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For the thermal stability function 4,, used to calculate heat and moisture fluxes in the surface layer, we choose a formulation which has the theoretically correct free convection limit (-z/L)-'". We then use the experimental result that z/L = Ri to deduce a formulation with an exponent -l/6 for the momentum stability function I$,,,. This formulation also resolves the matching problem at the interface between the surface and Ekman layers. The proposed functions are found to remain reasonably close to another formulation that is well supported by observations and has exponents -112 for & and -114 for &,. The intent of the proposals is mainly to clarify and simplify the parameterization of the convective boundary layer in present day atmospheric models, without significantly altering the results.

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The evolution of the structure of the atmospheric boundary layer during the cooling phase of the diurnal cycle is studied with the help of a one-dimensional numerical model. The model uses a turbulent energy equation for the determination of the eddy exchange coefficients, which also involve the local value of the Monin-Obukhov length. The surface temperature is prescribed as a function of time and the geostrophic wind is held constant. Results are presented in nondimensional form and cover a wide range of possible values for the external parameters. After several hours of cooling the inversion layer is found to reach a maximum depth, which depends strongly upon the magnitude of the geostrophic wind and, to a lesser extent, on the cooling rate of the ground surface. * Present affiliation: Dynamic Prediction Research Division, Environment ofCanada, West Isle Office Tower, 5th Floor, 2121Trans-Canada Highway, Dorval, Quebec, Canada.

A two dimensional model has been set up to investigate the circulation induced by an urban heat island in the absence of synoptic winds. The boundary conditions need to be formulated carefully and due to difficulties arising here, we restrict our attention to cases of initially stable thermal stratification. Heat island circulations are allowed to develop from rest and prior to the appearance of the final symmetric double cell pattern, a transitional multi-cell pattern is observed in some cases. The influence on the steady state circulation of various parameters is studied, among which are eddy transfer coefficients, the heat island intensity, the initial temperature stratification and the heat island size. Some results are presented for a case in which differential surface cooling beneath an initially stable atmosphere produces a circulation and an unstable layer capped by an elevated inversion over the city. It is hoped that this case is vaguely representative of the night-time heat island with no geostrophic wind.