Discussion on the Choice of Decomposition Level for Wavelet Based Hydrological Time Series Modeling

The combination of wavelet analysis methods with data-driven models is a prevalent approach to conducting hydrological time series forecasting, but the results are affected by the accuracy of the wavelet decomposition of the series. The choice of decomposition level is one of the key factors for the wavelet decomposition. In this paper, the data of daily precipitation and streamflow time series measured in the upper reach of the Heihe River Basin in Northwest China were used as an example, and the influence of the decomposition level on wavelet-based hydrological time series forecasting was investigated. The true components of the precipitation series were identified, and the modeling results using 10 decomposition levels and two decomposition types were compared. The results affirmed that the wavelet-based modeling performance is sensitive to the choice of decomposition level, which is determined by the time series analyzed, but has no relation with the decomposition type used. The essence of the choice of decomposition level is to reveal the complex variability of hydrological time series under multi-temporal scales, and first knowing the true components of series could guide the choice of decomposition level. Through this study, the relationship among original series' characteristics, the choice of decomposition level, and the accuracy of wavelet-based hydrological time series forecasting can be more clearly understood, and it can be an improvement for wavelet-based data-driven modeling.