The theoretical calculations of the distribution of photochemically‐formed ozone in the atmosphere

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Abstract
The paper consists of a calculation of the distribution of ozone with height as it would be in an undisturbed photochemical steady state under the influence of solar radiation considered as that of a black body at a temperature of 6000°K. An expression is derived for the number of ozone molecules as a function of height, in terms respectively of a numerical constant, the concentration of oxygen and of total air molecules as a function of height, and the number of quanta absorbed by oxygen and by ozone as a function of height. The latter two quantities are in principle integrals over frequency‐ranges, and they are evaluated by summing over finite frequency‐strips. Moreover, the number of quanta absorbed by ozone at any height depends of course upon the concentration of the ozone itself. The complete expression is, therefore, evaluated by the method of successive approximations for a series of heights, the available intensity of the radiation absorbed by ozone being derived as the remainder from the last greater height. The ozone concentration, once evaluated for a particular height, is assumed constant over the interval of which this is the midpoint in evaluating the depletion of the radiation in this interval; then, by deduction, the remaining radiation available for the next lower interval is determined. The numerical constant is perhaps best looked upon as evaluated from the known total atmospheric ozone path, though its order of magnitude is indicated by the facts of experimental photochemistry. In this way a distribution of ozone is found which resembles rather closely that which from observation is now known approximately to obtain in the atmosphere. The values of the absorption‐coefficient of ozone and oxygen in the region where the two absorptions meet, that is, about 2200Å, prove to be very important, two possible sets of values being used in this narrow interval for illustration.

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