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Remote sensing of the earth with satellites yields datasets that can be massive in size, nonstationary in space, and non-Gaussian in distribution. To overcome computational challenges, we make use of the reduced-rank Spatial Random Effec ts (SRE) model in our statistical analysis of cloud mask data from NASA’s Moderate Resolut ion Imaging Spectroradiometer (MODIS) instrument on board NASA’s Terra satellite, launch ed in December 1999. Clouds are the biggest source of uncertainty in future projections of Earth’s climate and explain the wide spread of climate sensitivity calculated by climate models due to their inherent differences in parameterized cloud processes. An accurate quantification of the spatial distributions of clouds, as well as a rigorously estimated pixel-scale clear -sky-probability process, is needed to establish reliable estimates of cloud-distributional changes and trends caused by climate change. In this article, we give a hierarchical spatial statistical modeling approach for a very large spatial dataset of size 2 . 75 million pixels, corresponding to a granule of the MODIS cloud mask, and then we use spatial change-of-support relationships to estimate cloud fraction at coarser resolutions. Our model is non-Gaussian; it postulates a hidden process for the prob- ability of a clear sky that makes use of the SRE model, EM estimation, and optimal (empirical Bayes) spatial prediction of the clear-sky-probability process. Measures of uncertainty of the resulting optimal map are also given.