Monthly runoff prediction using gated recurrent unit neural network based on variational modal decomposition and optimized by whale optimization algorithm

To further increase the forecast precision of non-stationary non-linear monthly runoff series and improve the effectiveness of pretreatment of monthly runoff series, the whale optimization algorithm (WOA) is introduced to optimize the variational mode decomposition (VMD), and the WOA–VMD–GRU prediction model is constructed by coupling with the gating cycle unit (GRU) neural network. First, the variation modal decomposition is optimized by the whale optimization algorithm, to find the best decomposition modal number k and penalty factor α, then several IMF components are obtained according to VMD processing runoff sequences; finally, results are obtained by adding those of each component. Taking Manwan Hydropower, Hongjiadu Hydropower, and Changshui Hydrological Station as examples, the BP model, the GRU model, the EMD–GRU model, the CEEMDAN–GRU model, and the VMD–GRU model are compared. Four quantitative indexes were used to estimate the model performance. The results show that the proposed WOA–VMD–GRU model has the best prediction accuracy, with correlation coefficients and Nash coefficients above 0.99 and 0.97 in the prediction results of the three hydrological stations, respectively, and avoids the low efficiency of VMD decomposition parameters in manual trial computation, providing a new way for monthly runoff prediction. Graphical Abstract