Matching of Monin-Obukhov Similarity theory to LES Subgrid Closures
MO flux is estimated at the half-level above the surface. Flux divergence, however, is estimated, across the full first cell. After all, MOST is only an approximation and the MO flux at the first half-level has higher-order correction terms (such as the linear correction for stratification and other that are normally neglected). Try to improve the estimate based on the resolved or total flux at the second half-level above the surface, the gradient across the second grid cell, and/or the flux divergence across the second grid cell such that a consistent profile of the eddy viscosity and Kármán measure emerges.