The ratio of primary scattering to total scattering of sky radiance

Abstract

Recently Eschelbach has computed from theory spectral radiance values for a turbid atmosphere taking into account the effect of multiple scattering. In the present work these computational data were used to investigate the ratio of primary to total scattering. This quotient is a measure of multiple scattering because of the relation: Total Scattering (TS) is equal to Primary Scattering (PS) plus Multiple Scattering (MS), i.e. PS/TS = 100 ‐ MS/TS (%). It is discussed in which way multiple scattering in the solar almucantar depends on the solar elevation, turbidity, scattering angle, wavelength and albedo. The present work shows in which way multiple scattering is related to the optical thickness, i.e. the extinction. The accuracy of this relation lies within the tolerance of radiance measurements. The relationship found enables one to simplify a comparison between the results from experimental measurements and those from computational models, at least for primary scattering. This is advantageous insofar as numerous computational models for primary scattering are readily available. Furthermore, measurements taken at a fixed solar elevation, namely Hμ = 24°, were used to investigate in which way multiple scattering depends on the wavelength and the scattering angle as a function of 3 different turbidity coefficients and 2 different values of the albedo. This was done with and without accounting for aerosol absorption in the sun's vertical and in the solar almucantar. One series of measurements of the sky radiance and the total extinction was used as an example to evaluate the above‐described method. The values compare satisfactorily with the model computations. We can show that our newly developed method enables one to draw conclusions on aerosol absorption.

A Qualitative and Quantitative Evaluation of 8 Clear Sky Models

“…This seems logical since multiple scattering is ignored in this model. This also indicates that, in the measured values, multiple scattering is responsible for one third of the sky irradiance, which seems consistent with [22] (especially the values from Table 1, for a turbidity T = 2). The RMSE between the Nishita93 model and the measurements, summed over the 17 daytimes, 81 direction samples, and the wavelengths between 360 and 720 nm, is 26.6 mW/(m 2 .sr.nm).…”