Using a physically based, high-resolution spectral radiation model, instantaneous clear-sky beam irradiance is parameterized with simple atmospheric functions and polynomial expansions of the sine of the solar elevation angle. This construction permits analytic integration to obtain an expression for estimating potential daily clear-sky beam irradiation. By forcing the model with monthly-averaged climate data, turbidity is estimated at an array of weather-station locations in South Africa. Findings include new estimates of turbidity trends and variability over South Africa. The methodology makes use of available climate data, is not restricted to clear-sky conditions, and can be applied at any location where the requisite data are available.