A novel time-varying stepwise decomposition ensemble framework for forecasting nonstationary and nonlinear streamflow

Many current decomposition ensemble streamflow forecasting models have been incorrectly developed and their parameter solving methods are tedious, which undermines their application to forecasting in the real-world. This study, therefore, developed a time-varying stepwise decomposition ensemble (TV-SDE) framework for nonsta-tionary and nonlinear streamflow series, along with an optimization strategy combining a two-stage calibration strategy with a particle swarm optimization algorithm, namely, TSC-PSO-PSO for parameter optimization. To test the efficiency of the developed TV-SDE framework, a TV-SDE model, based on variational mode decomposition and support vector machine, namely, TV-VMD-SVM, was built and was compared with single models. The monthly streamflow data from nine hydrological stations in China were used to assess the models. Results showed that (1) the time-varying decomposition ensemble models were superior to the single models, (2) the TSC-PSO-PSO optimization strategy outperformed the optimization strategy combining a two-stage calibration strategy with a particle swarm optimization algorithm and Cross Validation algorithm for the TV-SDE frame-work, and (3) the TV-VMD-SVM model based on the TSC-PSO-PSO optimization strategy was a significant improvement over each single model and had the best streamflow forecasting performance among all models, with the Nash-Sutcliffe coefficient greater than 0.83 and Willimot Index greater than 0.79. The TV-SDE frame-work has potential to have a wide range of applications in the hydrology and water resources filed, as well as other fields..

Automated summary

This study developed a time-varying stepwise decomposition ensemble framework for nonsta-tionary and nonlinear streamflow series, along with an optimization strategy combining a two-stage calibration strategy with a particle swarm optimization algorithm. The results showed that the time-varying decomposition ensemble models were superior to the single models, and the TSC-PSO-PSO optimization strategy outperformed other optimization strategies. The TV-VMD-SVM model based on the TSC-PSO-PSO optimization strategy had the best streamflow forecasting performance.