Modification of the standard ε-equation for the stable ABL through enforced consistency with Monin-Obukhov similarity theory

A condition is derived for consistency of the standard epsilon-equation with Monin-Obukhov ( MO) similarity theory of the stably-stratified surface layer. The condition is derived by extending the procedure used to derive the analogous condition for neutral theory to stable stratification. It is shown that consistency with MO theory requires a function of flux Richardson number, Ri(f), to be absorbed into either of two closure parameters, c(epsilon1) or c(epsilon2). Inconsistency, on the other hand, results if constant values of these are maintained for all Rif, as is done in standard application of the equation, and the large overpredictions of turbulence found in such application to the one-dimensional stable atmospheric boundary layer (1D-SBL) are traced to this inconsistency. Guided by this, we formulate a MO-consistent epsilon-equation by absorbing the aforementioned function into c(epsilon1), and combine this with a Level-2.5 second-order closure model for vertical eddy viscosity and diffusivities. Numerical predictions of the 1D-SBL by the modified model converge to a quasi-steady state, rectifying the predictive failure of the standard epsilon-equation for the case. Quasi-steady predictions of non-dimensional variables agree strongly with Nieuwstadt's theory. Qualitative accuracy of predictions is inferred from comparisons to field data, large-eddy simulation results and Rossby-number similarity relationships.