Sensitivity analysis of the equations for a convective mixed layer

TLDR: In this paper, the authors analyzed the sensitivity of the solutions of the model equations to variations in the entrainment formulation and in the initial and boundary conditions, and showed that the initial conditions for the mixed-layer height (h) and potential temperature (m) quickly lose their influence.

Abstract: Jump or slab models are frequently used to calculate the depth of the convectively mixed layer and its potential temperature during the course of a clear day. Much attention has been paid theoretically to the parameterization of the budget for turbulent kinetic energy that is required in these models. However, for practical applications the sensitivity of the solutions of the model equations to variations in the entrainment formulation and in the initial and boundary conditions is also very important. We analyzed this sensitivity on the basis of an analytical solution for the model which uses the well-known constant heat flux ratio. The initial conditions for the mixed-layer height (h) and potential temperature (θ m ) quickly lose their influence. Only the initial temperature deficit is important. The mixed-layer temperature at noon on convective days is insensitive to the entrainment coefficient c. It is governed by the integral of the heat input and by the stable lapse rate. A change in c from 0.2 to 0.5 leads to a variation of 20% in h. This is not very much considering the accuracy in the determination of h from actual observations.