On the <i>u</i>_⋆−<i>U</i> Relationship in the Stable Atmospheric Boundary Layer over Arctic Sea Ice

Abstract

A relationship between the friction velocity u⋆ and mean wind speed U in a stable atmospheric boundary layer (ABL) over Arctic sea ice was considered. To that aim, the observations collected during the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment were used. The observations showed the so-called “hockey-stick” shape of the u⋆−U relationship, which consists of a slow increase of u⋆ with increasing wind speed for UUtr and a more rapid almost linear increase of u⋆ for U>Utr, where Utr is the wind speed of transition between the two regimes. Such a relationship is most pronounced at the highest observational levels, namely at 9 and 14 m, and is also sharper when the air-surface temperature difference exceeds its average values for stable conditions. It is shown that the Monin–Obukhov similarity theory (MOST) reproduces the observed u⋆−U relationship rather well. This suggests that at least for the SHEBA dataset, there is no contradiction between MOST and the “hockey-stick” shape of the u⋆−U relationship. However, the SHEBA data, as well as the single-column simulations show that for cases with strong stability, u⋆ significantly decreases with height due to the shallowness of the ABL. It was shown that when u⋆ was assumed independent of height, the value of the normalized drag coefficient, i.e., of the so-called stability correction function for momentum, calculated using observations at a certain level, can be significantly underestimated. To overcome this, the decrease of u⋆ with height was taken into account in the framework of MOST using local scaling instead of the scaling with surface fluxes. Using such an extended MOST brought the estimates of the normalized drag coefficient closer to the Businger–Dyer relation.

Keywords

• stable atmospheric boundary layer
• Monin–Obukhov similarity theory