为进一步提高中长期径流预报精度，以兰西水文站1959-2014年径流深数据为例，分别利用灰色模型和BP神经网络模型对径流深数据进行预测，采用马尔可夫链推求状态概率对预测结果校正，用最小二乘法对双模型校正结果进行耦合。模型所得组合校正预测结果通过平均相对误差、均方差和合格率进行统计描述，校正后的组合预测结果平均相对误差和均方差分别为12.72%和11.70，均要优于灰色模型和BP神经网络模型且90.91%的预报结果满足相对误差小于20%的控制条件。可见，耦合模型能有效规避单一模型已存在的缺点，基于马尔可夫链的修正结果可使预测精度进一步提升。因此，本研究提供的组合校正模型在一定程度上具有更好的拟合效果和预报精度，是一种具有实用价值的预测模型。

In order to further improve the accuracy of mid and long term runoff prediction,taking the runoff data series of 1959-2014 in Lanxi Hydrological Station for case study,the grey model and BP neural network model are applied to predict the runoff depth respectively,and the prediction results are corrected with the state probability derived from the Markov chain,and,furthermore,the corrected results of both models are coupled by least square method.The statistical descriptions of the corrected and combined prediction results show 12.72% in average relative error,11.70 in mean square deviation of better than the grey model and BP neural network model,and 90.91% of the prediction results,satisfying with the threshold of relative error. less than 20%.The shortcomings of the single model may be effectively overcome by applying the coupled model,and the prediction precision be further improved by adopting the corrected results based on the Markov chain.With more efficient fitting and more accurate prediction,the corrected and combined model suggested in this study is of practical value in prediction of the mid and long term runoff.

国家自然科学基金(51509088)；河南省高校科技创新团队(18IRTSTHN009)；陕西省语音与图像信息处理重点实验室开放基金(2018)；河南省水环境模拟与治理重点实验室(2017016)