Parameter space methods in joint parameter estimation for groundwater flow models

The joint estimation of model parameters using hydraulic head and tracer concentration data is examined using methods based on parameter space analysis. Response surfaces and confidence regions can indicate how multiple data sets interact to reduce parameter uncertainty. Each data set produces a unique response surface and confidence region. If these surfaces are oriented differently for the two data sets, parameter uncertainties are significantly reduced when the second data set is included in the inversion. If these surfaces are similar for the two data sets, the second data set will not reduce the parameter uncertainty significantly. The axes of the linearized confidence ellipsoid are analyzed to determine the difference in orientation of the confidence regions for the two data sets. The use of confidence regions can be extended to predict the value of a second data set in reducing the uncertainty of parameter estimates, before the data are collected. Parameter space approaches are also introduced for selecting the relative weights for the individual data sets in joint parameter estimation. The conventional method based on the analysis of data residuals is compared to three other methods: with the weights selected to maximize parameter stability, to minimize the volume of the confidence region, or to minimize the longest axis of the confidence region. Each criterion can lead to substantially different weights applied to each of the data sets. The application of these methods is demonstrated using hydraulic head measurements and 14C concentrations to calibrate a model of groundwater flow in the San Juan Basin, New Mexico.

[1]  S. P. Neuman,et al.  Estimation of aquifer parameters under transient and steady-state conditions: 2 , 1986 .

[2]  W. Yeh,et al.  Identification of Parameter Structure in Groundwater Inverse Problem , 1985 .

[3]  C. Voss,et al.  Behavior of sensitivities in the one-dimensional advection-dispersion equation: Implications for parameter estimation and sampling design , 1987 .

[4]  William W.-G. Yeh,et al.  Coupled inverse problems in groundwater modeling - 1. Sensitivity analysis and parameter identification. , 1990 .

[5]  Soroosh Sorooshian,et al.  Response surface parameter sensitivity analysis methods for postcalibration studies , 1982 .

[6]  Jesús Carrera,et al.  Coupled estimation of flow and solute transport parameters , 1996 .

[7]  J. Witmer,et al.  Nonlinear Regression Modeling. , 1984 .

[8]  F. P. Lyford,et al.  Estimates of vertical hydraulic conductivity and regional ground-water flow rates in rocks of Jurassic and Cretaceous age, San Juan Basin, New Mexico and Colorado , 1982 .

[9]  Joel Massmann,et al.  Hydrogeological Decision Analysis: 1. A Framework , 1990 .

[10]  Soroosh Sorooshian,et al.  The Analysis of Structural Identifiability: Theory and Application to Conceptual Rainfall-Runoff Models , 1985 .

[11]  W. Yeh.  Review of Parameter Identification Procedures in Groundwater Hydrology: The Inverse Problem , 1986 .

[12]  A. Long,et al.  An isotopic investigation of groundwater in the Central San Juan Basin, New Mexico: Carbon 14 dating as a basis for numerical flow modeling , 1989 .

[13]  J. Vogel.  INVESTIGATION OF GROUNDWATER FLOW WITH RADIOCARBON. , 1968 .

[14]  Mary C. Hill,et al.  Two-dimensional advective transport in ground-water flow parameter estimation , 1996 .

[15]  Steven M. Gorelick,et al.  Coupled process parameter estimation and prediction uncertainty using hydraulic head and concentration data , 1991 .

[16]  E. Poeter,et al.  Inverse Models: A Necessary Next Step in Ground‐Water Modeling , 1997 .

[17]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[18]  Allan D. Woodbury,et al.  Application of the Arnoldi Algorithm to the solution of the advection‐dispersion equation , 1990 .

[19]  S. Sorooshian,et al.  Automatic calibration of conceptual rainfall-runoff models: The question of parameter observability and uniqueness , 1983 .

[20]  Peter D. H. Hill,et al.  A Review of Experimental Design Procedures for Regression Model Discrimination , 1978 .

[21]  S. P. Neuman,et al.  A statistical approach to the inverse problem of aquifer hydrology: 1. Theory , 1979 .

[22]  Leslie Smith,et al.  Efficient and Responsible Use of Prior Information in Inverse Methods , 1998 .

[23]  Allan D. Woodbury,et al.  Simultaneous inversion of hydrogeologic and thermal data: 2. Incorporation of thermal data , 1988 .

[24]  M. Hill.  A computer program (MODFLOWP) for estimating parameters of a transient, three-dimensional ground-water flow model using nonlinear regression , 1992 .

[25]  W. Broecker,et al.  A 30,000 yr Continental Paleotemperature Record Derived from Noble Gases Dissolved in Groundwater from the San Juan Basin, New Mexico , 1995, Quaternary Research.