Contaminant transport models under random sources

While the discussion of model uncertainty has centered on spatial heterogeneity, it is possible that ground water models have not enjoyed much success as predictive tools often because the sources that were eventually imposed in the field differed from those represented in the simulations. This is because deterministic prediction of future conditions is often inaccurate due to the random nature of contaminant sources, in terms of their timing, location, and magnitude. This paper presents a stochastic framework for accommodating random contaminant sources in conventional, deterministic advection-dispersion transport models. The contaminant sources are first classified into two types: those occurring continuously with a deterministic component and random variations and those occurring randomly at instantaneous discrete-time intervals. For the first type, the governing partial differential equation (PDE) is replaced by a stochastic PDE. The random variations are modeled by Gaussian noise or Brownian motion, and the solution is obtained by using Ito's integration technique. For the second type, Markovian analysis is used for discrete-time contamination events. Both approaches use a deterministic transport model to generate response functions at any observation location and time. The response functions are then integrated to yield probabilistic description of contaminant transport, from which key statistical properties such as mean, standard deviation, and confidence interval can be drawn.