Improving mixing length-scale for the stable boundary layer in mesoscale models

It has been recognized that current numerical mesoscale models often represent the stable atmospheric boundary layer (SABL) poorly in terms of the SABL depth, near-surface inversion characteristics, low-level wind profiles and overall mixing properties. Namely, the models usually yield either too strong vertical diffusion, or lead to a so-called frictional decoupling. We use Prandtl model to deduce an improved mixing length-scale in a mesoscale model with a higher-order turbulence parameterization scheme (MIUU model). A thin SABL flow develops against calm stratified background atmosphere laying over a slightly inclined cooled surface; this is equivalent to a simple katabatic flow.

We forced MIUU model to reproduce the solution similar to that from the Prandtl model. In this way, we determine one of the coefficients in the mixing length-scale for stable "z-less" conditions, L = min[2a(TKE)^(1/2)/N, a(TKE)^(1/2)/S] where N and S are buoyancy frequency and absolute vertical wind shear and 2a = 0.537 is a standard coefficient in this model. Under weakly to moderately stable conditions, 0 < Ri ≤ 1, this new L, now including the wind shear explicitly (2nd term), is smaller than in the original MIUU formulation (1st term only, proportional to Ozmidov length). Without this inclusion, MIUU model gave too strong vertical mixing with an elevated inversion and low-level jet around 150–200 m instead of around 20 m.