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, written primarily in Fortran, and can compile and run on Microsoft Windows or Unix-like operating systems. The compiled program is a command line tool that reads text file inputs that define the model grid, boundary conditions, and simulation time frame. Extensions beyond the command line program are several actively developed commercial and non-commercial graphical user interfaces.
Groundwater flow equation The governing partial differential equation for a confined aquifer used in MODFLOW is:
where , and are the values of hydraulic conductivity along the x, y, and z coordinate axes (L/T) is the potentiometric head (L) 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) 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 density-dependent 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 non-orthogonal 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).
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 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.
The first version of MODFLOW 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 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. There are three final releases of MODFLOW-96: MODFLOW-96 (version 3.3, May 2, 2000) MODFLOW-96h (version 3.3h, July 10, 2000), with HYDMOD package MODFLOWP (version 3.2, Oct 9, 1997), MODFLOW-96 with parameter-estimation
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. 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: MF2K-GWM or GWM-2000 (version 1.1.4, May 31, 2011, branched from mf2k 1.17.2), with groundwater management capability using optimization MF2K-FMP (version 1.00, May 19, 2006, based on mf2k 1.15.03), with Farm Process MF2K-GWT (version 1.9.8, October 28, 2008, based on MF2K 1.17.02), groundwater flow and solute-transport model SEAWAT (version 4.00.05, October 19, 2012), variable-density flow and transport processes VSF (version 1.01, July 5, 2006), variably saturated flow
MODFLOW-2005 MODFLOW-2005 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. 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-CFP (version 1.8.00, February 23, 2011), conduit flow process to simulate turbulent or laminar groundwater flow conditions MODFLOW-LGR (version 2.0, September 19, 2013), local grid refinement GWM-2005 (version 1.4.2, March 25, 2013), groundwater management capability using optimization MF2005-FMP2 (version 1.0.00, October 28, 2009), estimate dynamically integrated supply-and-demand components of irrigated agriculture as part of the simulation of surface-water and ground-water flow MODFLOW-NWT(version 1.1.3, August 1, 2017), Newton formulation for solving problems involving drying and rewetting nonlinearities of the unconfined groundwater-flow equation. MODFLOW-OWHMv1 (version 1.00.12, October 1, 2016), The One-Water Hydrologic Flow Model (MF-OWHM1), developed cooperatively between the USGS and the U.S. Bureau of Reclamation, is a fusion of multiple versions of MODFLOW-2005 (NWT, LGR, FMP, SWR, SWI) into ONE version, contains upgrades and new features and allows the simulation of head-dependent flows, flow-dependent flows, and deformation dependent flows that collectively affect conjunctive use of water resources. MODFLOW-USG. All version of MODFLOW listed above are constructed on what is called a structured grid. That is, the grid is composed of rectilinear blocks. The only exception is the LGR capability, which allows locally refined grids to be inserted into the structure of a "parent" grid. The local area is again composed of rectilinear blocks, but the blocks are smaller. Experimentation with a much more flexible grid structure resulted in the release of MODFLOW-USG (version 1.3.00, December 1, 2015), designed to be adapted to a wide range of grid variations using unstructured grids. MODFLOW-USG has similar capabilities as MODFLOW 6, which provides grid capabilities with and intermediate level of flexibility. MODFLOW-USG Transport. An update of MODFLOW USG including multiple solute species transport, density dependent flow and transport, use of the Richard's equation for flow and transport in the unsaturated zone and air-water interface sorption. Some of the updates to the model have also been made to accommodate for transport of PFAS.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
MODFLOW 6 MODFLOW 6 (), first released in 2017, is a complete redevelopment of MODFLOW-2005 following an object-oriented programming paradigm in Fortran. MF6 provides a platform that includes the capabilities from several previous MODFLOW-2005 versions, including MODFLOW-NWT, MODFLOW-USG, and MODFLOW-LGR. 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..
MODFLOW-OWHM Version 2 The MODFLOW One-Water Hydrologic Flow Model version 2 (MF-OWHM) is a major rewrite of MF-OWHM1 released in 2020.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 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.