A conditional copula model to identify the response of runoff probability to climatic factors

Understanding the response of runoff to climate drivers is important to ensure rational water allocation and address the risk of drought. Many models that assess the effect of climate factors on the response of runoff volume have been developed and widely used. However, models that assess the response of the probability of runoff occurrence (runoff probability) are lacking. In this study, we developed a model by integrating a conditional probability distribution (CPD) and a copula function model to assess the effect of climate conditions on variation of the probability of runoff occurrence. The developed model was applied to the basin of Poyang Lake, the largest freshwater lake in China. The study showed that Frank copula was the copula that had the best-fitted effect to identify the impact of climate factors (except for precipitation and air temperature [AT] in low flow period [LFP]) on the probability of runoff occurrence. The copulas with the best-fitted effect of precipitation and AT is the Gumbel copula and Clayton copula during LFP, respectively. Precipitation, relative humidity (RH), and water vapor pressure (WP) were positive with streamflow variation, while wind speed (WS), potential evapotranspiration (ET0), and sunshine duration (SD) were negative with runoff, but AT had an inverse relation with the streamflow during high flow period (HFP) and LFP. Sensitivity analysis indicated that precipitation has a weaker effect on the likelihood of extreme hydrological events than many other climate factors (such as RH and SD). Moreover, the sensitivity of runoff probability to climatic factors tended to be relatively stable during HFP, which was in contrast to that during LFP. This research highlights the significance of considering change conditions when evaluating runoff response to climate drivers, which is consistent with the objective of achieving more accurate runoff predictions to combat climate change and extreme weather conditions