Modification of $\mathit{k-\epsilon }$ Model for Sensible Heat and Momentum Flux Reconstruction from Surface Temperature Data

We present a modified $\mathit{k-\epsilon }$ model with a set of wall-functions suitable for reconstruction of sensible heat and momentum fluxes from the observations data (e.g., surface temperature evolution during the diurnal cycle). The modification takes into account stability and buoyancy effects in the Reynolds stress parametrization which affects turbulence production and turbulent heat flux. The single-cell and single-column versions of the model are presented. The model is tested based on CASES-99 observations data for dry ABL. It is shown that the presented modification improves the predictions of sensible heat flux magnitude and leads to a faster onset of a daytime instability, compared to the non-modified $\mathit{k-\epsilon }$ model and its scale-limited modification based on Monin-Obukhov similarity theory.