Axially Symmetric Steady-State Models of the Basic State for Instability and Climate Studies. Part I. Linearized Calculations

Edwin K. Schneider Department of Meteorology, Massachusetts Institute of Technology, Cambridge 02139

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Richard S. Lindzen Division of Engineering and Applied Physics, Harvard University, Cambridge, O2138

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Abstract

A linearized numerical model of the steady axially symmetric motions on a sphere is developed and applied to the earth's atmosphere. The motions are driven by radiative cooling, conduction of heat from the surface and applied heat sources. The applied heat sources are meant to represent the zonally averaged effect on the large scale of cumulus convection. Frictional effects included are small-scale turbulent mixing in the vertical, represented by eddy viscosity, and “cumulus friction.” The model results show that cumulus heating and friction drive a meridional circulation comparable to the observed. Detrainment of tall cumulus leads to a horizontal temperature gradient reversal near the tropical tropopause, as is observed. Sea surface temperature gradients are shown to drive a significant meridional circulation below 800 mb. If the cumulus precipitation is proportional to the moisture convergence in the lower atmospheric layers, the moisture convergence produced by the mass circulation driven by sea surface temperature gradients will produce an ITCZ near the latitude of maximum sea surface temperature. Preference for a certain latitude of frictional convergence due to upper level heating (CISK) could alter this conclusion, but it is shown that the most unstable CISK perturbation occurs at the equator.

Abstract

A linearized numerical model of the steady axially symmetric motions on a sphere is developed and applied to the earth's atmosphere. The motions are driven by radiative cooling, conduction of heat from the surface and applied heat sources. The applied heat sources are meant to represent the zonally averaged effect on the large scale of cumulus convection. Frictional effects included are small-scale turbulent mixing in the vertical, represented by eddy viscosity, and “cumulus friction.” The model results show that cumulus heating and friction drive a meridional circulation comparable to the observed. Detrainment of tall cumulus leads to a horizontal temperature gradient reversal near the tropical tropopause, as is observed. Sea surface temperature gradients are shown to drive a significant meridional circulation below 800 mb. If the cumulus precipitation is proportional to the moisture convergence in the lower atmospheric layers, the moisture convergence produced by the mass circulation driven by sea surface temperature gradients will produce an ITCZ near the latitude of maximum sea surface temperature. Preference for a certain latitude of frictional convergence due to upper level heating (CISK) could alter this conclusion, but it is shown that the most unstable CISK perturbation occurs at the equator.

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