5.4 Case Study IV: A Ground Water Model with Discontinuous Probability Distributions

Uncertainty Analysis of Tritium Contamination in a Landfill using the EPACMTP Model

Characterization of exposure due to leakage of hazardous contaminants from a land disposal unit involves significant uncertainty due to inherent variability in the hydrogeologic properties of the site, and due to incomplete understanding of the processes involved in transport of contaminants. Since the exposure estimates are utilized in making policy decisions, it is important that any exposure characterization should take into account the variability and uncertainty involved with the physical system, and with the modeling process.

Here, a case study is presented in relation to characterization of uncertainty in estimated tritium exposure at a receptor well. The main source for the contamination is a hypothetical landfill unit in the southern United States. The fate and transport model used in this work is the EPA's Composite Model for leachate Migration and Transformation Products (EPACMTP). In the following sections, a brief description of the model used, the estimates of the model parameters and the uncertainty analysis methods is given. The variability and uncertainty associated with the hydrogeologic parameters and with the physical properties of the landfill unit are considered to characterize the uncertainty in the calculated concentrations of tritium. Environmental metrics considered are the estimated maximum concentration of tritium in a ``receptor'' well and the estimated time of occurrence of the maximum concentration.

5.4.1 EPACMTP Model

The EPA's Composite Model for leachate Migration and Transformation Products (EPACMTP) provides estimates of potential human exposure to hazardous chemicals leaching from land disposal facilities [64]. EPACMTP simulates the subsurface fate and transport of contaminants released from land disposal sites, and predicts the associated groundwater exposure in a domestic drinking water receptor well. This model is an improvement over the EPA's Composite Model for Landfills (EPACML) [62]. EPACML accounts for the first-order decay and sorption of chemicals, but disregards the formation and transport of transformation products. In addition, EPACML can describe only uniform, unidirectional groundwater flow. On the other hand, EPACMTP can take into consideration: (i) chain decay reactions and transport of daughter and grand-daughter products, (ii) effects of water-table mounding on groundwater flow and contaminant migration, (iii) finite source as well as continuous source scenarios, and (iv) metals transport.

EPACMTP consists of two modules: an unsaturated zone module called Finite Element and semi-analytical Contaminant Transport in the Unsaturated Zone (FECTUZ), and a saturated zone module called Combined Analytical-Numerical SAturated Zone in 3-Dimensions (CANSAZ-3D). FECTUZ is a one-dimensional model that simulates vertically downward steady-state flow and contaminant transport through the unsaturated zone above an unconfined aquifer. CANSAZ-3D simulates 3-D steady-state groundwater flow and transient or steady state contaminant transport. EPACMTP currently uses a simplified 2-D version of the CANSAZ-3D, and the modules are optimized for computational efficiency. Appendix D provides detailed description of the formulation and implementation of FECTUZ and CANSAZ-3D modules.

5.4.2 Data Sources for the Application of EPACMTP

Data for the site characteristics, infiltration rates, the volume and area of the landfills, and the probability distributions for the hydrogeologic parameters are obtained from a review conducted by the Hydrogeologic Inc. [64]. In this review, a number of different sources were used for the development of this site-based approach. Four of these sets were selected to derive the regional characteristics of important parameters for each sampled site:

• the OPPI survey of waste management units (EPA,1986),
• the infiltration and recharge analysis performed by OSW,
• the USGS state-by-state inventory of groundwater resources, and
• the Hydrogeologic Database for Modeling (HGDB), developed from a survey of hazardous waste field sites in the U.S.

These datasets were used in conjunction with the soil mapping database provided by the Soil Conservation Service (SCS), the data sets from the National Oceanic and Atmospheric Administration, and simulations from the HELP model [180]. The data for the hypothetical scenario in this case study were adapted from a data set provided by Hydrogeologic Inc.

5.4.3 Implementation of the Monte Carlo Method in EPACMTP

The Monte Carlo method requires that for each input parameter that has associated uncertainty or variability, a probability distribution (or a frequency distribution) be provided. The method involves the repeated generation of pseudo-random values of the uncertain input variables (drawn from the known distribution and within the range of any imposed bounds) and the application of the model using these values to generate a set of model responses or outputs (for example, the receptor well concentration, $C_{RW}$). These responses are then statistically analyzed to yield the probability distribution of the model output. The various steps involved in the application of a Monte Carlo simulation are:

• selection of representative cumulative probability distribution functions for the relevant input variables,
• generation of a pseudo-random number from the selected distributions, representing a possible set of values (a realization) for the input variables,
• checking whether the realization satisfies the constraints or bounds on the distribution (and resampling till a reasonable realization is obtained),
• application of the model to compute the derived inputs and outputs,
• repeated application of the above steps for a specified number of iterations, and
• statistical analysis of the series of the output values generated.

  

Table 5.3: Probability distributions used for the EPACMTP model parameters for the uncertainty analysis

5.4.4 Uncertainty Analysis

This case study consists of a site based landfill modeling for tritium contamination at a groundwater well resulting from a hypothetical landfill unit in the souther United States. The landfill is a finite source, of 0.35 km$^2$ area, with a leaching duration of 20 years, and a recharge rate of 0.381 m/yr. The receptor well is located at a distance of 1635 m from the landfill. The EPACMTP model is used to simulate the radioactive decay and transport of tritium through the saturated and unsaturated zone underlying the landfill. The data used here is adapted from data provided by Hydrogeologic Inc.

The probability distributions of the site-specific parameters for the land fill at the Old Burial Ground are given in Table 5.3, and the values of the constant model parameters for EPACMTP are given in Table 5.4.

  

Table 5.4: Deterministic Parameters in the EPACMTP model for the case study

5.4.5 Results and Discussion

Figure 5.21 shows the uncertainty associated with the estimation of maximum tritium concentration in the ground water, as a result of the leaching from the landfill unit. Figure 5.22 shows the uncertainty associated with the estimated time of occurrence of the maximum tritium concentration in the ground water at the well. The figures show the pdfs estimated by the Monte Carlo simulations and by the SRSM. Results of the SRSM with 350 model runs are compared with those of Monte Carlo simulations with 1000, 3000 and 5000 model runs.

  

Figure 5.21: Uncertainty in estimated maximum tritium concentration in a receptor well

  

Figure 5.22: Uncertainty in estimated time of occurrence of maximum tritium concentration in a receptor well

The results indicate that the SRSM shows close agreement with the Monte Carlo results, while requiring much fewer number of runs. Further, there are certain other advantages in using the SRSM, that are focused in the ongoing research:

• The relationships between inputs and outputs can be easily estimated, since both the input and output pdfs are expressed as a series expansion in srvs. This implies that SRSM provides insight into the relative contribution of each uncertain input each output, thus giving extensive sensitivity and uncertainty information. Conventional Monte Carlo methods do not provide such information.
• Correlation between outputs can be easily estimated since all outputs are expressed in terms of srvs. On the other hand, Monte Carlo methods require significantly large number of model simulations to obtain a reasonably good approximation of the correlation between outputs.
• The algebraic expressions for the outputs in terms of the srvs are smooth and continuous and could efficiently model the tails of the probability distributions of the outputs (which typically correspond to either high risk or worst case scenarios).

One of the limitations of the Stochastic Response Surface Method, that is a focus of the ongoing research, is as follows: the current implementation of the SRSM does not take into account constraints on the input probability distributions that make the distributions discontinuous. In short, this method assumes that the probability distributions are continuous. In the present work, such constraints are modeled as truncated probability distributions, and the results shown in Figures 5.21 and 5.22 for the SRSM are obtained in such a manner, indicating that they represent only an approximate estimate. Current work in progress involves the refinement of the SRSM so that all types of constraints can be propagated, and discontinuities in probability distributions can be fully addressed.