﻿896 On Radiative Equilibrium. 



of the change of height of the tropopause no longer holds, 

 at least without further examination. 



In view of these considerations, it seems on the whole 

 tenable that the outward radiation from the equator is 

 less than from higher latitudes, and that the variation of 

 stratospheric temperature must be principally due to the 

 general circulation of the air in the convective region. 

 (The connexion between the variation of temperature of 

 the stratosphere and the observed uniformity of pressure 

 at 20 km. over the whole earth has been pointed out by 

 W. H. Dines *.) The higher upper-air temperatures of 

 high latitudes may still be helped by the increased direct 

 absorption there, in the way we have seen. 



§ 15. Summary. — It is shown that if the atmosphere is 

 divided into two shells — a lower one (the troposphere) in 

 convective equilibrium, and an isothermal one (the strato- 

 sphere), — then the stratosphere cannot be in strict radiative 

 equilibrium unless its optical thickness for low-temperature 

 radiation is zero, even if it is in radiative equilibrium as a 

 whole. The only exception is when the lower region is also 

 in radiative equilibrium as a whole and when, in addition, a 

 special relation (cosa = -Jn, or cos\ — n/^/2 when rotation 

 is allowed for) exists between the angle of incidence of the 

 solar radiation and the ratio of the coefficients of absorption 

 of solar and terrestrial radiation. The theory of atmospheres 

 in radiative equilibrium subject to insolation is discussed in 

 detail for various cases, including the dependence of the 

 temperature distribution on the angle of incidence of the 

 solar radiation. An integral equation for the temperature 

 is obtained. Comparison is made with Emden's work. 

 From an application of the results to the earth's atmosphere 

 it is inferred that the variation of the temperature of the 

 stratosphere with latitude cannot be accounted for on 

 radiation principles unless the total radiation of the earth 

 to space is greater in high latitudes than in low latitudes. 

 This is probably the case, and the observed distribution 

 of stratospheric temperature is probably connected with 

 the general circulation of the air ; however, the increased 

 direct absorption of solar energy in the upper levels in 

 high latitudes must have some effect. 



It is intended to insist principally on the general theory, 

 and the applications are only made tentatively. 



July 17, 1922. 



* Geophysical Memoirs, No. 13, p. 71 (1919). 



4 



