Characterizing flood hazard at two spatial scales with the use of stochastic models: An application to the contiguous United States of America and the Houston Ship Channel

Flooding is the most common and one of the most damaging natural hazards globally. It has severe societal, economic and environmental consequences. Damages from floods are expected to worsen with changing climate and increasing population andwealthworldwide. Within the last decades, advances in computational power and increases in the number of global databases have enabled the development of global flood risk models (GFRMs). These are valuable tools for agencies, practitioners and stakeholders to learn, communicate and plan effective flood risk mitigation strategies. However, the current limitations of GFRMs directly affect their usefulness for concrete applications. They often only capture riverine flooding for major world catchments which renders them of limited use and accuracy for smaller catchment scales or in coastal areas. The drivers of floods are diverse and their co-occurrence can significantly exacerbate the severity of the flood hazard. Finally, the complex structure of conventional flood hazard models is often computationally very expensive. This thesis focuses on improving flood risk characterization by applying stochastic models for flood hazard quantification. The use of stochastic models, such as Bayesian Network (BN) models, is a possible alternative to conventional GFRM approaches because they substantially reduce computational time and are flexible in structure. In this thesis, the dependence structure in the BN is represented by the Gaussian copula. The research was divided into two parts: global- and local-scale applications. First, a Global BN model is developed to derive discharge for the contiguous United States (US). This continental-scale riverine flood hazard model is considered to be global because of the geographic and climatological diversity of the US. Second, a Local BN model is developed to represent the interaction between riverine and coastal flooding at the catchment scale. The local-scale model is coupled with a simple one-dimensional (1D) steady state process-based hydraulicmodel to derive water surface elevations. The Global BN model is a hydrologic model, a non-parametric Bayesian Network, based on the work of Paprotny andMorales Nápoles [2016] for Europe. Annual maximumdaily river discharge,Q, is collected at 4765US stations and 1841 European stations. The statistical dependencies between Q and seven variables, based on catchment area, steepness, climate and land use, are derived from global databases and used to build the Global BN. The model is sampled to infer the conditional probability distribution of Q, which is used to perform frequency analysis using a log-logistic distribution for different return periods in the US. The performance of themodel is measured based on the coefficient of determination, R2, and theNash- Sutcliffe efficiency coefficient, NSE. The mean discharge, QMAMX , obtained from the model for all US stations is compared to the equivalent discharge obtained from historical observations. Overall, the model shows a moderate performance (R2=0.86, NSE=0.76). Spatial representation of the ratio of the modeled to the observed mean discharge, the relative error e, shows distinct regional patterns. Stations located inwarmtemperate climate regions are modeled the best (R2=0.91, NSE=0.77), and in arid regions the worst (R2=0.69, NSE=-0.12). Similarly, stations with large catchment areas, i.e. larger than 10000 km2, exhibit much higher performance results than others (R2=0.91, NSE=0.75). It is understood that these two factors drive the overall performance. While the model performed worse when compared to the BN-approach applied to Europe (R2=0.92, NSE=0.92), the Global BN still captures betterQMAMX than another global flood hazard model developed by Smith et al. [2015]. The Local BN model is build to capture the statistical dependencies between mean daily discharges in the Buffalo Bayou River catchment and the maximum daily residual height at the tide gauge Galveston Pier 21 (GP21) in southeast Texas. In coastal catchments, an elevated downstream water level, resulting from high tide and/or storm surge, impedes drainage creating a backwater effect that may exacerbate flooding in the riverine environment. However, conventional flood hazard studies do not explicitly model this interaction. In this study, the Local BN model is sampled to infer boundary conditions (discharges at six stations) for the river reach and explicitly include their dependence. The surge height at the Lynchburg Landing site (LL), the downstream boundary of the hydraulic model, is calculated as the conditional expectation given the residual at GP21. Stochastic boundary conditions corresponding to selected bivariate return periods, 50- to 1000-year, are modeled. Marginal distributions of mean daily river discharges and maximum daily residuals are parametrized using a Generalized Extreme Value distribution and a Gaussian mixture model, respectively. The water levels in the river reach are modeled using a 1D hydraulic model to obtain water surface profiles (WSPs) for the modeled stochastic boundary conditions. The modeled WSPs show a higher difference in water surface elevations in the upstream section of the river reach (8.12m for the 100-year return period WSPs) than downstream at LL (0.96m). The selected design 100-year WSP is compared to the 100-year WSP used in the FEMA model [FEMA,2017]. The water surface elevation obtained in this study at LL is 2.23m-NAVD88 and a total discharge of 8685m3/s, against 4.85m-NAVD88 and 6749m3/s for FEMA. Since water levels in the lower reach are particularly sensitive to the imposed downstream boundary condition, the design WSP is lower than what would be obtained using the water levels reported by FEMA in the selected reach. However, the model results show that the mid- and upper reaches are particularly sensitive to the backwater effects caused by the interaction between high river discharges and storm surge. This suggests that conventional methods may underestimate the flood hazard associated with compound flooding in the riverine environment and that such interactions should be carefully investigated in future coastal flood hazard studies. This research shows that BN-based models are an useful addition to conventional flood hazardmodels. Their flexible structure can simply and intuitively represent complex flood hazards while explicitly including dependencies between variables. Future studies further investigating the sensitivity and appropriate simplification of flood mechanisms will strengthen the accuracy and applicability of probabilistic models both at global- and local-scales.Civil Engineering and GeosciencesHydraulic Engineerin