A New K–ε Turbulence Parameterization for Mesoscale Meteorological Models

Abstract

Abstract A new one-dimensional 1.5-order planetary boundary layer (PBL) scheme, based on the K–ε turbulence closure applied to the Reynolds-averaged Navier–Stokes (RANS) equations, is developed and implemented within the Weather Research and Forecasting (WRF) Model. The new scheme includes an analytic solution of the coupled equations for turbulent kinetic energy and dissipation rate. Different versions of the PBL scheme are proposed, with increasing levels of complexity, including a model for the calculation of the Prandtl number, a correction to the dissipation rate equation, and a prognostic equation for the temperature variance. Five different idealized cases are tested: four of them explore convective conditions, and they differ in initial thermal stratification and terrain complexity, while one simulates the very stable boundary layer case known as GABLS. For each case study, an ensemble of different large-eddy simulations (LES) is taken as reference for the comparison with the novel PBL schemes and other state-of-the-art 1- and 1.5-order turbulence closures. Results show that the new PBL K–ε scheme brings improvements in all the cases tested in this study. Specifically, the more significant are obtained with the turbulence closure including a prognostic equation for the temperature variance. Moreover, the largest benefits are obtained for the idealized cases simulating a typical thermal circulation within a two-dimensional valley. This suggests that the use of prognostic equations for dissipation rate and temperature variance, which take into account their transport and history, is particularly important with the increasing complexity of PBL dynamics.