Compound flooding caused by high rainfalls and tides may salinize the soil, deteriorate the water quality, and damage the ecosystems in coastal areas. Traditionally, compound flood risk is estimated using the joint probabilities of a rainfall and a tide level when they are simultaneously or individually exceeded. This results in bias because flood risk should represent the exceeding probability of a flood magnitude, not of the triggers’ values. In this study, a new approach is proposed to determine the exceedance probability for a flood depth induced by the compound effects of rainfall and tide through the combination of copula analysis, numerical simulation, multiple regression, and Monte Carlo integration. A frequently flooded coastal area in Chiayi, Taiwan, was selected as the study subject. The results show that realistic flood risk should range between the joint probabilities of rainfall and tide levels being simultaneously or individually exceeded. Thus, when the joint probabilities are used to determine the thresholds of rainfall and tide for flood warning and hydraulic design, the misestimation of flood risk will result in errors such as incorrect alarms and inaccurate protections with a ratio of 37% in a case study with 10-year return period. These errors can be reduced using a hybrid cumulative probability function developed in this study for selecting the best rainfall and tide thresholds with local maximum or minimum cumulative flood probabilities. The proposed approach is efficient and general, so it can be promoted in different fields for risk assessment influenced by bivariate variables.
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