Guest essay by Saburo Nonogaki
It has been said that the averaged earth surface temperature would be 255K if no green-house-effect(g-h-e) gases were contained in the atmosphere, and is 288Ｋ at present where the atmosphere contains g-h-e gases. The estimation of 255K is based on the earth’s long-term radiative equilibrium and Stefan-Boltzmann’s law which states that the total amount of radiative energy from a black body at absolute temperature T is proportional to T 4.
As the earth’s long-term radiative equilibrium will be reached also in the case where the atmosphere contains g-h-e gases, we obtain the following equation under the condition that the long-term input energy from the sun remains constant.
(1–a )T 4 = constant (1)
Here, T is the averaged earth surface absolute temperature and a the ratio of radiative energy retained by the g-h-e gases in the atmosphere to the total radiative energy. By replacing T in equation (1) with 255Ｋ and 288Ｋ, we obtain the following equation.
(1–0)×2554 = (1–a )×2884 (2)
From equation (2), we obtain the value of a as follows.
a = 0.385 (3)
Jack Barrett* has reported that, in the case of 100m-thick atmosphere, the doubling of pre-industrial concentration of CO2 will result in the increase in infrared absorption by g-h-e gases by 0.5%. The reason why the increase is so small is based mainly on the saturation tendency of infrared absorption by CO2. As the re-emission of a part of energy absorbed by g-h-e gases into the universe takes place, the increase in a is less than 0.5%. According to equations (1), (2) and (3), the increase in a by less than 0.5% results in the increase in T by less than 0.6K.
As the actual thickness of the atmosphere is about 8000m at ordinary atmospheric pressure, the saturation of infrared absorption by CO2 will be almost complete and the actual increase in a caused by the doubling of CO2 concentration must be much less than 0.5% and the resulted increase in T must be also actually much less than 0.6K.