Copula entropy coupled with artificial neural network for rainfall-runoff simulation

The rainfall-runoff relationship is not only nonlinear and complex but also difficult to model. Artificial neural network (ANN), as a data-driven technique, has gained significant attention in recent years and has been shown to be an efficient alternative to traditional methods for hydrological modeling. However, for different input combinations, ANN models can yield different results. Therefore, input variables and ANN types need to be carefully considered, when using an ANN model for stream flow forecasting. This study proposes the copula-entropy (CE) theory to identify the inputs of an ANN model. The CE theory permits to calculate mutual information (MI) and partial MI directly which avoids calculating the marginal and joint probability distributions. Three different ANN models, namely multi-layer feed (MLF) forward networks, radial basis function networks and general regression neural network, were applied to predict stream flow of Jinsha River, China. Results showed that the inputs selected by the CE method were better than those by the traditional linear correlation analysis, and the MLF ANN model with the inputs selected by CE method obtained the best predicted results for the Jinsha River at Pingshan gauging station.