Predictive inference for big, spatial, non-Gaussian data: MODIS cloud data and its change-of-support

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 use the reduced-rank spatial random effects (SRE) model in a statistical

analysis of cloud-mask data from NASA’s Moderate Resolution Imaging Spectroradiometer

(MODIS) instrument on board NASA’s Terra satellite. Parameterisations of cloud processes

are the biggest source of uncertainty and sensitivity in different climate models’ future

projections of Earth’s climate. An accurate quantification of the spatial distribution 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. Here we give a hierarchical spatial-statistical modelling approach for a very large

spatial dataset of 2.75 million pixels, corresponding to a granule of MODIS cloud-mask

data, and 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 clear-sky

probability that makes use of the SRE model, EM-estimation, and optimal (empirical Bayes)

spatial prediction of the clear-sky-probability process. Measures of prediction uncertainty

are also given.