The effect of ozone on the temperature of the upper atmosphere. —II

Source abstract

Abstract A graphical method of calculating the radiative equilibrium temperature of the upper regions of the atmosphere, taking into account the variation of absorption with wave-length, has already been described in detail.* The equation of radiative equilibrium is most simply written in the form: 2 ∫0∞ KλBλT0dλ = ∫0∞ Kλ (Sλ + Eλ + Aλ) dλ, where, for any arbitrary layer, Kλ is the absorption, BλT0 is the black body radiation at temperature T0 degrees absolute, Sλ, Eλ, and Aλ are respectively the solar, terrestrial, and atmospheric radiations reaching the layer, all at wave-length λ. On account of the irregular variations of Kλ the integrations can only be performed graphically, and one cannot solve directly for the temperature. The term Aλ for any layer depends on the temperatures of all the other layers of the stratosphere, and unfortunately it is much too large to be neglected. Therefore it is evident that the process of determining the temperature distribution with height has to be one of successive approximation. On the basis of an assumed temperature distribution the terms of the equation are calculated. The total of the right-hand side then gives the energy that must be radiated by any layer. In general this is not equal to the radiation shown by the left-hand side for the assumed temperature. By calculating the left hand side for various other temperatures and plotting a curve, an estimate may be made of how near the agreement is. This serves as a guide in making a fresh assumption of the temperature distribution in order to start again. Such a process is continued until satisfactory agreement between assumed and calculated values is reached for all layers. At the end of the first paper it was concluded that, given the layer of ozone, a theoretical consideration of an assumed condition of radiative equilibrium for water vapour and ozone, under solar and terrestrial radiation, indicates the existence of a warm region above 40 km. In this paper the work is carried much further, various changes in fundamental assumptions are tested, and the effects of some varying physical conditions are calculated.