基于多模型比选耦合的降水预测

变化环境下水文时间序列的模拟预测难度不断加大，以往研究大多聚焦在模型的不同组合尝试与应用探索，但缺乏针对不同组合模型适用性与稳定性的系统研究。选择经验模态分解（empirical mode decomposition，EMD）、总体平均经验模态分解（ensemble empirical mode decomposition，EEMD）、改进的总体平均经验模态分解（modified ensemble empirical mode decomposition，MEEMD）和变分模态分解（variational mode decomposition，VMD）4种常用的分解算法，与多元线性回归（multivariable linear regression，MLR）、随机森林（random forest，RF）、BP神经网络（back propagation，BP）、卷积神经网络（convolutional neural networks，CNN）和长短期记忆神经网络（long short-term memory，LSTM）5种具有代表性的模型结合，构建20种基于“分解-预测-重构”模式的组合模型，并以华北地区密云、官厅两流域年和汛期降水为例，进行模型适用性与稳定性综合对比分析。结果表明：单一模型对密云流域年降水和汛期降水的预测结果优于官厅流域，但整体预测结果均不理想；结合分解算法后的组合模型预测结果明显优于单一模型，且该预测结果存在正负误差抵消现象，因此有助于进一步提高组合模型的整体预测精度；与基于EMD系列的分解算法相比，VMD算法对模型预测精度提升效果最显著，组合模型适用性和稳定性整体上表现为VMD-MLR＞VMD-LSTM＞VMD-BP＞VMD-CNN。

Precipitation prediction based on decomposition algorithm-based models

Prediction of hydrological time series is a challenging issue due to complicated hydrologic processes, which would greatly impact the water resources management and hydraulic engineering design. Related studies indicated that combined models, which are based on the decomposition-prediction-reconstruction mode usually perform much better for the prediction of hydrological time series than single models. A great number of studies have been conducted on diverse combinations and applications of combined models, however, a comprehensive evaluation of the applicability and stability of different combined models is lacking, leaving a research gap for this important issue. Four commonly used decomposition methods were applied, namely empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), modified ensemble empirical mode decomposition (MEEMD), and variational mode decomposition (VMD). The four decomposition methods were further combined with five representative prediction models, namely multivariable linear regression (MLR), random forest (RF), back propagation (BP), convolutional neural networks (CNN), and long short-term memory (LSTM), to establish a total of 20 combined models. These 20 combined models were used to predict the annual precipitation and flood season precipitation and conducted a comparative analysis of the models in the Miyun basin and Guanting basin in North China.in North China.Results showed that: (1) The single models predicted both annual precipitation and flood season precipitation more accurately in the Miyun basin than in the Guanting basin, but the single model’s performances were overall poor in the two basins. (2) The prediction results from the combined models after coupling with decomposition algorithms become much better than those from the single models, and the positive errors could be offset by the negative errors during the prediction processes when using the combined models, which could improve the overall prediction accuracy of precipitation. (3) Compared with the EMD and other algorithms, the VMD algorithm has the most significant effect on improving the prediction accuracy of precipitation, and the applicability and stability of the combined models is VMD-MLR> VMD-LSTM> VMD-BP> VMD-CNN.Moreover, the results indicated a single model can not accurately grasp the complex characteristics of the precipitation time series. The prediction accuracy of a single model could be approved through parameters optimization, however, the effect is not obvious. Compared with a single model, the combined models based on decomposition algorithms can effectively improve the prediction results. In the combined models, the effectiveness of decomposition algorithms (such as EMD and VMD) in decomposing the original time series directly affects the models'' prediction results. After combining with the decomposition algorithm, the models'' performance improves significantly, and their applicability and stability are greatly enhanced. After combining with the decomposition algorithm, even some simple models (such as MLR) can be used to accurately predict precipitation time series with complex variability patterns. Different model combinations and predictors lead to differences in prediction results among combined models. Therefore, more influencing factors (such as climate indicators) and more complex combined models based on the decomposition-prediction-reconstruction mode should be explored in future research to optimize the prediction model and prediction process, to further improve the prediction accuracy and reliability of the precipitation in this study area.