Multiple Equilibria in Radiative-Convective Atmospheres

                                   by

                            Nilton O. Renno,
                   Dept Atmospheric Sci Univ Arizona

                 JWB 335, 4:15pm  Monday, May 6, 1996
            Joint Seminar with the Department of Meteorology

                                Abstract

  A one-dimensional, radiative-convective model is used to study the
  equilibria conditions of moist atmospheres. We show that when the
  hydrologic cycle is included in the model a subcritical bifurcation
  occurs, leading to two linearly stable solutions to the
  radiative-convective equilibria. In this case, when the external
  forcing is larger than a critical value, a finite amplitude
  instability can lead to two equilibria. Furthermore, another finite
  amplitude instability can lead to a runaway greenhouse regime when the
  solar forcing is larger than a second critical value. In general,
  previous climate studies with radiative-convective models did not
  include a hydrologic cycle. Instead, the atmosphere's water vapor
  mixing ratio was diagnosed based on the climatological profile of
  relative humidity. We show that fixing the water vapor profile at the
  climatological value (in the computation of the radiation fluxes only)
  leads to a unique stable solution to the radiative-convective
  equilibria. Thus, the crucial part of the hydrologic cycle which
  allows multiple solutions is the relaxation of the assumption of a
  climatological water vapor profile. The first equilibrium corresponds
  to an optically thin atmosphere. In this regime, the system is nearly
  linear and is in a state of small dissipation. The second equilibrium
  corresponds to an optically thick atmosphere. In this second regime,
  the system is highly nonlinear and is in a state of large dissipation.
  We argue that, of the two linearly stable equilibria, one corresponds
  to the weakest heat engine while the other corresponds to the most
  powerful heat engine possible within the constraints of moist
  convection for a given forcing value. In the weakest heat engine
  regime, the bulk of the emission of radiation to space originates in
  the warm surface and low troposphere. This regime is stable to finite
  amplitude perturbations when the radiation emitted by the opaque
  version of the planet is larger than the absorbed solar radiation. In
  the most powerful heat engine regime, the bulk of the emission of
  radiation to space originates in the cold upper troposphere.

 Nilton O. Renno
 Department of Atmospheric Sciences
 The University of Arizona
 Tucson, AZ 85721

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