This paper extends the theoretical analysis of the estimation of the surface UV irradiance from satellite ozone and reflectivity data from a clear-sky case to a cloudy atmosphere and snow-covered surface. Two methods are compared for the estimation of cloud-transmission factor CT, the ratio of cloudy to clear-sky surface irradiance: (1) the Lambert equivalent reflectivity (LER) method and (2) a method based on radiative transfer calculations for a homogeneous (plane parallel) cloud embedded into a molecular atmosphere with ozone absorption. The satellite-derived CT from the NASA Total Ozone Mapping Spectrometer (TOMS) is compared with ground-based CT estimations from the Canadian network of Brewer spectrometers for the period 1989--1998. For snow-free conditions the TOMS derived CT at 324 nm approximately agrees with Brewer data with a correlation coefficient of ~0.9 and a standard deviation of ~0.1. The key source of uncertainty is the different size of the TOMS FOV (~100 km field of view) and the much smaller ground instrument FOV. As expected, the standard deviations of weekly and monthly CT averages were smaller than for daily values. The plane-parallel cloud method produces a systematic CT bias relative to the Brewer data (+7% at low solar zenith angles to -10% at large solar zenith angles.) The TOMS algorithm can properly account for conservatively scattering clouds and snow/ice if the regional snow albedo RS is known from outside data. Since RS varies on a daily basis, using a climatology will result in additional error in the satellite-estimated CT. The CT error has the same sign as the RS error and increases over highly reflecting surfaces. Finally, clouds polluted with absorbing aerosols transmit less radiation to the ground than conservative clouds for the same satellite reflectance and flatten spectral dependence of CT. Both effects reduce CT compared to that estimated assuming conservative cloud scattering. The error increases if polluted clouds are over snow. ¿ 2001 American Geophysical Union