[Abridged] To simulate the kinds of observations that will eventually be obtained for exoplanets, the Deep Impact spacecraft obtained light curves of Earth at seven wavebands spanning 300-1000 nm as part of the EPOXI mission of opportunity. In this paper we analyze disc-integrated light curves, treating Earth as if it were an exoplanet, to determine if we can detect the presence of oceans and continents. We present two observations each spanning one day, taken at gibbous phases. The rotation of the planet leads to diurnal albedo variations of 15-30%, with the largest relative changes occuring at the reddest wavelengths. To characterize these variations in an unbiased manner we carry out a principal component analysis of the multi-band light curves; this analysis reveals that 98% of the diurnal color changes of Earth are due to only 2 dominant eigencolors. We use the time-variations of these two eigencolors to construct longitudinal maps of the Earth, treating it as a non-uniform Lambert sphere. We find that the spectral and spatial distributions of the eigencolors correspond to cloud-free continents and oceans; this despite the fact that our observations were taken on days with typical cloud cover. We also find that the near-infrared wavebands are particularly useful in distinguishing between land and water. Based on this experiment we conclude that it should be possible to infer the existence of water oceans on exoplanets with time-resolved broadband observations taken by a large space-based coronagraphic telescope.
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