The modification of clear-sky global and diffuse irradiances and the direct-to-diffuse irradiance ratio by the aerosol single scattering albedo, ω, as a function of aerosol optical depth, τa, and solar zenith angle (SZA) is investigated using radiative-transfer model calculations. The model-derived relations are combined with UV irradiances at the surface and the aerosol optical depth measured with a Brewer MkIII spectroradiometer, with the aim to develop and test an indirect method of estimating an effective single scattering albedo. The uncertainties introduced from different sources are quantitatively discussed in order to determine the overall uncertainty of the method. The overall accuracy in determining ω indirectly depends strongly on the radiation quantity used and the amount of aerosols, increasing the uncertainty of the method in situations with τa at 340 nm below 0.2. From the three radiation quantities, the direct-to-diffuse irradiance ratio provides the highest accuracy in the estimation of the effective ω. As an example, the effective ω is determined for 2 days with different aerosol loadings and composition. Finally, 5 years of measurements of global irradiance and τa under cloud-free conditions are analysed in order to estimate the range of variation of the effective ω at Thessaloniki, Greece. For τa at 340 nm larger than 0.8, ω ranges between 0.85 and 0.99, while for lower-aerosol optical depths the derived effective ω covers the entire range from 0.64 to 0.99.