MODFLOW

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MODFLOW simulation Mf2k 1 17.png
MODFLOW simulation

MODFLOW is the U.S. Geological Survey modular finite-difference 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 source code is free public domain software, [1] written primarily in Fortran, and can compile and run on Microsoft Windows or Unix-like operating systems.

Contents

3-dimensional grid MODFLOW 3D grid.png
3-dimensional grid

Since its original development in the early 1980s, [2] the USGS has made six major releases, and is now considered to be the de facto standard code for aquifer simulation. There are several actively developed commercial and non-commercial graphical user interfaces for MODFLOW.

MODFLOW was constructed in what was in 1980's called a modular design. This means it has many of the attributes of what came to be called object-oriented programming. For example, capabilities (called "packages") that simulate subsidence or lakes or streams, can easily be turned on and off and the execution time and storage requirements of those packages go away entirely. If a programmer wants to change something in MODFLOW, the clean organization makes it easy. Indeed, this kind of innovation is exactly what was anticipated when MODFLOW was designed.

Importantly, the modularity of MODFLOW makes it possible for different Packages to be written that are intended to address the same simulation goal in different ways. This allows differences of opinion about how system processes function to be tested. Such testing is an important part of multi-modeling, or alternative hypothesis testing. Models like MODFLOW make this kind of testing more definitive and controlled. This results because other aspects of the program remain the same. Tests become more definitive because they become less prone to being influenced unknowingly by other numerical and programming differences.

Groundwater flow equation

The governing partial differential equation for a confined aquifer used in MODFLOW is:

where

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

Versions

Cover image from McDonald & Harbaugh (1983), which illustrates a computer surrounded by modules and arrays used by MODFLOW. This was said at the time to resemble a "component stereo system". Modflow original.png
Cover image from McDonald & Harbaugh (1983), which illustrates a computer surrounded by modules and arrays used by MODFLOW. This was said at the time to resemble a "component stereo system".

"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 Three-Dimensional Finite-Difference Ground-Water Flow Model", or informally as "The Modular Model". The name MODFLOW was coined several years after the initial code development, which started in 1981. [2]

The first version of MODFLOW [3] 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 83-875 referred to above.

MODFLOW-88

This version of MODFLOW [4] was rewritten in FORTRAN 77, and was originally released on July 24, 1987. The current version of MODFLOW-88 is 2.6, released on September 20, 1996.

MODPATH, was initially developed in 1989 to post-process the steady-state MODFLOW-88 data to determine three-dimensional pathlines of particles. This innovation has been indispensable for the fields of contaminant hydrogeology. It is still used as a post-processor 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 MODFLOW-2000.

MODFLOW-96

MODFLOW-96 (version 3.0) was originally released on December 3, 1996, and is a cleaned-up and revised continuation of MODFLOW-88. [5] [6] There are three final releases of MODFLOW-96:

Several graphical interfaces were first developed using the MODFLOW-96 code.

MODFLOW-2000

MODFLOW-2000 (version 1.0; version numbering was reset) was released on July 20, 2000, which merged MODFLOWP and HYDMOD codes into the main program and has integrated observation, sensitivity analysis, parameter estimation, and uncertainty evaluation capabilities. [7] 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 was coded in a mixture of FORTRAN 77, Fortran 90, and one solver was programmed in C. MODFLOW-2000 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 parallelization capability is designed to support the sensitivity analysis, parameter estimation, and uncertainty analysis capabilities of MODFLOW-2000.

The final version of MODFLOW-2000 (or MF2K) is version 1.19.01, released on March 25, 2010. There are four related or branched codes based on MODFLOW-2000:

MODFLOW-2005

MODFLOW-2005 [8] differs from MODFLOW-2000 in that the sensitivity analysis, parameter estimation, and uncertainty evaluation capabilities are removed. Thus, the support for these capabilities now falls to "clip on" codes that are supported externally to the MODFLOW support effort. In addition, the code was reorganized to support multiple models within one MODFLOW run, as needed for the LGR (Local Grid Refinement) capability. [9] MODFLOW-2005 is written primarily in Fortran 90 and C, with C being used for one solver.

The current version of MODFLOW-2005 is version 1.12.00, released on February 3, 2017. Related or branched codes include:

MODFLOW 6

MODFLOW 6 (MF6), first released in 2017, is the sixth core version of MODFLOW to be released by the USGS. [16] This release is a rewrite of MODFLOW following an object-oriented programming paradigm in Fortran, and provides a platform that includes the capabilities from several previous MODFLOW-2005 versions, including MODFLOW-NWT, MODFLOW-USG, and MODFLOW-LGR. [17] MODFLOW 6 supports structured or unstructured grids, has full support for the Newton-Raphson formulation, and has a unique Water Mover Package that allows flows to be routed between the advanced packages, including the Streamflow Routing, Lake, Multi-Aquifer Well, and Unsaturated Zone Flow Packages. MODFLOW 6 also contains a Groundwater Transport (GWT) model that simulates transient three-dimensional solute transport on structured or unstructured grids and through the advanced flow and mover packages. An Application Programming Interface (API) is also available for MODFLOW 6, which allows the program to be coupled with other models or controlled with popular scripting languages, such as Python. While there are a few features lacking in the current release that are supported in MODFLOW-2005, most of the popular capabilities in previous MODFLOW versions are available in MODFLOW 6. The current version is 6.2.2, released July 30, 2021. [18]

MODFLOW-OWHM Version 2

The MODFLOW One-Water Hydrologic Flow Model version 2 [19] (MF-OWHM) is a major rewrite of MF-OWHM1 [11] released in 2020. [20] MF-OWHM is a MODFLOW-2005 based integrated hydrologic model designed for the analysis of conjunctive-use management. The term “integrated” refers to the tight coupling of groundwater flow, surface-water flow, landscape processes, aquifer compaction and subsidence, reservoir operations, and conduit (karst) flow. This fusion results in a simulation software capable of addressing water-use and sustainability problems, including conjunctive-use, water-management, water-food-security, and climate-crop-water scenarios. [21]

As a second core version of MODFLOW-2005, MF-OWHM maintains backward compatibility with existing MODFLOW-2005 versions. Existing models developed using MODFLOW-2005, [8] MODFLOW-NWT, [10] MODFLOW-SWI, [22] MODFLOW-SWR, [23] MODFLOW-LGR, [24] and MODFLOW-CFP [25] can also be simulated using MF-OWHM. The Farm Process (FMP) [26] is part of MF-OWHM but is the only component that does not maintain input backward compatibility with past releases (see the FMP_Template for new input structure). MF-OWHM also includes a Surface Water Operations Module [27] (SWO) with a Fortran-like scripting language, Slang, that can specify dynamic reservoir and stream operations. A current major application of MF-OWHM, developed by the USGS, is the California Central Valley (CVHM2). [28]

The current USGS Approved Software version is 2.3.0 [29] [30] released on January 15, 2024, and current preliminary-beta release of 2.3.1b-4 [31] released on February 27, 2025.

Packages

The names in this table are the labels used to turn MODFLOW capabilities on and off via a key input file. Most capabilities have many alternatives or can be omitted, but the ones related to the BASIC Package are always required. Many of the capabilities introduced are supported in later versions, though the grid change enabled with MODFLOW-USG and MODFLOW 6 meant that such backward compatibility was rather selective.

NameLong nameVersion introduced
Basic Package and its Components
BASBasic Packageoriginal
OCOutput Controloriginal
DIS Discretization MODFLOW-2000 (1.0)
DISU Unstructured DiscretizationMODFLOW-USG (1.0)
DISVDiscretization by VerticesMODFLOW 6 (1.00)
IC Initial Conditions MODFLOW 6 (1.00)
Groundwater flow packages
BCFBlock-Centered Flow Packageoriginal
CLNConnected Linear Network ProcessMODFLOW-USG (1.0)
GNCGhost Node Correction PackageMODFLOW-USG (1.0)
HFBHorizontal Flow Barrier PackageMODFLOW-88
HUFHydrogeologic Unit Flow PackageMODFLOW-2000 (1.1)
LPFLayer-Property Flow PackageMODFLOW-2000 (1.0)
NPFNode Property FlowMODFLOW 6 (1.00)
SWI2Seawater Intrusion PackageMODFLOW-2005 (1.11)
UPWUpstream Weighting PackageMODFLOW-NWT (1.0)
UZFUnsaturated-Zone Flow PackageMODFLOW-2005 (1.2)
Conjunctive Use and Land Use Simulation
FMPFarm ProcessMODFLOW-FMP
SWOSurface Water OperationsMODFLOW-OWHM (2.0)
Specified Head boundary packages
CHDConstant-Head Boundary / Time-Variant Specified-HeadMODFLOW-88
FHBFlow and Head Boundary PackageMODFLOW-96 (3.2)
Specified flux boundary packages
FHBFlow and Head Boundary PackageMODFLOW-96 (3.2)
RCH Recharge Packageoriginal
WEL Well Packageoriginal
Head-dependent flux boundary packages
DAFDAFLOWMODFLOW-96
DRN Drain Packageoriginal
DRTDrain Return PackageMODFLOW-2000 (1.1)
ETSEvapotranspiration Segments PackageMODFLOW-2000 (1.1)
EVT Evapotranspiration Packageoriginal
GHBGeneral-Head Boundary Packageoriginal
LAK Lake PackageMODFLOW-2000 (1.1)
MAWMulti-Aquifer WellMODFLOW 6 (1.00)
MNWMulti-Node, Drawdown-Limited Well PackageMODFLOW-2000 (1.11)
RES Reservoir PackageMODFLOW-88 (2.6)
RIP Riparian Evapotranspiration PackageMODFLOW-OWHM (1.0)
RIV River Packageoriginal
SFRStreamflow-Routing PackageMODFLOW-2000 (1.14.00)
STR Stream PackageMODFLOW-88
SWRSurface-Water Routing ProcessMODFLOW-NWT 1.08
UZFUnsaturated-Zone Flow PackageMODFLOW-2005 (1.2)
Solvers
DE4Direct Solver PackageMODFLOW-88 (2.5)
GMGGeometric Multigrid SolverMODFLOW-2000 (1.15.00)
LMGLink-AMG PackageMODFLOW-2000 (1.4) [Note 1]
NWTNewton-RaphsonMODFLOW-NWT (1.0)
PCGPreconditioned Conjugate-Gradient PackageMODFLOW-88
PCGNPreconditioned Conjugate Gradient Solver with Improved Nonlinear ControlMODFLOW-2005 (1.9.0)
SIPStrongly Implicit Procedure Packageoriginal
SMS Sparse Matrix SolverMODFLOW-USG (1.0)
SORSlice Successive Over-Relaxation Packageoriginal
Miscellaneous packages
GAGGageMODFLOW-2000
HYDHYDMODMODFLOW-2000 (1.1)
IBSInterbed-StorageMODFLOW-88
KDEPHydraulic-Conductivity Depth-Dependence CapabilityMODFLOW-2000 (1.12)
LMTLink-MT3DMS MODFLOW-2000 (1.5)
LVDAModel-Layer Variable-Direction Horizontal Anisotropy CapabilityMODFLOW-2000 (1.12)
MVRWater MoverMODFLOW 6 (1.00)
STO Storage MODFLOW 6 (1.00)
SUBSubsidence and Aquifer-System CompactionMODFLOW-2000 (1.12)
SWTSubsidence and Aquifer-System Compaction Package for Water-Table AquifersMODFLOW-2000 (1.18)
CSUBSkeletal Storage, Compaction, and SubsidenceMODFLOW 6 (6.1.0)
UTLUtilityoriginal
Observation process input files
OBSInput File For All ObservationsMODFLOW-2000
HOBHead-ObservationMODFLOW-2000
DROBDrain ObservationMODFLOW-2000
DTOBDrain Return ObservationMODFLOW-2000
RVOBRiver ObservationMODFLOW-2000
GBOBGeneral-Head-Boundary ObservationMODFLOW-2000
CHOBConstant-Head Flow ObservationMODFLOW-2000
ADVAdvective-Transport ObservationMODFLOW-2000 (1.0)
STOBStream ObservationMODFLOW-2000
Obsolete packages
GFDGeneral Finite-DifferenceMODFLOW-88 to 96
TLKTransient LeakageMODFLOW-88 to 96
  1. Due to licensing restrictions, the USGS is no longer able to publicly distribute the Algebraic Multi-Grid

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.

Non-commercial interfaces

Non-commercial MODFLOW versions are free, however, their licensing usually limit the use to non-profit educational or research purposes.

Commercial programs

Commercial MODFLOW programs are typically used by governments and consultants for practical applications of MODFLOW to real-world groundwater problems. Professional versions of MODFLOW are generally priced at a minimum of around $1000 and typically range upward to US$7000. This is a list of commercial programs for 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

See also

References

  1. Water Webserver Team (March 5, 2014). "Software User Rights Notice". Water Resources of the United States. U.S. Department of the Interior, U.S. Geological Survey. Retrieved 2014-05-27.
  2. 1 2 McDonald M.G. & Harbaugh, A.W. (2003). "The History of MODFLOW". Ground Water. 41 (2): 280–283. Bibcode:2003GrWat..41..280M. doi:10.1111/j.1745-6584.2003.tb02591.x. PMID   12656294. S2CID   21781355.
  3. 1 2 3 McDonald, M.G. & Harbaugh, A.W. (December 28, 1983). A modular three-dimensional finite-difference ground-water flow model. Open-File Report 83-875. U.S. Geological Survey.[ permanent dead link ]
  4. McDonald, M.G. & Harbaugh, A.W. (1988). A modular three-dimensional finite-difference ground-water flow model (PDF). Techniques of Water-Resources Investigations, Book 6. U.S. Geological Survey.
  5. Harbaugh, A.W. & McDonald, M.G. (1996a). User's documentation for MODFLOW-96, an update to the U.S. Geological Survey modular finite-difference ground-water flow model (PDF). Open-File Report 96-485. U.S. Geological Survey.
  6. Harbaugh, A.W. & McDonald, M.G. (1996). Programmer's documentation for MODFLOW-96, an update to the U.S. Geological Survey modular finite-difference ground-water flow model (PDF). Open-File Report 96-486. U.S. Geological Survey.
  7. Harbaugh, A.W., Banta, E.R., Hill, M.C., and McDonald, M.G. (2000). MODFLOW-2000, the U.S. Geological Survey modular ground-water model — User guide to modularization concepts and the Ground-Water Flow Process (PDF). Open-File Report 00-92. U.S. Geological Survey.{{cite book}}: CS1 maint: multiple names: authors list (link)
  8. 1 2 Harbaugh, Arlen W. (2005). MODFLOW-2005, The U.S. Geological Survey Modular Ground-Water Model—the Ground-Water Flow Process. Techniques and Methods 6–A16. U.S. Geological Survey.
  9. Mehl, Steffen (2005). MODFLOW-2005, The U.S. Geological Survey Modular Ground-Water Model—Documentation of Shared Node Local Grid Refinement (LGR) and the Boundary Flow and Head (BFH) Package. Techniques and Methods 6–A12. U.S. Geological Survey.[ permanent dead link ]
  10. 1 2 Niswonger, Richard G.; Panday, Sorab; Ibaraki, Motomu (2011), "MODFLOW-NWT, A Newton Formulation for MODFLOW-2005", Techniques and Methods, Techniques and Methods 6-A37, Reston, VA: U.S. Geological Survey, doi:10.3133/tm6A37
  11. 1 2 Hanson, Randall T.; Boyce, Scott E.; Schmid, Wolfgang; Hughes, Joseph D.; Mehl, Steffen W.; Leake, Stanley A.; Maddock, Thomas, III; Niswonger, Richard G. (2014), "One-Water Hydrologic Flow Model (MODFLOW-OWHM)", Techniques and Methods, Techniques and Methods 6-A51, Reston, VA: U.S. Geological Survey, p. 134, doi: 10.3133/tm6A51 {{citation}}: CS1 maint: multiple names: authors list (link)
  12. "Mf-Owhm | Modflow Owhm". 9 April 2020.
  13. Panday, Sorab; Langevin, Christian D.; Niswonger, Richard G.; Ibaraki, Motomu; Hughes, Joseph D. (2013), "MODFLOW–USG Version 1: An Unstructured Grid Version of MODFLOW for Simulating Groundwater Flow and Tightly Coupled Processes Using a Control Volume Finite-Difference Formulation" , USGS Report, Techniques and Methods 6-A45, Reston, VA: U.S. Geological Survey: 44, Bibcode:2013usgs.rept...44P, doi:10.3133/tm6A45
  14. Panday, Sorab (2024); USG-Transport Version 2.4.0: Transport and Other Enhancements to MODFLOW-USG, GSI Environmental, http://www.gsi-net.com/en/software/free-software/USG-Transport.html
  15. Hort, Hiroko M.; Stockwell, Emily B.; Newell, Charles J.; Scalia, Joseph; Panday, Sorab (2024). "Modeling and Evaluation of PFOS Retention in the Unsaturated Zone above the Water Table" . Groundwater Monitoring & Remediation. 44 (3): 38–48. Bibcode:2024GMRed..44c..38H. doi:10.1111/gwmr.12662. ISSN   1069-3629.
  16. Hughes, Joseph D.; Langevin, Christian D.; Banta, Edward R. (2017). "Documentation for the MODFLOW 6 framework". Techniques and Methods. Techniques and Methods 6-A57. p. 40. doi:10.3133/tm6A57.
  17. Langevin, Christian D.; Hughes, Joseph D.; Banta, Edward R.; Niswonger, Richard G.; Panday, Sorab; Provost, Alden M. (2017). "Documentation for the MODFLOW 6 Groundwater Flow Model". Techniques and Methods. Techniques and Methods 6-A55. doi:10.3133/tm6A55.
  18. "MODFLOW 6: USGS Modular Hydrologic Model".
  19. Boyce, Scott E.; Hanson, Randall T.; Ferguson, Ian; Schmid, Wolfgang; Henson, Wesley R.; Reimann, Thomas; Mehl, Steffen W.; Earll, Marisa M. (2020). "One-Water Hydrologic Flow Model: A MODFLOW based conjunctive-use simulation software". Techniques and Methods (Report). U.S. Geological Survey. doi: 10.3133/tm6a60 .
  20. Boyce, S.E., 2020, MODFLOW One-Water Hydrologic Flow Model (MF-OWHM) Conjunctive Use and Integrated Hydrologic Flow Modeling Software, version 2.0.0: U.S. Geological Survey Software Release, https://doi.org/10.5066/P9P8I8GS
  21. "MODFLOW One-Water Hydrologic Flow Model (MF-OWHM) | U.S. Geological Survey". www.usgs.gov. 2020-04-07. Retrieved 2025-03-18.
  22. Bakker, Mark; Schaars, Frans; Hughes, Joseph D.; Langevin, Christian D.; Dausman, Alyssa M. (2013). Documentation of the seawater intrusion (SWI2) package for MODFLOW (Report). U.S. Geological Survey.
  23. Hughes, Joseph D.; Langevin, Christian D.; Chartier, Kevin L.; White, Jeremy T. (2012). Documentation of the Surface-Water Routing (SWR1) Process for modeling surface-water flow with the U.S. Geological Survey Modular Ground-Water Model (MODFLOW-2005) (Report). U.S. Geological Survey. pp. i–113.
  24. Mehl, Steffen W.; Hill, Mary C. (2013). MODFLOW–LGR—Documentation of ghost node local grid refinement (LGR2) for multiple areas and the boundary flow and head (BFH2) package (Report). U.S. Geological Survey.
  25. Shoemaker, W.B., Kuniansky, E.L., Birk, S., Bauer, S., and Swain, E.D., 2008, Documentation of a Conduit Flow Process (CFP) for MODFLOW-2005: U.S. Geological Survey Techniques and Methods, Book 6, Chapter A24, 50 p., https://pubs.usgs.gov/tm/tm6a24/
  26. Schmid, Wolfgang, and Hanson, R.T., 2009, The Farm Process Version 2 (FMP2) for MODFLOW-2005—Modifications and Upgrades to FMP1: U.S. Geological Survey Techniques and Methods 6-A-32, 102 p., https://pubs.usgs.gov/tm/tm6a32/
  27. Ferguson, I.M.., Llewellyn, D., Hanson, R.T., and Boyce S.E., 2016, User guide to the surface water operations process—An integrated approach to simulating large-scale surface water management in MODFLOW-based hydrologic models: Denver, Colo., Bureau of Reclamation Technical Memorandum no. 86-68210–2016-02, 96 p.
  28. Faunt, Claudia C.; Traum, Jonathan A.; Boyce, Scott E.; Seymour, Whitney A.; Jachens, Elizabeth R.; Brandt, Justin T.; Sneed, Michelle; Bond, Sandra; Marcelli, Marina F. (2024-04-22). "Groundwater Sustainability and Land Subsidence in California's Central Valley". Water. 16 (8): 1189. Bibcode:2024Water..16.1189F. doi: 10.3390/w16081189 . ISSN   2073-4441.
  29. Boyce, S.E., 2024, MODFLOW One-Water Hydrologic Flow Model (MF-OWHM) Conjunctive Use and Integrated Hydrologic Flow Modeling Software, version 2.3.0: U.S. Geological Survey Software Release, https://doi.org/10.5066/P9P8I8GS
  30. Boyce, S.E. and Ferguson, I.M., 2024, MODFLOW One-Water Hydrologic Flow Model (MF-OWHM) Conjunctive Use and Integrated Hydrologic Flow Modeling Software with Surface Water Operations, version 2.3.0: U.S. Geological Survey Software Release, https://doi.org/10.5066/P9P8I8GS
  31. Boyce, S.E., 2025, MODFLOW One-Water Hydrologic Flow Model (MF-OWHM) Conjunctive Use and Integrated Hydrologic Flow Modeling Software, version 2.3.1-b4: U.S. Geological Survey Software Release, https://doi.org/10.5066/P9P8I8GS
  32. Wen-Hsing Chiang (2005). 3D-Groundwater Modeling with PMWIN (Second ed.). Springer. doi:10.1007/3-540-27592-4. ISBN   978-3-540-27590-9.