 km plane area corresponding to each frame of data as the regional standard. According to the range of radar data after processing and the stratification strategy, the Z_H value (256 × 256 km) is stratified in this paper. Finally, a total of 2215 hierarchical processing data values were obtained. The distribution of radar echo Z_H after stratification is shown in Figure 3.

The Z_H contour plot is divided into five gradients of (0, 13), [13, 26), [26, 39), [39, 52), [52, 65] with 13 dBZ as the gradient. This study was carried out with an example of a precipitation event in the dataset, as shown in Figure 4.

In this study, a precipitation event is used as an example to plot Z_H contour maps under each stratum separately. Figure 5 shows that the Z_H values of this precipitation event are concentrated in the Ⅱ and Ⅲ intervals. Since the relationship between radar reflectivity and precipitation intensity is empirically exponential, this indicates that the rainfall is moderate-intensity rainfall.

4.2. Analysis of MI Results

Combining the hierarchically processed data and the MI analysis method, this study performs correlation analysis on the radar echo data of 1 km, 3 km, and 7 km. The time step of Z_H, Z_DR, and K_DP data is set to 5, and there are a total of 36 prediction factors in each interval. Too low or too high input data dimension will lead to underfitting and overfitting problems in the model. This study comprehensively considers all model features, and finally sets the model’s input dimension to 15.

Table 2. The model’s input factors of different intervals.

Interval	Input Factors
Ⅰ	$\begin{array}{l}{Z}_{DR}^{1\mathrm{km}}(t),Z_{DR}^{1\mathrm{km}}(t-5),Z_{DR}^{1\mathrm{km}}(t-4),Z_{DR}^{1\mathrm{km}}(t-1),Z_{DR}^{1\mathrm{km}}(t-2),Z_{DR}^{1\mathrm{km}}(t-3),Z_{DR}^{7\mathrm{km}}(t),Z_{DR}^{7\mathrm{km}}(t-2)\\ Z_H^{7\mathrm{km}}(t-2),Z_{DR}^{7\mathrm{km}}(t-5),Z_H^{7\mathrm{km}}(t-5),Z_{DR}^{7\mathrm{km}}(t-1),Z_H^{7\mathrm{km}}(t-4),Z_H^{7\mathrm{km}}(t),Z_{DR}^{7\mathrm{km}}(t-3)\end{array}$
Ⅱ	$\begin{array}{l}{Z}_H^{7\mathrm{km}}(t-3),Z_H^{7\mathrm{km}}(t-5),Z_H^{7\mathrm{km}}(t-4),Z_H^{7\mathrm{km}}(t-2),Z_H^{7\mathrm{km}}(t-1),Z_H^{7\mathrm{km}}(t),Z_H^{3\mathrm{km}}(t-3)\\ Z_H^{3\mathrm{km}}(t-4),Z_H^{3\mathrm{km}}(t-2),Z_H^{3\mathrm{km}}(t-5),Z_H^{3\mathrm{km}}(t),Z_H^{3\mathrm{km}}(t-1),Z_H^{1\mathrm{km}}(t-5),Z_H^{1\mathrm{km}}(t-1),Z_H^{1\mathrm{km}}(t-2)\end{array}$
Ⅲ	$\begin{array}{l}{Z}_H^{1\mathrm{km}}(t),Z_H^{1\mathrm{km}}(t-2),Z_H^{1\mathrm{km}}(t-1),Z_H^{1\mathrm{km}}(t-3),Z_H^{1\mathrm{km}}(t-4),Z_H^{1\mathrm{km}}(t-5),Z_H^{3\mathrm{km}}(t-4)\\ Z_H^{3\mathrm{km}}(t),Z_H^{3\mathrm{km}}(t-1),Z_H^{3\mathrm{km}}(t-2),Z_H^{3\mathrm{km}}(t-5),Z_H^{3\mathrm{km}}(t-3),Z_H^{7\mathrm{km}}(t),Z_H^{7\mathrm{km}}(t-1),Z_H^{7\mathrm{km}}(t-2)\end{array}$
Ⅳ	$\begin{array}{l}{Z}_{DR}^{1\mathrm{km}}(t),Z_H^{1\mathrm{km}}(t),Z_{DR}^{1\mathrm{km}}(t-1),Z_{DR}^{1\mathrm{km}}(t-2),Z_H^{1\mathrm{km}}(t-1),Z_{DR}^{1\mathrm{km}}(t-3),Z_H^{1\mathrm{km}}(t-2),Z_{DR}^{1\mathrm{km}}(t-4)\\ Z_H^{1\mathrm{km}}(t-3),Z_{DR}^{1\mathrm{km}}(t-5),Z_H^{1\mathrm{km}}(t-4),Z_H^{1\mathrm{km}}(t-5),Z_H^{3\mathrm{km}}(t),Z_H^{3\mathrm{km}}(t-1),Z_H^{3\mathrm{km}}(t-3)\end{array}$
Ⅴ	$\begin{array}{l}{Z}_{DR}^{1\mathrm{km}}(t),Z_{DR}^{3\mathrm{km}}(t),Z_H^{1\mathrm{km}}(t),Z_{DR}^{1\mathrm{km}}(t-1),Z_{DR}^{3\mathrm{km}}(t-1),Z_{DR}^{1\mathrm{km}}(t-2),Z_{DR}^{3\mathrm{km}}(t-2),Z_{DR}^{3\mathrm{km}}(t-3)\\ Z_{DR}^{3\mathrm{km}}(t-4),Z_{DR}^{1\mathrm{km}}(t-3),Z_{DR}^{1\mathrm{km}}(t-4),Z_{DR}^{3\mathrm{km}}(t-5),Z_{DR}^{1\mathrm{km}}(t-5),Z_H^{1\mathrm{km}}(t-1),Z_H^{3\mathrm{km}}(t)\end{array}$

lists the top 15 input features of each interval MI value, and Figure 6 shows the MI vertical diagrams corresponding to 15 input features. Table 2 shows that precipitation events of different intensities are most strongly associated with Z_H and Z_DR at 1 km, followed by Z_H and Z_DR at 3 km. This indicates that the higher radar echo data have a limited contribution to the assessment of near-surface precipitation. Meanwhile, the radar echo data’s correlation with precipitation gradually decreases with the increase in time step. Combined with Figure 6, it can be seen that interval IV has the highest MI value and interval I has the lowest MI value. This indicates that there is a complex correlation between the MI value and the intensity of precipitation events.

4.3. Interval Evaluation Effect

In this study, the Bayesian optimization method described in Section 3.4.5 was used to optimize the hyperparameters of the RF, SVR, GRU and LSTM models. As an example, Figure 7 shows the optimization process of the SVR model for precipitation events Ⅰ-Ⅴ under the Bayesian optimization framework. In this process, the objective function was adjusted according to the research needs, and the BoxConstraint and KernelScale kept changing until the best combination was found. As can be seen in Figure 7, the potential optimal values in the pre-Bayes optimization period are obtained by random search. In this study, the 25 Bayesian iterations process is set, and the model gradually locks in the best combination of parameters. From the final result, the optimization process is very reasonable, and the objective function achieves the minimum requirement.

Based on the Bayesian optimization results of the model, this study establishes an assessment method for precipitation events.

Table 3. Interval Ⅰ–Ⅴ model precipitation assessment results.

Data Range	Model	Period	r	RMSE	MAE
Interval Ⅰ	Bayes–KF-RF	Calibration	0.93	8.83	3.96
		Validation	0.60	7.48	5.08
	Bayes–KF-SVR	Calibration	0.71	23.19	18.25
		Validation	0.57	18.18	17.14
	Bayes–KF-GRU	Calibration	0.73	15.37	7.98
		Validation	0.57	9.21	7.05
	Bayes–KF-LSTM	Calibration	0.87	11.23	5.46
		Validation	0.69	5.67	4.36
Interval Ⅱ	Bayes–KF-RF	Calibration	0.80	22.31	18.09
		Validation	0.62	13.81	13.67
	Bayes–KF-SVR	Calibration	0.68	9.61	5.09
		Validation	0.73	4.22	3.31
	Bayes–KF-GRU	Calibration	0.73	8.78	4.38
		Validation	0.75	4.30	3.10
	Bayes–KF-LSTM	Calibration	0.73	8.64	4.06
		Validation	0.77	5.09	3.59
Interval Ⅲ	Bayes–KF-RF	Calibration	0.93	1.72	0.99
		Validation	0.72	2.78	2.42
	Bayes–KF-SVR	Calibration	0.88	2.61	1.92
		Validation	0.82	1.98	1.63
	Bayes–KF-GRU	Calibration	0.82	2.57	1.81
		Validation	0.83	1.88	1.48
	Bayes–KF-LSTM	Calibration	0.91	1.88	1.42
		Validation	0.83	1.81	1.35
Interval Ⅳ	Bayes–KF-RF	Calibration	0.98	3.50	2.46
		Validation	0.82	15.19	12.41
	Bayes–KF-SVR	Calibration	0.97	4.49	3.75
		Validation	0.82	18.16	15.65
	Bayes–KF-GRU	Calibration	0.97	4.24	3.04
		Validation	0.80	9.77	7.58
	Bayes–KF-LSTM	Calibration	0.97	4.66	3.32
		Validation	0.77	13.75	11.62
Interval Ⅴ	Bayes–KF-RF	Calibration	0.94	73.73	41.77
		Validation	0.88	93.38	61.19
	Bayes–KF-SVR	Calibration	0.93	34.86	29.60
		Validation	0.87	43.65	37.26
	Bayes–KF-GRU	Calibration	0.93	26.29	13.59
		Validation	0.84	54.86	36.69
	Bayes–KF-LSTM	Calibration	0.98	13.76	7.91
		Validation	0.93	38.56	26.37

demonstrates the precipitation assessment effect for each interval. The thickened data shows that the corresponding model performs better in this interval. The data in Table 3 show that the performance of precipitation event assessment for each interval is better overall, and the assessment effect of the calibration period is generally better than that of the validation period. This phenomenon may be due to the greater noise in the validation period data. Except for interval 4, the Bayes–KF-LSTM model has the most prominent assessment effect in other intervals, and thus it is recommended as the main precipitation assessment method. It should be noted that interval Ⅰ is relatively poorly assessed, which may be due to the under-representation of the data in the calibration period.

4.4. Representative Cases

In order to evaluate the effectiveness of specific precipitation events, we utilize heat maps to visualize the model’s assessment accuracy before and after applying optimized parameters, combined with typical precipitation events. In Figure 8, we select a total of five typical precipitation event processes, and each typical precipitation time includes the observed value of the precipitation event, the interval stratification value, and the precipitation assessment value. Figure 9 shows that the assessment model’s precipitation events, which accurately predict the likely intensity of upcoming precipitation events, are in good agreement with the observed values, particularly in the region of strong convective precipitation. This makes the practical application of the model better. As the interval increases, that is, as the precipitation intensity continues to increase, the better the forecast effect. This is mainly because the larger the interval level, the fewer the corresponding heavy precipitation events. There are many 0 values in the data, which affect the final evaluation index.

In order to evaluate the computational efficiency of different models and intervals, this study sets the number of Bayes optimizations for each model to 25, and the average of its time is taken for each run 10 times.

Table 4. Average running time for each model and interval.

Model	Interval	Running Time/s	Model	Interval	Running Time/s
Bayes–KF–RF	Ⅰ	30.67	Bayes–KF–GRU	Ⅰ	274.13
	Ⅱ	26.56		Ⅱ	266.89
	Ⅲ	28.87		Ⅲ	258.02
	Ⅳ	24.20		Ⅳ	267.91
	Ⅴ	26.18		Ⅴ	250.48
Bayes–KF–SVR	Ⅰ	314.31	Bayes–KF–LSTM	Ⅰ	108.16
	Ⅱ	68.69		Ⅱ	91.62
	Ⅲ	137.20		Ⅲ	88.08
	Ⅳ	92.42		Ⅳ	118.77
	Ⅴ	165.28		Ⅴ	72.30

shows the average computational time of different models under each interval, and Figure 10 shows the box plots of the running time of different models and intervals. Overall, RF has the shortest running time and the highest computational efficiency; GRU has the longest running time and the lowest computational efficiency, which may be related to the model’s structure and parameter settings. Combined with Figure 10, it can be seen that, except for the anomalies, the model’s running time is essentially within a reasonable range. At the same time, with the increase in rainfall intensity (Ⅰ–V), the running time of the whole model shows a weak downward trend. This may be due to the fact that there are more 0 values in layers Ⅳ–V after the stratification of heavy rainfall events.

5. Summary and Discussion

This research work is driven by Z_H and Z_DR data from dual-polarization radar, and a data-layering strategy is proposed to reduce the data dimensionality. Further, this paper constructs the Bayes–KF-Models for evaluating strong convective precipitation events. The example verification shows that the data stratification strategy proposed in this paper can significantly reduce the data dimension and greatly improve the operation efficiency of the model. Kalman filtering can reduce the interference of radar echo data noise on the model to a certain extent. The radar data after stratification contains microphysical information such as rainfall intensity, which can provide a data basis for model construction. The results of the precipitation assessment model in this paper are very close to the near-surface precipitation data. The correlation coefficient r of the calibration period of the calibration intervals Ⅲ-Ⅴ can reach about 0.9. Among them, the Bayes–KF-LSTM model has the best evaluation effect, followed by the Bayes–KF-RF model. However, the Bayes–KF-RF model has the highest computational efficiency, which has the strong practicability. Considering that the model needs to have better applicability in precipitation events of different intensities, Bayes–KF-RF or Bayes–KF-LSTM are recommended as the main methods for the assessment of intense convective precipitation events.

The evaluation model of strong convective precipitation events constructed in this paper has good applicability and promotion value. However, this research work still requires further discussion, which can be further studied and improved in the future. For example, this study focuses only on the post-processing and assessment of severe convective precipitation events, and is understudied with respect to forecasting issues; the evaluation results of different models are quite different; and the uncertainty characteristics of severe convective precipitation events are difficult to quantify. In the future, research work can consider increasing the fusion results of multi-model evaluation effects to reduce the impact of data noise and system errors. Meanwhile, we need to pay more attention to the precipitation event forecasting method itself. The generalization performance and stability of the model can be improved through the above research. In summary, this study fully exploits the potential of dual-polarimetric radar Z_H and Z_DR data in precipitation event assessment. This research work can provide new ideas for the assessment of strong convective precipitation events, which has broad application prospects.