Fully elucidating the precipitation–runoff relationship (PRR) is of great significance for better water resources planning and management and understanding hydrological cycle processes. For investigating the multi-scale PRR variability in the Weihe River basin in 1960–2010, a new hybrid method is proposed in which ensemble empirical mode decomposition (EEMD) and cross wavelet transform and wavelet transform coherence are used in combination. With the application of mutual information entropy, monthly precipitation and runoff are decomposed into two parts: high- (HFC) and low-frequency components (LFC). The results show that HFCs are characterized by inter- and intra-annual variations in precipitation and runoff, whereas LFCs display approximately two-year periodicity and contain abundant abnormal information of the raw data. Therefore, the PRR between HFCs exhibited significant correlations at the 95% confidence level over the whole time period. However, the correlations of the PRR between LFCs are not significant for many of the time-frequency domains. Additionally, the phase relations are disordered in these time-frequency domains, and no certain trend in phase angle variations can be identified. Through comparative analysis of the anthropogenic activities and climatic events with PRR variations, it can be concluded that the hybrid method can efficiently capture the PRR in various time-frequency domains.

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