Impacts of Wave-Current Interaction in Coupled Storm Surge-Wave Model

In existing two-dimensional (depth integrated) storm surge models coupled with wave models, the surface wave effect is traditionally included as the radiation stress gradient forcing, which accounts for momentum transfer from surface waves to currents. However, recent studies on wave-current interactions indicate that radiation stress alone does not fully capture the impact of waves on ocean currents and sea surface elevation. In this study, we derive new governing equations for two-dimensional storm surge models to incorporate more comprehensive wave-current interactions. Instead of using vertically integrated Eulerian currents, our formulation is based on vertically integrated Lagrangian currents, which include the wave Stokes drift. The resulting momentum equations include a new wave-induced forcing term that depends on both waves and currents, in addition to the radiation stress gradient. We incorporated the new term into the Advanced Circulation storm surge model, coupled with the Wavewatch III wave model, and simulated storm surges during Hurricanes Michael (2018) and Ian (2022). Our results indicate that, while the radiation stress forcing significantly increases water levels (by 0.4 m or more) over a large area to the right of the storm track, the new wave-induced forcing causes a notable reduction in water levels (up to 0.3 m) near the storm track shortly before the storm makes landfall. This reduction is attributed to the alignment of strong currents and waves in the alongshore direction.