Extending the Joint Probability Method to Compound Flooding: Transition Zone Delineation, Flood Depth Attribution, and Design Event Selection

Abstract

Quantifying the frequency of compound flood depths is a fundamental challenge in low-gradient coastal watersheds, where flood hazards arise from the nonlinear interaction of storm surge, rainfall, and riverine flooding. Existing approaches often characterize either the joint occurrence of flood drivers or the flood response for prescribed events, but they do not derive the long-term frequency distribution of compound flood depths from probabilistic descriptions of rainfall and antecedent hydrologic conditions. Traditionally, coastal flood frequency has been quantified using the Joint Probability Method (JPM), which represents storm surge probabilistically. Although recent studies have incorporated rainfall into JPM-based analyses, rainfall is treated as a deterministic function of JPM storm characteristics rather than as a conditional probability distribution. Here, we extend the JPM by coupling its event-scale stochastic description of storm characteristics with probabilistic rainfall realizations and stochastic antecedent hydrologic conditions, thereby enabling propagation of these stochastic processes through the flood response to derive the compound flood-depth distribution. The framework provides a statistical basis for delineating compound flood transition zones, probabilistically attributing flood depths to hydrologic and coastal processes, and selecting response-based design storms for specified annual exceedance probabilities (or return periods). Application to the Lake Maurepas basin, Louisiana, shows that the statistically defined compound flood transition zone is more than twice the area identified from event-based analyses and that compound interactions increase flood depths by up to 0.7 m. This extended JPM establishes a probabilistic foundation for compound flood hazard assessment and response-based design.