Finding large-scale spatial trends in massive, global, environmental datasets
by
Noel Cressie
Ohio State University
Coauthors: Gardar Johannesson (Ohio State University)

As technology progresses, the availability of massive environmental data with global spatial coverage has become quite common. An example of such data is Total Column Ozone (TCO) remotely sensed from a satellite. In their raw form, these data are often spatially (and temporally) dense, but irregular. However, for practical use, the data are typically aggregated on a space-time grid at a given resolution. The resolution of the spatial grid that covers the entire globe needs to be sufficiently fine to be of use in answering a large variety of environmental questions, but there is a practical drawback of creating massive datasets that can be difficult to manage. The problem considered here is one of detecting large-scale spatial trend at a given time point (actually, in a given time interval). We propose a sequential aggregation method, producing different levels of coarser (spatial) resolution data and, at the same time, preserving both the local information content and the locations of the raw data. Each dataset of coarser resolution is used to estimate the large-scale trend in the data. In estimating the large-scale trend, we consider different parameterizations of a smooth spatial trend on the sphere, all linear in the data and satisfying the topological constraints imposed by the sphere. These parameterizations include spherical harmonics, tensor products of splines, and a spatial-covariance-based method. Each trend type is fitted to coarser resolution data and the fit is used to predict at the finest resolution, where comparison can be made to the original fine-resolution data. Results are obtained on the relative losses incurred by using different trend types and coarser-resolution data.

Date received: January 23, 2002