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Mary C. Hill

Publications and source records attributed to Mary C. Hill.

At least 19 recordsLinked to original sources
USGS2017

An update of the Death Valley regional groundwater flow system transient model, Nevada and California

Since the original publication of the Death Valley regional groundwater flow system (DVRFS) numerical model in 2004, more information on the regional groundwater flow system in the form of new data and interpretations has been compiled. Cooperators such as the Bureau of Land Management, National Park Service, U.S. Fish and Wildlife Service, the Department of Energy, and Nye County, Nevada, recognized a need to update the existing regional numerical model to maintain its viability as a groundwater management tool for regional stakeholders. The existing DVRFS numerical flow model was converted to MODFLOW-2005, updated with the latest available data, and recalibrated. Five main data sets were revised: (1) recharge from precipitation varying in time and space, (2) pumping data, (3) water-level observations, (4) an updated regional potentiometric map, and (5) a revision to the digital hydrogeologic framework model. The resulting DVRFS version 2.0 (v. 2.0) numerical flow model simulates groundwater flow conditions for the Death Valley region from 1913 to 2003 to correspond to the time frame for the most recently published (2008) water-use data. The DVRFS v 2.0 model was calibrated by using the Tikhonov regularization functionality in the parameter estimation and predictive uncertainty software PEST. In order to assess the accuracy of the numerical flow model in simulating regional flow, the fit of simulated to target values (consisting of hydraulic heads and flows, including evapotranspiration and spring discharge, flow across the model boundary, and interbasin flow; the regional water budget; values of parameter estimates; and sensitivities) was evaluated. This evaluation showed that DVRFS v. 2.0 simulates conditions similar to DVRFS v. 1.0. Comparisons of the target values with simulated values also indicate that they match reasonably well and in some cases (boundary flows and discharge) significantly better than in DVRFS v. 1.0.

California, Nevada↗
USGS2014

Simulation of water-table aquifers using specified saturated thickness

Simulating groundwater flow in a water-table (unconfined) aquifer can be difficult because the saturated thickness available for flow depends on model-calculated hydraulic heads. It is often possible to realize substantial time savings and still obtain accurate head and flow solutions by specifying an approximate saturated thickness a priori, thus linearizing this aspect of the model. This specified-thickness approximation often relies on the use of the “confined” option in numerical models, which has led to confusion and criticism of the method. This article reviews the theoretical basis for the specified-thickness approximation, derives an error analysis for relatively ideal problems, and illustrates the utility of the approximation with a complex test problem. In the transient version of our complex test problem, the specified-thickness approximation produced maximum errors in computed drawdown of about 4% of initial aquifer saturated thickness even when maximum drawdowns were nearly 20% of initial saturated thickness. In the final steady-state version, the approximation produced maximum errors in computed drawdown of about 20% of initial aquifer saturated thickness (mean errors of about 5%) when maximum drawdowns were about 35% of initial saturated thickness. In early phases of model development, such as during initial model calibration efforts, the specified-thickness approximation can be a very effective tool to facilitate convergence. The reduced execution time and increased stability obtained through the approximation can be especially useful when many model runs are required, such as during inverse model calibration, sensitivity and uncertainty analyses, multimodel analysis, and development of optimal resource management scenarios.

Ground Water↗
USGS2014

Distributed Evaluation of Local Sensitivity Analysis (DELSA), with application to hydrologic models

This paper presents a hybrid local-global sensitivity analysis method termed the Distributed Evaluation of Local Sensitivity Analysis (DELSA), which is used here to identify important and unimportant parameters and evaluate how model parameter importance changes as parameter values change. DELSA uses derivative-based “local” methods to obtain the distribution of parameter sensitivity across the parameter space, which promotes consideration of sensitivity analysis results in the context of simulated dynamics. This work presents DELSA, discusses how it relates to existing methods, and uses two hydrologic test cases to compare its performance with the popular global, variance-based Sobol' method. The first test case is a simple nonlinear reservoir model with two parameters. The second test case involves five alternative “bucket-style” hydrologic models with up to 14 parameters applied to a medium-sized catchment (200 km 2 ) in the Belgian Ardennes. Results show that in both examples, Sobol' and DELSA identify similar important and unimportant parameters, with DELSA enabling more detailed insight at much lower computational cost. For example, in the real-world problem the time delay in runoff is the most important parameter in all models, but DELSA shows that for about 20% of parameter sets it is not important at all and alternative mechanisms and parameters dominate. Moreover, the time delay was identified as important in regions producing poor model fits, whereas other parameters were identified as more important in regions of the parameter space producing better model fits. The ability to understand how parameter importance varies through parameter space is critical to inform decisions about, for example, additional data collection and model development. The ability to perform such analyses with modest computational requirements provides exciting opportunities to evaluate complicated models as well as many alternative models.

Water Resources Research↗
USGS2014

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.

Environmental Modelling and Software↗
USGS2013

Evaluating model structure adequacy: The case of the Maggia Valley groundwater system, southern Switzerland

Model adequacy is evaluated with alternative models rated using model selection criteria (AICc, BIC, and KIC) and three other statistics. Model selection criteria are tested with cross-validation experiments and insights for using alternative models to evaluate model structural adequacy are provided. The study is conducted using the computer codes UCODE_2005 and MMA (MultiModel Analysis). One recharge alternative is simulated using the TOPKAPI hydrological model. The predictions evaluated include eight heads and three flows located where ecological consequences and model precision are of concern. Cross-validation is used to obtain measures of prediction accuracy. Sixty-four models were designed deterministically and differ in representation of river, recharge, bedrock topography, and hydraulic conductivity. Results include: (1) What may seem like inconsequential choices in model construction may be important to predictions. Analysis of predictions from alternative models is advised. (2) None of the model selection criteria consistently identified models with more accurate predictions. This is a disturbing result that suggests to reconsider the utility of model selection criteria, and/or the cross-validation measures used in this work to measure model accuracy. (3) KIC displayed poor performance for the present regression problems; theoretical considerations suggest that difficulties are associated with wide variations in the sensitivity term of KIC resulting from the models being nonlinear and the problems being ill-posed due to parameter correlations and insensitivity. The other criteria performed somewhat better, and similarly to each other. (4) Quantities with high leverage are more difficult to predict. The results are expected to be generally applicable to models of environmental systems.

Water Resources Research↗
USGS2013

Modeling unsaturated zone flow and runoff processes by integrating MODFLOW-LGR and VSF, and creating the new CFL package

In this paper two modifications to the MODFLOW code are presented. One concerns an extension of Local Grid Refinement (LGR) to Variable Saturated Flow process (VSF) capability. This modification allows the user to solve the 3D Richards’ equation only in selected parts of the model domain. The second modification introduces a new package, named CFL (Cascading Flow), which improves the computation of overland flow when ground surface saturation is simulated using either VSF or the Unsaturated Zone Flow (UZF) package. The modeling concepts are presented and demonstrated. Programmer documentation is included in appendices.

Journal of Hydrology↗
USGS2013

Knowledge, transparency, and refutability in groundwater models, an example from the Death Valley regional groundwater flow system

This work demonstrates how available knowledge can be used to build more transparent and refutable computer models of groundwater systems. The Death Valley regional groundwater flow system, which surrounds a proposed site for a high level nuclear waste repository of the United States of America, and the Nevada National Security Site (NNSS), where nuclear weapons were tested, is used to explore model adequacy, identify parameters important to (and informed by) observations, and identify existing old and potential new observations important to predictions. Model development is pursued using a set of fundamental questions addressed with carefully designed metrics. Critical methods include using a hydrogeologic model, managing model nonlinearity by designing models that are robust while maintaining realism, using error-based weighting to combine disparate types of data, and identifying important and unimportant parameters and observations and optimizing parameter values with computationally frugal schemes. The frugal schemes employed in this study require relatively few (10–1000 s), parallelizable model runs. This is beneficial because models able to approximate the complex site geology defensibly tend to have high computational cost. The issue of model defensibility is particularly important given the contentious political issues involved.

California, Nevada↗
USGS2013

MODFLOW–LGR—Documentation of ghost node local grid refinement (LGR2) for multiple areas and the boundary flow and head (BFH2) package

This report documents the addition of ghost node Local Grid Refinement (LGR2) to MODFLOW-2005, the U.S. Geological Survey modular, transient, three-dimensional, finite-difference groundwater flow model. LGR2 provides the capability to simulate groundwater flow using multiple block-shaped higher-resolution local grids (a child model) within a coarser-grid parent model. LGR2 accomplishes this by iteratively coupling separate MODFLOW-2005 models such that heads and fluxes are balanced across the grid-refinement interface boundary. LGR2 can be used in two-and three-dimensional, steady-state and transient simulations and for simulations of confined and unconfined groundwater systems. Traditional one-way coupled telescopic mesh refinement methods can have large, often undetected, inconsistencies in heads and fluxes across the interface between two model grids. The iteratively coupled ghost-node method of LGR2 provides a more rigorous coupling in which the solution accuracy is controlled by convergence criteria defined by the user. In realistic problems, this can result in substantially more accurate solutions and require an increase in computer processing time. The rigorous coupling enables sensitivity analysis, parameter estimation, and uncertainty analysis that reflects conditions in both model grids. This report describes the method used by LGR2, evaluates accuracy and performance for two-and three-dimensional test cases, provides input instructions, and lists selected input and output files for an example problem. It also presents the Boundary Flow and Head (BFH2) Package, which allows the child and parent models to be simulated independently using the boundary conditions obtained through the iterative process of LGR2.

Techniques and Methods↗
USGS2012

MT3DMS: Model use, calibration, and validation

MT3DMS is a three-dimensional multi-species solute transport model for solving advection, dispersion, and chemical reactions of contaminants in saturated groundwater flow systems. MT3DMS interfaces directly with the U.S. Geological Survey finite-difference groundwater flow model MODFLOW for the flow solution and supports the hydrologic and discretization features of MODFLOW. MT3DMS contains multiple transport solution techniques in one code, which can often be important, including in model calibration. Since its first release in 1990 as MT3D for single-species mass transport modeling, MT3DMS has been widely used in research projects and practical field applications. This article provides a brief introduction to MT3DMS and presents recommendations about calibration and validation procedures for field applications of MT3DMS. The examples presented suggest the need to consider alternative processes as models are calibrated and suggest opportunities and difficulties associated with using groundwater age in transport model calibration.

Transactions of the ASABE↗
USGS2012

Uncertainty quantification for environmental models

Environmental models are used to evaluate the fate of fertilizers in agricultural settings (including soil denitrification), the degradation of hydrocarbons at spill sites, and water supply for people and ecosystems in small to large basins and cities—to mention but a few applications of these models. They also play a role in understanding and diagnosing potential environmental impacts of global climate change. The models are typically mildly to extremely nonlinear. The persistent demand for enhanced dynamics and resolution to improve model realism [17] means that lengthy individual model execution times will remain common, notwithstanding continued enhancements in computer power. In addition, high-dimensional parameter spaces are often defined, which increases the number of model runs required to quantify uncertainty [2]. Some environmental modeling projects have access to extensive funding and computational resources; many do not. The many recent studies of uncertainty quantification in environmental model predictions have focused on uncertainties related to data error and sparsity of data, expert judgment expressed mathematically through prior information, poorly known parameter values, and model structure (see, for example, [1,7,9,10,13,18]). Approaches for quantifying uncertainty include frequentist (potentially with prior information [7,9]), Bayesian [13,18,19], and likelihood-based. A few of the numerous methods, including some sensitivity and inverse methods with consequences for understanding and quantifying uncertainty, are as follows: Bayesian hierarchical modeling and Bayesian model averaging; single-objective optimization with error-based weighting [7] and multi-objective optimization [3]; methods based on local derivatives [2,7,10]; screening methods like OAT (one at a time) and the method of Morris [14]; FAST (Fourier amplitude sensitivity testing) [14]; the Sobol' method [14]; randomized maximum likelihood [10]; Markov chain Monte Carlo (MCMC) [10]. There are also bootstrapping and cross-validation approaches.Sometimes analyses are conducted using surrogate models [12]. The availability of so many options can be confusing. Categorizing methods based on fundamental questions assists in communicating the essential results of uncertainty analyses to stakeholders. Such questions can focus on model adequacy (e.g., How well does the model reproduce observed system characteristics and dynamics?) and sensitivity analysis (e.g., What parameters can be estimated with available data? What observations are important to parameters and predictions? What parameters are important to predictions?), as well as on the uncertainty quantification (e.g., How accurate and precise are the predictions?). The methods can also be classified by the number of model runs required: few (10s to 1000s) or many (10,000s to 1,000,000s). Of the methods listed above, the most computationally frugal are generally those based on local derivatives; MCMC methods tend to be among the most computationally demanding. Surrogate models (emulators)do not necessarily produce computational frugality because many runs of the full model are generally needed to create a meaningful surrogate model. With this categorization, we can, in general, address all the fundamental questions mentioned above using either computationally frugal or demanding methods. Model development and analysis can thus be conducted consistently using either computation-ally frugal or demanding methods; alternatively, different fundamental questions can be addressed using methods that require different levels of effort. Based on this perspective, we pose the question: Can computationally frugal methods be useful companions to computationally demanding meth-ods? The reliability of computationally frugal methods generally depends on the model being reasonably linear, which usually means smooth nonlin-earities and the assumption of Gaussian errors; both tend to be more valid with more linear

SIAM News↗
USGS2011

Comment on “An unconfined groundwater model of the Death Valley Regional Flow System and a comparison to its confined predecessor” by R.W.H. Carroll, G.M. Pohll and R.L. Hershey [Journal of Hydrology 373/3–4, pp. 316–328]

Carroll et al. (2009) state that the United States Geological Survey (USGS) Death Valley Regional Flow System (DVRFS) model, which is based on MODFLOW, is “conceptually inaccurate in that it models an unconfined aquifer as a confined system and does not simulate unconfined drawdown in transient pumping simulations.” Carroll et al. (2009) claim that “more realistic estimates of water availability” can be produced by a SURFACT-based model of the DVRFS that simulates unconfined groundwater flow and limits withdrawals from wells to avoid excessive drawdown. Differences in results from the original MODFLOW-based model and the SURFACT-based model stem primarily from application by Carroll et al. (2009) of head limits that can also be applied using the existing MODLOW model and not from any substantial difference in the accuracy with which the unconfined aquifer is represented in the two models. In a hypothetical 50-year predictive simulation presented by Carroll et al. (2009), large differences between the models are shown when simulating pumping from the lower clastic confining unit, where the transmissivity is nearly two orders of magnitude less than in an alluvial aquifer. Yet even for this extreme example, drawdowns and pumping rates from the MODFLOW and SURFACT models are similar when the head-limit capabilities of the MODFLOW MNW Package are applied. These similarities persist despite possible discrepancies between assigned hydraulic properties. The resulting comparison between the MODFLOW and SURFACT models of the DVRFS suggests that approximating the unconfined system in the DVRFS as a constant-saturated-thickness system (called a “confined system” by Carroll et al., 2009) performs very well.

Death Valley↗
USGS2011

MODFLOW-LGR-Modifications to the streamflow-routing package (SFR2) to route streamflow through locally refined grids

This report documents modifications to the Streamflow-Routing Package (SFR2) to route streamflow through grids constructed using the multiple-refined-areas capability of shared node Local Grid Refinement (LGR) of MODFLOW-2005. MODFLOW-2005 is the U.S. Geological Survey modular, three-dimensional, finite-difference groundwater-flow model. LGR provides the capability to simulate groundwater flow by using one or more block-shaped, higher resolution local grids (child model) within a coarser grid (parent model). LGR accomplishes this by iteratively coupling separate MODFLOW-2005 models such that heads and fluxes are balanced across the shared interfacing boundaries. Compatibility with SFR2 allows for streamflow routing across grids. LGR can be used in two- and three-dimensional, steady-state and transient simulations and for simulations of confined and unconfined groundwater systems.

Techniques and Methods↗
USGS2011

MODPATH-LGR; documentation of a computer program for particle tracking in shared-node locally refined grids by using MODFLOW-LGR

The computer program described in this report, MODPATH-LGR, is designed to allow simulation of particle tracking in locally refined grids. The locally refined grids are simulated by using MODFLOW-LGR, which is based on MODFLOW-2005, the three-dimensional groundwater-flow model published by the U.S. Geological Survey. The documentation includes brief descriptions of the methods used and detailed descriptions of the required input files and how the output files are typically used. The code for this model is available for downloading from the World Wide Web from a U.S. Geological Survey software repository. The repository is accessible from the U.S. Geological Survey Water Resources Information Web page at http://water.usgs.gov/software/ground_water.html. The performance of the MODPATH-LGR program has been tested in a variety of applications. Future applications, however, might reveal errors that were not detected in the test simulations. Users are requested to notify the U.S. Geological Survey of any errors found in this document or the computer program by using the email address available on the Web site. Updates might occasionally be made to this document and to the MODPATH-LGR program, and users should check the Web site periodically.

Techniques and Methods↗
USGS2010

Comment on RamaRao et al. [1995] and LaVenue et al. [1995]

A method for stochastic modeling of groundwater flow systems using a combination of pilot point parameterization and conditional simulation was presented by RamaRao et. al [1995] and LaVenue et. al [1995]. (We will collectively term these two papers RLMM and term the method developed in RLMM the CS method here.) RLMM (pp. 478-479) state that the CS method is intended to provide a frequency distribution of possible alternative spatial transmissivity T distributions that (1) are statistically similar to the observed T distribution, (2) are equally likely given the calibration data, and (3) closely reproduce the measured pressures. The frequency distribution of transmissivities is then used to form frequency distribution of derived functions, such as travel times, which are summarized in the form of uncertainty measures, such as (RLMM, p. 512) "confidence (or tolerance) intervals," on the actual values, which in the case of travels times, are values that could occur sometime in the future (RLMM, p.513). Cooley [2000] analyzes the RLMM method using linearization and bootstrap theory and concludes that that the method can yield accurate uncertainty estimates but only under some limited circumstances. In this comment we use Cooley's analysis to critique the method. We also identify and discuss some statements made my by RLMM about model calibration and their methodology that appear to be misleading. It is unusual to comment on a paper so long after publication. Subsequent work has expanded the method of RLMM, and the method was used advantageously in the testing documented by Zimmerman et. al [1998], so it is clear the method has significant strengths. We go back to the 1995 papers for this comment, however, because they display most clearly the methodological difficulties with which we are concerned.

Water Resources Research↗
USGS2010

Solving groundwater flow problems by conjugate-gradient methods and the strongly implicit procedure

The performance of the preconditioned conjugate-gradient method with three preconditioners is compared with the strongly implicit procedure (SIP) using a scalar computer. The preconditioners considered are the incomplete Cholesky (ICCG) and the modified incomplete Cholesky (MICCG), which require the same computer storage as SIP as programmed for a problem with a symmetric matrix, and a polynomial preconditioner (POLCG), which requires less computer storage than SIP. Although POLCG is usually used on vector computers, it is included here because of its small storage requirements. In this paper, published comparisons of the solvers are evaluated, all four solvers are compared for the first time, and new test cases are presented to provide a more complete basis by which the solvers can be judged for typical groundwater flow problems. Based on nine test cases, the following conclusions are reached: (1) SIP is actually as efficient as ICCG for some of the published, linear, two-dimensional test cases that were reportedly solved much more efficiently by ICCG; (2) SIP is more efficient than other published comparisons would indicate when common convergence criteria are used; and (3) for problems that are three-dimensional, nonlinear, or both, and for which common convergence criteria are used, SIP is often more efficient than ICCG, and is sometimes more efficient than MICCG.

Water Resources Research↗
USGS2010

Comment on “Two statistics for evaluating parameter identifiability and error reduction” by John Doherty and Randall J. Hunt

Doherty and Hunt (2009) present important ideas for first-order-second moment sensitivity analysis, but five issues are discussed in this comment. First, considering the composite-scaled sensitivity (CSS) jointly with parameter correlation coefficients (PCC) in a CSS/PCC analysis addresses the difficulties with CSS mentioned in the introduction. Second, their new parameter identifiability statistic actually is likely to do a poor job of parameter identifiability in common situations. The statistic instead performs the very useful role of showing how model parameters are included in the estimated singular value decomposition (SVD) parameters. Its close relation to CSS is shown. Third, the idea from p. 125 that a suitable truncation point for SVD parameters can be identified using the prediction variance is challenged using results from Moore and Doherty (2005) . Fourth, the relative error reduction statistic of Doherty and Hunt is shown to belong to an emerging set of statistics here named perturbed calculated variance statistics. Finally, the perturbed calculated variance statistics OPR and PPR mentioned on p. 121 are shown to explicitly include the parameter null-space component of uncertainty. Indeed, OPR and PPR results that account for null-space uncertainty have appeared in the literature since 2000.

Journal of Hydrology↗