A computational scheme for an improved Mellor–Yamada (M–Y) Level-3 model with condensation physics is proposed and its performance is examined against large-eddy-simulation data on radiation fog. The improved M–Y model greatly corrects several shortcomings of the original M–Y model: the underestimations of the mixed-layer depth and the magnitude of turbulent kinetic energy, and the discrepancies in the formation and dissipation times of the fog. In addition the improved M–Y model can reproduce the occurrence of Kelvin–Helmholtz instability and periodic oscillations due to its energy cycle. It is shown that the optimization of both the closure constants and the master length scale is required for this improvement.
The improved M–Y model has an improvement also in the Level-2.5 version. Although the performance of the Level-2.5 version is not so good as that of the Level-3 version, the former has the advantage of relatively low computational cost and is popularly used in operational weather forecasts. Our computational scheme for the improved M–Y model allows us to switch its hierarchy levels easily according to the purpose.