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Scientific Investigations Report 2006–5009

MODOPTIM: A General Optimization Program for Ground-Water Flow Model Calibration and Ground-Water Management with MODFLOW

By Keith J. Halford

Version 1.0


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MODOPTIM is a non-linear ground-water model calibration and management tool that simulates flow with MODFLOW-96 as a subroutine. A weighted sum-of-squares objective function defines optimal solutions for calibration and management problems. Water levels, discharges, water quality, subsidence, and pumping-lift costs are the five direct observation types that can be compared in MODOPTIM. Differences between direct observations of the same type can be compared to fit temporal changes and spatial gradients. Water levels in pumping wells, wellbore storage in the observation wells, and rotational translation of observation wells also can be compared. Negative and positive residuals can be weighted unequally so inequality constraints such as maximum chloride concentrations or minimum water levels can be incorporated in the objective function. Optimization parameters are defined with zones and parameter-weight matrices. Parameter change is estimated iteratively with a quasi-Newton algorithm and is constrained to a user-defined maximum parameter change per iteration. Parameters that are less sensitive than a user-defined threshold are not estimated. MODOPTIM facilitates testing more conceptual models by expediting calibration of each conceptual model. Examples of applying MODOPTIM to aquifer-test analysis, ground-water management, and parameter estimation problems are presented.

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   Purpose and Scope

The Optimization Problem
   Objective Function
      Observation Types
   Optimization Parameters
      Zonation and Parameter-Weight Matrices
      Parameter-Weight Matrices from Iso-Value Contours
   Optimization Algorithm
      Minimization Algorithms
      Parameter Sensitivity and Ranking of Parameters Parameter Scaling
   Implementation of Minimization Algorithm in MODOPTIM

MODOPTIM—Organization and Structure
   Coordinate Systems
   Parameter-Weight Matrices
   Optimization Parameters
      Interpolation of Point Observations
      Special Cases for Water-Level Observations
         Water-Levels in Pumping Wells
         Wellbore Storage in Observation Wells
         Rotation of Observation Wells
      Subsidence Observations
      Flow Observations
      Optimization Constraints
      Comparison of Observation Differences
   Weighting of Observations
      Inequality Comparisons
      Different Observation Types
   Output and Analysis of Results
      Parameter Estimates and Optimization Results
      Residuals and Sensitivities

Comparison to Other Programs


Appendix A. Input structures used in MODOPTIM files

Appendix B. Input for main optimization file

Appendix C. Input for composite MODFLOW/MODOPTIM file with parameters to be estimated

Appendix D. Input for grid discretization file

Appendix E. Time-variant hydraulic-property package (VAR1)

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Send questions or comments about this report to the author, Keith Halford at, 775.887.7614.
For more information about USGS activities in Nevada, visit the Nevada Water Science Center home page.

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