MODFLOW

MODFLOW is the U.S. Geological Survey modular finitedifference flow model, which is a computer code that solves the groundwater flow equation. The program is used by hydrogeologists to simulate the flow of groundwater through aquifers. The code is free software, written primarily in Fortran, and can compile and run on DOS, Windows or Unixlike operating systems.
Since its original development in the early 1980s,^{[1]} the USGS have released four major releases, and is now considered to be the de facto standard code for aquifer simulation. Currently, there are at least five actively developed commercial and noncommercial graphical user interfaces for MODFLOW.
Contents
Groundwater flow equation
The governing partial differential equation used in MODFLOW is:
where
 K_{xx}, K_{yy} and K_{zz} are the values of hydraulic conductivity along the x, y, and z coordinate axes (L/T)
 h is the potentiometric head (L)
 W is a volumetric flux per unit volume representing sources and/or sinks of water, where negative values are extractions, and positive values are injections (T^{−1})
 S_{S} is the specific storage of the porous material (L^{−1}); and
 is time (T)
Finite difference
The finite difference form of the partial differential in a discretized aquifer domain (represented using rows, columns and layers) is:
where
 is the hydraulic head at cell i,j,k at time step m
 CV, CR and CC are the hydraulic conductances, or branch conductances between node i,j,k and a neighboring node
 is the sum of coefficients of head from source and sink terms
 is the sum of constants from source and sink terms, where is flow out of the groundwater system (such as pumping) and is flow in (such as injection)
 is the specific storage
 are the dimensions of cell i,j,k, which, when multiplied, represent the volume of the cell; and
 is the time at time step m
This equation is formulated into a system of equations to be solved as:
where
or in matrix form as:
where
 A is a matrix of the coefficients of head for all active nodes in the grid
 is a vector of head values at the end of time step m for all nodes in the grid; and
 is a vector of the constant terms, RHS, for all nodes of the grid.
Limitations
 The water must have a constant density, dynamic viscosity (and consequently temperature) throughout the modelling domain (SEAWAT is a modified version of MODFLOW which is designed for densitydependent groundwater flow and transport)
 The principal components of anisotropy of the hydraulic conductivity used in MODFLOW is displayed on the right. This tensor does not allow nonorthogonal anisotropies, as could be expected from flow in fractures. Horizontal anisotropy for an entire layer can be represented by the coefficient "TRPY" (Data Item 3 Page 153 ^{[2]}.
Versions
"Modular Model"
The USGS throughout the 1970s had developed several hundred models, written in different dialects of FORTRAN. At the time, it was common practice to rewrite a new model to fit the need of a new groundwater scenario. The concept for MODFLOW was originally designed in 1981 to provide a common modular groundwater model, which could be compiled on multiple platforms without major (or any) modification, and can read and write common formats. Different aspects of the groundwater system would be handled using the modules, similar to the idea of a "component stereo system". The original name of the code was "The USGS Modular ThreeDimensional FiniteDifference GroundWater Flow Model", or informally as "The Modular Model." The name MODFLOW was coined several years after the initial code development, which started in 1981.^{[1]}
The first version of MODFLOW^{[2]} was published on December 28, 1983, and was coded entirely in FORTRAN 66. The source code for this version is listed in USGS Open File Report 83875 referred to above.
MODFLOW88
This version of MODFLOW^{[3]} was rewritten in FORTRAN 77, and was originally released on July 24, 1987. The current version of MODFLOW88 is 2.6, released on September 20, 1996.
MODPATH, was initially developed in 1989 to postprocess the steadystate MODFLOW88 data to determine threedimensional pathlines of particles. This innovation has been indispensable for the fields of contaminant hydrogeology. It is still used as a postprocessor in recent versions of MODFLOW.
A separate program, MODFLOWP, was developed in 1992 to estimate various parameters used in MODFLOW. This program was eventually built into MODFLOW2000.
MODFLOW96
MODFLOW96 (version 3.0) was originally released on December 3, 1996, and is a cleanedup and revised continuation of MODFLOW88.^{[4]}^{[5]} There are three final releases of MODFLOW96:
 MODFLOW96, version 3.3 (May 2, 2000)
 MODFLOW96h (with HYDMOD package), version 3.3h (July 10, 2000)
 MODFLOWP (MODFLOW96 with parameterestimation), version 3.2 (Oct 9, 1997)
Several graphical interfaces were first developed using the MODFLOW96 code.
MODFLOW2000
MODFLOW2000 (version 1.0; version numbering was reset) was released on July 20, 2000, which merged MODFLOWP and HYDMOD codes into the main program.^{[6]} Many new packages and enhancements were also included, including new solvers, stream and saturated flow packages. The internal design concepts also changed from previous versions, such that packages, processes and modules are distinct. This version is coded in a mixture of FORTRAN 77, Fortran 90, and C. MODFLOW2000 can also be compiled for parallel computing, which can allow multiple processors to be used to increase model complexity and/or reduce simulation time.
The current version of MODFLOW2000 (or MF2K) is version 1.19.01, released on March 25, 2010. There are four related or branched codes based on MODFLOW2000:
 MF2KGWM or GWM2000, with groundwater management capability using optimization, version 1.1.1 (March 15, 2007), branched from mf2k 1.17.02
 MF2KFMP, with Farm Process, version 1.00 (May 19, 2006), based on mf2k 1.15.03
 MF2KGWT, groundwater flow and solutetransport model, version 1.9.8 (October 28, 2008), based on MF2K 1.17.02
 SEAWAT, variabledensity flow and transport processes, version 4.00.03 (September 21, 2009), based on MF2K 1.18.01
MODFLOW2005
This is the present development version of MODFLOW.^{[7]} It is written primarily in Fortran 90 and C.
The current version of MODFLOW2005 is version 1.8.00, released on December 18, 2009. Related or branched codes include:
 MODFLOWLGR with local grid refinement, version 1.2 (May 18, 2010)
 GWM2005, with groundwater management capability using optimization, version 1.2.01 (January 26, 2010), built from MODFLOWLGR version 1.1.2
 MF2005FMP2, estimate dynamically integrated supplyanddemand components of irrigated agriculture as part of the simulation of surfacewater and groundwater flow, version 1.0.00 (October 28, 2009), based on MODFLOW2005 version 1.6.01
Packages
Name Long name Version introduced Required packages BAS Basic original OC Output Control original Groundwater flow packages BCF BlockCentered Flow original LPF LayerProperty Flow MODFLOW2000 (1.0) HUF Hydrogeologic Unit Flow MODFLOW2000 (1.1) HFB Horizontal Flow Barrier MODFLOW88 UZF UnsaturatedZone Flow MODFLOW2005 (1.2) Solvers DE4 Direct Solver MODFLOW88 (2.5) GMG Geometric Multigrid Solver MODFLOW2000 (1.15.00) LMG LinkAMG MODFLOW2000 (1.4) ^{[Note 1]} PCG Preconditioned ConjugateGradient MODFLOW88 SIP Strongly Implicit Procedure original SOR Slice Successive OverRelaxation original Headdependent flux boundary packages DAF DAFLOW MODFLOW2000 (1.11) DRN Drain original DRT Drain Return MODFLOW2000 (1.1) ETS Evapotranspiration Segments MODFLOW2000 (1.1) EVT Evapotranspiration original GHB GeneralHead Boundary original LAK Lake MODFLOW2000 (1.1) MNW MultiNode, DrawdownLimited Well MODFLOW2000 (1.11) RES Reservoir MODFLOW88 (2.6) RIV River original SFR StreamflowRouting MODFLOW2000 (1.14.00) STR Stream MODFLOW88 Other stress packages WEL Well original CHD ConstantHead Boundary MODFLOW88 FHB Flow and Head Boundary MODFLOW96 (3.2) RCH Recharge original Miscellaneous packages DIS Discretization MODFLOW2000 (1.0) GAG Gage MODFLOW2000 HYD HYDMOD MODFLOW2000 (1.1) IBS InterbedStorage MODFLOW88 KDEP HydraulicConductivity DepthDependence Capability MODFLOW2000 (1.12) LMT LinkMT3DMS MODFLOW2000 (1.5) LVDA ModelLayer VariableDirection Horizontal Anisotropy Capability MODFLOW2000 (1.12) SUB Subsidence and AquiferSystem Compaction MODFLOW2000 (1.12) SWT Subsidence and AquiferSystem Compaction Package for WaterTable Aquifers MODFLOW2000 (1.18) UTL Utility original Observation process input files OBS Input File For All Observations MODFLOW2000 HOB HeadObservation MODFLOW2000 DROB Drain Observation MODFLOW2000 DTOB Drain Return Observation MODFLOW2000 RVOB River Observation MODFLOW2000 GBOB GeneralHeadBoundary Observation MODFLOW2000 CHOB ConstantHead Flow Observation MODFLOW2000 ADV AdvectiveTransport Observation MODFLOW2000 (1.0) STOB Stream Observation MODFLOW2000 Obsolete packages GFD General FiniteDifference MODFLOW88 to 96 TLK Transient Leakage MODFLOW88 to 96  ^ Due to licensing restrictions, the USGS is no longer able to publicly distribute the Algebraic MultiGrid
Graphical user interfaces
There are several graphical interfaces to MODFLOW, which often include the compiled MODFLOW code with modifications. These programs aid the input of data for creating MODFLOW models.
Noncommercial interfaces
Noncommercial MODFLOW versions are free, however, their licensing usually limit the use to nonprofit educational or research purposes.
 MODFLOWGUI – Made by the USGS: it is updated often to match the current USGS MODFLOW development. It supports MODFLOW96, MODFLOW2000, MODFLOW2005, MODPATH, ZONEBUDGET, GWT, MT3DMS, SEAWAT, and GWM. Source code for MODFLOWGUI is included. It depends on Argus ONE: a commercial interface for constructing generic models. There are no license restrictions beyond those of Argus ONE.
 PMWIN – "Processing MODFLOW" (for Windows) – powerful freeware for MODFLOW processing and visualization, provided alongside an instructional book;^{[9]} also available in Traditional Chinese. The license for this version is limited to noncommercial use.
 ModelMuse is a gridindependent graphical user interface from the USGS for MODFLOW2005, MODPATH, and PHAST. There are no license restrictions. The source code is included. ModelMuse
Commercial programs
Commercial MODFLOW programs are typically used by governments and consultants for practical applications of MODFLOW to realworld groundwater problems. Professional versions of MODFLOW are generally priced at a minimum of around $1000 and typically range upward to $7000 USD. This is a list of commercial programs for MODFLOW:
 GMS – Groundwater Modeling System
 Groundwater Vistas
 Processing Modflow
 Visual MODFLOW
All current versions of these programs run only on Microsoft Windows, however previous versions of GMS (up to Version 3.1) were compiled for several Unix platforms.
Former graphical interfaces
 Graphic Groundwater – Windowsbased interface
 ModelCad – A Windowsbased interface, developed by Geraghty and Miller, Inc.
 ModIME – A DOSbased interface by S.S. Papadopulos & Associates, Inc.
Other Commonly Used Groundwater Models
References
 ^ ^{a} ^{b} McDonald M.G. and Harbaugh, A.W. (2003). "The History of MODFLOW". Ground Water 41 (2): 280–283. doi:10.1111/j.17456584.2003.tb02591.x. PMID 12656294.
 ^ ^{a} ^{b} ^{c} McDonald, M.G., and Harbaugh, A.W. (December 28, 1983). A modular threedimensional finitedifference groundwater flow model. OpenFile Report 83875. U.S. Geological Survey. http://pubs.er.usgs.gov/usgspubs/ofr/ofr83875.
 ^ McDonald, M.G., and Harbaugh, A.W. (1988) (PDF). A modular threedimensional finitedifference groundwater flow model. Techniques of WaterResources Investigations, Book 6. U.S. Geological Survey. http://pubs.usgs.gov/twri/twri6a1/.
 ^ Harbaugh, A.W., and McDonald, M.G. (1996a). User's documentation for MODFLOW96, an update to the U.S. Geological Survey modular finitedifference groundwater flow model. OpenFile Report 96485. U.S. Geological Survey. http://water.usgs.gov/software/code/ground_water/modflow/doc/ofr96485.pdf.
 ^ Harbaugh, A.W., and McDonald, M.G. (1996). Programmer's documentation for MODFLOW96, an update to the U.S. Geological Survey modular finitedifference groundwater flow model. OpenFile Report 96486. U.S. Geological Survey. http://water.usgs.gov/software/code/ground_water/modflow/doc/ofr96486.pdf.
 ^ Harbaugh, A.W., Banta, E.R., Hill, M.C., and McDonald, M.G. (2000). MODFLOW2000, the U.S. Geological Survey modular groundwater model — User guide to modularization concepts and the GroundWater Flow Process. OpenFile Report 0092. U.S. Geological Survey. http://water.usgs.gov/nrp/gwsoftware/modflow2000/ofr0092.pdf.
 ^ Harbaugh, Arlen W. (2005). MODFLOW2005, The U.S. Geological Survey Modular GroundWater Model—the GroundWater Flow Process. Techniques and Methods 6–A16. U.S. Geological Survey. http://pubs.usgs.gov/tm/2005/tm6A16/.
 ^ WenHsing Chiang (2005). 3DGroundwater Modeling with PMWIN (Second ed.). Springer. doi:10.1007/3540275924. ISBN 9783540275909.
External links
Categories: Hydrology models
 Geology software
 United States Geological Survey
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