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.

An improved Mellor-Yamada (MY) turbulence closure model (MYNN model: Mellor-YamadaNakanishi-Niino model) that we have developed is summarized and its performance is demonstrated against a large-eddy simulation (LES) of a convective boundary layer. Unlike the original MY model, the MYNN model considers e¤ects of buoyancy on pressure covariances and e¤ects of stability on the turbulent length scale, with model constants determined from a LES database. One-dimensional simulations of Day 33 of the Wangara field experiment, which was conducted in a flat area of southeastern Australia in 1967, are made by the MY and MYNN models and the results are compared with horizontal-average statistics obtained from a threedimensional LES. The MYNN model improves several weak points of the MY model such as an insu‰cient growth of the convective boundary layer, and underestimates of the turbulent kinetic energy and the turbulent length scale; it reproduces fairly well the results of the LES including the vertical distributions of the mean and turbulent quantities. The improved performance of the MYNN model relies mainly on the new formulation of the turbulent length scale that realistically increases with decreasing stability, and partly on the parameterization of the pressure covariances and the expression for stability functions for third-order turbulent fluxes.

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