Multiscale streamflow forecasting using a new Bayesian Model Average based ensemble multi-wavelet Volterra nonlinear method

Over the last five years, wavelet transform based models have begun to be explored for hydrologic forecasting applications. In general, a particular wavelet transform (and a particular set of levels of decomposition) is selected as the ‘optimal’ wavelet transform to be used for forecasting purposes. However, different wavelets have different strengths in capturing the different characteristics of particular hydrological processes. Therefore, relying on a single model based on a single wavelet often leads to predictions that capture some phenomena at the expenses of others. Ensemble approaches based on the use of multiple different wavelets, in conjunction with a multi model setup, could potentially improve model performances and also allow for uncertainty estimation. In this study, a new multi-wavelet based ensemble method was developed for the wavelet Volterra coupled model. Different wavelets, levels of decomposition, and model setups are used in this new approach to generate an ensemble of forecasts. These ensembles are combined using Bayesian Model Averaging (BMA) to develop more skilful and reliable forecasts. The new BMA based ensemble multi-wavelet Volterra approach was applied for forecasting stream flow at different scales (daily, weekly and monthly) observed at two stations in the USA. The results of this study reveal that the proposed BMA based ensemble multi-wavelet Volterra nonlinear model outperforms the single best wavelet Volterra model, as well as the mean averaged ensemble wavelet Volterra model.