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An experiment has been proposed to measure the zenith sky intensity and directly transmitted solar flux density at several wavelengths in the near ultraviolet from an aircraft platform located at about 15 km. From these measurements, the vertical distribution of ozone above the platform is to be inferred, by inversion of the equation of radiative transfer. The present study is an analysis of the errors to be expected in a real experiment, due to atmospheric fluctuations, numerical procedures, and ignorance of various parameters necessary for the calculation of the intensities and fluxes to be expected. These errors are found to vary from 17% at the shorter wavelengths to about 3% at the longer wavelengths used. It is shown elsewhere (Twomey et al., 1977) that unacceptable levels of instability and non-uniqueness of results will be found if the error levels in the measurements upon which we wish to invert exceed 3%. On the basis of this, it is concluded that with the present instrumentation and the present knowledge of necessary ancillary parameters, this experiment will not be feasible.

An extension of the Chahine relaxation method (1970) for inverting the radiative transfer equation is presented. This method is superior to the original method in that it takes into account in a realistic manner the shape of the kernel function, and its extension to nonlinear systems is much more straightforward. A comparison of the new method with a matrix method due to Twomey (1965), in a problem involving inference of vertical distribution of ozone from spectroscopic measurements in the near ultraviolet, indicates that in this situation this method is stable with errors in the input data up to 4%, whereas the matrix method breaks down at these levels. The problem of non-uniqueness of the solution, which is a property of the system of equations rather than of any particular algorithm for solving them, remains, although it takes on slightly different forms for the two algorithms.

Results are reported for a field test that was aimed at acquiring a sufficient set of measurements of aerosol properties required as input for radiative-transfer calculations relevant to the earth's radiation balance. These measurements include aerosol extinction and size distributions, vertical profiles of aerosols, and radiation fluxes. Physically consistent, vertically inhomogeneous models of the aerosol characteristics of a turbid atmosphere over a desert and an agricultural region are constructed by using direct and indirect sampling techniques. These results are applied for a theoretical interpretation of airborne radiation-flux measurements. The absorption term of the complex refractive index of aerosols is estimated, a regional variation in the refractive index is noted, and the magnitude of solar-radiation absorption by aerosols and atmospheric molecules is determined.