MODELING THE SPATIAL VARIABILITY OF NATURAL TRACE-ELEMENT CONCENTRATIONS IN GROUNDWATER

A conceptual stochastic model is developed that describes the natural spatial variability of nonreactive solute concentrations in large grou ndwater systems. The spatial variation in aqueous concentration is ass ociated with dissolution from source areas of high mineral enrichment in the aquifer matrix. The stochastic model considers randomly varying inputs of a solute species from source deposits that occur as a two-d imensional spatial Poisson process. A steady state advective-dispersiv e transport equation is utilized to predict the downgradient movement of the solute from the source areas. The total groundwater concentrati on at any location is calculated from the superposition of the individ ual contributions from each source area in the aquifer. A spatially va rying concentration field results, described mathematically by a filte red Poisson process model. The theoretical concentration field is nons tationary, with the mean and variance increasing, and the coefficient of variation decreasing, in the direction of groundwater flow. Gaussia n fields for abundant elements and highly skewed probability distribut ions for trace elements are indicated by the filtered Poisson process model. Evaluation of elemental concentration data from the Sherwood aq uifer in England demonstrates how field data may be analyzed in the co ntext of the stochastic model.