A Stochastic Advection-Diffusion Model for the Rocky Flats Soil Plutonium Data

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.