Thermal Equilibrium of the Atmosphere with a Given Distribution of Relative Humidity

Radiative convective equilibrium of the atmosphere with a given distribution of relative humidity is computed as the asymptotic state of an initial value problem. The results show that it takes almost twice as long to reach the state of radiative convective equilibrium for the atmosphere with a given distribution of relative humidity than for the atmosphere with a given distribution of absolute humidity. Also, the surface equilibrium temperature of the former is almost twice as sensitive to change of various factors such as solar constant, CO2 content, O3 content, and cloudiness, than that of the latter, due to the adjustment of water vapor content to the temperature variation of the atmosphere. According to our estimate, a doubling of the CO2 content in the atmosphere has the effect of raising the temperature of the atmosphere (whose relative humidity is fixed) by about 2C. Our model does not have the extreme sensitivity of atmospheric temperature to changes of CO2 content which was adduced by Möller.