Fast, resolution-consistent spatial prediction of global processes from satellite data

Polar orbiting satellites remotely sense the earth and its atmosphere, producing datasets that give daily global coverage. For any given day, the data are many and measured at spatially irregular locations. Our goal in this article is to predict values that are spatially regular at different resolutions; such values are often used as input to general circulation models (GCMs) and the like. Not only do we wish to predict optimally, but because data acquisition is relentless, our algorithm must also process the data very rapidly. This article applies a multiresolution autoregressive tree-structured model, and presents a new statistical prediction methodology that is resolution consistent (i.e., preserves "mass balance" across resolutions) and computes spatial predictions and prediction (co)variances extremely fast. Data from the Total Ozone Mapping Spectrometer (TOMS) instrument, on the Nimbus-7 satellite, are used for illustration.