In search of non-stationary dependence between estuarine river discharge and storm surge based on large-scale climate teleconnections

Compound floods may happen in low-lying estuarine environments when sea level above normal tide co-occurs with high river flow. Thus, comprehensive flood risk assessments for estuaries should not only account for the individual hazard arising from each environmental variable in isolation, but also for the case of bivariate hazard. Characterization of the dependence structure of the two flood drivers becomes then crucial, especially under climatic variability and change that may affect their relationship. In this article, we demonstrate our search for evidence of non-stationarity in the dependence between river discharge and storm surge along the East and Gulf coasts of the United States, driven by large-scale climate variability, particularly El-Ni & ntilde;o Southern Oscillation and North Atlantic Oscillation (NAO). Leveraging prolonged overlapping observational records and copula theory, we recover parameters of both stationary and dynamic copulas using state-of-theart Markov Chain Monte Carlo methods. Physics-informed copulas are developed by modeling the magnitude of dependence as a linear function of large-scale climate indices, i.e., Oceanic Ni & ntilde;o Index or NAO index. After model comparison via suitable Bayesian metrics, we find no strong indication of such non-stationarity for most estuaries included in our analysis. However, when non-stationarity due to these climate modes cannot be neglected, this work highlights the importance of appropriately characterizing bivariate hazard under nonstationarity assumption. As an example, we find that during a strong El-Ni & ntilde;o year, Galveston Bay, TX, is much more likely to experience a coincidence of abnormal sea level and elevated river stage.