1. General Model Information

Name: USGS 2-D Method Of Characteristics transport model

Acronym: MOC

Main medium: terrestrial
Main subject: biogeochemistry, hydrology
Organization level: ecosystem
Type of model: partial differential equations (finite differences,2D), ordinary differential equations
Main application:
Keywords: groundwater, solute transport, pollution, adsorption, ion-exchange, convection-dispersion equation, method of characteristics, MOC, finite difference numerics, first order degradation, nonlinear adsorption isotherms, confined aquifers


U.S. Geological Survey
Hydrologic Analysis Software Support Team
R. Steven Regan
437 National Center
Reston, VA 20192
Fax :
email: h2osoft@usgs.gov


Authors: L.F. Konikow and J.D. Bredehoeft (U.S. Geological Survey)


MOC is a two-dimensional model for the simulation of non-conservative solute transport in saturated ground-water systems. The model is both general in its applicability and flexible in its design. Thus, it can be applied to a wide range of problems. It computes changes in the spatial concentration distribution over time caused by convective transport, hydrodynamic dispersion, mixing or dilution from recharge and chemical reactions. The chemical reactions include first-order irreversible rate reaction (such as radioactive decay), reversible equilibrium-controlled sorption with linear, Freundlich, or Langmuir isotherms, and reversible equilibrium-controlled ion exchange for monovalent or divalent ions. The model assumes that fluid density variations, viscosity changes, and temperature gradients do not affect the velocity distribution. MOC allows modeling heterogeneous and anisotropic, confined aquifers. MOC solves the ground-water flow equation and the non-conservative solute-transport equation in a step-wise (uncoupled) fashion. The computer program uses the Alternating Direction Implicit (ADI) method or the Strongly Implicit Procedure (SIP) to solve the finite-difference approximation of the ground-water flow equation. The SIP procedure for solving the ground-water flow equation is most useful when areal discontinuities in transmissivity exist or when the ADI solution does not converge. MOC uses the method of characteristics to solve the solute transport equation. It uses a particle tracking procedure to represent convective transport and a two-step explicit procedure to solve the finite-difference equation that describes the effects of hydrodynamic dispersion, fluid sources and sinks, and divergence of velocity. The explicit procedure is subject to stability criteria, but the program automatically determines and implements the time step limitations necessary to satisfy the stability criteria. MOC uses a rectangular, block-centered finite-difference grid for flux and transport calculations. The grid size for flow and transport equations allows up to 100 rows and 100 columns. The program allows spatially varying diffuse recharge or discharge, saturated thickness, transmissivity, boundary conditions, initial heads and initial concentrations, and an unlimited number of injection or withdrawal wells. Up to five nodes can be designated as observation points for which a summary table of head and concentration versus time is printed at the end of the calculations. An interactive preprocessor, PREMOC, developed by the IGWMC and updated by the USGS, is included with the program to facilitate user-friendly data entry and editing. The program produces tabular output which can be processed in a commercial contouring package. The MOC package includes the preprocessor, PREMOC, and two versions of the MOC program, one that can handle a 40 by 40 grid and a big version that can handle a 100 by 100 grid. A batch file capability is also included for conducting multiple runs during calibration and sensitivity analysis. MOC is distributed with source code, executable image and example data sets. The users manual includes installation procedures, data input formats, and various documentation reports prepared by the USGS.

Source of the Abstract: IGWMC

Note that, in the meantime, a 3D-Version of MOC has been developed : USGS-MOC3D

II. Technical Information

II.1 Executables:

Operating System(s): DOS - IBM-compatible PC, 386 or higher with math coprocessor, Data General AViiON DG/UX , Silicon Graphics Indigo, Sun SPARCstation Solaris

II.2 Source-code:

Programming Language(s): FORTRAN

II.3 Manuals:

Available in Postscript and PDF Format, download from MOC software page

II.4 Data:

MOC example data files

III. Mathematical Information

III.1 Mathematics

III.2 Quantities

III.2.1 Input

III.2.2 Output

IV. References

Konikow, L.F., Granato, G.E., and Hornberger, G.Z., 1994, User's guide to revised method-of-characteristics solute-transport model (MOC--Version 3.1): U.S. Geological Survey Water-Resources Investigations Report 94-4115.
Goode, D.J., and Konikow, L.F., 1989 , Modification of a method-of- characteristics solute-transport model to incorporate decay and equilibrium-controlled sorption or ion exchange: U.S. Geological Survey Water-Resources Investigations Report 89-4030, 65 p.
Konikow, L.F., and Bredehoeft, J.D., 1978, Computer model of two- dimensional solute transport and dispersion in ground water: U.S. Geological Survey Techniques of Water-Resources Investigations, book 7, chap. C2, 90 p.

The basic MODFLOW documentation is contained in the following three reports:

McDonald, M.G., and Harbaugh, A.W., 1988, A modular three- imensional finite-difference ground-water flow model: U.S. Geological Survey Techniques of Water-Resources Investigations, book 6, chap. A1, 586 p.
Harbaugh, A.W., and McDonald, M.G., 1996, User's documentation for MODFLOW-96, and update to the U.S. Geological Survey modular finite-difference ground-water flow model: U.S. Geological Survey Open-File Report 96-485, 56 p.
Harbaugh, A.W., and McDonald, M.G., 1996, Programmer's documentation for MODFLOW-96, and update to the U.S. Geological Survey modular finite-difference ground-water flow model: U.S. Geological Survey Open-File Report 96-486, 220 p.

V. Further information in the World-Wide-Web

VI. Additional remarks

Last review of this document by: T. Gabele: 24. 6. 1997 -
Status of the document:
last modified by Tobias Gabele Wed Aug 21 21:44:45 CEST 2002

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