Multi-Point BME Space/Time Mapping Of Environmental Variables

Abstract

The multi-point Bayesian Maximum Entropy (BME) approach considers physical data analysis from a modern geostatistical perspective, promoting the view that a deeper understanding of a theory of knowledge is an important prerequisite for the improved mathematical modelling and mapping of spatiotemporal environmental variables. A spatiotemporal map should depend on what we know about the phenomenon it represents, as well as how we know it (i.e., how we collect and process knowledge). BME's rich theoretical basis provides guidelines for the adequate interpretation and processing of all knowledge bases available. BME is formulated in a way that preserves earlier geostatistical results, which are its limiting cases, but it also provides novel and more general results that could not be obtained within traditional geostatistics. Numerical comparisons of BME vs. simple and indicator kriging are discussed via a porosity data set and a synthetic example. 1 Spatiotemporal Mapping For a very large number of environmental problems, the required outcome of the analysis is one or more spatiotemporal maps. These maps may be the visual representation of information regarding the distribution of environmental variables in space/time (e.g., spring water solute contents; calcium, nitrate and chloride ions), usually obtained from data sets. Or, they may involve broader knowledge bases (general knowledge, analytic beliefs, mathematical models representing physical laws given some boundary/initial conditions, etc.). While the first viewpoint is more descriptive, the second one is more explanatory. This work favors a perspective that combines both: a spatiotemporal map representing the evolution of an environmental variable in space/time should be the outcome of an analysis that incorporates the set of observations available in space/time as well as other important knowledge bases. Bayesian Maximum Entropy (BME) is a stochastic method for studying spatiotemporal distributions of environmental variables in terms of random fields. The main advantage of random fields is that they allow the rigorous characterization of Transactions on Ecology and the Environment vol 17, © 1998 WIT Press, www.witpress.com, ISSN 1743-3541