A Hybrid Model Integrating Elman Neural Network with Variational Mode Decomposition and Box–Cox Transformation for Monthly Runoff Time Series Prediction

Precise and reliable monthly runoff prediction plays a vital role in the optimal management of water resources, but the nonstationarity and skewness of monthly runoff time series can pose major challenges for developing appropriate prediction models. To address these issues, this paper proposes a novel hybrid prediction model by introducing variational mode decomposition (VMD) and Box–Cox transformation (BC) into the Elman neural network (Elman), named the VMD-BC-Elman model. First, the observed runoff is decomposed into sub-time series using VMD for better frequency resolution. Second, the input datasets are transformed into a normal distribution using Box–Cox, and as a result, skewedness in the data is removed, and the correlation between the input and output variables is enhanced. The proposed VMD-BC preprocessing technology is expected to overcome the problems arising from nonstationary and skewed runoff data. Finally, Elman is used to simulate the respective sub-time series. The proposed model is evaluated using monthly runoff time series at Zhangjiashan, Zhuangtou and Huaxian hydrological stations in the Wei River Basin in China. The model performances are compared with those of single models (SVM, Elman), decomposition-based (VMD-SVM, VMD-Elman et al.) and BC-based models (BC-SVM and BC-Elman) by employing four metrics. The results show that the hybrid models outperform single models, and the VMD-BC-Elman model performs best in all considered hybrid models with an NSE greater than 0.95, R greater than 0.98, NMSE less than 4.7%, and PBIAS less than 0.4% in both the training and testing periods. The study indicates that the VMD-BC-Elman model is a satisfactory data-driven approach to predict nonstationary and skewed monthly runoff time series, representing an effective tool for predicting monthly runoff series.