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Michael Hantel
and
Herbert Langholz

Abstract

The diabatic heating of the atmosphere can be very closely represented by the convergence of a vertical energy flux. It consists of two components: the flux of net radiation and the flux of precipitation. The latter comprises the vertical flux of water in condensed form (rain, snow, ice). The concept of precipitation flux is investigated employing the zonal mean equation of potential heat. Input data are radiation flux from a model, adjusted at the top and bottom of the atmosphere with observed data; horizontal advective heat flux convergence and heat storage with the data of the MIT Library; and vertical sub-synoptic eddy flux of sensible heat (a small quantity) from a parameterization. Output is the precipitation flux in the free atmosphere. Time scale is 1 month, space domain is the zonal mean Northern Hemisphere.

The precipitation flux is downward everywhere. It is maximum in the tropics. Comparison of the flux across the 1000 mb level with the observed surface precipitation shows satisfactory agreement. The balance in the potential heat equation is largely between radiation and precipitation; thus the atmosphere can be characterized by an approximate radiative-precipitative equilibrium. The accuracy of the method (±10 W m−2) depends critically on the validity of the radiation data.

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Michael Hantel
,
Dietmar Dedenbach
, and
Herbert Hüster

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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Hermann Flohn
,
Michael Hantel
, and
Eberhardt Ruprecht

Abstract

No abstract available.

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Michael Hantel
and
Hans-Reinhard Baader

Abstract

The diabatic heating Q is the ultimate driving force of the general circulation and climate. We present seasonal and zonal mean estimates of Q (order of magnitude 10−5 K s−1) for the atmosphere from 15°S-90°N and from 50–1000 mb. Q comprises radiation, condensation, conduction, dissipation and diffusion; the first two terms are large, the last three are small. We compile Q indirectly by specifying (from the synoptic general circulation statistics of the MIT Library) sensible heat advective and storage terms, including the adiabatic heating, which together balance Q in the First Law of thermodynamics. An important component of the advective terms is subsynoptic-scale advection. We show that it is not restricted to boundary layer heating but also has convective-scale components of potential significance and seems to be active even in the stratosphere. However, we are not able to specify the total subsynoptic-scale advection since it is subject to considerable compensation. This causes a systematic error of the order of 10−6 K s−1 in our synoptic estimates of Q.

The meridional diabatic heating profiles show four latitude belts of different Q climate. The tropics and midlatitudes are characterized by net heating, the subtropics and the polar cap by net cooling. This pattern is visible throughout the year and reflects the net effect of the two governing, and partly balancing, components of Q: condensational heating dominates in the rainbelts, radiational cooling dominates in the dry belts. A new feature in the Q field is persistent strong beating at and above the jet stream level between 30–40°N throughout the year. We speculatively explain this effect with the subsynoptic advective terms.

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