Geology topics

M. C. Hill

Publications and source records attributed to M. C. Hill.

At least 19 recordsLinked to original sources

USGS2013

Advective transport observations with MODPATH-OBS--documentation of the MODPATH observation process

The MODPATH-OBS computer program described in this report is designed to calculate simulated equivalents for observations related to advective groundwater transport that can be represented in a quantitative way by using simulated particle-tracking data. The simulated equivalents supported by MODPATH-OBS are (1) distance from a source location at a defined time, or proximity to an observed location; (2) time of travel from an initial location to defined locations, areas, or volumes of the simulated system; (3) concentrations used to simulate groundwater age; and (4) percentages of water derived from contributing source areas. Although particle tracking only simulates the advective component of conservative transport, effects of non-conservative processes such as retardation can be approximated through manipulation of the effective-porosity value used to calculate velocity based on the properties of selected conservative tracers. This program can also account for simple decay or production, but it cannot account for diffusion. Dispersion can be represented through direct simulation of subsurface heterogeneity and the use of many particles. MODPATH-OBS acts as a postprocessor to MODPATH, so that the sequence of model runs generally required is MODFLOW, MODPATH, and MODPATH-OBS. The version of MODFLOW and MODPATH that support the version of MODPATH-OBS presented in this report are MODFLOW-2005 or MODFLOW-LGR, and MODPATH-LGR. MODFLOW-LGR is derived from MODFLOW-2005, MODPATH 5, and MODPATH 6 and supports local grid refinement. MODPATH-LGR is derived from MODPATH 5. It supports the forward and backward tracking of particles through locally refined grids and provides the output needed for MODPATH_OBS. For a single grid and no observations, MODPATH-LGR results are equivalent to MODPATH 5. MODPATH-LGR and MODPATH-OBS simulations can use nearly all of the capabilities of MODFLOW-2005 and MODFLOW-LGR; for example, simulations may be steady-state, transient, or a combination. Though the program name MODPATH-OBS specifically refers to observations, the program also can be used to calculate model prediction of observations. MODPATH-OBS is primarily intended for use with separate programs that conduct sensitivity analysis, data needs assessment, parameter estimation, and uncertainty analysis, such as UCODE_2005, and PEST. In many circumstances, refined grids in selected parts of a model are important to simulated hydraulics, detailed inflows and outflows, or other system characteristics. MODFLOW-LGR and MODPATH-LGR support accurate local grid refinement in which both mass (flows) and energy (head) are conserved across the local grid boundary. MODPATH-OBS is designed to take advantage of these capabilities. For example, particles tracked between a pumping well and a nearby stream, which are simulated poorly if a river and well are located in a single large grid cell, can be simulated with improved accuracy using a locally refined grid in MODFLOW-LGR, MODPATH-LGR, and MODPATH-OBS. The locally-refined-grid approach can provide more accurate simulated equivalents to observed transport between the well and the river. The documentation presented here includes a brief discussion of previous work, description of the methods, and detailed descriptions of the required input files and how the output files are typically used.

Techniques and Methods↗

USGS2012

Methods and guidelines for effective model calibration

This paper briefly describes nonlinear regression methods, a set of 14 guidelines for model calibration, how they are implemented in and supported by two public domain computer programs, and a demonstration and a test of the methods and guidelines. Copyright ASCE 2004.

Conference Paper↗

USGS2012

Modeling the Death Valley regional ground-water flow system

The development of a regional ground-water flow model of the Death Valley region in the southwestern United States is discussed in the context of the fourteen guidelines of Hill. This application of the guidelines demonstrates how they may be used for model calibration and evaluation, and to direct further model development and data collection.

California, Nevada↗

USGS2012

Evaluating observations in the context of predictions for the death valley regional groundwater system

When a model is calibrated by nonlinear regression, calculated diagnostic and inferential statistics provide a wealth of information about many aspects of the system. This work uses linear inferential statistics that are measures of prediction uncertainty to investigate the likely importance of continued monitoring of hydraulic head to the accuracy of model predictions. The measurements evaluated are hydraulic heads; the predictions of interest are subsurface transport from 15 locations. The advective component of transport is considered because it is the component most affected by the system dynamics represented by the regional-scale model being used. The problem is addressed using the capabilities of the U.S. Geological Survey computer program MODFLOW-2000, with its Advective Travel Observation (ADV) Package. Copyright ASCE 2004.

Conference Paper↗

USGS2011

Effects of sediment-associated extractable metals, degree of sediment grain sorting, and dissolved organic carbon upon Cryptosporidium parvum removal and transport within riverbank filtration sediments, Sonoma County, California

Oocysts of the protozoan pathogen Cryptosporidium parvum are of particular concern for riverbank filtration (RBF) operations because of their persistence, ubiquity, and resistance to chlorine disinfection. At the Russian River RBF site (Sonoma County, CA), transport of C. parvum oocysts and oocyst-sized (3 μm) carboxylate-modified microspheres through poorly sorted (sorting indices, σ 1 , up to 3.0) and geochemically heterogeneous sediments collected between 2 and 25 m below land surface (bls) were assessed. Removal was highly sensitive to variations in both the quantity of extractable metals (mainly Fe and Al) and degree of grain sorting. In flow-through columns, there was a log–linear relationship ( r 2 = 0.82 at p < 0.002) between collision efficiency (α, the probability that colloidal collisions with grain surfaces would result in attachment) and extractable metals, and a linear relationship ( r 2 = 0.99 at p < 0.002) between α and σ 1 . Collectively, variability in extractable metals and grain sorting accounted for ∼83% of the variability in α (at p < 0.0002) along the depth profiles. Amendments of 2.2 mg L –1 of Russian River dissolved organic carbon (DOC) reduced α for oocysts by 4–5 fold. The highly reactive hydrophobic organic acid (HPOA) fraction was particularly effective in re-entraining sediment-attached microspheres. However, the transport-enhancing effects of the riverine DOC did not appear to penetrate very deeply into the underlying sediments, judging from high α values (∼1.0) observed for oocysts being advected through unamended sediments collected at ∼2 m bls. This study suggests that in evaluating the efficacy of RBF operations to remove oocysts, it may be necessary to consider not only the geochemical nature and size distribution of the sediment grains, but also the degrees of sediment sorting and the concentration, reactivity, and penetration of the source water DOC.

California↗

USGS2010

Analysis of accuracy of approximate, simultaneous, nonlinear confidence intervals on hydraulic heads in analytical and numerical test cases

Inaccuracies in parameter values, parameterization, stresses, and boundary conditions of analytical solutions and numerical models of groundwater flow produce errors in simulated hydraulic heads. These errors can be quantified in terms of approximate, simultaneous, nonlinear confidence intervals presented in the literature. Approximate confidence intervals can be applied in both error and sensitivity analysis and can be used prior to calibration or when calibration was accomplished by trial and error. In this paper, the method is expanded for use in numerical problems, and the accuracy of the approximate intervals is evaluated using Monte Carlo runs. Four test cases are used to compare results. In two numerical test cases, the approximate, simultaneous confidence intervals are generally accurate and are calculated efficiently enough to indicate that the method is useful for real-world problems. In one of the two analytical test cases considered, the approximate intervals are too wide to be of practical interest. Improving the method used to approximate the uncertainty of the model inputs could make the confidence intervals useful in more problems.

Water Resources Research↗

USGS2010

Grid-size dependence of Cauchy boundary conditions used to simulate stream-aquifer interactions

This work examines the simulation of stream–aquifer interactions as grids are refined vertically and horizontally and suggests that traditional methods for calculating conductance can produce inappropriate values when the grid size is changed. Instead, different grid resolutions require different estimated values. Grid refinement strategies considered include global refinement of the entire model and local refinement of part of the stream. Three methods of calculating the conductance of the Cauchy boundary conditions are investigated. Single- and multi-layer models with narrow and wide streams produced stream leakages that differ by as much as 122% as the grid is refined. Similar results occur for globally and locally refined grids, but the latter required as little as one-quarter the computer execution time and memory and thus are useful for addressing some scale issues of stream–aquifer interactions. Results suggest that existing grid-size criteria for simulating stream–aquifer interactions are useful for one-layer models, but inadequate for three-dimensional models. The grid dependence of the conductance terms suggests that values for refined models using, for example, finite difference or finite-element methods, cannot be determined from previous coarse-grid models or field measurements. Our examples demonstrate the need for a method of obtaining conductances that can be translated to different grid resolutions and provide definitive test cases for investigating alternative conductance formulations.

Advances in Water Resources↗

USGS2010

Local sensitivity analysis for inverse problems solved by singular value decomposition

Local sensitivity analysis provides computationally frugal ways to evaluate models commonly used for resource management, risk assessment, and so on. This includes diagnosing inverse model convergence problems caused by parameter insensitivity and(or) parameter interdependence (correlation), understanding what aspects of the model and data contribute to measures of uncertainty, and identifying new data likely to reduce model uncertainty. Here, we consider sensitivity statistics relevant to models in which the process model parameters are transformed using singular value decomposition (SVD) to create SVD parameters for model calibration. The statistics considered include the PEST identifiability statistic, and combined use of the process-model parameter statistics composite scaled sensitivities and parameter correlation coefficients (CSS and PCC). The statistics are complimentary in that the identifiability statistic integrates the effects of parameter sensitivity and interdependence, while CSS and PCC provide individual measures of sensitivity and interdependence. PCC quantifies correlations between pairs or larger sets of parameters; when a set of parameters is intercorrelated, the absolute value of PCC is close to 1.00 for all pairs in the set. The number of singular vectors to include in the calculation of the identifiability statistic is somewhat subjective and influences the statistic. To demonstrate the statistics, we use the USDA’s Root Zone Water Quality Model to simulate nitrogen fate and transport in the unsaturated zone of the Merced River Basin, CA. There are 16 log-transformed process-model parameters, including water content at field capacity (WFC) and bulk density (BD) for each of five soil layers. Calibration data consisted of 1,670 observations comprising soil moisture, soil water tension, aqueous nitrate and bromide concentrations, soil nitrate concentration, and organic matter content. All 16 of the SVD parameters could be estimated by regression based on the range of singular values. Identifiability statistic results varied based on the number of SVD parameters included. Identifiability statistics calculated for four SVD parameters indicate the same three most important process-model parameters as CSS/PCC (WFC1, WFC2, and BD2), but the order differed. Additionally, the identifiability statistic showed that BD1 was almost as dominant as WFC1. The CSS/PCC analysis showed that this results from its high correlation with WCF1 (-0.94), and not its individual sensitivity. Such distinctions, combined with analysis of how high correlations and(or) sensitivities result from the constructed model, can produce important insights into, for example, the use of sensitivity analysis to design monitoring networks. In conclusion, the statistics considered identified similar important parameters. They differ because (1) with CSS/PCC can be more awkward because sensitivity and interdependence are considered separately and (2) identifiability requires consideration of how many SVD parameters to include. A continuing challenge is to understand how these computationally efficient methods compare with computationally demanding global methods like Markov-Chain Monte Carlo given common nonlinear processes and the often even more nonlinear models.

Book↗

USGS2008

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.

Computers & Geosciences↗

USGS2008

Data error and highly parameterized groundwater models

Strengths and weaknesses of highly parameterized models, in which the number of parameters exceeds the number of observations, are demonstrated using a synthetic test case. Results suggest that the approach can yield close matches to observations but also serious errors in system representation. It is proposed that avoiding the difficulties of highly parameterized models requires close evaluation of: (1) model fit, (2) performance of the regression, and (3) estimated parameter distributions. Comparisons to hydrogeologic information are expected to be critical to obtaining credible models. Copyright ?? 2008 IAHS Press.

Conference Paper↗

USGS2007

Testing alternative ground water models using cross-validation and other methods

Many methods can be used to test alternative ground water models. Of concern in this work are methods able to (1) rank alternative models (also called model discrimination) and (2) identify observations important to parameter estimates and predictions (equivalent to the purpose served by some types of sensitivity analysis). Some of the measures investigated are computationally efficient; others are computationally demanding. The latter are generally needed to account for model nonlinearity. The efficient model discrimination methods investigated include the information criteria: the corrected Akaike information criterion, Bayesian information criterion, and generalized cross-validation. The efficient sensitivity analysis measures used are dimensionless scaled sensitivity (DSS), composite scaled sensitivity, and parameter correlation coefficient (PCC); the other statistics are DFBETAS, Cook's D, and observation-prediction statistic. Acronyms are explained in the introduction. Cross-validation (CV) is a computationally intensive nonlinear method that is used for both model discrimination and sensitivity analysis. The methods are tested using up to five alternative parsimoniously constructed models of the ground water system of the Maggia Valley in southern Switzerland. The alternative models differ in their representation of hydraulic conductivity. A new method for graphically representing CV and sensitivity analysis results for complex models is presented and used to evaluate the utility of the efficient statistics. The results indicate that for model selection, the information criteria produce similar results at much smaller computational cost than CV. For identifying important observations, the only obviously inferior linear measure is DSS; the poor performance was expected because DSS does not include the effects of parameter correlation and PCC reveals large parameter correlations. ?? 2007 National Ground Water Association.

Ground Water↗

USGS2007

A new ghost-node method for linking different models and initial investigations of heterogeneity and nonmatching grids

A flexible, robust method for linking parent (regional-scale) and child (local-scale) grids of locally refined models that use different numerical methods is developed based on a new, iterative ghost-node method. Tests are presented for two-dimensional and three-dimensional pumped systems that are homogeneous or that have simple heterogeneity. The parent and child grids are simulated using the block-centered finite-difference MODFLOW and control-volume finite-element FEHM models, respectively. The models are solved iteratively through head-dependent (child model) and specified-flow (parent model) boundary conditions. Boundary conditions for models with nonmatching grids or zones of different hydraulic conductivity are derived and tested against heads and flows from analytical or globally-refined models. Results indicate that for homogeneous two- and three-dimensional models with matched grids (integer number of child cells per parent cell), the new method is nearly as accurate as the coupling of two MODFLOW models using the shared-node method and, surprisingly, errors are slightly lower for nonmatching grids (noninteger number of child cells per parent cell). For heterogeneous three-dimensional systems, this paper compares two methods for each of the two sets of boundary conditions: external heads at head-dependent boundary conditions for the child model are calculated using bilinear interpolation or a Darcy-weighted interpolation; specified-flow boundary conditions for the parent model are calculated using model-grid or hydrogeologic-unit hydraulic conductivities. Results suggest that significantly more accurate heads and flows are produced when both Darcy-weighted interpolation and hydrogeologic-unit hydraulic conductivities are used, while the other methods produce larger errors at the boundary between the regional and local models. The tests suggest that, if posed correctly, the ghost-node method performs well. Additional testing is needed for highly heterogeneous systems. ?? 2007 Elsevier Ltd. All rights reserved.

Advances in Water Resources↗

USGS2006

The practical use of simplicity in developing ground water models

The advantages of starting with simple models and building complexity slowly can be significant in the development of ground water models. In many circumstances, simpler models are characterized by fewer defined parameters and shorter execution times. In this work, the number of parameters is used as the primary measure of simplicity and complexity; the advantages of shorter execution times also are considered. The ideas are presented in the context of constructing ground water models but are applicable to many fields. Simplicity first is put in perspective as part of the entire modeling process using 14 guidelines for effective model calibration. It is noted that neither very simple nor very complex models generally produce the most accurate predictions and that determining the appropriate level of complexity is an ill-defined process. It is suggested that a thorough evaluation of observation errors is essential to model development. Finally, specific ways are discussed to design useful ground water models that have fewer parameters and shorter execution times.

Conference Paper↗

USGS2006

Comparison of local grid refinement methods for MODFLOW

Many ground water modeling efforts use a finite-difference method to solve the ground water flow equation, and many of these models require a relatively fine-grid discretization to accurately represent the selected process in limited areas of interest. Use of a fine grid over the entire domain can be computationally prohibitive; using a variably spaced grid can lead to cells with a large aspect ratio and refinement in areas where detail is not needed. One solution is to use local-grid refinement (LGR) whereby the grid is only refined in the area of interest. This work reviews some LGR methods and identifies advantages and drawbacks in test cases using MODFLOW-2000. The first test case is two dimensional and heterogeneous; the second is three dimensional and includes interaction with a meandering river. Results include simulations using a uniform fine grid, a variably spaced grid, a traditional method of LGR without feedback, and a new shared node method with feedback. Discrepancies from the solution obtained with the uniform fine grid are investigated. For the models tested, the traditional one-way coupled approaches produced discrepancies in head up to 6.8% and discrepancies in cell-to-cell fluxes up to 7.1%, while the new method has head and cell-to-cell flux discrepancies of 0.089% and 0.14%, respectively. Additional results highlight the accuracy, flexibility, and CPU time trade-off of these methods and demonstrate how the new method can be successfully implemented to model surface water-ground water interactions. Copyright ?? 2006 The Author(s).

Conference Paper↗

USGS2006

Ground-water modeling of the Death Valley Region, Nevada and California

The Death Valley regional ground-water flow system (DVRFS) of southern Nevada and eastern California covers an area of about 100,000 square kilometers and contains very complex geology and hydrology. Using a computer model to represent the complex system, the U.S. Geological Survey simulated ground-water flow in the Death Valley region for use with U.S. Department of Energy projects in southern Nevada. The model was created to help address contaminant cleanup activities associated with the underground nuclear testing conducted from 1951 to 1992 at the Nevada Test Site and to support the licensing process for the proposed geologic repository for high-level nuclear waste at Yucca Mountain, Nevada.

California, Nevada↗

USGS2006

Using models to manage systems subject to sustainability indicators

Mathematical and numerical models can provide insight into sustainability indicators using relevant simulated quantities, which are referred to here as predictions. To be useful, many concerns need to be considered. Four are discussed here: (a) mathematical and numerical accuracy of the model; (b) the accuracy of the data used in model development, (c) the information observations provide to aspects of the model important to predictions of interest as measured using sensitivity analysis; and (d) the existence of plausible alternative models for a given system. The four issues are illustrated using examples from conservative and transport modelling, and using conceptual arguments. Results suggest that ignoring these issues can produce misleading conclusions.

Conference Paper↗

USGS2006

New ghost-node method for linking different models with varied grid refinement

A flexible, robust method for linking grids of locally refined ground-water flow models constructed with different numerical methods is needed to address a variety of hydrologic problems. This work outlines and tests a new ghost-node model-linking method for a refined "child" model that is contained within a larger and coarser "parent" model that is based on the iterative method of Steffen W. Mehl and Mary C. Hill (2002, Advances in Water Res., 25, p. 497-511; 2004, Advances in Water Res., 27, p. 899-912). The method is applicable to steady-state solutions for ground-water flow. Tests are presented for a homogeneous two-dimensional system that has matching grids (parent cells border an integer number of child cells) or nonmatching grids. The coupled grids are simulated by using the finite-difference and finite-element models MODFLOW and FEHM, respectively. The simulations require no alteration of the MODFLOW or FEHM models and are executed using a batch file on Windows operating systems. Results indicate that when the grids are matched spatially so that nodes and child-cell boundaries are aligned, the new coupling technique has error nearly equal to that when coupling two MODFLOW models. When the grids are nonmatching, model accuracy is slightly increased compared to that for matching-grid cases. Overall, results indicate that the ghost-node technique is a viable means to couple distinct models because the overall head and flow errors relative to the analytical solution are less than if only the regional coarse-grid model was used to simulate flow in the child model's domain.

Conference Paper↗

USGS2005

A controlled experiment in ground water flow model calibration

Nonlinear regression was introduced to ground water modeling in the 1970s, but has been used very little to calibrate numerical models of complicated ground water systems. Apparently, nonlinear regression is thought by many to be incapable of addressing such complex problems. With what we believe to be the most complicated synthetic test case used for such a study, this work investigates using nonlinear regression in ground water model calibration. Results of the study fall into two categories. First, the study demonstrates how systematic use of a well designed nonlinear regression method can indicate the importance of different types of data and can lead to successive improvement of models and their parameterizations. Our method differs from previous methods presented in the ground water literature in that (1) weighting is more closely related to expected data errors than is usually the case; (2) defined diagnostic statistics allow for more effective evaluation of the available data, the model, and their interaction; and (3) prior information is used more cautiously. Second, our results challenge some commonly held beliefs about model calibration. For the test case considered, we show that (1) field measured values of hydraulic conductivity are not as directly applicable to models as their use in some geostatistical methods imply; (2) a unique model does not necessarily need to be identified to obtain accurate predictions; and (3) in the absence of obvious model bias, model error was normally distributed. The complexity of the test case involved implies that the methods used and conclusions drawn are likely to be powerful in practice.

Groundwater↗