The effects of the cloudiness and satellite-based ozone measurements on erythemally effective ultraviolet (EUV) radiation were examined using a non-linear regression model. Instead of the widely used ozone transmissivity exponential function, we proposed a new approach based on a quantum transmission model using hyperbolic attenuation of the EUV radiation. The radiation data were collected at the Czech Johann Gregor Mendel Station, James Ross Island, Antarctica (63° 48′ S, 57° 53′ W), between 14 March 2007 and 3 March 2009. The total ozone content and effective surface reflectivity at 360 nm were obtained from the Ozone Monitoring Instrument on board the EOS-Aura spacecraft for the geographical coordinates of the J. G. Mendel Station. The model predicted 98.6% variability of the EUV radiation. The residuals between the measured and predicted EUV radiation intensities were evaluated separately for the ranges of solar elevation angle, total ozone content and surface reflectivity. The results of this study were compared to previous findings where the influence of ground-based and satellite-based ozone measurements and model usefulness was discussed.