  Reflected light photometry of terrestrial exoplanets could reveal the
presence of oceans and continents, hence placing direct constraints on the
current and long-term habitability of these worlds. Inferring the albedo map of
a planet from its observed light curve is challenging because different maps
may yield indistinguishable light curves. This degeneracy is aggravated by
changing clouds. It has previously been suggested that disk-integrated
photometry spanning multiple days could be combined to obtain a cloud-free
surface map of an exoplanet. We demonstrate this technique as part of a
Bayesian retrieval by simultaneously fitting for the fixed surface map of a
planet and the time-variable overlying clouds. We test this approach on
synthetic data then apply it to real disk-integrated observations of the Earth.
We find that eight days of continuous synthetic observations are sufficient to
reconstruct a faithful low resolution surface albedo map, without needing to
make assumptions about cloud physics. For lightcurves with negligible
photometric uncertainties, the minimal top-of-atmosphere albedo at a location
is a good estimate of its surface albedo. When applied to observations from the
Earth Polychromating Imaging Camera aboard the DSCOVR spacecraft, our approach
removes only a small fraction of clouds. We attribute this difficulty to the
full-phase geometry of observations combined with the short correlation length
for Earth clouds. For exoplanets with Earth-like climatology, it may be hard to
do much better than a cloud-averaged map. We surmise that cloud removal will be
most successful for exoplanets imaged near quarter phase that harbour large
cloud systems.
