Eileen P. Poeter

Field example of data fusion in site characterization

Application of data fusion to characterization of the Fountain and Lyons Formations at a field site incorporates geologic knowledge, geophysical log data, cross-hole seismic tomography, hydraulic test data, and observations of head to reduce uncertainty associated with subsurface interpretation. These formations consist of channel and overbank deposits that have undergone variable diagenesis, resulting in more hydrofacies than would have been encountered in the original, unaltered deposits. The disparate types of available data are integrated to yield a coherent hydrofacies classification through use of discriminant analysis and soft data techniques. This data fusion improves definition of the complex hydrofacies and increases knowledge of their spatial correlation. Two hundred multiple-indicator, conditional, stochastic simulations of the site are generated, 100 with only hard data and 100 with both hard and soft data. Forward groundwater flow modeling using estimates of hydraulic conductivity from field testing yields smaller head residuals for realizations which include soft data. Inverse modeling is used to eliminate hydrofacies realizations that do not honor hydraulic data and to estimate hydrofacies hydraulic conductivity ranges for the hard and hard/soft data ensembles. Inverse parameter estimation substantially decreases head residuals for both ensembles. Standard deviations of hydraulic conductivities estimated through inverse modeling are smaller when both hard and soft data are used to generate the simulations, even though head residuals are similar within the two ensembles when these estimated hydraulic conductivities are used.

UCODE, a computer code for universal inverse modeling

Abstract This article presents the US Geological Survey computer program UCODE, which was developed in collaboration with the US Army Corps of Engineers Waterways Experiment Station and the International Ground Water Modeling Center of the Colorado School of Mines. UCODE performs inverse modeling, posed as a parameter-estimation problem, using nonlinear regression. Any application model or set of models can be used; the only requirement is that they have numerical (ASCII or text only) input and output files and that the numbers in these files have sufficient significant digits. Application models can include preprocessors and postprocessors as well as models related to the processes of interest (physical, chemical and so on), making UCODE extremely powerful for model calibration. Estimated parameters can be defined flexibly with user-specified functions. Observations to be matched in the regression can be any quantity for which a simulated equivalent value can be produced, thus simulated equivalent values are calculated using values that appear in the application model output files and can be manipulated with additive and multiplicative functions, if necessary. Prior, or direct, information on estimated parameters also can be included in the regression. The nonlinear regression problem is solved by minimizing a weighted least-squares objective function with respect to the parameter values using a modified Gauss–Newton method. Sensitivities needed for the method are calculated approximately by forward or central differences and problems and solutions related to this approximation are discussed. Statistics are calculated and printed for use in (1) diagnosing inadequate data or identifying parameters that probably cannot be estimated with the available data, (2) evaluating estimated parameter values, (3) evaluating the model representation of the actual processes and (4) quantifying the uncertainty of model simulated values. UCODE is intended for use on any computer operating system: it consists of algorithms programmed in perl, a freeware language designed for text manipulation and Fortran90, which efficiently performs numerical calculations.

Geohydrologic, geochemical, and geologic controls on the occurrence of radon in ground water near Conifer, Colorado, USA

Abstract Integrated studies of geohydrology, geochemistry, and geology of crystalline rocks in the vicinity of Conifer, Colorado, reveal that radon concentrations do not correlate with variations in concentrations of other dissolved species. Concentrations of major ions show systematic variations along selected groundwater flowpaths, whereas radon concentrations are dependent on local geochemical and geologic phenomena (such as localized uranium concentration in the rock or the presence of faults or folds). When radon enters the flow system, concentrations do not increase along flowpaths because its decay rate is fast relative to groundwater flow rates. Radon-222 is not in secular equilibrium with 238U and 226Ra in the water. Therefore, most of the 238U and 226Ra necessary to support the waterborne 222Rn must be present locally in the rock. High concentrations of dissolved radon are not found in zones of high transmissivity, and transmissivity is not correlated with rock type in the study area. A higher transmissivity can be indicative of higher water-volume to rock-surface-area ratios, which could effectively dilute 222Rn entering the water and/or may indicate that emanated radon is carried away more rapidly. Water samples collected from individual wells over periods of several months showed significant fluctuations in the dissolved 222Rn content. This fluctuation may be controlled by changes in the contributions of water-producing zones within the well resulting from seasonal fluctuations of the water table and/or pumping stresses.

Relationships between 222Rn dissolved in ground water supplies and indoor 222Rn concentrations in some Colorado front range houses.

Indoor 222Rn concentrations were measured in 37 houses with alpha track detectors placed in water-use rooms near water sources (bathrooms, laundry rooms, and kitchens) and in non-water-use living rooms, dining rooms, and bedrooms away from water sources. Results show that relative contributions of 222Rn to indoor air from water use are insignificant when soil-gas concentrations are high but become increasingly important as the ratio of 222Rn-in-water: 222Rn-in-soil gas increases. High soil-gas 222Rn concentrations may mask 222Rn contributions from water even when waterborne 222Rn concentrations are as high as 750 kBq m-3. Ground water in Precambrian Pikes Peak granite averages 340 kBq m-3 222Rn, vs. 170 kBq m-3 in Precambrian migmatite, but average 222Rn concentrations in soil gas are also lower in migmatite. Because the ratio of 222Rn-in-water: 222Rn-in-soil gas may be consistently higher for houses in migmatite than in Pikes Peak granite, indoor air in houses built on migmatite may have a greater relative contribution from water use even though average 222Rn concentrations in the water are lower. Continuous monitoring of 222Rn concentrations in air on 15-min intervals also indicates that additions to indoor concentrations from water use are significant and measurable only when soil-gas concentrations are low and concentrations in water are high. When soil-gas concentrations were mitigated to less than 150 Bq m-3 in one house, water contributes 20-40% of the annual indoor 222Rn concentration in the laundry room (222Rn concentration in water of 670 kBq m-3). Conversely, when the mitigation system is inactive, diurnal fluctuations and other variations in the soil-gas 222Rn contribution swamp the variability due to water use in the house. Measurable variations in indoor concentrations from water use were not detected in one house despite a low soil-gas contribution of approximately 150 Bq m-3 because waterborne 222Rn concentrations also are low (80 kBq m-3). This result suggests that 222Rn concentrations in water near the recommended EPA limit in drinking water of 11 kBq m-3 may not contribute measurable amounts of 222Rn to indoor air in most houses.

UNCERT: geostatistics, uncertainty analysis and visualization software applied to groundwater flow and contaminant transport modeling

UNCERT is a 2D and 3D geostatistics, uncertainty analysis and visualization software package applied to ground water flow and contaminant transport modeling. It is a collection of modules that provides tools for linear regression, univariate statistics, semivariogram analysis, inverse-distance gridding, trend-surface analysis, simple and ordinary kriging and discrete conditional indicator simulation. Graphical user interfaces for MODFLOW and MT3D, ground water flow and contaminant transport models, are provided for streamlined data input and result analysis. Visualization tools are included for displaying data input and output. These include, but are not limited to, 2D and 3D scatter plots, histograms, box and whisker plots, 2D contour maps, surface renderings of 2D gridded data and 3D views of gridded data. By design, UNCERT’s graphical user interface and visualization tools facilitate model design and analysis. There are few built in restrictions on data set sizes and each module (with two exceptions) can be run in either graphical or batch mode. UNCERT is in the public domain and is available from the World Wide Web with complete on-line and printable (PDF) documentation. UNCERT is written in ANSI-C with a small amount of FORTRAN77, for UNIX workstations running X-Windows and Motif (or Lesstif). This article discusses the features of each module and demonstrates how they can be used individually and in combination. The tools are applicable to a wide range of fields and are currently used by researchers in the ground water, mining, mathematics, chemistry and geophysics, to name a few disciplines. # 1999 Elsevier Science Ltd. All rights reserved.

A computer program for uncertainty analysis integrating regression and Bayesian methods

This work develops a new functionality in UCODE_2014 to evaluate Bayesian credible intervals using the Markov Chain Monte Carlo (MCMC) method. The MCMC capability in UCODE_2014 is based on the FORTRAN version of the differential evolution adaptive Metropolis (DREAM) algorithm of Vrugt et al. (2009), which estimates the posterior probability density function of model parameters in high-dimensional and multimodal sampling problems. The UCODE MCMC capability provides eleven prior probability distributions and three ways to initialize the sampling process. It evaluates parametric and predictive uncertainties and it has parallel computing capability based on multiple chains to accelerate the sampling process. This paper tests and demonstrates the MCMC capability using a 10-dimensional multimodal mathematical function, a 100-dimensional Gaussian function, and a groundwater reactive transport model. The use of the MCMC capability is made straightforward and flexible by adopting the JUPITER API protocol. With the new MCMC capability, UCODE_2014 can be used to calculate three types of uncertainty intervals, which all can account for prior information: (1) linear confidence intervals which require linearity and Gaussian error assumptions and typically 10s-100s of highly parallelizable model runs after optimization, (2) nonlinear confidence intervals which require a smooth objective function surface and Gaussian observation error assumptions and typically 100s-1,000s of partially parallelizable model runs after optimization, and (3) MCMC Bayesian credible intervals which require few assumptions and commonly 10,000s-100,000s or more partially parallelizable model runs. Ready access allows users to select methods best suited to their work, and to compare methods in many circumstances.

Building model analysis applications with the Joint Universal Parameter IdenTification and Evaluation of Reliability (JUPITER) API

The open-source, public domain JUPITER (Joint Universal Parameter IdenTification and Evaluation of Reliability) API (Application Programming Interface) provides conventions and Fortran-90 modules to develop applications (computer programs) for analyzing process models. The input and output conventions allow application users to access various applications and the analysis methods they embody with a minimum of time and effort. Process models simulate, for example, physical, chemical, and (or) biological systems of interest using phenomenological, theoretical, or heuristic approaches. The types of model analyses supported by the JUPITER API include, but are not limited to, sensitivity analysis, data needs assessment, calibration, uncertainty analysis, model discrimination, and optimization. The advantages provided by the JUPITER API for users and programmers allow for rapid programming and testing of new ideas. Application-specific coding can be in languages other than the Fortran-90 of the API. This article briefly describes the capabilities and utility of the JUPITER API, lists existing applications, and uses UCODE_2005 as an example.

222Rn transport in a fractured crystalline rock aquifer: Results from numerical simulations

Abstract Dissolved 222 Rn concentrations in ground water from a small wellfield underlain by fractured Middle Proterozoic Pikes Peak Granite southwest of Denver, Colorado range from 124 to 840 kBq m −3 (3360-22700 pCi L −1 ). Numerical simulations of flow and transport between two wells show that differences in equivalent hydraulic aperture of transmissive fractures, assuming a simplified two-fracture system and the parallel-plate model, can account for the different 222 Rn concentrations in each well under steady-state conditions. Transient flow and transport simulations show that 222 Rn concentrations along the fracture profile are influenced by 222 Rn concentrations in the adjoining fracture and depend on boundary conditions, proximity of the pumping well to the fracture intersection, transmissivity of the conductive fractures, and pumping rate. Non-homogeneous distribution (point sources) of 222 Rn parent radionuclides, uranium and 226 Ra, can strongly perturb the dissolved 222 Rn concentrations in a fracture system. Without detailed information on the geometry and hydraulic properties of the connected fracture system, it may be impossible to distinguish the influence of factors controlling 222 Rn distribution or to determine location of 222 Rn point sources in the field in areas where ground water exhibits moderate 222 Rn concentrations. Flow and transport simulations of a hypothetical multifracture system consisting of ten connected fractures, each 10 m in length with fracture apertures ranging from 0.1 to 1.0 mm, show that 222 Rn concentrations at the pumping well can vary significantly over time. Assuming parallel-plate flow, transmissivities of the hypothetical system vary over four orders of magnitude because transmissivity varies with the cube of fracture aperture. The extreme hydraulic heterogeneity of the simple hypothetical system leads to widely ranging 222 Rn values, even assuming homogeneous distribution of uranium and 226 Ra along fracture walls. Consequently, it is concluded that 222 Rn concentrations vary, not only with the geometric and stress factors noted above, but also according to local fracture aperture distribution, local groundwater residence time, and flux of 222 Rn from parent radionuclides along fracture walls.

Improving groundwater project analysis with geophysical data

When interpreting the earth’s subsurface for groundwater contamination, we face a fundamental problem — we typically sample one‐millionth of the relevant material. If only these data are used to determine the material between boreholes and the continuity of high hydraulic conductivity units, the answers will be ambiguous For example, consider a site where three boreholes intersect two hydrofacies (Figure 1). If no other information is available, all of the interpretations shown (and many more not shown) are equally likely.

Iterative use of the Bruggeman-Hanai-Sen mixing model to determine water saturations in sand

The accuracy of the Bruggeman-Hanai-Sen (BHS) mixing model has been previously demonstrated for two-material mixtures during BHS model development. Using permittivities determined from modeling ground-penetrating radar (GPR) data, the BHS model has been iteratively applied to three-material mixtures of water, sand, and a dense, nonaqueous-phase liquid (DNAPL). However, the accuracy of this application has not been verified. A 10-cm air-line system driven by a network analyzer is used to measure bulk permittivitities when the water saturations in a sand are varied (frequency range of 20 to 200 MHz). Through iterative use of the BHS mixing model, the measured permittivities are used to calculate water saturations, which are compared to known saturation values. An iterative BHS mixing model for an air/water/sand system must consider which two-material end member (air/sand or water/sand) represents the matrix term in the original two-material BHS model. An air/sand matrix provides the best accuracy for low water saturations, and a water/sand matrix provides the best accuracy for high water saturations; thus, a new weighted model is developed. For a given porosity and a measured bulk permittivity, water saturation is most accurately determined by proportionally weighting the water saturation values determined using air/sand as the matrix and water/sand as the matrix in the BHS model.