A Critical Evaluation of a Simple Mixed-Layer Model with Penetrative Convection

Abstract

A simple mixed-layer model with variable inversion strengths is validated with data. An algorithm is developed to obtain mixed-layer heights by analytically solving a cubic polynomial equation which is derived from, but much simpler than, the more familiar system of differential equations. Using a value of 0.2 for the ratio of the magnitudes of the heat fluxes at the inversion base and at the surface, this model obtained a correlation coefficient of 0.933 between the predicted and observed mixed-layer heights. Thus, it is suggested that this model may be readily adopted by existing regional-scale models for incorporation of diurnal variations of mixed-layer heights. To the best of our knowledge no such attempt has yet appeared in the literature.