Application of a Large Eddy Simulation Database to Optimization of First   Order Closures for Neutral and Stably Stratified Boundary Layers
  Large-eddy simulation (LES) is a well-established numerical technique, which resolves the most energetic turbulent fluctuations in the planetary boundary layers. Averaging these fluctuations, high-quality profiles of mean values and turbulence statistics can be obtained in experiments with well-defined initial and boundary conditions. Hence, the LES data can be beneficial for assessment and optimization of turbulence closure schemes. A database of 80 LES runs for neutral and stably stratified PBLs (DATABASE64) is applied in this study to optimize the first-order turbulence closure (FOC). Approximations for the mixing length scale and stability correction functions have been tuned to minimise a relative root-mean square error over the entire DATABASE64. New stability functions have correct asymptotes describing regimes of strong and week mixing found in theoretical exercises, atmospheric data and LES. The correct asymptotes exclude the need for a critical Richardson number in the FOC formulation. Further, we analysed the FOC quality as functions of the integral PBL stability and the vertical model resolution. We show that the FOC is never perfect because the turbulence in the upper half of the PBL is not generated by the local gradients. Accordingly, the parameterized and LES fluxes decorrelate in the upper PBL. With this imperfection in mind, we show that there is no systematic quality deterioration of the FOC in strongly stable PBLs provided the vertical model resolution is better than 10 levels within the PBL. In agreement with previous studies, we found that the quality improves slowly with the vertical resolution refinement. It is generally wise to not overstretch the mesh in the lowest 500 m of the atmosphere where majority of the observed, simulated and theoretically predicted stably stratified PBLs are located. 
Igor N. Esau, Oyvind Byrkjedal