Energy Streamfunctions in the Vertical-Meridional Plane for the Northern Atmosphere

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  • 1 Geophysical Fluid Dynamics Program, Princeton University Princeton, N. J.
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Abstract

The zonal mean flux vector of atmospheric heat transports is very closely nondivergent in the vertical-meridional plane. This is demonstrated for potential (cpT + gz) and latent heat. Thus the heat flux vector fields can be represented by streamfunctions. The top of the atmosphere is a streamline for latent heat. For potential heat, the radiation flux across the top determines the upper boundary condition.

The conservation equations are invariant with respect to arbitrarily choosing a constant reference heat but the streamfunctions are not. The impact on the streamfunctions of shifting the reference heat is equivalent to subtracting the mass transport, scaled with that constant, from the heat flux. To remove this ambiguity it is postulated that the curt of the heat flux vector in the vertical-meridional plane be minimized in the least-squares sense. This principle of minimum mean enstrophy is rationalized by analogy to electro-dynamics. It yields a formula for the reference heat in terms of hemispheric integrals of heat and mass flux curl. The formula is applied to the circulation statistics of the MIT-Library. The reference constants turn out to be numerically identical to the observed hemispheric annual mean of the respective heat form (∼324 J g−1 for potential heat and ∼6 J g−1, corresponding to 2.6 g kg−1, for latent heat).

Streamfunctions reduced in this way are presented for the seasons. The potential heat circulation is highly variable. It changes sign from summer to winter over the entire northern atmosphere. The water circulation is less variable; it changes sign only in the tropics and fluctuates in intensity in the extratropics. It is shown that there is no further ambiguity in the streamfunction concept. The interrelationships between kinetic energy and potential, latent and static heat flux are discussed with the main result that the potential heat circulation is largely governed by radiation and precipitation flux but very little by the kinetic energy flux and not at all by the water vapor, and further that the streamfunction concept is not applicable to the kinetic energy flux. The main virtue of the streamfunctions is that they quantitatively represent the net heat flux on all scales and phases.

Abstract

The zonal mean flux vector of atmospheric heat transports is very closely nondivergent in the vertical-meridional plane. This is demonstrated for potential (cpT + gz) and latent heat. Thus the heat flux vector fields can be represented by streamfunctions. The top of the atmosphere is a streamline for latent heat. For potential heat, the radiation flux across the top determines the upper boundary condition.

The conservation equations are invariant with respect to arbitrarily choosing a constant reference heat but the streamfunctions are not. The impact on the streamfunctions of shifting the reference heat is equivalent to subtracting the mass transport, scaled with that constant, from the heat flux. To remove this ambiguity it is postulated that the curt of the heat flux vector in the vertical-meridional plane be minimized in the least-squares sense. This principle of minimum mean enstrophy is rationalized by analogy to electro-dynamics. It yields a formula for the reference heat in terms of hemispheric integrals of heat and mass flux curl. The formula is applied to the circulation statistics of the MIT-Library. The reference constants turn out to be numerically identical to the observed hemispheric annual mean of the respective heat form (∼324 J g−1 for potential heat and ∼6 J g−1, corresponding to 2.6 g kg−1, for latent heat).

Streamfunctions reduced in this way are presented for the seasons. The potential heat circulation is highly variable. It changes sign from summer to winter over the entire northern atmosphere. The water circulation is less variable; it changes sign only in the tropics and fluctuates in intensity in the extratropics. It is shown that there is no further ambiguity in the streamfunction concept. The interrelationships between kinetic energy and potential, latent and static heat flux are discussed with the main result that the potential heat circulation is largely governed by radiation and precipitation flux but very little by the kinetic energy flux and not at all by the water vapor, and further that the streamfunction concept is not applicable to the kinetic energy flux. The main virtue of the streamfunctions is that they quantitatively represent the net heat flux on all scales and phases.

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