Multiple equilibria in radiative-convective atmospheres

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 2 linearly stable solutions to the radiative-convective equilibria. In this case, when the net forcing is larger than a critical value, two equilibria are possible. Furthermore, a 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 relative humidity 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 relative humidity profile. Our results do not apply directly to any real planet because of large uncertainties in our calculation due to the absence of clouds and the use of a one-dimensional model. The 1st equilibrium corresponds to an optically thin atmosphere. In this regime, the system is nearly linear and is in a state of small dissipation. The 2nd equilibrium corresponds to an optically thick atmosphere. In this 2nd regime, the system is highly nonlinear and is in a state of large dissipation.