Geostrophic drag coefficients over sea ice

ABSTRACT The geostrophic drag coefficient, Cg ≡ u*/G, and turning angle, α were measured October through November 1988 from a 120 km array of 6 drifting buoys and a drifting ship in the northern Barents Sea/Arctic Ocean during CEAREX; u* is the friction velocity, G is the geostrophic wind, and α is the angle between surface stress and \vec G . The median Cg was 0.029 with hinge values (quartiles) of 0.023 and 0.034 and the median α was 25° with hinge values of 15° and 32°. The median values are representative for the nonsummer Arctic away from marginal seas and marginal ice zones. Surface air temperature, cloud amount, and the lapse rate above the inversion base were not good predictors of the influence of boundary layer stability on Cg. The geostrophic drag coefficient was most sensitive to the temperature difference across the boundary layer from the surface to the top of the inversion. A first order correction to account for airmass stability is C_g = 0.037 - 8.3 \times 10^{ - 3} \left( {{{N_{900} } \over {\bar N_{900} }}} \right)^4 ,{\rm \alpha = 11}{\rm .7 + 13}{\rm .1}\left( {{{N_{900} } \over {\bar N_{900} }}} \right)^2 . This stability correction represents a 17% improvement over using a constant drag value, based on reduction of variance with the CEAREX data set. The formula uses an external stability parameter, N9002, proportional to the difference between the potential temperature measured at 900 mb, \theta _{900} , which is representative of the temperature at the top of the arctic inversion, and at the surface, \theta _{\rm s} :N_{900}^2 = \left( {{g / {\bar \theta }}} \right)\Delta {\theta / {h_{900} }},\Delta \theta = \theta _{900} - \theta _{\rm s} ,\bar \theta = {{\left( {\theta _{900} + \theta _{\rm s} } \right)} / 2},h_{900} = 67.4\bar \theta \log _{10} \left( {{{P_{\rm s} } / {{\rm 900}}} \right),\bar N_{900} = 0.024{\rm s}^{{\rm - 1}},PS is surface pressure and g is gravity. \theta _{900} can be obtained from atmospheric models or satellite‐derived temperature soundings. Formulas are also developed based on the standard level of 850 mb; the reduction in variance is less, 11%, because this level is sometimes above the top of the arctic inversion. We reason that because most of the boundary layer above the surface layer is near a critical Richardson number, the total amount of shear that can be maintained in the boundary layer, and thus the reduction in Cg, is given by the external temperature difference rather than the detailed internal