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Mary C. Hill

Publications and source records attributed to Mary C. Hill.

At least 55 records · Page 3Linked to original sources
USGS2005

UCODE_2005 and six other computer codes for universal sensitivity analysis, calibration, and uncertainty evaluation constructed using the JUPITER API

This report documents the computer codes UCODE_2005 and six post-processors. Together the codes can be used with existing process models to perform sensitivity analysis, data needs assessment, calibration, prediction, and uncertainty analysis. Any process model or set of models can be used; the only requirements are that models have numerical (ASCII or text only) input and output files, that the numbers in these files have sufficient significant digits, that all required models can be run from a single batch file or script, and that simulated values are continuous functions of the parameter values. Process models can include pre-processors and post-processors as well as one or more models related to the processes of interest (physical, chemical, and so on), making UCODE_2005 extremely powerful. An estimated parameter can be a quantity that appears in the input files of the process model(s), or a quantity used in an equation that produces a value that appears in the input files. In the latter situation, the equation is user-defined. UCODE_2005 can compare observations and simulated equivalents. The simulated equivalents can be any simulated value written in the process-model output files or can be calculated from simulated values with user-defined equations. The quantities can be model results, or dependent variables. For example, for ground-water models they can be heads, flows, concentrations, and so on. Prior, or direct, information on estimated parameters also can be considered. Statistics are calculated to quantify the comparison of observations and simulated equivalents, including a weighted least-squares objective function. In addition, UCODE_2005 can be used fruitfully in model calibration through its sensitivity analysis capabilities and its ability to estimate parameter values that result in the best possible fit to the observations. Parameters are estimated using nonlinear regression: a weighted least-squares objective function is minimized with respect to the parameter values using a modified Gauss-Newton method or a double-dogleg technique. Sensitivities needed for the method can be read from files produced by process models that can calculate sensitivities, such as MODFLOW-2000, or can be calculated by UCODE_2005 using a more general, but less accurate, forward- or central-difference perturbation technique. Problems resulting from inaccurate sensitivities and solutions related to the perturbation techniques are discussed in the report. Statistics are calculated and printed for use in (1) diagnosing inadequate data and identifying parameters that probably cannot be estimated; (2) evaluating estimated parameter values; and (3) evaluating how well the model represents the simulated processes. Results from UCODE_2005 and codes RESIDUAL_ANALYSIS and RESIDUAL_ANALYSIS_ADV can be used to evaluate how accurately the model represents the processes it simulates. Results from LINEAR_UNCERTAINTY can be used to quantify the uncertainty of model simulated values if the model is sufficiently linear. Results from MODEL_LINEARITY and MODEL_LINEARITY_ADV can be used to evaluate model linearity and, thereby, the accuracy of the LINEAR_UNCERTAINTY results. UCODE_2005 can also be used to calculate nonlinear confidence and predictions intervals, which quantify the uncertainty of model simulated values when the model is not linear. CORFAC_PLUS can be used to produce factors that allow intervals to account for model intrinsic nonlinearity and small-scale variations in system characteristics that are not explicitly accounted for in the model or the observation weighting. The six post-processing programs are independent of UCODE_2005 and can use the results of other programs that produce the required data-exchange files. UCODE_2005 and the other six codes are intended for use on any computer operating system. The programs consist of algorithms programmed in Fortran 90/95, which efficiently performs numerical calculations. The model runs required to obtain perturbation sensitivities can be performed using multiple processors. The programs are constructed in a modular fashion using JUPITER API conventions and modules. For example, the data-exchange files and input blocks are JUPITER API conventions and many of those used by UCODE_2005 are read or written by JUPITER API modules. UCODE-2005 includes capabilities likely to be required by many applications (programs) constructed using the JUPITER API, and can be used as a starting point for such programs.

Techniques and Methods↗
USGS2004

A method for evaluating the importance of system state observations to model predictions, with application to the Death Valley regional groundwater flow system

We develop a new observation‐prediction (OPR) statistic for evaluating the importance of system state observations to model predictions. The OPR statistic measures the change in prediction uncertainty produced when an observation is added to or removed from an existing monitoring network, and it can be used to guide refinement and enhancement of the network. Prediction uncertainty is approximated using a first‐order second‐moment method. We apply the OPR statistic to a model of the Death Valley regional groundwater flow system (DVRFS) to evaluate the importance of existing and potential hydraulic head observations to predicted advective transport paths in the saturated zone underlying Yucca Mountain and underground testing areas on the Nevada Test Site. Important existing observations tend to be far from the predicted paths, and many unimportant observations are in areas of high observation density. These results can be used to select locations at which increased observation accuracy would be beneficial and locations that could be removed from the network. Important potential observations are mostly in areas of high hydraulic gradient far from the paths. Results for both existing and potential observations are related to the flow system dynamics and coarse parameter zonation in the DVRFS model. If system properties in different locations are as similar as the zonation assumes, then the OPR results illustrate a data collection opportunity whereby observations in distant, high‐gradient areas can provide information about properties in flatter‐gradient areas near the paths. If this similarity is suspect, then the analysis produces a different type of data collection opportunity involving testing of model assumptions critical to the OPR results.

Water Resources Research↗
USGS2004

Investigating the Macrodispersion Experiment (MADE) site in Columbus, Mississippi, using a three‐dimensional inverse flow and transport model

Flowmeter‐measured hydraulic conductivities from the heterogeneous MADE site have been used predictively in advection‐dispersion models. Resulting simulated concentrations failed to reproduce even major plume characteristics and some have concluded that other mechanisms, such as dual porosity, are important. Here an alternative possibility is investigated: that the small‐scale flowmeter measurements are too noisy and possibly too biased to use so directly in site‐scale models and that the hydraulic head and transport data are more suitable for site‐scale characterization. Using a calibrated finite element model of the site and a new framework to evaluate random and systematic model and measurement errors, the following conclusions are derived. (1) If variations in subsurface fluid velocities like those simulated in this work (0.1 and 2.0 m per day along parallel and reasonably close flow paths) exist, it is likely that classical advection‐dispersion processes can explain the measured plume characteristics. (2) The flowmeter measurements are possibly systematically lower than site‐scale values when the measurements are considered individually and using common averaging methods and display variability that obscures abrupt changes in hydraulic conductivities that are well supported by changes in hydraulic gradients and are important to the simulation of transport.

Water Resources Research↗
USGS2004

Calibration strategies for a groundwater model in a highly dynamic alpine floodplain

Most surface flows to the 20-km-long Maggia Valley in Southern Switzerland are impounded and the valley is being investigated to determine environmental flow requirements. The aim of the investigation is the devel-opment of a modelling framework that simulates the dynamics of the ground-water, hydrologic, and ecologic systems. Because of the multi-scale nature of the modelling framework, large-scale models are first developed to provide the boundary conditions for more detailed models of reaches that are of eco-logical importance. We describe here the initial (large-scale) groundwa-ter/surface water model and its calibration in relation to initial and boundary conditions. A MODFLOW-2000 model was constructed to simulate the inter-action of groundwater and surface water and was developed parsimoniously to avoid modelling artefacts and parameter inconsistencies. Model calibration includes two steady-state conditions, with and without recharge to the aquifer from the adjoining hillslopes. Parameters are defined to represent areal re-charge, hydraulic conductivity of the aquifer (up to 5 classes), and streambed hydraulic conductivity. Model performance was investigated following two system representation. The first representation assumed unknown flow input at the northern end of the groundwater domain and unknown lateral inflow. The second representation used simulations of the lateral flow obtained by means of a raster-based, physically oriented and continuous in time rainfall-runoff (R-R) model. Results based on these two representations are compared and discussed.

Conference Paper↗
USGS2003

MODFLOW-2000, the U.S. Geological Survey modular ground-water model -- Three additions to the Hydrogeologic-Unit Flow (HUF) Package: Alternative storage for the uppermost active cells, Flows in hydrogeologic units, and the Hydraulic-conductivity depth-dependence (KDEP) capability

The Hydrogeologic-Unit Flow (HUF) Package is an internal flow package for MODFLOW-2000 that allows the vertical geometry of the system hydrogeology to be defined differently than the definition of model layers. Effective hydraulic properties for the model layers are calculated using the hydraulic properties of the hydrogeologic units. The HUF Package can be used instead of the Block-Centered Flow (BCF) or the Layer Property Flow (LPF) Packages. This report documents three additions to the HUF Package.

Open-File Report↗
USGS2003

MODFLOW-2000, the U.S. Geological Survey modular ground-water model -- Documentation of MOD-PREDICT for predictions, prediction sensitivity analysis, and evaluation of uncertainty

This document describes the MOD-PREDICT program, which helps evaluate userdefined sets of observations, prior information, and predictions, using the ground-water model MODFLOW-2000. MOD-PREDICT takes advantage of the existing Observation and Sensitivity Processes (Hill and others, 2000) by initiating runs of MODFLOW-2000 and using the output files produced. The names and formats of the MODFLOW-2000 input files are unchanged, such that full backward compatibility is maintained. A new name file and input files are required for MOD-PREDICT. The performance of MOD-PREDICT 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 using the email address available at the web address below. Updates might occasionally be made to this document, to the MOD-PREDICT program, and to MODFLOW- 2000. Users can check for updates on the Internet at URL http://water.usgs.gov/software/ground water.html/.

Open-File Report↗
USGS2003

Using sensitivity analysis in model calibration efforts

In models of natural and engineered systems, sensitivity analysis can be used to assess relations among system state observations, model parameters, and model predictions. The model itself links these three entities, and model sensitivities can be used to quantify the links. Sensitivities are defined as the derivatives of simulated quantities (such as simulated equivalents of observations, or model predictions) with respect to model parameters. We present four measures calculated from model sensitivities that quantify the observation-parameter-prediction links and that are especially useful during the calibration and prediction phases of modeling. These four measures are composite scaled sensitivities (CSS), prediction scaled sensitivities (PSS), the value of improved information (VOII) statistic, and the observation prediction (OPR) statistic. These measures can be used to help guide initial calibration of models, collection of field data beneficial to model predictions, and recalibration of models updated with new field information. Once model sensitivities have been calculated, each of the four measures requires minimal computational effort. We apply the four measures to a three-layer MODFLOW-2000 (Harbaugh et al., 2000; Hill et al., 2000) model of the Death Valley regional ground-water flow system (DVRFS), located in southern Nevada and California. D’Agnese et al. (1997, 1999) developed and calibrated the model using nonlinear regression methods. Figure 1 shows some of the observations, parameters, and predictions for the DVRFS model. Observed quantities include hydraulic heads and spring flows. The 23 defined model parameters include hydraulic conductivities, vertical anisotropies, recharge rates, evapotranspiration rates, and pumpage. Predictions of interest for this regional-scale model are advective transport paths from potential contamination sites underlying the Nevada Test Site and Yucca Mountain.

California, Nevada↗
USGS2002

Evaluation of a local grid refinement method for steady-state block-centered finite-difference groundwater models

A new method of local grid refinement for two-dimensional block-centered finite difference meshes that uses an iteration-based feedback to couple two separate grids has been developed. Its convergence properties have been evaluated and comparisons with alternative methods have been completed (Mehl and Hill, in review a). This work further investigates a difficulty encountered with the traditional telescopic mesh refinement (TMR) methods that lack a feedback. Results indicate: (1) Coupling the coarse grid with the refined grid in a numerically rigorous way that allows for a feedback can improve the coarse grid results; this improvement is not possible using the TMR methods because there is no feedback. (2) The TMR methods work well in situations where the better resolution of the locally refined grid has little influence on the overall flow-system dynamics, but if this is not true, lack of a feedback mechanism produced errors in head up to 6.8% and errors in cell-to-cell fluxes up to 7.1% for the case presented. (3) For the TMR methods, coupling using flux boundary conditions produces significant inconsistencies in the head distribution at the boundary interface. TMR inaccuracies can substantially effect parameter estimation (Mehl and Hill, in review b).

Developments in Water Science↗
USGS2002

MODFLOW-2000, the U.S. Geological Survey modular ground-water model -- Documentation of the Model-Layer Variable-Direction Horizontal Anisotropy (LVDA) capability of the Hydrogeologic-Unit Flow (HUF) package

This report documents the model-layer variable-direction horizontal anisotropy (LVDA) capability of the Hydrogeologic-Unit Flow (HUF) Package of MODFLOW-2000. The LVDA capability allows the principal directions of horizontal anisotropy to be different than the model-grid row and column directions, and for the directions to vary on a cell-by-cell basis within model layers. The HUF Package calculates effective hydraulic properties for model grid cells based on hydraulic properties of hydrogeologic units with thicknesses defined independently of the model layers. These hydraulic properties include, among other characteristics, hydraulic conductivity and a horizontal anisotropy ratio. Using the LVDA capability, horizontal anisotropy direction is defined for model grid cells within which one or more hydrogeologic units may occur. For each grid cell, the HUF Package calculates the effective horizontal hydraulic conductivity along the primary direction of anisotropy using the hydrogeologic-unit hydraulic conductivities, and calculates the effective horizontal hydraulic conductivity along the orthogonal anisotropy direction using the effective primary direction hydraulic conductivities and horizontal anisotropy ratios. The direction assigned to the model layer effective primary hydraulic conductivity is specified using a new data set defined by the LVDA capability, when active, to calculate coefficients needed to solve the ground-water flow equation. Use of the LVDA capability is illustrated in four simulation examples, which also serve to verify hydraulic heads, advective-travel paths, and sensitivities calculated using the LVDA capability. This version of the LVDA capability defines variable-direction horizontal anisotropy using model layers, not the hydrogeologic units defined by the HUF Package. This difference needs to be taken into account when designing model layers and hydrogeologic units to produce simulations that accurately represent a given field problem. This might be a reason, for example, to make model layer boundaries coincide with hydrogeologic-unit boundaries in all or part of a model grid.

Open-File Report↗
USGS2002

Is it More Important to Characterize Heterogeneity or Differences in Hydraulic Conductivity Measurements?

As a first step toward understanding the role of sedimentary structures in flow and transport through porous media, this work deterministically examines how transport simulations compare to observed transport through simple, artificial structures in a laboratory experiment. Small-scale laboratory-measured values of hydraulic conductivity were used to simulate transport in an intermediate-scale (10-m long), two-dimensional, heterogeneous porous medium (s 2 lnK=1.26, mlnK = 4.18, where K is cm hr-1 ). Results were judged based on how well the simulated transport matched observed transport through the tank. Permeameter and column experiments produced laboratory measurements of hydraulic conductivity for each of the five sands used in the intermediate-scale experiments. Despite explicit numerical representation of the heterogeneity, predictions using the laboratory-measured values under-estimated the mean arrival time by as much as 35%. The significance of differences between simulated and observed mean arrival time was investigated by comparing variability of transport predictions using the different measurement methods to that produced by different realizations of the heterogeneous distribution. Results indicate that the variations in measured hydraulic conductivity were more important to transport than variations between realizations of the heterogeneous distribution of hydraulic conductivity.

Conference Paper↗
USGS2001

A new tracer‐density criterion for heterogeneous porous media

Tracer experiments provide information about aquifer material properties vital for accurate site characterization. Unfortunately, density‐induced sinking can distort tracer movement, leading to an inaccurate assessment of material properties. Yet existing criteria for selecting appropriate tracer concentrations are based on analysis of homogeneous media instead of media with heterogeneities typical of field sites. This work introduces a hydraulic‐gradient correction for heterogeneous media and applies it to a criterion previously used to indicate density‐induced instabilities in homogeneous media. The modified criterion was tested using a series of two‐dimensional heterogeneous intermediate‐scale tracer experiments and data from several detailed field tracer tests. The intermediate‐scale experimental facility (10.0×1.2×0.06 m) included both homogeneous and heterogeneous (σ ln k 2 = 1.22) zones. The field tracer tests were less heterogeneous (0.24 < σ ln k 2 < 0.37), but measurements were sufficient to detect density‐induced sinking. Evaluation of the modified criterion using the experiments and field tests demonstrates that the new criterion appears to account for the change in density‐induced sinking due to heterogeneity. The criterion demonstrates the importance of accounting for heterogeneity to predict density‐induced sinking and differences in the onset of density‐induced sinking in two‐ and three‐dimensional systems.

Water Resources Research↗
USGS2001

Predictive modeling of flow and transport in a two‐dimensional intermediate‐scale, heterogeneous porous medium

As a first step toward understanding the role of sedimentary structures in flow and transport through porous media, this work deterministically examines how small‐scale laboratory‐measured values of hydraulic conductivity relate to in situ values of simple, artificial structures in an intermediate‐scale (10 m long), two‐dimensional, heterogeneous, laboratory experiment. Results were judged based on how well simulations using measured values of hydraulic conductivities matched measured hydraulic heads, net flow, and transport through the tank. Discrepancies were investigated using sensitivity analysis and nonlinear regression estimates of the in situ hydraulic conductivity that produce the best fit to measured hydraulic heads and net flow. Permeameter and column experiments produced laboratory measurements of hydraulic conductivity for each of the sands used in the intermediate‐scale experiments. Despite explicit numerical representation of the heterogeneity the laboratory‐measured values underestimated net flow by 12–14% and were distinctly smaller than the regression‐estimated values. The significance of differences in measured hydraulic conductivity values was investigated by comparing variability of transport predictions using the different measurement methods to that produced by different realizations of the heterogeneous distribution. Results indicate that the variations in measured hydraulic conductivity were more important to transport than variations between realizations of the heterogeneous distribution of hydraulic conductivity.

Water Resources Research↗
USGS2001

Preliminary evaluation of the importance of existing hydraulic-head observation locations to advective-transport predictions, Death Valley regional flow system, California and Nevada

When a model is calibrated by nonlinear regression, calculated diagnostic statistics and measures of uncertainty provide a wealth of information about many aspects of the system. This report presents a method of ranking the likely importance of existing observation locations using measures of prediction uncertainty. It is suggested that continued monitoring is warranted at more important locations, and unwarranted or less warranted at less important locations. The report develops the methodology and then demonstrates it using the hydraulic-head observation locations of a three-layer model of the Death Valley regional flow system. The predictions of interest are subsurface transport from beneath Yucca Mountain and 14 Underground Test Areas. The advective component of transport is considered because it is the component most affected by the system dynamics represented by the 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, and an additional computer program developed for this work. The methods presented in this report are used in three ways. (1) The ratings for individual observations are obtained by manipulating the measures of prediction uncertainty, and do not involve recalibrating the model. In this analysis, observation locations are each omitted individually and the resulting increase in uncertainty in the predictions is calculated. The uncertainty is quantified as standard deviations on the simulated advective transport. The increase in uncertainty is quantified as the percent increase in the standard deviations caused by omitting the one observation location from the calculation of standard deviations. In general, observation locations associated with larger increases are rated as more important. (2) Ratings for largely geographically based groups are obtained using a straightforward extension of the method used for individual observation locations. This analysis is needed where observations are clustered to determine whether the area is important to the predictions of interest. (3) Finally, the method is used to evaluate omitting a set of 100 observation locations. The locations were selected because they had low individual ratings and were not one of the few locations at which hydraulic heads from deep in the system were measured. The major results of the three analyses, when applied to the three-layer DVRFS ground-water flow system, are described in the following paragraphs. The discussion is labeled using the numbers 1 to 3 to clearly relate it to the three ways the method is used, as listed above. (1) The individual observation location analysis indicates that three observation locations are most important. They are located in Emigrant Valley, Oasis Valley, and Beatty. Of importance is that these and other observations shown to be important by this analysis are far from the travel paths considered. This displays the importance of the regional setting within which the transport occurs, the importance of including some sites throughout the area in the monitoring network, and the importance of including sites in these areas in particular. The method considered in this report indicates that the 19 observation locations that reflect hydraulic heads deeper in the system (in model layers 1, 2, and 3) are not very important. This appears to be because the locations of these observations are in the vicinity of shallow observation locations that also generally are rated as low importance, and because the model layers are hydraulically well connected vertically. The value of deep observations to testing conceptual models, however, is stressed. As a result, the deep observations are rated higher than is consistent with the results of the analysis presented, and none of these observations are omitted in the scenario discussed under (3) below. (2) The geographic grouping of the observations found one major area of importance not identified by the individual observation analysis. Five of the 49 groups are categorized as most highly important. The most important groups were those that, when omitted, produced mean increases greater than 10 percent at any UGTA site or Yucca Mountain. Four of the five groups were dominated by one individual observation. However, one group, located in Ash Meadows, had no individual observations ranked of high importance but collectively, when omitted, increased uncertainty substantially. Other groups also located in Ash Meadows, including intermediate depth observations, consistently ranked as more important than all other groups. (3) To demonstrate the importance of omitting a set of low-rated observations, one scenario is considered in which the 100 individually lowest-rated shallow and intermediate-depth observation locations are omitted. The measure of overall prediction uncertainty increased by just 0.59 percent, indicating that the wells associated with these observations probably could prudently be measured less frequently.

California, Nevada↗
USGS2000

MODFLOW-2000, the U.S. Geological Survey modular ground-water model; user guide to the observation, sensitivity, and parameter-estimation processes and three post-processing programs

This report documents the Observation, Sensitivity, and Parameter-Estimation Processes of the ground-water modeling computer program MODFLOW-2000. The Observation Process generates model-calculated values for comparison with measured, or observed, quantities. A variety of statistics is calculated to quantify this comparison, including a weighted least-squares objective function. In addition, a number of files are produced that can be used to compare the values graphically. The Sensitivity Process calculates the sensitivity of hydraulic heads throughout the model with respect to specified parameters using the accurate sensitivity-equation method. These are called grid sensitivities. If the Observation Process is active, it uses the grid sensitivities to calculate sensitivities for the simulated values associated with the observations. These are called observation sensitivities. Observation sensitivities are used to calculate a number of statistics that can be used (1) to diagnose inadequate data, (2) to identify parameters that probably cannot be estimated by regression using the available observations, and (3) to evaluate the utility of proposed new data. The Parameter-Estimation Process uses a modified Gauss-Newton method to adjust values of user-selected input parameters in an iterative procedure to minimize the value of the weighted least-squares objective function. Statistics produced by the Parameter-Estimation Process can be used to evaluate estimated parameter values; statistics produced by the Observation Process and post-processing program RESAN-2000 can be used to evaluate how accurately the model represents the actual processes; statistics produced by post-processing program YCINT-2000 can be used to quantify the uncertainty of model simulated values. Parameters are defined in the Ground-Water Flow Process input files and can be used to calculate most model inputs, such as: for explicitly defined model layers, horizontal hydraulic conductivity, horizontal anisotropy, vertical hydraulic conductivity or vertical anisotropy, specific storage, and specific yield; and, for implicitly represented layers, vertical hydraulic conductivity. In addition, parameters can be defined to calculate the hydraulic conductance of the River, General-Head Boundary, and Drain Packages; areal recharge rates of the Recharge Package; maximum evapotranspiration of the Evapotranspiration Package; pumpage or the rate of flow at defined-flux boundaries of the Well Package; and the hydraulic head at constant-head boundaries. The spatial variation of model inputs produced using defined parameters is very flexible, including interpolated distributions that require the summation of contributions from different parameters. Observations can include measured hydraulic heads or temporal changes in hydraulic heads, measured gains and losses along head-dependent boundaries (such as streams), flows through constant-head boundaries, and advective transport through the system, which generally would be inferred from measured concentrations. MODFLOW-2000 is intended for use on any computer operating system. The program consists of algorithms programmed in Fortran 90, which efficiently performs numerical calculations and is fully compatible with the newer Fortran 95. The code is easily modified to be compatible with FORTRAN 77. Coordination for multiple processors is accommodated using Message Passing Interface (MPI) commands. The program is designed in a modular fashion that is intended to support inclusion of new capabilities.

Open-File Report↗
USGS2000

MODFLOW-2000, The U.S. Geological Survey modular ground-water model: User guide to modularization concepts and the ground-water flow process

MODFLOW is a computer program that numerically solves the three-dimensional ground-water flow equation for a porous medium by using a finite-difference method. Although MODFLOW was designed to be easily enhanced, the design was oriented toward additions to the ground-water flow equation. Frequently there is a need to solve additional equations; for example, transport equations and equations for estimating parameter values that produce the closest match between model-calculated heads and flows and measured values. This report documents a new version of MODFLOW, called MODFLOW-2000, which is designed to accommodate the solution of equations in addition to the ground-water flow equation. This report is a user's manual. It contains an overview of the old and added design concepts, documents one new package, and contains input instructions for using the model to solve the ground-water flow equation.

Open-File Report↗
USGS1999

Editorial

No abstract available.

Advances in Water Resources↗