Analyzing time-resolved disk-integrated spectral images of the Earth can provide a baseline for future exoplanet characterization. The Earth Polychromatic Imaging Camera (EPIC) onboard the Deep Space Climate Observatory (DSCOVR) provides ~5000 full-disk sunlit Earth images each year in ten wavelengths from the ultraviolet to the near-infrared. A whole-disk radiative transfer model can improve our understanding of the temporal variation of Earth's disk-integrated reflected radiance ("light curves") at different wavelengths and create a pool of possible observations of Earth-like exoplanets. We use the two-stream-exact-single-scattering line-by-line radiative transfer model to build the Earth Spectrum Simulator (ESS) and reconstruct DSCOVR/EPIC spectral observations. Atmospheric effects, such as scattering by air molecules, clouds, aerosols, and gaseous absorption, are included. Surface contributions are treated using appropriate bidirectional reflectance distribution functions. We simulate ~300 images in each channel for observations collected in 2016, with a spatial resolution of ~2000 pixels over the visible disk. ESS provides a simultaneous fit to the observed light curves, with time-averaged reflectance differences typically less than 7% and root-mean-square errors less than 1%. The only exceptions are in the oxygen absorption channels, where reflectance biases can be as large as 19.55%; this is a consequence of simplified assumptions about clouds; especially their vertical placement. We also recover principal components of the spectrophotometric light curves and correlate them with atmospheric and surface features.