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

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

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Abstract

The linearized model presented in Part I of this study (Schneider and Lindzen, 1977) is extended to include the nonlinear advections of angular momentum by the meridional circulation. A crude cumulus heating parameterization is also introduced in certain calculations to simulate the effect of an internal hydrological cycle. The nonlinear (steady-state) boundary value problem is solved by means of an iterative scheme. The results from the nonlinear model are viewed as a reasonable basic state whose stability may be studied. It is seen that this basic state is similar in many respects to the observed zonally averaged general circulation. Surface easterlies and westerlies appear at the correct latitudes with the right magnitudes, the tropical Hadley cell has near the observed mass flux and geometry, with an ITCZ forming at the sea surface temperature maximum, mid-latitude Ferrel cells appear (although fluxes by baroclinic eddies are not modeled) with somewhat less mass flux than the observations indicate and the tropical tropospheric temperature fields are close to the observed. The main departures of the model results from the observations is in the excessive magnitude of the upper level zonal winds in middle latitudes. This difference is ascribed to the neglect of fluxes by large-scale eddies (baroclinic, barotropic and topographic) in the model. The similarity of the observed surface winds to those computed in the model is in opposition to some classical pictures [such as that of Jeffreys (1926)] in which the mid-latitude westerlies are maintained by poleward transports of zonal momentum by large-scale eddies. Results from the numerical model are used to develop arguments showing that the horizontal scale of the tropical Hadley circulation is a suitably defined global Rossby radius of deformation, and that the vertical scale cf the Hadley circulation and the tropical static stability can be adequately approximated by simple one-dimensional radiative-convective models (see the Appendix).

Abstract

The linearized model presented in Part I of this study (Schneider and Lindzen, 1977) is extended to include the nonlinear advections of angular momentum by the meridional circulation. A crude cumulus heating parameterization is also introduced in certain calculations to simulate the effect of an internal hydrological cycle. The nonlinear (steady-state) boundary value problem is solved by means of an iterative scheme. The results from the nonlinear model are viewed as a reasonable basic state whose stability may be studied. It is seen that this basic state is similar in many respects to the observed zonally averaged general circulation. Surface easterlies and westerlies appear at the correct latitudes with the right magnitudes, the tropical Hadley cell has near the observed mass flux and geometry, with an ITCZ forming at the sea surface temperature maximum, mid-latitude Ferrel cells appear (although fluxes by baroclinic eddies are not modeled) with somewhat less mass flux than the observations indicate and the tropical tropospheric temperature fields are close to the observed. The main departures of the model results from the observations is in the excessive magnitude of the upper level zonal winds in middle latitudes. This difference is ascribed to the neglect of fluxes by large-scale eddies (baroclinic, barotropic and topographic) in the model. The similarity of the observed surface winds to those computed in the model is in opposition to some classical pictures [such as that of Jeffreys (1926)] in which the mid-latitude westerlies are maintained by poleward transports of zonal momentum by large-scale eddies. Results from the numerical model are used to develop arguments showing that the horizontal scale of the tropical Hadley circulation is a suitably defined global Rossby radius of deformation, and that the vertical scale cf the Hadley circulation and the tropical static stability can be adequately approximated by simple one-dimensional radiative-convective models (see the Appendix).

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