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Hantel & Princeton University 1976
Hantel, M. and Princeton University, y.F.D.P. (1976). On the vertical Eddy transports in the Northern Atmosphere 1. Vertical Eddy Heat Transport for Summer and Winter. Journal of Geophysical Research 81: doi: 10.1029/JC081i009p01577. issn: 0148-0227.

The zonal mean hemispheric budget of heat in the form of moist static energy is considered. While the horizontal heat flux is synoptic, the vertical flux is largely subsynoptic and thus unknown. It represents, however, a significant link in the heat budget. The heat balance equation composes radiational heating, heat storage, and meridional and vertical heat flux divergence. The first three of these are specified, and the fourth is determined as being residual. The domain is the entire northern atmosphere, divided into 16 equal mass boxes. A model is used for radiation, climatological data are used for the surface boundary fluxes, and the statistics of the MIT library are used for storage and horizontal heat fluxes. The various sources create box imbalances of the order of 7 W/m2; this reflects the overall accuracy of contemporary hemispheric heat budget estimates. A least squares technique is employed to compute the residual vertical fluxes which are of the order of 100 W/cm2, well above the noise level; they are due to eddies of all scales. The eddy fluxes are practically always upward and have the same magnitude at all latitudes except over the polar cap, where they are weaker. To first order, the eddy flux balances the radiation flux and constitutes the radiative-convective equilibrium of the atmosphere. The data do not allow one to split the vertical eddies into a synoptic and a subsynoptic term. Information from the Geophysical Fluid Dynamics Laboratory global climate model is used for a tentative apportionment into a grid and a subgrid scale term. The model indicates almost equal size of both in the lower troposphere but dominance of the grid scale vertical heat flux in the middle and upper troposphere.

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Journal of Geophysical Research
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