An Efficient Non-iterative Bulk Parametrization of Surface Fluxes for Stable Atmospheric Conditions Over Polar Sea-Ice

In climate and weather prediction models the near-surface turbulent fluxes of heat and momentum and related transfer coefficients are usually parametrized on the basis of Monin–Obukhov similarity theory (MOST). To avoid iteration, required for the numerical solution of the MOST equations, many models apply parametrizations of the transfer coefficients based on an approach relating these coefficients to the bulk Richardson number \(Ri_{b}\). However, the parametrizations that are presently used in most climate models are valid only for weaker stability and larger surface roughnesses than those documented during the Surface Heat Budget of the Arctic Ocean campaign (SHEBA). The latter delivered a well-accepted set of turbulence data in the stable surface layer over polar sea-ice. Using stability functions based on the SHEBA data, we solve the MOST equations applying a new semi-analytic approach that results in transfer coefficients as a function of \(Ri_{b}\) and roughness lengths for momentum and heat. It is shown that the new coefficients reproduce the coefficients obtained by the numerical iterative method with a good accuracy in the most relevant range of stability and roughness lengths. For small \(Ri_{b}\), the new bulk transfer coefficients are similar to the traditional coefficients, but for large \(Ri_{b}\) they are much smaller than currently used coefficients. Finally, a possible adjustment of the latter and the implementation of the new proposed parametrizations in models are discussed.