Many large-scale environmental data bases have been produced in recent years for the purpose of knowledge discovery related to processes such as greenhouse gas cycling, large scale hydrology etc. These data bases typically extend over a period of 20 to 50 years and over large spatial domains, such as continents, hemispheres, or even the entire global terrestrial domain. The possible existence of (temporal) trends is one of the primary topics of interest to environmental scientists. The standard approach is to estimate trends separately at each location and to generate a spatial plot of the results. However statistical power of detecting significant trends is reduced by the fact that this procedure ignores similarities between locations that are at close proximity of each other. Spatial statistics approaches have not been successfully applied in this setting partly due to the sheer size of the data involved.
We propose to utilize a formulation of the spatial Gaussian conditional autoregression (CAR) as introduced by (Pettitt et al., 2000) and to extend it for local trend estimation in the spatial temporal setting. This model is suitable for spatially irregularly sampled data since it posits a weight function that represents the degree of spatial interaction. Furthermore it allows for an elegant calculation of the determinant of the precision matrix, which greatly speeds up any iterative estimation procedure. To this end we examine a Markov Chain Monte Carlo (MCMC) implementation of this model. We achieve additional computational efficiency by initial orthonormal data transformation within the spatial domain. This guarantees that only fast and elementary calculations are needed for each step within the Markov chain.
The presented model and computational approaches are illustrated by an application from hydrology. We describe the estimation of trends in precipitation and/or temperature data bases of pan-arctic drainage basins. The hydrology of the pan-arctic is believed to be an important indicator for shifts in global climate.