Coastal and Riverine Flooding: A Joint Probability Approach for Evaluating Storm Surge, Tides, and Extreme Rainfall Under Climate Change

In 2023, floods and flash floods caused around 2.1 billion U.S. dollars' worth of property and crop damage across the United States. Though many of these floods were caused by a single factor (e.g. extreme rainfall, coastal storm surges), compound events pose even more severe threats to communities by combining the impacts of storm surge, tides, and high river flows. The effects of sea level rise and changes to extreme rainfall event probability due to climate change are already causing underestimation of the flood risk, and that risk will only increase as global temperatures rise in the future. This requires that flood studies now incorporate potential compound events, as well as projecting future changes to probability due to climate change. Flood damage can be caused by one of three types of flooding. 1. Pluvial Flooding: when extreme rainfall causes runoff to exceed the collection system capacity 2. Riverine Flooding: when extreme rainfall causes river elevations to exceed bank and flood wall elevations 3. Coastal Flooding: a combination of high tides and storm surge. Floods in coastal and riverine environments are frequently subject to dual causes. In rivers discharging to coastal areas, storm surge and sea levels combined with high river discharge can result in widespread flooding of low-lying areas, but also can prevent storm sewers from discharging, resulting in pluvial flooding in more inland, higher elevation areas. In areas adjacent to tidally influenced rivers away from the coast, the same dual effect can be seen due to riverine flooding and exacerbated pluvial flooding. The dual cause study examined in this paper calculates flooding in a tidal river discharging to another tidal river. Flood elevations are subject to extreme upstream discharge from the upriver watershed, compounded by tides and extreme elevations of the receiving tidal river. This study shows that floods arising from multiple, simultaneous causes interact in complex ways, leading to significantly higher flood elevations and damage compared to floods driven by a single cause. Assessing joint probabilities is crucial for understanding the likelihood of flooding in various contexts, such as: coastal areas (where storm surge and pluvial flooding coincide), tidal riverine areas (where high river flows combine with tidal surges), and inland river areas (where high river flows and pluvial flooding intersect). By integrating joint probability analysis with practical methodologies to assess climate change impacts, it is possible to better estimate flood elevations and probabilities leading to better adaptation, planning and flood protection design. Vine Street in Philadelphia, PA, experienced severe flooding during Hurricane Ida in 2021. The Schuylkill River is tidally influenced as it is a tributary to the tidally influenced Delaware River. Flooding occurred at a location where tidal influences, storm surge, and the discharge in both the tributary and main river all contributed to historic flooding on Vine Street. Hurricane Ida highlighted the importance of accounting for all potential contributors to flooding, especially under a future with higher sea levels. It demonstrated that flood probabilities based on multiple factors are significantly higher than those calculated using the more common approach of considering a single cause. This study addressed the complexity of assessing flood probability at a site exposed to extreme riverine flows, tidal effects, storm surges and sea level rise. It was designed to evaluate site specific flood probabilities and elevations, incorporating a copula-based joint probability analysis to assess compounded flood risk. Utilizing historical data, future projections and defined flood thresholds, an innovative method yielded actionable insights, including probabilistic water elevations under current and future scenarios that are being used to assess flood protection measures. The key finding of the study was that assuming flooding is caused by only one factor can result in a significant underestimation of current flood risk. An initial estimate of the return interval for the critical flood elevation that caused overbank flooding at Vine Street was made using upstream discharge probabilities and a HEC-RAS model to estimate resulting flood elevations in the tidal section of the river. Even with a conservative downstream boundary condition for the model, the return interval for the critical flood elevation of 14 feet due to high flows emanating from the Schuylkill River watershed was estimated to be about 20-years. Although tidal surge on the receiving Delaware River does not cause elevation increases anywhere close to the critical flood elevation in the Schuylkill River and probabilities are low for elevation in the Delaware River above about 5 feet, the resulting return intervals for the critical flood elevation were much lower when joint probabilities were considered. The resulting estimated current probability for the critical flood elevation at Vine Street was reduced to about 10-years. Adding climate change to the current estimates of flood probability were also projected using estimates of changes to extreme rainfall and runoff in the river watershed coupled with sea level rise effects on storm surge probability. This caused a further reduction by mid-century to return intervals for the critical flood elevation of less than 5-years, and end-of-century projections of annual flooding. Because of the relatively high probability of a reoccurrence of flooding at Vine Street, protective measures are being investigated. With climate change affecting both the Delaware River water levels as well as the extreme discharges from the upstream Schuylkill River, ignoring the joint probability of flooding and trends related to climate change can result in an increasing underestimation of flood risk over time. Flood probability estimates are needed to make key decisions about current and future risk of flooding to plan and design flood protection measures for critical infrastructure. The results of this study illustrate the importance of considering both compound causes and the changing probabilities of flood elevations due to multiple climate impacts. . These estimates provide a good basis to calculate depth-damage functions and annualized losses over time to assess the benefit cost ratio of potential protection measures to avoid flooding of Vine Street in the future.