A STOCHASTIC ADVECTION-DIFFUSION MODEL FOR THE ROCKY FLATS SOIL PLUTONIUM DATA

JAROSLAV MOHAPL*

Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

(Received October 27, 1997; revised September 28, 1998)

Abstract. An advection-diffusion equation with time and space dependent random coefficients is derived as a model for the plutonium concentration changes in the surface soil around the Rocky Flats Plant northwest of Denver, Colorado. The equation is used to fit a set of temporal-spatial data sampled annually over a 23 year period from 71 sites around the plant. The coefficients of the advection-diffusion equation are derived from the estimated covariance function of the observed random field using a combination of maximum likelihood and quasi-likelihood techniques. Goodness-of-fit of the model to the data is also assessed. Finally we interpret the model in terms of the advection-diffusion mechanism.

Key words and phrases: Temporal-spatial data, temporal-spatial process, random field, parameter estimation, stochastic partial differential equation, stochastic modeling.