A Rate Equation for the Nocturnal Boundary-Layer Height

Abstract

A rate equation is derived which describes the development of the boundary-layer height under stable conditions as a function of time. It takes the form of a linear relaxation equation; its solution is forced toward an equilibrium value. The equilibrium height is connected to the work done by the ageostrophic wind in the boundary layer. The time scale of the relaxation process increases monotonically from a few hours shortly after sunset to a value of the order of 10 h later on. This means that the boundary-layer height evolves very slowly, which may lead to the unwarranted impression that stationary conditions have been reached. The main features of the rate equation are confirmed by comparison with the results of computer simulations and with field observations of the boundary-layer height during clear nights.