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Steady state solutions for axially-symmetric climatic variables

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Summary

Equations governing the axially-symmetric time-average state of the atmosphere and the transient departures from this mean state are set down. As a first step toward a solution of this system for seasonal average conditions, a model is formulated based on the thermodynamical energy equation for the vertical average of the mean state, and on the perturbation solutions of the linearized equations governing the baroclinic growth of transient eddies. All forms of non-adiabatic heating within the atmosphere and at the earth's surface are parameterized. The resulting differential equation governing the axially-symmetric mean potential temperature distribution takes the form of a steadystate diffusion equation in surface spherical coordinates, with a variable Austausch coefficient which is to be determined iteratively as a dependent variable.

Global solutions, for winter and summer equilibrium conditions, are obtained for the thermal structure, the heat balance components, the transient eddy variances of temperature and meridional wind speed, and the covariance representing the meridional eddy heat transport. These solutions are for different types of surface conditions (ocean, land), and for a successively more complete variety of modes of heat transfer ranging from pure radiation to a combination of radiation, latent heat processes, and conduction and convection within the atmosphere and the subsurface layers. The results for this latter complete case seem to be a reasonable first order approximation to the observed distributions. Suggestions are made for improving and generalizing the study.

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Saltzman, B. Steady state solutions for axially-symmetric climatic variables. PAGEOPH 69, 237–259 (1968). https://doi.org/10.1007/BF00874919

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Keywords

  • Diffusion Equation
  • Meridional Wind
  • Perturbation Solution
  • Transient Eddy
  • Thermodynamical Energy