Dynamic Inversion Algorithm for Rainfall Intensity Based on Dual-Mode Microwave Radar Combined Rain Gauge
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摘要: 微波气象雷达探测降雨特征的应用前景较为广泛，但其数据维度单一，测量精度受限于传统反演算法局限性。该文提出基于双模(FMCW-CW)微波雷达联合雨量计的数据进行融合反演降雨强度。针对FMCW模式的雨滴谱数据特征，该文提出基于注意力机制(Attention)连接双层长短期记忆网络(LSTM)的融合算法(LSTM-Attention-LSTM)，通过Attention和 LSTM提取雨滴谱数据与实际降雨强度之间的依赖关系，聚焦重要特征并进行解码预测。同时，针对CW模式反演算法难以获取雨滴谱数据，仅能依赖反射率因子和降雨率(Z-R)关系的问题，提出基于扩展卡尔曼算法(EKF)优化Z-R关系，通过动态建模Z-R参数、融合多源数据、施加物理约束，以便准确拟合Z-R关系。实验结果表明：(1) LSTM-Attention-LSTM显著提升降雨率反演精度，相较实际测量降雨强度相关系数(R2)达到0.95，均方根误差(RMSE)为
0.1623 mm/h。(2) 基于EKF优化动态Z-R关系法能够更加精准地确定Z-R关系的参数，拟合结果与实际数据分布情况相关度最高R2为0.972，RMSE为0.1076 mm/h。-
关键词:
- 微波雷达 /
- 降雨强度 /
- 长短期记忆神经网络 /
- 反射率因子和降雨率关系 /
- 扩展卡尔曼滤波
Abstract:Objective Microwave meteorological radar has broad application potential in rainfall detection due to its non-contact measurement, high spatiotemporal resolution, and multi-parameter retrieval capability. However, in the context of climate change, increasingly complex rainfall events require monitoring systems to deliver high-precision, multi-dimensional, real-time data to support disaster warning and climate research. Conventional single-mode radars, constrained by fixed functionalities, cannot fully meet these requirements, which has led to the development of multi-mode radar technology. The dual-mode radar examined in this study employs Frequency Modulated Continuous Wave (FMCW) and Continuous Wave (CW) modes. These modes adopt different algorithmic principles for raindrop velocity measurement: FMCW enables spatially stratified detection and strong anti-interference performance, whereas CW provides more accurate measurements of raindrop fall speed, yielding integral rainfall information in the vertical column. Despite these advantages, retrieval accuracy remains limited by the reliance of traditional algorithms on fixed empirical parameters, which restrict adaptability to regional climate variations and dynamic microphysical precipitation processes, and hinder real-time response to variations in rain Drop Size Distribution (DSD). Ground rain gauges, by contrast, provide near-true reference data through direct measurement of rainfall intensity. To address the above challenges, this paper proposes a dynamic inversion algorithm that integrates dual-mode (FMCW–CW) radar with rain gauge data, enhancing adaptability and retrieval accuracy for rainfall monitoring. Methods Two models are developed for the two radar modes. For the FMCW mode, which can retrieve DSD parameters, a fusion algorithm based on Attention integrated with a double-layer Long Short-Term Memory (LSTM) network (LSTM–Attention–LSTM) is proposed. The first LSTM extracts features from DSD data and rain gauge–measured rainfall intensity through its hidden state output, with a dropout layer applied to randomly discard neurons and reduce overfitting. The Attention mechanism calculates feature similarity using dot products and converts it into attention weights. The second LSTM then processes the time series and integrates the hidden-layer features, which are passed through a fully connected layer to generate the retrieval results. For the CW mode, which cannot directly retrieve DSD parameters and is constrained to the reflectivity factor–Rainfall rate (Z–R) relationship (Z=aRb), an algorithm based on the Extended Kalman Filter (EKF) is proposed to optimize this relationship. The method dynamically models the Z–R parameters, computes the residual between predicted rainfall intensity and rain gauge observations, and updates the prior estimates accordingly. Physical constraints are applied to parameters a and b during state updates to ensure consistency with physical laws, thereby enabling accurate fitting of the Z–R relationship. Results and Discussions Experimental results show that both models enhance the accuracy of rainfall intensity retrieval. For the FMCW mode, the LSTM–Attention–LSTM model applied to the test dataset outperforms traditional physical models, single-layer LSTM, and double-layer LSTM. It effectively captures the temporal variation of rainfall intensity, with the absolute error relative to observed values remaining below 0.25 mm/h ( Fig. 5 ). Compared with the traditional physical model, the LSTM–Attention–LSTM reduces RMSE and MAE by 46% and 38%, achieving values of0.1623 mm/h and 0.147 mm/h, respectively, and increases R2 by 14.5% to 0.95 (Table 2 ). For the CW mode, the Z–R relationship optimized by the EKF model provides the best fit for the Z and R distribution in the validation dataset (Fig. 6 ). Rainfall intensity retrieved with this algorithm on the test set exhibits the smallest deviation from actual observations compared with convective cloud empirical formulas, Beijing plain area empirical formulas, and the dynamic Z–R method. The corresponding RMSE, MAE, and R2 reach0.1076 mm/h, 0.094 mm/h, and 0.972, respectively (Fig. 7 ;Table 4 ).Conclusions This study proposes two multi-source data fusion schemes that integrate dual-mode radar with rain gauges for short-term rainfall monitoring. Experimental results confirm that both methods significantly improve the accuracy of rainfall intensity retrieval and demonstrate strong dynamic adaptability and robustness. -
表 2 FMCW模式各模型反演结果指标
模型 RMSE MAE R2 雨滴谱算法
LSTM
双层LSTM
LSTM-attention-LSTM0.3009 0.2773 0.2260 0.1623 0.2371 0.2156 0.1982 0.1470 0.8285 0.8544 0.9032 0.9501 
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表 4 CW模式各Z-R模型反演结果指标
模型 RMSE MAE R2 对流型经验公式
北京平原经验公式
动态Z-R
EKF优化Z-R0.2059 0.1770 0.1466 0.1076 0.1799 0.1479 0.1186 0.0940 0.9197 0.9207 0.9593 0.9720
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