A Forecast Heuristic of Back Propagation Neural Network and Particle Swarm Optimization for Annual Runoff Based on Sunspot Number

Runoff prediction is of great importance to water utilization and water-project regulation. Although sun activity has been considered an important factor in runoff, little modeling has been constructed. This study put forward a forecast heuristic combining back propagation neural network (BPNN) and particle swarm optimization (PSO) for annual runoff based on sunspot number and applied it to the Yellow River of China for the period 1956–2016 and assessed the contribution of the sunspot number by placing sole BPNN modeling on the time series as a contrast. First, the heuristic is made up of BPNN calibration and PSO optimization: (1) we use historical data to calibrate BPNN models and obtain a prediction of the sunspot number for training and testing stages; (2) we use the PSO to minimize the difference between the predicted runoff of both BPNN and a linear equation for forecasting stage. Second, the application offers interesting findings: (1) while BPNN calibration obtains first-class forecasting with the ratio >85% with <20% absolute error in training and testing stages, the PSO can achieve similar performance in the forecasting stage; (2) the heuristic can achieve better prediction in years with a lower sunspot number; (3) besides the influence of the sun activity, atmospheric circulation, water usage, and water-project regulation do play important roles on the measured or natural runoff to some extent. This study could provide useful insights into further forecasting of measured and natural runoff under this forecast heuristic in the world.