Sea Surface Roughness and Drag Coefficient as Functions of Neutral Wind Speed

Near the surface, it is commonly believed that the behavior of the (turbulent) atmospheric flow can be well described by a constant stress layer. In the case of a neutrally stratified surface layer, this leads to the well-known logarithmic wind profile that determines the relation between near-surface wind speed and magnitude of stress. The profile is set by a surface roughness length, which, over the ocean surface, is not constant; rather, it depends on the underlying (ocean wave) sea state. For instance, at the European Centre for Medium-Range Weather Forecasts this relation is parameterized in terms of surface stress itself, where the scale is set by kinematic viscosity for light wind and a Charnock parameter for strong wind. For given wind speed at a given height, the determination of the relation between surface wind and stress (expressed by a drag coefficient) leads to an implicit equation that is to be solved in an iterative way. In this paper a fit is presented that directly expresses the neutral drag coefficient and surface roughness in terms of wind speed without the need for iteration. Since the fit is formulated in purely dimensionless quantities, it is able to produce accurate results over the entire range in wind speed, level height, and values for the Charnock parameter for which the implicit set of equations is believed to be valid.