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Mary C. Hill


U.S. Geological Survey Water-Resources Investigations Report 98-4005

By Mary C. Hill


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.

Method 1

Composite scaled sensitivities for parameters of the initial Death Valley regional ground-water flow system model of D'Agnese and others (1998, in press). K* are hydraulic-conductivity parameters, ANIV* are vertical anisotropy parameters, RCH is an areal recharge parameter, and ETM is a maximum evapotranspiration parameter. The composite scaled sensitivities indicate that the available data provide the most information about parameters K4 and RCH.

Method 2

Composite scaled sensitivities for the parameters of the final calibrated Death Valley regional ground-water system model of D'Agnese and others (in press). Parameters estimated by regression have black bars; parameters defined but not estimated by regression have gray bars.

Full PDF Document (wr984005.pdf) and Errata (wr98-4005errata.pdf).

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Last Modified: March 17, 1999