An Improved Mellor–Yamada Level-3 Model: Its Numerical Stability and Application to a Regional Prediction of Advection Fog

This note describes a numerically stable version of the improved Mellor–Yamada (M–Y) Level-3 model proposed by Nakanishi and Niino [Nakanishi, M. and Niino, H.: 2004, Boundary-Layer Meteorol. 112, 1–31] and demonstrates its application to a regional prediction of advection fog. In order to ensure the realizability for the improved M–Y Level-3 model and its numerical stability, restrictions are imposed on computing stability functions, on L/q, the temperature and water-content variances, and their covariance, where L is the master length scale and q ²/2 the turbulent kinetic energy per unit mass. The model with these restrictions predicts vertical profiles of mean quantities such as temperature that are in good agreement with those obtained from large-eddy simulation of a radiation fog. In a regional prediction, it also reasonably reproduces the satellite-observed horizontal distribution of an advection fog.