Article ID: 2022-013
It is desirable that a surface layer scheme in an atmospheric numerical model is consistent with an atmospheric boundary layer scheme incorporated in the same model. In this study, stability functions based on Monin–Obukhov similarity theory for momentum and heat, ϕm and ϕh, in the stable surface layer are derived from the Mellor–Yamada–Nakanishi–Niino (MYNN) scheme modified so that turbulent diffusivity coefficients have no critical gradient Richardson number. The resulting stability functions are approximated by ϕm = 1 + 4.8z/L and ϕh = 0.74 + 6.0z/L, which can be analytically integrated with respect to height z to obtain momentum and heat fluxes, where L is the Obukhov length. The fluxes thus obtained are compared with those obtained from stability functions in four previous studies: they turn out to be nearly the same as those from two of them, and show better agreement with observational data of the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) over sea ice than those from the other two studies. Detailed comparisons of the results of the MYNN scheme with the SHEBA data suggest that significant variations of the fluxes observed for a period of “winter” when the ice was covered with dry snow may have been caused by those of the surface roughness around the observational site. The stability functions obtained from the MYNN scheme predict that the bulk and flux Richardson numbers approach critical values of 0.26 and 0.21, respectively, in the limit of z/L → ∞. These critical values result from Kolmogorov hypothesis applied to the turbulent dissipation in the MYNN scheme and are considered to correspond to a transition from Kolmogorov to non-Kolmogorov turbulence.
