Many aspects of ground-water flow and transport resist standard, deterministic modeling techniques: either there exist elements which are overly complex or which are simply unpredictable. These elements may have either a spatial character, as heterogeneity in porous media, or a temporal character, as recharge events to an aquifer. Provided that an adequate representation can be found, then these aspects of flow and transport frequently are better modeled by taking the complex or unpredictable element to be a stochastic process. Given an adequate representation, then the following questions may be addressed: (1) What is the implication of these elements for flow and transport in porous media? (2) Given observations of the physical process (hydraulic heads, concentrations, discharges), can the stochastic element be characterized (variances, length scales)? (3) Can an adequate monitoring program be designed when the physical process incorporates complex or unpredictable elements? The principal objective of this research is a better understanding of flow and transport phenomena when the underlying physical process contains one or more stochastic elements. A subsidiary objective is the development of a network model to evaluate sampling schemes when the physical process contains a stochastic element. An inverse procedure whereby the statistical properties of the stochastic element can be determined from the outputs of the physical process will be a necessity if these models are to be utilized. Where practicable, investigation will include development of usable computer codes.
