Using temporal variability to improve spatial mapping with application to satellite data
The National Aeronautics and Space Administration (NASA) has a remote-sensing program with a large array of satellites whose mission is earth-system science. To carry out this mission. NASA produces data at various levels; level-2 data have been calibrated to the satellite's footprint at high temporal resolution, although there is often a lot of missing data. Level-3 data are produced on a regular latitude longitude grid over the whole globe at a coarser spatial and temporal resolution (such as a clay, a month, or a repeat-cycle of the satellite), and there are still missing data. This article demonstrates that spatio-temporal statistical models can be made operational and provide a way to estimate level-3 values over the whole grid and attach to each value a measure of its uncertainty. Specifically, a hierarchical statistical model is presented that includes a spatio-temporal random effects (STRE) model as a dynamical component and a temporally independent spatial component for the tine-scale variation. Optimal spatio-temporal predictions and their mean squared prediction errors are derived in terms of a fixed-dimensional Kalman filter. The predictions provide estimates of missing values and filter out unwanted noise. The resulting fixed-rank filter is scalable, in that it can handle very large data sets. Its functionality relies on estimation of the model's parameters, which is presented in detail. It is demonstrated how both past and current remote-sensing observations on aerosol optical depth (AOD) can be combined, yielding an optimal statistical predictor of AOD on the log scale along with its prediction standard error. The Canadian Journal of Statistics 38: 271-289; 2010 (C) 2010 Statistical Society of Canada
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