Remote sensing of the earth by satellites yields datasets that can be massive in size. To overcome computational challenges, we make use of the reduced-rank Spatial Random Effects (SRE) model in our statistical analysis of cloud mask data from NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) instrument on board NASA's Terra satellite, launched in December 1999. A set of retrieval algorithms has been developed by members of the MODIS atmospheric team for detecting clouds. Clouds play an important role in climate studies, and hence an accurate quantification of the the spatial distribution of clouds is necessary. In this paper, we build a statistical model for the underlying clear-sky-probability (or conversely, the cloud-probability) process, and we quantify the uncertainty in our predictions. We consider a hierarchical statistical model for analyzing the cloud data, where we postulate a hidden process for the probability of clear sky that makes use of the SRE model. Its advantages are considerable: It can represent many types of spatial behavior, it permits fast computations when datasets are very large, and it has attractive change-of-support properties.