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This paper presents multi-filter measurements of the night sky brightness atthe South African Astronomical Observatory (SAAO) in Sutherland in the presenceof a bright moon. The observations cover a wide range of sky directions, lunarphases and lunar positions. A revised simplified scattering model is developedfor estimating the sky brightness due to moonlight that more accuratelyreflects the atmospheric extinction of the lunar beam compared to modelsfrequently applied in astronomical studies. Contributions to night skybrightness due to sources other than moonlight are quantified and subtractedfrom the total sky background radiation to determine the spectral intensity andangular distribution of scattered moonlight. The atmospheric scattering phasefunction is then derived by comparing the sky brightening to the strength ofthe incoming lunar beam, estimated using a novel approach. The phase functionis shown to be an excellent match to the combined theoretical Rayleigh and Miescattering functions, the latter with a Henyey--Greenstein form instead of theexponential angular relationship often used in previous studies. Wheredeviations between measured and model sky brightness are evident in some bandsthese are explained by contributions from multiple scattering or airglow, andare quantified accordingly. The model constitutes an effective tool to predictsky brightness at SAAO in optical photometric bands, especially with a brightmoon present. The methodology can also be readily be adapted for use at otherastronomical sites. The paper furthermore presents $UBV(RI)_c$ andStr{\"o}mgren photometry for 49 stars, most with no prior such data.

A revised simplified scattering model for the moonlit sky brightness profile based on photometry at SAAO