Extending the Joint Probability Method to Compound Flooding: Statistical Delineation of Transition Zones and Design Event Selection

Abstract

Compound flooding from the combined effects of extreme storm surge, rainfall, and river flows poses significant risks to infrastructure and communities -- as demonstrated by hurricanes Isaac and Harvey. Yet, existing methods to quantify compound flood risk lack a unified probabilistic basis. Copula-based models capture the co-occurrence of flood drivers but not the likelihood of the flood response, while coupled hydrodynamic models simulate interactions but lack a probabilistic characterization of compound flood extremes. The Joint Probability Method (JPM), the foundation of coastal surge risk analysis, has never been formally extended to incorporate hydrologic drivers -- leaving a critical gap in quantifying compound flood risk and the statistical structure of compound flood transition zones (CFTZs). Here, we extend the JPM theory to hydrologic processes for quantifying the likelihood of compound flood depths across both tropical and non-tropical storms. This extended methodology incorporates rainfall fields, antecedent soil moisture, and baseflow alongside coastal storm surge, enabling: (1) a statistical description of the flood depth as the response to the joint distribution of hydrologic and coastal drivers, (2) a statistical delineation of the CFTZ based on exceedance probabilities, and (3) a systematic identification of design storms for specified return period flood depths, moving beyond design based solely on driver likelihoods. We demonstrate this method around Lake Maurepas, Louisiana. Results show a CFTZ more than double the area of prior event-specific delineations, with compound interactions increasing flood depths by up to 2.25 feet. This extended JPM provides a probabilistic foundation for compound flood risk assessment and planning.

Figures (16)

• Figure 1: The extended Joint Probability Method processes the probabilistic characteristics of storm events (including precipitation, and hydrology) through a flood depth response (based on respective models) and derives a probability distribution of the flood depth response for any point over the study region.
• Figure 2: In this extended JPM theory, utilizes synthetic cyclone storm tracks (blue lines), which roughly represent historical TC storm strack patterns, where the frequency and relative likelihood of tropical cyclone storm tracks are considered relative to the distance, $x_l$, along a line that starts at 0 and extends to $x_{l,\max}$. The line is drawn to cover all possible tropical cyclone storm tracks impacting the region of interest. Traditionally, the JPM tropical cyclone process was considered relative to a point---a so-called coastal reference location.
• Figure 3: The HEC-RAS 2D model domain with inflows from the 1D HEC-HMS at four major river inflows shown in red and coastal storm surge boundary conditions from ADCIRC at line segments with centers shown in yellow.
• Figure 4: Total accumulated rainfall from Analysis of Record for Calibration (AORC) observations (first column) and example synthetic ensemble rainfall fields (next three columns) generated from the parametric generator for Hurricane Isidore, Hurricane Katrina, Hurricane Gustav and Hurricane Isaac villarini2022probabilistic. TC tracks are shown as the magenta line.
• Figure 5: Compound flood depths for different return periods as derived from the PDF of Eq. (\ref{['eq:pA']}), which accounts for both tropical and non-tropical storms based on the storm responses of Eqs. (\ref{['eq:petaTC_PS']}) and (\ref{['eq:petaNT_PS']}) and the likelihood of the storm characteristics as described by the PDFs $p_{TC}(\mathbf{x}_{TC}(t))$ and $p_{NT}(\mathbf{x}_{NT}(t))$ of Eqs. (\ref{['eq:pTC_PS']}) and (\ref{['eq:pNT_PS']}), as discretized (see \ref{['sec:PDF_discretized']}).