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M. C. Hill

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

52 records · Page 3Linked to original sources
USGS1999

UCODE, a computer code for universal inverse modeling

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.

Computers & Geosciences↗
USGS1999

Death valley regional ground-water flow model calibration using optimal parameter estimation methods and geoscientific information systems

A regional-scale, steady-state, saturated-zone ground-water flow model was constructed to evaluate potential regional ground-water flow in the vicinity of Yucca Mountain, Nevada. The model was limited to three layers in an effort to evaluate the characteristics governing large-scale subsurface flow. Geoscientific information systems (GSIS) were used to characterize the complex surface and subsurface hydrogeologic conditions of the area, and this characterization was used to construct likely conceptual models of the flow system. Subsurface properties in this system vary dramatically, producing high contrasts and abrupt contacts. This characteristic, combined with the large scale of the model, make zonation the logical choice for representing the hydraulic-conductivity distribution. Different conceptual models were evaluated using sensitivity analysis and were tested by using nonlinear regression to determine parameter values that are optimal, in that they provide the best match between the measured and simulated heads and flows. The different conceptual models were judged based both on the fit achieved to measured heads and spring flows, and the plausibility of the optimal parameter values. One of the conceptual models considered appears to represent the system most realistically. Any apparent model error is probably caused by the coarse vertical and horizontal discretization.A regional-scale, steady-state, saturated-zone ground-water flow model was constructed to evaluate potential regional ground-water flow in the vicinity of Yucca Mountain, Nevada. The model was limited to three layers in an effort to evaluate the characteristics governing large-scale subsurface flow. Geoscientific information systems (GSIS) were used to characterize the complex surface and subsurface hydrogeologic conditions of the area, and this characterization was used to construct likely conceptual models of the flow system. Subsurface properties in this system vary dramatically, producing high contrasts and abrupt contacts. This characteristic, combined with the large scale of the model, make zonation the logical choice for representing the hydraulic-conductivity distribution. Different conceptual models were evaluated using sensitivity analysis and were tested by using nonlinear regression to determine parameter values that are optimal, in that they provide the best match between the measured and simulated heads and flows. The different conceptual models were judged based both on the fit achieved to measured heads and spring flows, and the plausibility of the optimal parameter values. One of the conceptual models considered appears to represent the system most realistically. Any apparent model error is probably caused by the coarse vertical and horizontal discretization.

Advances in Water Resources↗
USGS1998

Concentration data and dimensionality in groundwater models: Evaluation using inverse modelling

A three-dimensional inverse groundwater flow and transport model that fits hydraulic-head and concentration data simultaneously using nonlinear regression is presented and applied to a layered sand and silt groundwater system beneath the Grindsted Landfill in Denmark. The aquifer is composed of rather homogeneous hydrogeologic layers. Two issues common to groundwater flow and transport modelling are investigated: 1) The accuracy of simulated concentrations in the case of calibration with head data alone; and 2) The advantages and disadvantages of using a two-dimensional cross-sectional model instead of a three-dimensional model to simulate contaminant transport when the source is at the land surface. Results show that using only hydraulic heads in the nonlinear regression produces a simulated plume that is profoundly different from what is obtained in a calibration using both hydraulic-head and concentration data. The present study provides a well-documented example of the differences that can occur. Representing the system as a two-dimensional cross-section obviously omits some of the system dynamics. It was, however, possible to obtain a simulated plume cross-section that matched the actual plume cross-section well. The two-dimensional model execution times were about a seventh of those for the three-dimensional model, but some difficulties were encountered in representing the spatially variable source concentrations and less precise simulated concentrations were calculated by the two-dimensional model compared to the three-dimensional model. Summed up, the present study indicates that three dimensional modelling using both hydraulic heads and concentrations in the calibration should be preferred in the considered type of transport studies.

Grindsted Landfill↗
USGS1998

Methods and guidelines for effective model calibration; with application to UCODE, a computer code for universal inverse modeling, and MODFLOWP, a computer code for inverse modeling with MODFLOW

This report documents methods and guidelines for model calibration using inverse modeling. The inverse modeling and statistical methods discussed are broadly applicable, but are presented as implemented in the computer programs UCODE, a universal inverse code that can be used with any application model, and MODFLOWP, an inverse code limited to one application model. UCODE and MODFLOWP perform inverse modeling, posed as a parameter-estimation problem, by calculating parameter values that minimize a weighted least-squares objective function using nonlinear regression. Minimization is accomplished using a modified Gauss-Newton method, and prior, or direct, information on estimated parameters can be included in the regression. Inverse modeling in many fields is plagued by problems of instability and nonuniqueness, and obtaining useful results depends on (1) defining a tractable inverse problem using simplifications appropriate to the system under investigation and (2) wise use of statistics generated using calculated sensitivities and the match between observed and simulated values, and associated graphical analyses. Fourteen guidelines presented in this work suggest ways of constructing and calibrating models of complex systems such that the resulting model is as accurate and useful as possible.

Water-Resources Investigations Report↗
USGS1998

Documentation of UCODE: A computer code for universal inverse modeling

This report documents the computer program UCODE, which 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 pre-processors and post-processors as well as models related to the processes of interest (physical, chemical, and so on), making UCODE extremely powerful. An estimated parameter can be a quantity that appears in the input files of the application model(s), or that can be used in conjunction with user-defined functions to calculate a quantity that appears in the input files. Observations to be matched in the regression can be any quantity for which a simulated equivalent value can be produced, and simulated equivalent values are calculated using values that appear in the application model output files and a set of additive and multiplicative functions. 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 and identifying parameters that probably cannot be estimated; (2) evaluating estimated parameter values; (3) evaluating the model representation of the actual processes; and (4) quantifying the likely 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.

Water-Resources Investigations Report↗
USGS1996

Unrealistic parameter estimates in inverse modelling: A problem or a benefit for model calibration?

Estimation of unrealistic parameter values by inverse modelling is useful for constructed model discrimination. This utility is demonstrated using the three-dimensional, groundwater flow inverse model MODFLOWP to estimate parameters in a simple synthetic model where the true conditions and character of the errors are completely known. When a poorly constructed model is used, unreasonable parameter values are obtained even when using error free observations and true initial parameter values. This apparent problem is actually a benefit because it differentiates accurately and inaccurately constructed models. The problems seem obvious for a synthetic problem in which the truth is known, but are obscure when working with field data. Situations in which unrealistic parameter estimates indicate constructed model problems are illustrated in applications of inverse modelling to three field sites and to complex synthetic test cases in which it is shown that prediction accuracy also suffers when constructed models are inaccurate.

IAHS-AISH Publication↗
USGS1996

Identification of groundwater parameters at Columbus, Mississippi, using a 3D inverse flow and transport model

An extensive amount of data including hydraulic heads, hydraulic conductivities and concentrations of several solutes from controlled injections have been collected during the MADE 1 and MADE 2 experiments at a heterogeneous site near Columbus, Mississippi. In this paper the use of three-dimensional inverse groundwater models including simultaneous estimation of flow and transport parameters is proposed to help identify the dominant characteristics at the site. Simulations show that using a hydraulic conductivity distribution obtained from 2187 borehole flowmeter tests directly in the model produces poor matches to the measured hydraulic heads and tritium concentrations. Alternatively, time averaged hydraulic head maps are used to define zones of constant hydraulic conductivity to be estimated. Preliminary simulations suggest that in the case of conservative transport many, but not all, of the major plume characteristics can be explained by large-scale heterogeneity in recharge and hydraulic conductivity.

IAHS-AISH Publication↗
USGS1996

Death Valley regional groundwater flow model calibration using optimal parameter estimation methods and geoscientific information systems

A three-layer Death Valley regional groundwater flow model was constructed to evaluate potential regional groundwater flow paths in the vicinity of Yucca Mountain, Nevada. Geoscientific information systems were used to characterize the complex surface and subsurface hydrogeological conditions of the area, and this characterization was used to construct likely conceptual models of the flow system. The high contrasts and abrupt contacts of the different hydrogeological units in the subsurface make zonation the logical choice for representing the hydraulic conductivity distribution. Hydraulic head and spring flow data were used to test different conceptual models by using nonlinear regression to determine parameter values that currently provide the best match between the measured and simulated heads and flows.

IAHS-AISH Publication↗
USGS1992

Comparison of three newton-like nonlinear least-squares methods for estimating parameters of ground-water flow models

Three methods of solving nonlinear least-squares problems were compared for robustness and efficiency using a series of hypothetical and field problems. A modified Gauss-Newton/full Newton hybrid method (MGN/FN) and an analogous method for which part of the Hessian matrix was replaced by a quasi-Newton approximation (MGN/QN) solved some of the problems with appreciably fewer iterations than required using only a modified Gauss-Newton (MGN) method. In these problems, model nonlinearity and a large variance for the observed data apparently caused MGN to converge more slowly than MGN/FN or MGN/QN after the sum of squared errors had almost stabilized. Other problems were solved as efficiently with MGN as with MGN/FN or MGN/QN. Because MGN/FN can require significantly more computer time per iteration and more computer storage for transient problems, it is less attractive for a general purpose algorithm than MGN/QN.

Conference Paper↗
USGS1990

Relative efficiency of four parameter-estimation methods in steady-state and transient ground-water flow models

Parameters in numerical ground-water flow models have been successfully estimated using nonlinear-optimization methods such as the modified Gauss-Newton (GN) method and conjugate-direction methods. This paper investigates the relative efficiency of GN and three conjugate-direction parameter-estimation methods on two-dimensional, steady-state and transient ground-water flow test cases. The steady-state test cases are included to compare the performance of the algorithm with published examples. The three conjugate-direction methods are the Fletcher-Reeves (FR) and quasi-Newton (QN) regression methods, and combination Fletcher-Reeves quasi-Newton (FR-QN). All three are combined with Newton's method of calculating step size. The numerical ground-water flow model is described by McDonald and Harbaugh.

Conference Paper↗
USGS1989

Simulated effects of future withdrawals on water levels in the northeastern coastal plain aquifers of New Jersey

In the northeastern Coastal Plain of New Jersey, groundwater withdrawals have produced large cones of depression in all four major regional aquifers. Prior to development, water levels in the four aquifers were 20 to 120 ft above sea level and natural groundwater flow was towards Raritan Bay. In 1983, when total withdrawals exceeded 90 million gal/day, water levels were as low as 185 ft below sea level in the Wenonah-Mount Laurel aquifer, 225 ft below sea leval in the Englishtown aquifer system and 52 and 82 ft below sea level in the upper and middle aquifers of the Potomac-Raritan-Magothy aquifer system, respectively. With development, the natural direction of groundwater flow has been reversed, resulting in the movement of saltwater into parts of the upper and middle aquifers of the Potomac-Raritan-Magothy aquifer system. An 11-layer finite-difference model of the entire New Jersey Coastal Plain was used to simulate the effects of six scenarios of future groundwater withdrawals on water levels in the northeastern Coastal Plain of New Jersey through the year 2020. In the simulation with the most severe reduction, most of the groundwater withdrawals in the northeastern and west-central areas of the Coastal Plain were limited to 50% of 1983 withdrawals after 1990. Even with such restrictions, the lowest simulated water levels in the northeastern part of the Coastal Plain for 2010 are still well below sea level. (USGS)

Water-Resources Investigations Report↗