New Modified and Extended Stability Functions for the Stable Boundary Layer based on SHEBA and Parametrizations of Bulk Transfer Coefficients for Climate Models

Abstract

Climate models still have deficits in reproducing the surface energy and momentum budgets in Arctic regions. One of the reasons is that currently used transfer coefficients occurring in parameterizations of the turbulent fluxes are based on stability functions derived from measurements over land and not over sea ice. An improved parameterization is developed using the Monin–Obukhov similarity theory (MOST) and corresponding stability functions that reproduce measurements over sea ice obtained during the Surface Heat Budget of the Arctic Ocean (SHEBA) campaign. The new stability functions for the stable surface layer represent a modification of earlier ones also based on SHEBA measurements. It is shown that the new functions are superior to the former ones with respect to the representation of the measured relationship between the MOST stability parameter and the bulk Richardson number. Nevertheless, the functions fulfill the same criteria of applicability as the earlier functions and contain, as an extension, a dependence on the neutral-limit turbulent Prandtl number. Applying the new functions we develop an efficient noniterative parameterization of the near-surface turbulent fluxes of momentum and heat with transfer coefficients as a function of the bulk Richardson number (Rib) and roughness parameters. A hierarchy of transfer coefficients is recommended for weather and climate models. They agree better with SHEBA data for strong stability (Rib > 0.1) than previous parameterizations and they agree well with those based on the Businger–Dyer functions in the range Rib ≤ 0.1.