The neutral drag coefficient over polar sea ice with small floes and/or melt ponds

Neutral drag coefficients observed over polar sea ice vary over roughly a factor of five. The variability is due to the nonhomogeneous distribution of e.g., ridge heights, distances between ridges, sea ice freeboard, ice concentration and floe sizes. The small scales in the variability of these parameters as well as the difficulties in their determination from observations or from sea ice models cause difficulties in the parameterization of the drag coeffcients. Hence, attempts to relate the surface drag solely on sea ice concentration are attractive, since the latter is a parameter that can be determined most easily. We show in this contribution under which assumptions such simple parameterizations are valid. This is done on the basis of an analytical model determining the total surface drag as a sum of skin drag and form drag calculated as the dynamic pressure caused by the flow across floe edges. It is shown that the form drag equation can be simplified in several steps to an algebraic function which depends indeed on the sea ice concentration but also on the aspect ratios of either freeboard/floe length in regions with small floes or of freeboard/melt pond length in summer sea ice. The new parameterization is as simple as a polynomial presented recently by Andreas et al. (2010) as a result of a fit to observations. The new parameterization has the advantage to explain a part of the observed drag variability by the variability in the aspect ratios and it can be used to analyze the region of applicability of the Andreas et al (2010) parameterization. In its general form with drag coefficients depending on both sea ice concentration and aspect ratios the new parameterization can be used to estimate possible changes in sea ice roughness in a changing climate with a reduced sea ice thickness.

References

Andreas, E.L. et al.,(2010), Parametrizing turbulent exchange over summer sea ice and the marginal ice zone, Q.J.R.Meteorol. Soc. 136:927-943