An algorithm for estimating biologically active UV irradiance from satellite measurements of ozone and reflectivity is presented. In contrast to previous work, this technique treats bulk radiative properties of clouds explicitly, assuming that clouds are reflecting surfaces. This work addresses the following issue: If clouds are characterized as simple reflecting surfaces of a specified albedo at a specified altitude covering a fraction of the sky, how precisely can surface UV irradiance be determined? To address this issue, an Eddington radiative transfer model is used to calculate not only ground level irradiance but also an estimate of the backscattered radiance in the nadir direction using the formal solution to the radiative transfer equation. While this model does not simulate detailed angular distributions of radiation scattered off clouds, it is found that this model retrieves average measured biologically active surface UV irradiance around solar noon quite well and that different combinations of parameters yield strikingly similar estimates of surface UV irradiance. The model is tested using four years of continuous-scan SBUV data and Robertson-Berger meter data for nine cities.