BEYOND DIRECT PARAMETER SAMPLING FOR UNCERTAINTY ANALYSES OF FIELD SCALE GROUNDWATER SYSTEMS

Uncertainty analyses are commonly used to estimate the first two moments of the system dependent variables. For many problems however, it is not these moments that are important but rather it is the probability at the tails of the PDF that are critical. The classical problem of the first arrival of a contaminant at a receptor is an example. The public, regulators and courts are often concerned with the earliest possible arrival of a contaminant. Economic decisions are made on these low-probability occurrences. The difficulty for the analyst then is the robustness of the output PDF tails; the estimation of the higher moments may be critical.

The most common uncertainty method is direct parameter sampling based on either the Monte Carlo or Latin Hypercube techniques; the methods yield higher moments but parameters are generally assumed to be independent. The First-Order Second-Moment method is also popular with the sensitivity derivatives of the method usually being calculated using parameter perturbations. The First-Order and Second-Order Reliability Methods can also be implemented using direct parameter sampling. With an increase in the complexity of implementation, computational efficiency can be achieved using adjoint equations; correlated parameters can be readily included in the analysis.

There is generally an inverse relationship between the complexity of the spatial-temporal parameterization of the deterministic system and the mathematical complexity of the method chosen for uncertainty analysis. As field problems become detailed, there is a tendency to use simpler methods for uncertainty analysis. The tradeoffs include computational effort in solving the related deterministic problem, computational and implementation burden associated with the uncertainty method, the need for the preservation of system physics and dimensionality, and the ability to estimate higher moments.

The issues related to the application of uncertainty analysis to field scale problems are demonstrated in two case studies: the analysis of the arrival of a contaminant at a well field in Toms River NJ, and the allocation of a bankruptcy trust to individuals with health impacts attributed to contaminant exposure concentration and duration. In both cases, decisions were based on the earliest possible arrival of a contaminant.