A Numerical Diagnostic Model of the Zonally Averaged Circulation in Isentropic Coordinates

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  • 1 Department of Meteorology and Center for Climatic Research, University of Wisconsin, Madison 53706
  • 2 Department of Meteorology and Space Science and Engineering Center, University of Wisconsin. Madison 53706
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Abstract

In the linear theory of the isentropic zonally averaged circulation (Gallimore and Johnson, 1981), stable meridional circulations within the circumpolar vortex are forced by larger scale diabatic beating and angular momentum torques. The linear theory, however, could not describe important nonlinear interactions between the forcing of meridional circulations and the maintenance of the circumpolar vortex nor could the quasi-steady balance be ascertained.

In this study, an isentropic numerical model is developed to investigate the forcing of the meridional circulation and its role and the role of angular momentum torques in maintaining the circumpolar vortex. The model is based on a set of isentropic zonally averaged equations applied to the Northern Hemisphere. The horizontal resolution is 5° of latitude while nine equally spaced isentropic levels are used for vertical resolution. The basic forcing of the model is diabatic heating and zonal pressure and friction torques. The distribution of diabatic heating is prescribed from observational results while the meridional distribution of the zonal pressure torque is determined from a specified separation of the zonally averaged meridional mass transport into geostrophic and ageostrophic modes. The friction torque is internally time dependent. Eddy transport terms are not included and a fixed surface potential temperature is assumed at the lower boundary. The zonally averaged circulation and its forcing were studied in three experiments in which the meridional distribution of the diabatic heating and the pressure torque were varied. After 30 days of numerical simulation a slowly varying state was attained.

The simulation determined a realistic isentropic Hadley circulation spanning the Northern Hemisphere and a zonal wind structure with an upper tropospheric subtropical jet. The structure of the model's zonally averaged meridional circulation is consistent with observations and with the results of the linear theory, i.e., the vertical branches of the direct, stable circulation are forced through tropical heating and polar cooling while the meridional branches are forced by upper tropospheric sources and lower tropospheric sinks of pressure and friction torques. The zonal vortex is maintained through the balance of angular momentum torques and the convergence of the absolute angular momentum transport within the meridional circulation. The results further indicate that non-steady, freely convecting meridional circulations do not occur for realistic forcing.

A comparison of the results in which the heating is varied reveals that the changes in the intensity of the meridional circulation depend on the variations of the meridional heating distribution. Since changes occur in the meridional momentum transport, structural changes in the zonal momentum and torques are also produced. With the same heating, changes in the zonal vortex occur in conjunction with compensating changes in the meridional distribution of the zonal pressure and time-dependent friction torques while the intensity of the total meridional circulation remains independent of this factor.

Abstract

In the linear theory of the isentropic zonally averaged circulation (Gallimore and Johnson, 1981), stable meridional circulations within the circumpolar vortex are forced by larger scale diabatic beating and angular momentum torques. The linear theory, however, could not describe important nonlinear interactions between the forcing of meridional circulations and the maintenance of the circumpolar vortex nor could the quasi-steady balance be ascertained.

In this study, an isentropic numerical model is developed to investigate the forcing of the meridional circulation and its role and the role of angular momentum torques in maintaining the circumpolar vortex. The model is based on a set of isentropic zonally averaged equations applied to the Northern Hemisphere. The horizontal resolution is 5° of latitude while nine equally spaced isentropic levels are used for vertical resolution. The basic forcing of the model is diabatic heating and zonal pressure and friction torques. The distribution of diabatic heating is prescribed from observational results while the meridional distribution of the zonal pressure torque is determined from a specified separation of the zonally averaged meridional mass transport into geostrophic and ageostrophic modes. The friction torque is internally time dependent. Eddy transport terms are not included and a fixed surface potential temperature is assumed at the lower boundary. The zonally averaged circulation and its forcing were studied in three experiments in which the meridional distribution of the diabatic heating and the pressure torque were varied. After 30 days of numerical simulation a slowly varying state was attained.

The simulation determined a realistic isentropic Hadley circulation spanning the Northern Hemisphere and a zonal wind structure with an upper tropospheric subtropical jet. The structure of the model's zonally averaged meridional circulation is consistent with observations and with the results of the linear theory, i.e., the vertical branches of the direct, stable circulation are forced through tropical heating and polar cooling while the meridional branches are forced by upper tropospheric sources and lower tropospheric sinks of pressure and friction torques. The zonal vortex is maintained through the balance of angular momentum torques and the convergence of the absolute angular momentum transport within the meridional circulation. The results further indicate that non-steady, freely convecting meridional circulations do not occur for realistic forcing.

A comparison of the results in which the heating is varied reveals that the changes in the intensity of the meridional circulation depend on the variations of the meridional heating distribution. Since changes occur in the meridional momentum transport, structural changes in the zonal momentum and torques are also produced. With the same heating, changes in the zonal vortex occur in conjunction with compensating changes in the meridional distribution of the zonal pressure and time-dependent friction torques while the intensity of the total meridional circulation remains independent of this factor.

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