Flash floods can be characterized by several variables. Of these, soil moisture (SM) is an important environmental factor that plays a key role in hydrological and ecological processes and affects the mechanisms that cause flash floods. To more accurately determine the occurrence probability of flash floods, the combined effects of soil moisture and rainfall indexes were considered in this paper, and the copula function approach was explored for use in joint probability analyses of flash flood risks. The results showed that (1) the Clayton copula function offered the best fit for the bivariate joint distribution and captured the occurrence probability of the combination of both peak flow (PF) and SM, while the t-copula function achieved the best fit for the multivariate joint distribution, which presented different combinations of characteristic flash flood parameters. (2) The joint distribution probability of flash floods increased with increasing risk parameter thresholds. Return period analysis indicated that the return periods of the bivariate joint distribution were smaller than those of the multivariate joint distribution. (3) If PF and SM are fixed, the occurrence probability of flash floods is higher in regions where the maximum 1-h rainfall is higher. This study provides an effective and quantitative approach to improving flash flood prediction and advances the application of this approach for the management of future flash flood risks.

洪水泛滥可以通过几个变量来表征。其中，土壤水分（SM）是重要的环境因素，在水文和生态过程中起着关键作用，并影响导致山洪泛滥的机制。为了更准确地确定山洪暴发的发生概率，本文考虑了土壤水分和降雨指数的综合影响，并探索了copula函数方法用于山洪暴发风险的联合概率分析。结果表明：（1）Clayton copula函数最适合双变量关节分布，并捕获了峰值流量（PF）和SM组合出现的概率，而t-copula函数最适合于双变量关节分布。多元联合分布 给出了特征性洪水泛滥参数的不同组合。（2）洪水泛滥的联合分布概率随着风险参数阈值的增加而增加。回归期分析表明，二元联合分布的回归期小于多元联合分布的回归期。（3）如果PF和SM固定，则在最大1 h降雨量较高的地区，山洪泛滥的发生概率较高。这项研究提供了一种有效和定量的方法来改善山洪暴发的预测，并推动了这种方法在管理未来山洪暴发风险中的应用。回归期分析表明，二元联合分布的回归期小于多元联合分布的回归期。（3）如果PF和SM固定，则在最大1 h降雨量较高的地区，山洪泛滥的发生概率较高。这项研究提供了一种有效和定量的方法来改善山洪暴发的预测，并推动了这种方法在管理未来山洪暴发风险中的应用。回归期分析表明，二元联合分布的回归期小于多元联合分布的回归期。（3）如果PF和SM固定，则在最大1 h降雨量较高的地区，山洪泛滥的发生概率较高。这项研究提供了一种有效和定量的方法来改善山洪暴发的预测，并推动了这种方法在管理未来山洪暴发风险中的应用。