DYNAMIC-STOCHASTIC ESTIMATION OF PHYSICAL VARIABLES

A fundamental problem facing the physical sciences today is analysis o f natural variations and mapping of spatiotemporal processes. Derailed maps describing the space/time distribution of groundwater contaminan ts, atmospheric pollutant deposition processes, rainfall intensity var iables, external intermittency functions, etc. are tools whose importa nce in practical applications cannot be overestimated Such maps are va luable inputs for numerous applications including, for example, solute transport, storm modeling, turbulent-nonturbulent flow characterizati on, weather prediction, and human exposure to hazardous substances. Th e approach considered here uses the spatiotemporal random field theory to study natural space/time variations and derive dynamic stochastic estimates of physical variables. The random field model is constructed in a space/time continuum that explicitly involves both spatial and t emporal aspects and provides a rigorous representation of spatiotempor al variabilities and uncertainties. This has considerable advantages a s regards analytical investigations of natural processes. The model is used to study natural space/time variations of springwater calcium io n data from the Dyle River catchment area, Belgium. This dataset is ch aracterized by a spatially nonhomogeneous and temporally nonstationary variability that is quantified by random field parameters, such as or ders of space/time continuity and random field increments. A rich clas s of covariance models is determined from the properties of the random field increments. The analysis leads to maps of continuity orders and covariances reflecting space/time calcium ion correlations and trends . Calcium ion estimates and the associated statistical errors are calc ulated at unmeasured locations/instants over the Dyle region using a s pace/time kriging algorithm. In practice, the interpretation of the re sults of the dynamic stochastic analysis should take into consideratio n the scale effects.