Parameterization of the monthly mean vertical heat transfer at the earth’s surface

The monthly mean vertical flux of heat at the earth's surface is parameterized using a simplified representation of the atmospheric thermal eddy diffusivity in terms of the temperature lapse rate. The formula obtained expresses the dependence of this mean vertical heat flux not only on the mean temperature difference between the surface and the free atmosphere (as is specified in several statistical-dynamical models of the zonal climate and the diabatically-forced standing waves), but also on the intrinsic properties of the earth's surface (albedo, conductive capacity, and water availability) and on the free atmospheric variance of temperature associated with synoptic air mass movements. These latter factors enter as “rectifier” effects associated with the diurnal and synoptic temperature oscillations; they lead to significant net upward fluxes of heat, particularly over the continents in summer and lower latitudes in all seasons (the diurnal effect) and over the oceans off the east coasts of the continents in winter (the synoptic effect). A calculation of the heat flux from the formula expressing all of the above combined effects, for January and July mean conditions, shows good agreement with the distributions obtained independently by Budyko.