Watershed runoff modeling through a multi-time scale approach by multivariate empirical mode decomposition (MEMD)

Abstract

Accurate runoff modeling has an important role in water resource management. Attributable to the effects of climate variability and vegetation dynamics, runoff time series is nonstationary, resulting in the difficulty of runoff modeling. Detecting the temporal features of runoff and its potential influencing factors can help to increase the modeling accuracy. Selecting the Yihe watershed in the rocky mountainous area of northern China as a case study, multivariate empirical mode decomposition (MEMD) was adopted to analyze the time scales of the monthly runoff and its influencing factors, i.e., precipitation (P), normalized difference vegetation index (NDVI), temperature (T), relative humidity (RH), and potential evapotranspiration (PE). Using the MEMD technique, the original monthly runoff and its influencing factors were decomposed into six orthogonal and bandlimited functions, i.e., intrinsic mode functions (IMF1-6) and one residue, respectively. Each IMF is a counterpart of the simple harmonic function and represents a simple but general oscillatory mode in the original time series data. The results of the IMF contribution rate showed that the annual cycle had the most important role in runoff, P, NDVI, T and PE change. The contribution of quarterly oscillation was the largest contribution for the month RH variability. The monotonic residue showed that the predominant trends of runoff, P, NDVI, T, RH, and PE were decreasing from 2006 to 2015. Stepwise multiple linear regression (SMLR) was chosen to simulate the runoff IMFs and residue. The modeling results using the IMFs and residue of the potential influencing factors as input variables (R2 ranges from 0.53 to 1.0) were better than those using the original time series of influencing factors as input variables (R2 ranges from 0.17 to 0.6). By summing all the modeled IMFs and residues, the monthly runoff model was obtained, which increased the R2 value by 24.2% compared with the SMLR model using the original time series of influencing factors as input. The results indicated that MEMD was efficient for improving the accuracy of nonstationary runoff modeling.