A Study on the “Runaway Greenhouse Effect” with a One-Dimensional Radiative–Convective Equilibrium Model

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  • 1 Space Development Division, NEC Corporation, Midori, Yokohama, Japan
  • | 2 Department of Earth and Planetary Physics, Faculty of Science, University of Tokyo, Bunkyo, Tokyo, Japan
  • | 3 Water Research Institute, Nagoya University, Furou-cho, Chikusa, Nagoya, Japan
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Abstract

A simple one-dimensional radiative–convective equilibrium model is used to investigate the relationship between the surface temperature and the outgoing infrared radiation at the top of the atmosphere. The model atmosphere has a gray infrared absorption coefficient and is composed of a radiative equilibrium stratosphere and a moist adiabat troposphere.

An upper limit of the outgoing infrared radiation is found to exist. The existence of the upper limit is characterized by the radiation limits that appear when the optical depth of the entire atmosphere becomes sufficiently deep and the temperature structure around the levels where the optical depth is about unity approaches a fixed profile. This appearance of an upper limit differs from that found by Komabayashi and Ingersoll, which is obtained from the constraint of the stratospheric radiation balance.

As one of those radiation limits, the outgoing infrared radiation has an asymptotic limit as the surface temperature increases. This is caused by the tropospheric structure approaching the water vapor saturation curve. It is considered that the asymptotic limits appearing in the radiatively and thermodynamically more complicated models utilized by Abe and Matsui and Kasting are corresponding to this asymptotic limit indicated in our model.

Abstract

A simple one-dimensional radiative–convective equilibrium model is used to investigate the relationship between the surface temperature and the outgoing infrared radiation at the top of the atmosphere. The model atmosphere has a gray infrared absorption coefficient and is composed of a radiative equilibrium stratosphere and a moist adiabat troposphere.

An upper limit of the outgoing infrared radiation is found to exist. The existence of the upper limit is characterized by the radiation limits that appear when the optical depth of the entire atmosphere becomes sufficiently deep and the temperature structure around the levels where the optical depth is about unity approaches a fixed profile. This appearance of an upper limit differs from that found by Komabayashi and Ingersoll, which is obtained from the constraint of the stratospheric radiation balance.

As one of those radiation limits, the outgoing infrared radiation has an asymptotic limit as the surface temperature increases. This is caused by the tropospheric structure approaching the water vapor saturation curve. It is considered that the asymptotic limits appearing in the radiatively and thermodynamically more complicated models utilized by Abe and Matsui and Kasting are corresponding to this asymptotic limit indicated in our model.

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