Tropical cyclone (TC) storm surges are among the most destructive coastal hazards, yet quantifying the risk of low-probability, high-impact events remains limited by the prohibitive computational cost of physical surge models. This challenge is compounded by climate change, which is expected to alter the intensity and structure of the most powerful storms.

This thesis introduces a physics-informed framework to estimate the potential height: the maximum physically plausible storm surge a TC can generate under given climatic conditions. The approach constrains idealized cyclones by thermodynamic limits, combining established theory of TC potential intensity with a new reformulation of TC potential size. The revised potential size metric is benchmarked against observations (IBTrACS) and used to assess how storm size limits evolve in reanalysis (ERA5) and climate projections (CMIP6). To identify the storm trajectory that maximizes surge, the ADCIRC hydrodynamic model driven by idealized TCs is placed within a Bayesian optimization loop. Application to diverse U.S. coastlines shows that worst-case surge characteristics depend strongly on coastal geometry: enclosed basins favour very slow-moving cyclones, while open coasts favour faster storms. Under a high-emissions scenario, the potential storm surge height for New Orleans is projected to increase by \(\sim\)15% (2.4 m) between 2015 and 2100 in SSP5-8.5.

The utility of this physical upper bound is demonstrated through its integration with Extreme Value Theory (EVT). By treating the potential height as a known constraint, uncertainty in estimating rare, high-return-period events is substantially reduced. The generated extreme-event dataset further provides a controlled testbed for assessing extrapolation in surrogate models, with a proof-of-concept using a spatio-temporal Graph Neural Network.

Overall, this thesis establishes a coherent methodology for bridging thermodynamic cyclone theory, high-resolution surge modelling, and statistical risk analysis. By quantifying a physically constrained upper bound on TC storm surges, it advances the capacity to assess worst-case coastal hazards under current and future climate conditions.