Data representation and prediction model design play an important role in mid- to long-term runoff prediction. However, it is challenging to extract key factors that accurately characterize the changes in the runoff of a river basin because of the complex nature of the runoff process. In addition, the low accuracy is another problem for mid- to long-term runoff prediction. With an aim to solve these problems, two improvements are proposed in this paper. First, the partial mutual information (PMI)-based approach was employed for estimating the importance of various factors. Second, a deep learning architecture was introduced by using the deep belief network (DBN) with partial least-squares regression (PLSR), together denoted as PDBN, for mid- to long-term runoff prediction, which solves the problem of parameter optimization for the DBN using PLSR. The novelty of the proposed method lies in the key factor selection and a novel forecasting method for mid- to long-term runoff. Experimental results demonstrated that the proposed method can significantly improve the effect of mid- to long-term runoff prediction. Also, compared with the results obtained by current state-of-the-art prediction methods, i.e., DBN, backpropagation neural networks, and support vector machine models, our prediction results demonstrate the performance of the proposed method.

数据表示和预测模型设计在中长期径流预测中起着重要作用。但是，由于径流过程的复杂性，要​​提取准确表征流域径流变化特征的关键因素具有挑战性。另外，低精度是中长期径流预测的另一个问题。为了解决这些问题，本文提出了两个改进。首先，采用基于部分互信息（PMI）的方法来估计各种因素的重要性。其次，通过将深度信念网络（DBN）与偏最小二乘回归（PLSR）一起表示为PDBN引入深度学习架构，以进行中长期径流预测，从而解决了参数优化的问题使用PLSR的DBN。该方法的新颖之处在于关键因素的选择和中长期径流预报的新方法。实验结果表明，该方法可以显着提高中长期径流预报的效果。此外，与通过当前最新的预测方法（即DBN，反向传播神经网络和支持向量机模型）获得的结果相比，我们的预测结果证明了该方法的性能。