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Abstract The differential equations governing the strength Δ (a potential temperature difference) and the height h of inversions associated with dry penetrative convection are considered. No assumptions on the magnitude of the downward heat flux at the inversion base are needed to obtain an algebraic equation that relates h and Δ to the heating history of the boundary layer and to the initial conditions. After the nocturnal inversion has been filled in by heating, the inversion base generally grows linearly with time in the morning, but is proportional to the square root of time in the afternoon. The variation of Δ with time differs greatly from case to case.
H. Tennekes (Tue,) studied this question.