We determine the value of solar constant at which the runaway greenhouse state realize in three-dimensional gray atmosphere and perform the numerical integration of the runaway greenhouse state by use of simplified general circulation model(GCM). The radiative active gas is only water vapor. The vapor is transparent to solar radiation and has a gray infrared absorption coefficient. This model is equivalent to the system of Nakajima et al. (1992) which defined the runaway greenhouse state except for including the atmospheric dynamics.
Under the various values of solar constant, integrations of about 1000 day are performed. The atmospheric thermal structure reaches statistical equilibrium state in about 500 day when the value of solar constant is smaller than 1600 W/m2. However, the atmosphere cannot reach equilibrium states and thermally "runaway" under the solar constant whose value is larger than 1600 W/m2. Outgoing longwave radiation (OLR) cannot balance to the incident energy flux. The vapor content and the amount of the atmosphere continue to increase and atmospheric temperature and ground temperature continue to increase.
The pole-equator contrast of distributions of vapor and temperature
decrease with increasing the value of solar constant. As a result of
homogenization of the radiation structure, the value of solar constant
when "thermally runaway" state realize corresponds to the
upper limit of the outgoing radiation of the model of Nakajima et
al. (1992) with the constant value of relative humidity, 60%.
This value of relative humidity is the mean value in troposphere of
three-dimensional calculation. The "thermally runaway"
states realized when the value of the solar constant is larger than
1600 W/m2 correspond to the the state in which
one-dimensional model has no equilibrium solution, that is, runaway
greenhouse state.