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 $U<U_{tr}$ and a more rapid almost linear increase of $u_{☆}$ for $U>U_{tr}$, where $U_{tr}$ 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.

中文翻译：

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北极海冰上稳定大气边界层中的u☆-U关系

摩擦速度之间的关系 ${ü}_{☆}$考虑了北极海冰上稳定的大气边界层（ABL）中的平均风速U。为此，使用了在北冰洋地表热量收支（SHEBA）实验期间收集的观测结果。观察结果显示了所谓的“曲棍球棒”形状。${ü}_{☆}-ü$ 关系，其中包括 ${ü}_{☆}$ 随着风速的增加 $ü<{ü}_{Ť\mathrm{[R}}$ 并以更快的速度线性增长 ${ü}_{☆}$ 为了 $ü>{ü}_{Ť\mathrm{[R}}$， 在哪里 ${ü}_{Ť\mathrm{[R}}$是两种状态之间过渡的风速。这种关系在最高观测水平（即9和14 m）最为明显，当空气表面温度差超过稳定条件下的平均值时，这种关系也更加明显。结果表明，莫宁-奥布科夫相似理论（MOST）重现了观察到的${ü}_{☆}-ü$关系还不错。这表明，至少对于SHEBA数据集，MOST与“ S曲棍棒”形状之间没有矛盾。${ü}_{☆}-ü$关系。但是，SHEBA数据以及单列模拟表明，对于稳定性很强的情况，${ü}_{☆}$由于ABL的浅浅，高度随高度显着降低。结果表明，当${ü}_{☆}$如果假定与高度无关，则可以大大低估使用在一定水平上的观测值计算得出的归一化阻力系数的值，即所谓的动量稳定性修正函数的值。为了克服这个问题，减少了${ü}_{☆}$在MOST框架中，使用局部缩放而不是使用表面通量缩放来考虑高度的变化。使用这种扩展的MOST，可以使归一化阻力系数的估计值更接近Businger-Dyer关系。