An Improved Surface Boundary Condition for Large-Eddy Simulations Based on Monin–Obukhov Similarity Theory: Evaluation and Consequences for Grid Convergence in Neutral and Stable Conditions

Abstract

Monin–Obukhov similarity theory is used in large-eddy simulation (LES) models as a surface boundary condition to predict the surface shear stress and scalar fluxes based on the gradients between the surface and the first grid level above the surface. We outline deficiencies of this methodology, such as the systematical underestimation of the surface shear stress, and propose a modified boundary condition to correct for this issue. The proposed boundary condition is applied to a set of LES for both neutral and stable boundary layers with successively decreasing grid spacing. The results indicate that the proposed boundary condition reliably corrects the surface shear stress and the sensible heat flux, and improves grid convergence of these quantities. The LES data indicate improved grid convergence for the surface shear stress, more so than for the surface heat flux. This is either due to a limited performance of the Monin–Obukhov similarity functions or due to problems in the LES model in representing stable conditions. Furthermore, we find that the correction achieved using the proposed boundary condition does not lead to improved grid convergence of the wind-speed and temperature profiles. From this we conclude that the sensitivity of the wind-speed and temperature profiles in the LES model to the grid spacing is more likely related to under-resolved near-surface gradients and turbulent mixing at the boundary-layer top, to the SGS model formulation, and/or to numerical issues, and not to deficiencies due to the use of improper surface boundary conditions.