Abstract The thermal interaction between the atmosphere and the underlying earth, as related to the diurnal heat wave, is investigated through the use of a modified virtual conduction model in which the influences of turbulence and thermal convection are simulated by diffusion while the influence of terrestrial radiation is approximated partly by diffusion and partly by a Newtonian cooling, the ratio between the two parts increasing from summer to winter. The virtual thermal diffusivity is assumed to vary both in time and in space in order to represent the various physical processes involved in accomplishing the actual heat transfer. It is shown that a mean upward transport of heat is maintained through the diurnal variation of the transfer process although the mean lapse rate is stable, thereby removing a long-standing difficulty in evalutating the turbulent heat flux from the mean potential temperature distribution. The solar energy received at the surface is found to be partitioned into the two media a...