## 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 and to space in proportion to the effective heat capacities and the surface radiation factor; the former are defined as 1) the product of the respective heat capacity ρ*c _{p}* and the square roots of the frequency

*q*and the thermal dffiusivity

*K*in case

*K*is constant, and 2) the product of ρ

*c*and the vertical gradient of

_{p}*K*when

*dK*/

*dz*is very large near the surface. Further, a large

*dK*/

*dz*tends to increase the attenuation rate and to reduce the time lag of the temperature wave, therefore tending to maintain a steep temperature gradient at the boundary. The effect of the terrestrial radiation at the surface is to increase the cooling rate in the afternoon and to reduce it during the night, thereby helping to shift the time of the temperature maximum forward.

The analysis also shows that the temperature wave in the lowest few hundred meters of the atmosphere is influenced appreciably by the absorption of the solar radiation and by the interactions between *K* and *T* waves, and this is especially so for the mean temperature. Comparison of the theoretical results with observations made at O'Neill in summer shows that the observed temperature wave in the first 500 m can be approximated closely by the solution corresponding to a *K* profile which increases from a small value (from 3–10 cm^{2} sec^{−1}) at the surface to about 10^{5} cm^{2} sec^{−1} at 10 m, and by consideration of the direct absorption of solar radiation and *K*–*T* interaction terms. The winter observations are approximated very closely by the solutions of the simple one-layer power law diffusivity models without consideration of the absorption of solar radiation and the interaction terms, provided a much larger surface value of the diffusivity is used. These results indicate that the transfer of terrestrial radiation is of importance at the surface in winter.