A regression strategy for analyzing environmental data generated by spatio-temporal processes

Highly complex spatio-temporal environmental data sets are becoming common in ecology because of the increasing use of large-scale simulation models and automated data collection devices. The spatial and temporal dimensions present real and difficult challenges for the interpretation of these data. A particularly difficult problem is that the relationship among variables can vary in dramatically in response to environmental variation; consequently, a single model may not provide adequate fit. The temporal dimension presents both opportunities for improved prediction because explanatory variables sometimes exert delayed effects on response variables, and problems because variables are often serially correlated. This article presents a regression strategy for accommodating these problems and exploiting serial correlation. The strategy is illustrated by a case study of simulated net primary production (SNPP) that compares ocean-atmosphere indices to terrestrial climate variables as predictors of SNPP across the conterminous United States, and describes spatial variation in the relative importance of terrestrial climate variables towards predicting SNPP. We found that the relationship between ocean-atmosphere indices and SNPP varies substantially over the United States, and that there is evidence of a substantive link only in the western portions of the United States. Evidence of multi-year delays in the effect of terrestrial climate effects on SNPP were also found.