• nonlinearity;
  • wavelet transform;
  • change point;
  • wavelet power spectrum


Rainfall–runoff processes appear to be highly nonlinear in Bayinbluk watersheds of the northwestern China. In this study, the time-scale wavelet transform has been used for the analysis of this nonstationary system. The Haar and Morlet wavelet transform were used to analyse the rainfall–runoff conversion relationship. Wavelet power spectrum and change point methods are also employed to analyse rainfall rates and runoffs measured at daily to half-hourly sampling rate. The four experimental sites (Luoto, Haer, Kuce and Shengl) are located in the Tianshan Mountains (Xinjiang province, China). Correlation analysis and wavelet transform are first applied to runoff process in different underlying surfaces. Wavelet analyses of rainfall rates and runoffs also give meaningful information on the temporal variability of the rainfall–runoff relationship. Change point and wavelet power spectrum analysis provide simple interpretation of energy distribution between different scales. The results indicate that wavelet transform is a good method for analysing the nonlinear relationship of temporal–spatial responses between rainfall and runoff. This method allowed quantification of the processes affecting runoff and provided an insight into their implications in surface water management. Copyright © 2011 John Wiley & Sons, Ltd.