Synergistic effects of multiple driving factors on the runoff variations in the Yellow River Basin, China

River runoff plays an important role in watershed ecosystems and human survival, and it is controlled by multiple environmental factors. However, the synergistic effects of various large-scale circulation factors and meteorological factors on the runoff on different time-frequency scales have rarely been explored. In light of this, the underlying mechanism of the synergistic effects of the different environmental factors on the runoff variations was investigated in the Yellow River Basin of China during the period 1950–2019 using the bivariate wavelet coherence (WTC) and multiple wavelet coherence (MWC) methods. First, the continuous wavelet transform (CWT) method was used to analyze the multiscale characteristics of the runoff. The results of the CWT indicate that the runoff exhibited significant continuous or discontinuous annual and semiannual oscillations during the study period. Scattered inter-annual time scales were also observed for the runoff in the Yellow River Basin. The meteorological factors better explained the runoff variations on seasonal and annual time scales. The average wavelet coherence (AWC) and the percent area of the significant coherence (PASC) between the runoff and individual meteorological factors were 0.454 and 19.89%, respectively. The circulation factors mainly regulated the runoff on the inter-annual and decadal time scales with more complicated phase relationships due to their indirect effects on the runoff. The AWC and PASC between the runoff and individual circulation factors were 0.359 and 7.31%, respectively. The MWC analysis revealed that the synergistic effects of multiple factors should be taken into consideration to explain the multiscale characteristic variations of the runoff. The AWC or MWC ranges were 0.320–0.560, 0.617–0.755, and 0.819–0.884 for the combinations of one, two, and three circulation and meteorological factors, respectively. The PASC ranges were 3.53%–33.77%, 12.93%–36.90%, and 20.67%–39.34% for the combinations one, two, and three driving factors, respectively. The combinations of precipitation, evapotranspiration (or the number of rainy days), and the Arctic Oscillation performed well in explaining the variability in the runoff on all time scales, and the average MWC and PASC were 0.847 and 28.79%, respectively. These findings are of great significance for improving our understanding of hydro-climate interactions and water resources prediction in the Yellow River Basin.