Jeffrey D. Cawlfield

Probabilistic sensitivity analysis for one-dimensional contaminant transport in the vadose zone

Abstract A reliability algorithm is coupled to a van Genuchten model-based unsaturated flow and transport numerical solution to develop a probabilistic model of one-dimensional non-reactive and reactive contaminant transport in the vadose zone. The reliability approach provides two important quantitative results: an estimate of the probability that a contaminant concentration is exceeded at some time and location, and a probabilistic sensitivity measure which quantifies the relative importance of each uncertain variable to the probabilistic outcome. The method requires that each uncertain variable be assigned at least a mean and standard deviation but marginal distributions and correlation structure may be incorporated. Transport through an idealized soil column with fixed boundary conditions and constant source concentration is analyzed. The uncertain variables include the van Genuchten model shape parameters, the saturated and residual water contents, saturated hydraulic conductivity, dispersivity, dispersion coefficient, first-order decay terms, bulk density and partitioning coefficient. The objective is to examine the relative importance of each uncertain variable and marginal distributions assigned to each variable. The influence of correlation structure is not considered in this study. Results indicate that the probabilistic outcome is generally very sensitive to likely changes in the saturated water content. Uncertainty associated with the diffusion coefficient, residual water content and first-order decay coefficients is often not a significant issue with respect to the probabilistic outcome; thus, these variables may be treated as deterministic constants. Although these results are limited by the assumptions of the numerical code and by the conceptual setup of the idealized soil column, they provide insight into the critical issues to consider in a probabilistic analysis of contaminant transport in the vadose zone. Such information concerning the most important uncertain parameters can be used to guide field and laboratory investigations.

Probabilistic sensitivity and modeling of two-dimensional transport in porous media

A reliability approach is used to develop a probabilistic model of two-dimensional non-reactive and reactive contaminant transport in porous media. The reliability approach provides two important quantitative results: an estimate of the probability that contaminant concentration is exceeded at some location and time, and measures of the sensitivity of the probabilistic outcome to likely changes in the uncertain variables. The method requires that each uncertain variable be assigned at least a mean and variance; in this work we also incorporate and investigate the influence of marginal probability distributions. Uncertain variables includex andy components of average groundwater flow velocity,x andy components of dispersivity, diffusion coefficient, distribution coefficient, porosity and bulk density. The objective is to examine the relative importance of each uncertain variable, the marginal distribution assigned to each variable, and possible correlation between the variables. Results utilizing a two-dimensional analytical solution indicate that the probabilistic outcome is generally very sensitive to likely changes in the uncertain flow velocity. Uncertainty associated with dispersivity and diffusion coefficient is often not a significant issue with respect to the probabilistic analysis; therefore, dispersivity and diffusion coefficient can often be treated for practical analysis as deterministic constants. The probabilistic outcome is sensitive to the uncertainty of the reaction terms for early times in the flow event. At later times, when source contaminants are released at constant rate throughout the study period, the probabilistic outcome may not be sensitive to changes in the reaction terms. These results, although limited at present by assumptions and conceptual restrictions inherent to the closed-form analytical solution, provide insight into the critical issues to consider in a probabilistic analysis of contaminant transport. Such information concerning the most important uncertain parameters can be used to guide field and laboratory investigations.

Probabilistic sensitivity measures applied to numerical models of flow and transport

First- and second-order reliability algorithms (FORM AND SORM) have been adapted for use in modeling uncertainty and sensitivity related to flow in porous media. They are called reliability algorithms because they were developed originally for analysis of reliability of structures. FORM and SORM utilize a general joint probability model, the Nataf model, as a basis for transforming the original problem formulation into uncorrelated standard normal space, where a first-order or second-order estimate of the probability related to some failure criterion can easily be made. Sensitivity measures that incorporate the probabilistic nature of the uncertain variables in the problem are also evaluated, and are quite useful in indicating which uncertain variables contribute the most to the probabilistic outcome. In this paper the reliability approach is reviewed and the advantages and disadvantages compared to other typical probabilistic techniques used for modeling flow and transport. Some example applications of F...

Application of a Mass Balance-Based Stochastic Transport Model

The definition of contaminant source release is a necessary element of contaminant mass transport simulation in the saturated zone. At many sites the release history is unknown, and there has been a significant body of research to develop inverse models to define finite release histories. Instead of rigorously defining the source history, a mass balance-based approach is tested to explicitly account for uncertainty in rectangular pulse release variables. The approach has been incorporated into a spreadsheet model which uses a one-dimensional solution to the advection dispersion equation, which readily lends itself to Monte Carlo applications. After the model was tested with synthetic data sets, the model was calibrated and verified using a concentration data set collected at a Superfund site. Model calibration with synthetic and actual data resulted in a reasonable domain of source history parameters and the model provided reasonable results when the mass of contaminant in the aquifer was assumed to be ra...