  [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.
