A Rate Equation for the Inversion Height in a Nocturnal Boundary Layer

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Abstract
The application of a self-similar profile in the integration of the temperature equation across the stable boundary layer leads to a rate equation for the inversion height. An analytic solution of the resulting equation is derived. Its behavior is determined by two processes; cooling by turbulent mixing and cooling by internal radiation, the latter is parameterized in terms of the surface cooling rate. This parameterization, which attributes the temperature change in the boundary layer close to the surface completely to internal radiation, leads to a monotonic growth of the inversion depth. When the radiation term is neglected and only the turbulent heat flux is taken into account, the solution is governed by a relaxation process.

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