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The results of measurements of the aerosol optical thickness (AOT) of the atmosphere by CIMEL Sun-sky radiometers are analysed. In arid zones, days with values of AOT not greater than 0.02 are common. In these cases, the sky radiance in backward hemisphere in the visible wavelength range is practically fully determined by the molecular scattering, which is well studied up to date. This fact opens up possibilities to estimate the errors in measuring sky radiance comparing observed and calculated data, as well as to separate them into random and systematic.