Modelling the height,temperature and relative humidity of a well-mixed planetary boundary layer over a water surface

A vertically integrated model of a developing boundary layer over a wet surface is presented, and the expected change in the relative humidity is discussed. For the case of cold air moving over a water surface of constant temperature, analytical solutions of the model equations are obtained, giving the height, temperature and relative humidity of the boundary layer as functions of the distance travelled by the air column. The relation to the problem of sea smoke is discussed.