为提高年径流预测精度，引入黏菌算法（slime mould algorithm，SMA）和变分模态分解算法（variational mode decomposition，VMD），提出一种基于卷积神经网络（convolutional neural network，CNN）和门控循环单元（gated recurrent unit，GRU）神经网络的组合预测模型（VMD-SMA-CNN-GRU）。利用VMD对径流数据进行分解；采用SMA优化CNN-GRU模型参数，构建模型对每个分量进行预测；各分量结果相加得到最终结果。以兰西水文站为例，将所建模型与CEEMDAN (complete ensemble empirical mode decomposition with adaptive noise)-CNN-GRU、VMD-CNN-LSTM（long short-term memory）、VMD-LSTM、VMD-GRU、VMD-PSO (particle swarm optimization)CNN-GRU、SMA-CNN-GRU和CNN-GRU预测模型进行对比分析。结果表明：SMA优化的VMD-CNN-GRU模型预测精度不仅高于上述7种模型，而且避免了人工试算确定CNN-GRU模型参数效率低的不足，为年径流预测提供了一种新方法。

Medium and long-term hydrological forecasting is an essential link in management,optimization of water resources,flood control,drought relief,and reservoir optimal operation.With the rapid development of science and technology,many modern artificial intelligence (AI) models have been applied to hydrological forecasting,such as back-propagation artificial neural network,support vector machine and long short-term memory neural network.Among the AI models,convolutional neural network (CNN) is a unique deep network,which can fully excavate the correlation between data.Gated recurrent unit neural network (GRU),a kind of the recurrent neural network,is a variant of long short-term memory neural network (LSTM).GRU is often used in time-series data prediction and can solve the problem of gradient disappearance.The combined model of convolutional neural network and gated recurrent unit neural network (CNN-GRU) was applied in various fields except runoff prediction.Additionally,for the setting of the parameters of CNN-GRU hybrid neural network,most people used the control variable method for trial calculation,which was not only low in efficiency and low in accuracy.Hence,a combined prediction model (VMD-SMA-CNN-GRU) based on convolutional neural network and gated recurrent unit neural network was proposed by introducing slime mould algorithm (SMA) and variational mode decomposition (VMD). The four main steps of the present VMD-SMA-CNN-GRU forecasting model can be summarized as follows:The original runoff series was decomposed by VMD to obtain several intrinsic mode functions and a residual.The slime mould population size n and the maximum iteration M was set.Subsequently,SMA was used to optimize key parameters such as the number of convolution layers,the number of neurons in the hidden layer of GRU,training times and learning rate.The mean square error (MAE) was chosen as the objective function of the optimization algorithm.SMA-CNN-GRU model was used to predict all the subseries.The predicted values obtained above were accumulated to deduce the ultimate prediction results. Lanxi hydrological station was selected as an example to illustrate the advantages of VMD-SMA-CNN-GRU model using annual runoff data from 1959 to 2014.The data from 1959 to 2002 was selected as a training set while from 2003 to 2014 took as a test set.The proposed hybrid model was compared with CEEMDAN (Complete ensemble empirical mode decomposition with adaptive noise)-CNN-GRU model,VMD-CNN-LSTM model,VMD-LSTM model， VMD-GRU model,VMD-PSO (Particle swarm optimization)-CNN-GRU model,SMA-CNN-GRU model,and CNN-GRU model.Additionally,three standard statistical performances measures,namely root mean squared error (RMSE),mean absolute error (MAE) and mean absolute percentage error (MAPE) were employed to evaluate the performances of the six models mentioned above.In the training phase,all models except the CEEMDAN-CNN-GRU model achieved a better fit.In the validation phase,the VMD-SMA-CNN-GRU model predicted significantly better than several other models,especially in the case of predicted peaks.Results show that the SMA optimized VMD-CNN-GRU model has the best fitting effect,and the prediction accuracy is greater than that of the above seven comparison models. According to the results,there are several conclusions as follows:Runoff series has the characteristics of nonlinearity and non-stationarity.Therefore,VMD can decompose the original sequence into several relatively stable sub-sequences,which can be better fitted while increasing data.Low efficiency of manual trial calculations is avoided by SMA to determine the parameters of CNN-GRU model.The CNN-GRU model has the advantage of utilizing two neural networks simultaneously.The VMD-SMA-CNN-GRU model established effectively improves the accuracy of runoff prediction and provides a new method for annual runoff prediction.