The spectral properties of outdoor illumination functions can vary significantly due to atmospheric conditions and scene geometry. We show using a statistical analysis of a comprehensive physical model that the variation in outdoor illumination functions over both the visible range (0.33µm-0.7µm) and the visible/near-infrared range (0.4µm-2.5µm) can be represented accurately by use of seven-dimensional linear models. The physical model includes solar and scattered radiation as well as the effects of atmospheric gases and aerosols. The MODTRAN 3.5 code was employed for computing radiative transfer aspects of the model. We show that the new model has strong agreement over the visible wavelengths with the empirical study of Judd et al. [J. Opt. Soc. Am. (54)1031 (1964)]. We also demonstrate the accuracy of the model over the 0.4µm-2.5µm spectral range using measured outdoor illumination functions.