Estimating nearshore infragravity wave conditions at large spatial scales

Infragravity waves may contribute significantly to coastal flooding, especially during storm conditions. However, in many national and continental to global assessments of coastal flood risk, their contribution is not accounted for, mostly because of the high computational expense of traditional wave-resolving numerical models. In this study, we present an efficient stationary wave energy solver to estimate the evolution of incident and infragravity waves from offshore to the nearshore for large spatial scales. This solver can be subsequently used to provide nearshore wave boundary conditions for overland flood models. The new wave solver builds upon the stationary wave energy balance for incident wave energy and extends it to include the infragravity wave energy balance. To describe the energy transfer from incident to infragravity waves, an infragravity wave source term is introduced. This term acts as a sink term for incident waves and as a complementary source term for infragravity waves. The source term is simplified using a parameterized infragravity wave shoaling parameter. An empirical relation is derived using observed values of the shoaling parameter from a synthetic dataset of XBeach simulations, covering a wide range of wave conditions and beach profiles. The wave shoaling parameter is related to the local bed slope and relative wave height. As validation, we show for a range of cases from synthetic beach profiles to laboratory tests that infragravity wave transformation can be estimated using this wave solver with reasonable to good accuracy. Additionally, the validity in real-world conditions is verified successfully for DELILAH field case observations at Duck, NC, USA. We demonstrate the wave solver for a large-scale application of the full Outer Banks coastline in the US, covering 450 km of coastline, from deep water up to the coast. For this model, consisting of 4.5 million grid cells, the wave solver can estimate the stationary incident and infragravity wave field in a matter of seconds for the entire domain on a regular laptop PC. This computational efficiency cannot be provided by existing process-based wave-resolving models. Using the presented method, infragravity wave-driven flooding can be incorporated into large-scale coastal compound flood models and risk assessments.