Determination of Input for Artificial Neural Networks for Flood Forecasting Using the Copula Entropy Method

Abstract

Artificial neural networks (ANNs) have proved to be an efficient alternative to traditional methods for hydrological modeling. One of the most important steps in the ANN development is the determination of significant input variables. This study proposes a new method based on the copula-entropy (CE) theory to identify the inputs of an ANN model. The CE theory permits to calculate mutual information (MI) and partial mutual information (PMI), which characterizes the dependence between potential model input and output variables directly instead of calculating the marginal and joint probability distributions. Two tests were carried out for verifying the accuracy and performance of the CE method. The CE theory-based input determination methodology was applied to identify suitable inputs for a flood forecasting model for a real-world case study involving the three gorges reservoir (TGR) in China. Test results of application of the flood forecasting model to the upper Yangtze River indicates that the proposed method appropriately identifies inputs for the ANN with the smallest root-mean-square error (RMSE) for training, testing, and validation data.