Surface wave impacts on turbulent roughness length parameterization

The interactions between sea surface waves and ocean circulation are often represented using simplified parameterizations that rely on open-ocean calibrations whilst using local wind conditions. More refined estimates of these interactions and their impact on hydrodynamics can be achieved by using explicit forcing from a wave model. This transition from implicit to explicit wave-dependence requires revisiting existing turbulence scheme parameterizations, particularly in coastal waters where the scale of wave-ocean interactions differs from the open ocean and wave growth is often limited by fetch or wind duration. In this study, we optimize the roughness length parameterization in the generic length-scale (GLS) turbulence scheme, using regional wave data from the Baltic and North Seas, and assess the impacts on thermal stratification. The recalibrated parameterization reduces the roughness length under high winds, better representing the regional limitations for wave-growth, and leads to an improved representation of sea surface temperature (SST). We find recalibration particularly important for moderating the impacts of explicit wave-modified ocean-side stress, which is conceptually different from the bulk stress, and leads to large discrepancies with the default parameterization, especially under active wave-growth. Although thermocline depth representation is improved in wave-forced experiments, the definition may still lead to overly enhanced mixing under fetch-limited conditions. The regional limitations are best captured by scaling roughness length with significant wave height, but existing formulations should take account of the energetically distinct wind-sea and swell regimes. In wave-forced setups, this can be achieved by replacing wave-height-based flux estimates with wave-model-computed turbulent kinetic energy (TKE).