An improved nonlinear dynamical model for monthly runoff prediction for data scarce basins

Making accurate and reliable predictions for monthly runoff in data scarce basins is still a major challenge. In this study, a new model, the CL-NDM, is developed by combining Convolutional Neural Network-Long Short-term Memory (CNN-LSTM) and a nonlinear dynamic model. The CL-NDM can overcome the deficiency of observed data by fusing spatial and temporal dependencies in runoff sequences at different stations. First, phase space reconstruction is used to enlarge the dimensions of the runoff sequences and reconstruct the attractors of the runoff sequences. Then, the CNN-LSTM is employed to construct the mapping between non-delay and delay attractors. Finally, the prediction set of the target variable is obtained by embedding multiple times. The CL-NDM is performed for monthly runoff prediction at eleven hydrological stations in the Weihe River, China. Compared with the CNN, LSTM and CNN-LSTM models, which require a large amount of training samples, the CL-NDM behaves much better, especially in situations with small training sample sizes. The maximum increase in R is 74%, and the maximum NSE is as large as 0.8. The maximum improvement in RMSE and MAPE is 53% and 88%, respectively. The CL-NDM has stronger ability to capture peak value while LSTM, CNN-LSTM and CNN models show obvious time lag in the prediction of peak point. The improved nonlinear dynamical model may provide a valuable method for runoff prediction in data-scarce regions.