Analytical model coupling Ekman and surface layer structure in atmospheric boundary layer flows

Abstract

We introduce an analytical model that describes the vertical structure of Ekman boundary layer flows coupled to the Monin-Obukhov Similarity Theory (MOST) surface layer representation, which is valid for conventionally neutral (CNBL) and stable (SBL) atmospheric conditions. The model is based on a self-similar total stress distribution for both CNBL and SBL flows that merges the classic 3/2 power law profile with a MOST-consistent stress profile in the surface layer. The velocity profiles are then obtained from the Ekman momentum balance equation. The same stress model is used to derive a new self-consistent Geostrophic Drag Law (GDL). We determine the ABL depth (h) using an equilibrium boundary layer height model and parameterize the surface heat flux for quasi-steady SBL flows as a function of a prescribed surface temperature cooling rate. The ABL height and GDL equations can then be solved together to obtain the friction velocity and the cross-isobaric angle as a function of known input parameters such as the Geostrophic wind velocity magnitude and surface roughness. We show that the model predictions agree well with predictions from the literature and newly generated Large Eddy Simulation (LES). These results indicate that the proposed model provides an efficient and reasonably accurate self-consistent approach for predicting the mean wind velocity distribution in CNBL and SBL flows.