The Temperature of the Lower Atmosphere of the Earth

Abstract

From the known amounts of the various gases of the atmosphere from sea level to about 20 km, from the observed light absorption coefficients of the gases and from the albedo of the earth's surface the temperature of the atmosphere in radiative equilibrium is calculated on the assumption that the sunlight is the only source of energy. The calculation is perhaps more rigorous than has hitherto been attempted, although it contains a number of approximations. The sea level temperature comes out to be about 19\ifmmode^\circ\else\textdegree\fi{} above the observed world-wide average value 287\ifmmode^\circ\else\textdegree\fi{}K, and the temperature above about 3 km falls many degrees below the observed temperatures. The temperature gradient in levels from 3 to 6 km is greater than that of convective equilibrium and hence the atmosphere would not be dynamically stable if radiation equilibrium prevailed. Therefore air currents take place to bring about convective equilibrium. Continuing the calculation it is found that only when the convective region extends to about 12 km (as is observed), with radiative equilibrium above 12 km (as is observed), does the atmosphere satisfy the conditions of dynamic stability and thermal equilibrium with the received solar energy. For this case the calculated sea level temperature is 290\ifmmode^\circ\else\textdegree\fi{}K in good agreement with the observed value 287\ifmmode^\circ\else\textdegree\fi{}K. Calculation shows that doubling or tripling the amount of the carbon dioxide of the atmosphere increases the average sea level temperature by about 4\ifmmode^\circ\else\textdegree\fi{} and 7\ifmmode^\circ\else\textdegree\fi{}K, respectively; halving or reducing to zero the carbon dioxide decreases the temperature by similar amounts. Such changes in temperature are about the same as those which occur when the earth passes from an ice age to a warm age, or vice versa. Thus the calculation indicates that the carbon dioxide theory of the ice ages, originally proposed by Tyndall, is a possible theory.