The Dynamical Coupling of a Wave Model and a Storm Surge Model through the Atmospheric Boundary Layer

Abstract

The effect of a wave-dependent drag coefficient on the generation of storm surge in the North Sea is studied. To this end, a barotropic storm surge model is driven by stress that explicitly depend on the ocean waves. To estimate the effects of waves on the boundary layer the theory of Janssen is used. In this theory the aerodynamic drag depends on the fraction of the stress carried by the waves. For waves limited in growth by time, fetch, or depth this gives an enhancement of the drag. The importance to surges of radiation stress is also investigated. The coupled wave and storm surge models have been tested for three recent storm periods. The calculations with a Smith and Banke stress relation underestimate the surges by 20%. The calculations with the wave-dependent drag give a significant improvement. When corrected for the effects of an external surge, the storm surge caused by a fast moving depression was overestimated slightly. In this case, the generation of the storm surge was dominated by relatively young waves. In the other two cases, the wave-dependent stress reproduced the overall level of the surges within a few percent. The radiation stress increased the surge some 5% during one storm, but the effect was negligible during the other two storms. Most of the improvements can be reproduced by assuming an overall increase of the dimensionless roughness parameter. If the Smith and Banke relation is replaced by a Charnock one with a dimensionless constant of α = 0.032, the difference in water level between this formulation and the wave-dependent calculation is smaller than the uncertainty in the observations. Different basins would, however, give rise to different choices of α. Therefore, a wave-dependent drag is to be preferred for storm surge modeling.