Errors in parametrizations of convective boundary-layer turbulent momentum mixing

The structure of the wind profiles in the convective boundary layer is examined, through large-eddy simulation, across a wide parameter space. The stability and baroclinicity are varied independently, for cases with roughness lengths appropriate to both land and sea, and the impact of entrainment is isolated by comparing with simulations which do not permit fluxes through the boundary-layer top. Although entrainment is found to increase the shear in the upper boundary layer, it has little impact on the winds lower down which remain essentially well mixed except in cases with very strong baroclinicity and weak surface heating. The well-mixed structure of the wind profiles presents a problem for local turbulence closures which are typically used in numerical weather-prediction (NWP) models. Here it is shown that the resulting errors in the surface stress (magnitude and direction) depend strongly on the position in parameter space. For example, for cases over land, the main errors are underestimates (by up to around 20%) of the magnitude of the stress for deep boundary layers, but systematic direction errors (of around 5 degrees) for shallow boundary layers. Links are made with the errors shown in the verification statistics of two operational NWP models. The potential of a parametrization incorporating non-local momentum mixing to address these errors is also discussed.