The coincidence of fluvial and coastal flooding can lead to compound floods with substantial impacts on human life, property, and infrastructure. Low-lying coastal areas are particularly vulnerable to compound flooding because of exposure to multiple drivers such as extreme coastal high tides, storm surge, and fluvial flooding. In this study, we develop a bivariate non-stationary flood risk assessment that accounts for compound flooding from fluvial and coastal events with consideration of impacts of sea level rise (SLR). Extreme river discharge values were identified using peak over threshold method and were paired with the corresponding highest sea-water level within ±1 days of these events across the coastal contiguous United States. The statistical dependence between the paired data was assessed using Kendall’s rank correlation coefficient. For the locations with significant dependence, the best copula fit was used for bivariate dependence analysis by assuming non-stationarity in the marginal distribution of sea-water level data. The mixture Normal-Generalized Pareto Distribution model with SLR as the covariate is used to incorporate the non-stationary coastal flood frequency. The future risk was assessed using the notation of failure probability, which refers to the probability of occurrence of at least one major coastal flooding (i.e., water level exceed the major coastal flood threshold) or 100-year fluvial flood for a given design life. Failure probability was formulated to allow for changing exceeding probabilities over time. The results indicate that the joint exceedance probability of fluvial or coastal flooding can be higher when the dependence is considered. Ignoring the compounding effects may inappropriately underestimate the flood probability at locations that flood hazard can be influenced by the interaction of fluvial and coastal events. Moreover, with rising sea levels, the probability of exceedances of sea-water level over the flood threshold increases and consequently the compound flood probability increases as well. In the locations with less dependency between extreme river discharge and sea-water level, the frequency amplification of fluvial and major coastal flood events is higher.

Coastal cities are exposed to multiple flood drivers such as extreme coastal high tide, storm surge, and extreme river discharge. The interaction among these flood drivers may cause compound flooding events, which could exacerbate social and economic consequences. Climate change can put greater pressure on these areas by increasing the frequency and intensity of coastal and riverine flooding. In this study, a bivariate compound flooding risk assessment method is developed to incorporate sea level rise (SLR) and nonstationary river discharge conditions. Extreme sea water level (SWL) and river stage are identified using the peak-over-threshold method, and subsequently, pairs of extremes are selected when both SWL and river stage exceed their defined thresholds within ±1 day from each other. A copula-based approach is then used to estimate the joint distribution and return period of compound coastal riverine flooding by incorporating nonstationarity into the marginal distributions of extreme SWL and river stage. The future flood risk is assessed using the notation of failure probability, which here refers to (1) the probability of occurrence of at least one major coastal or riverine flooding for a given design life (i.e., total flood risk); and (2) the probability of occurrence of at least one compound major coastal riverine flooding for a given design life (i.e., compound flood risk). Compound flood risk assessment is conducted at 26 paired NOAA-USGS stations along the Contiguous United States coast with long‐term observed data and defined flood thresholds. The results indicate that in some regions the joint return period of coastal/riverine flooding are substantially lower when considering the projected future hydroclimate conditions and SLR. The importance impact of future SLR and hydroclimate conditions is discussed regionally in terms of changes in the frequency of compound major coastal riverine flooding events.