AQUIFEM-1

One of the first two-dimensional finite element groundwater flow codes to be used by third party users was AQUIFEM-1, developed at MIT in 1977-80 under the guidance of John L Wilson.

An early version of AQUIFEM was written by Antonio Sa da Costa in 1977-78, based on the code CAFE written by John Wang and Jerome Connor at MIT in the mid 1970s for circulation in coastal environments (cf. Wang and Connor (1975), Mathematical modelling of near coastal circulation, TR 200, Ralph M Parsons Laboratory for Water Resources and Hydrodynamics, MIT, April).

Lloyd Townley rewrote AQUIFEM-1 and prepared all documentation between October 1978 and February 1980. While never promoted as "open source" software, a complete listing of the Fortran source code was provided in the user's manual.

Two reports were published. (i) A 114-page manual by Wilson, Townley and Sa da Costa (1979) describes the theory of the finite element method and verification that the finite element method is able to reproduce analytical solutions. (ii) A 294-page user's manual by Townley and Wilson (1980) includes a "programmer's guide". Both reports were published twice: as Technical Reports 248 and 252 of MIT's Ralph M Parsons Laboratory for Water Resources and Hydrodynamics, and as TAP Reports 79-2 and 79-3 of MIT's Technology Adaptation Program.

The well-known reference book entitled Applied Groundwater Modeling: Simulation of Flow and Advective Transport by Anderson and Woessner (1991) used AQUIFEM-1 to explain finite element models, in comparison with finite difference models such as MODFLOW, first released in 1983 but better known since 1988. Many illustrations in the reference book come directly from the AQUIFEM-1 manuals. A Second Edition of this book, published by Anderson, Woessner and Hunt in 2015, uses FEFLOW as an example of finite element modelling software, but still refers to AQUIFEM-1 and AQUIFEM-N. By chance, the first version of FEFLOW was also released in 1979.

AQUIFEM-1 has no relationship with AQUIFEM developed by Pinder and Voss in Sweden in 1979 or AQUIFEM-SALT developed by Voss for the USGS in 1984. The name was chosen independently as a logical name for an AQUIfer Finite Element Model.

DYNFLOW by CDM Smith evolved from the same roots, from Antonio Sa da Costa's first version of AQUIFEM at MIT in 1978. A brief history of the 30 years of evolution of DYNSYSTEM was presented at the 2013 NGWA Summit in San Antonio TX. This history is interesting, but does not explain that the documented and released version of AQUIFEM-1 was completely rewritten by Lloyd Townley. In fact the developers of DYNSYSTEM also developed a model called AQUIFEM-N before renaming it DYNFLOW (DYNamic groundwater FLOW simulation model) in 1982.

One of the first published applications of AQUIFEM-1 was to the Nile Valley in Egypt in 1986.

In June 2020, optical character recognition (OCR) software was used to capture the source code from pages 266-294 of the AQUIFEM-1 user manual (Townley and Wilson, 1980). The code was first checked and aligned by eye, using Notepad++ with Language set to Fortran with Fixed format. The code was then compiled using Intel(R) Visual Fortran Compiler 19.1.1.216 [IA-32], within Microsoft Visual Studio Community 2019 Version 16.5.4. A few special compiler flags were needed, and a few minor edits were made, largely because modern compilers are not as forgiving as they were in the past. After 40 years, AQUIFEM-1 is still working as intended.

The source code, .exe file and a set of example data files will soon be made available.

If you have any questions or suggestions related to AQUIFEM-1, please contact us.

AQUIFEM-N

AQUIFEM-N is a multi-layered extension of AQUIFEM-1. It was distributed in Australia and internationally from the mid 1980s until the early 1990s. It has many similarities with early versions of MODFLOW, in that it was designed as a quasi-3D model, with vertical flow represented by a conductance or leakage coefficient. However development ceased after addition of conservative solute transport in the early 1990s.

AQUIFEM-N was developed in 1984-85 at the request of Richard Evans of the State Rivers and Water Supply Commission of Victoria. The SRWSC had an HP 3000 mainframe, which allowed 64 KB of RAM per user/process. The agreed specification was for a multi-layered finite element model with up to 10 layers, each with up to 400 nodes and 600 linear triangular elements, to run on the available hardware. AQUIFEM-N was developed on an XT PC with a single floppy drive and 128 KB of RAM. The software was uploaded and tested remotely using the AUSTPAC network operating at 15 baud.

The user's manual and other documentation will soon be made available.

AQUIFEM-P

AQUIFEM-P is a periodic version of AQUIFEM-1, developed in 1985 and documented in 1993. Many hydrogeological systems have piezometric heads and flows that fluctuate in response to fluctuations in forcing, such as seasonal variations in recharge, evapotranspiration and pumping (due to wet and dry seasons), tidal oscillations at boundaries and diurnal variation in plant water uptake. The purpose of AQUIFEM-P is to simulate the dynamic behaviour of fluctuating systems without time-stepping.

A simple idealisation is to consider sinusoidal fluctuations superimposed on long-term average behaviour. After linearising, the steady and sinusoidal components can be decoupled, simulated separately and recombined. Rather than representing sinusoidal fluctuations as a combination of sines and cosines (to represent phase lag), AQUIFEM-P is based on the use of complex variables, a technique used frequently in wave mechanics and in analysis of structural vibrations.

The user's manual and other documentation will soon be made available. We would love to find opportunities to demonstrate how this approach can help in analysis of the response time of hydrogeological systems.

CERT

CERT is a two-dimensional finite element groundwater flow code that includes parameter estimation and uncertainty analysis. CERT was written between June 1982 and April 1983, as part of Lloyd Townley's PhD research. It was documented in April-June 1983 as part of a project by INTERA Environmental Consultants for the US Office of Nuclear Waste Isolation (ONWI), documenting codes that could be applied to the design of radioactive waste management facilities.

CERT is based on the concept that all model parameters can and perhaps should be considered to be uncertain. Parameter estimation is implemented using both gradient-based and extended Kalman filter (EKF) search algorithms, minimising an objective function that combines measurements of heads and either measurements of or prior information about model parameters. This objective function can be justified based on Bayesian, Maximum Likelihood (ML), Maximum a Posteriori (MAP) or heuristic (weighted least squares) arguments. The gradient-based search uses adjoint methods and a novel (under-utilised) method to estimate the curvature of the objective function along the direction of each line search. Uncertainty analysis is implemented using the first order second moment (FOSM) method, later extended to include a second order correction to the mean, and also using Monte Carlo (MC) simulations.

One of the few examples of an application of CERT is in Neil Blandford's (1987) MS Thesis (7.7 MB).

While not specifically related to CERT, a paper by McLaughlin and Townley (1996) presents the groundwater inverse problem in the language of maximum-a-posteriori (MAP) estimation. In particular, the paper shows relationships between linear Bayesian methods, nonlinear least squares and maximum likelihood methods, the pilot point method and extended Kalman filtering, all of which have been applied in groundwater studies.

The CERT user's manual and other documentation will soon be made available.

FlowThru

FlowThru was developed by Lloyd Townley and Tony Barr at CSIRO during the period 1989-92, significantly extending the results of MSc research undertaken by Simon Nield at UWA. An interactive version of FlowThru is provided here.

FlowThru generates flow nets that show groundwater flow patterns beneath and near shallow water bodies such as lakes, wetlands, rivers and streams. The flow nets are automatically analysed to find stagnation points and dividing streamlines. Although this work was initially motivated by studies of shallow wetlands on the Swan Coastal Plain near Perth, Western Australia, the principles can be applied to every kind of surface water - groundwater interaction.

The FlowThru code allows the geometry of a vertical section to be defined in physical units, and also using non-dimensional ratios. Non-dimensional ratios allow the results to be applied to a wide range systems with the same ratios. We would love to embed FlowThru in other software, but would need support to do so.

The user's manual explains how flow regimes are identified based on the number and location of stagnation points (singularities) in the flow domain.

FlowThru was an outcome of years of research, summarised at www.townley.com.au under the heading "Research interests --> Surface water - groundwater interaction". The report by Townley et al. (1993a) was scanned in June 2015, 22 years after the report was completed and submitted as a Final Draft. It is now available for download.

Animations based on AQUIFEM-P

A number of animations are provided to illustrate the impact of seasonal fluctuations of recharge, rainfall and evapotranspiration on groundwater flow patterns in a 2D vertical section through shallow surface water bodies. The results combine the concepts of FlowThru with seasonal fluctuations, simulated using the periodic finite element model AQUIFEM-P. This work formed the basis for Tony Smith's PhD thesis, completed in 1999.

Most of the animations show flow-through regimes rather than recharge or discharge regimes, because this was the focus of our research at the time. We share these animations is not to provide answers, but to illustrate features of surface water - groundwater interaction that we understand well. We believe dynamics has an enormous influence on apparent mixing in groundwater, and hope to be able to explain more in the future.

PUWBS

The Perth Urban Water Balance Study (PUWBS) was a landmark study of the groundwater resources near Perth, Western Australia, undertaken during the period 1982-87. Lloyd Townley was a member of both the Steering Committee and the Project Team, guiding the direction of the project while at the same time involved in hands-on modelling. The final report has been scanned, 25 years after publication, to illustrate the level of technology available at that time. See Volume 1 (194 MB) and Volume 2 (10 MB).

The study was unique in a number of ways. The report was far more colourful than many modelling reports at the time, being targeted at a broad audience keen to understand the groundwater resources. Extensive use was made of GIS, using the first licence for ARC/INFO in Western Australia. The concept of a vertical flux model, coupled to an underlying regional scale single layer finite element model, was not unique, but may have been attempted in more detail than ever before in an urban environment.

Underground nuclear testing at Mururoa and Fangataufa Atolls in French Polynesia

In June 1995, President Jacques Chirac of France unexpectedly announced that France would conduct a final series of up to eight underground nuclear tests at Mururoa and Fangataufa Atolls in French Polynesia, prior to signing the proposed Comprehensive Test Ban Treaty. A total of six tests were carried out between 5 September 1995 and 27 January 1996. Responding to concerns and protests, the President invited two international groups to conduct separate independent investigations of the consequences of the underground tests.

Professor Charles Fairhurst was asked to select and lead a team of independent international experts, known as the International Geomechanical Commission (IGC) to study issues related to stability and hydrology. The International Atomic Energy Agency (IAEA) undertook a separate study of radiological issues.

The IGC's stability studies were led and coordinated by Professor Emmanuel Detournay, with detailed analysis being undertaken by Branko Damjanac, Peter Cundall and other staff from ITASCA in the USA. The hydrology studies were coordinated by Lloyd Townley and Professor Ghislain de Marsily, with detailed analysis being undertaken by Pierre Perrochet and Laurent Tacher of the Ecole Polytechnique Fédérale de Lausanne (EPFL) in Switzerland.

The IGC's findings were published in 1999 in hard copy, with additional files on an accompanying CD. The printed report is divided into three "parts". Part 1 is entitled General Results. Part 2 is entitled Technical Analyses, but includes only Chapter 1, which provides an overview of the IGC's analyses. Part 3 contains French Translations of Parts 1 and 2. The CD contains a number of files in PDF format, in this case entitled "volumes". Volumes 1 and 3 correspond to Parts 1 and 3. But Volume 2 is 480 pages in length, with Chapters 1 to 7 and Appendices A to V; it contains all of the technical analyses undertaken by the IGC.

A modified version of the IGC's final report (24.9 MB) has been assembled, 13 years after publication in hard copy. This version includes Volume 2 in place of Part 2.

Of particular interest to hydrologists and hydrogeologists are four sections in Volume 2: Chapter 6 on "atoll hydrology prior to nuclear testing", Chapter 7 on "hydrological impacts of underground nuclear tests", Appendix U on "analysis of periodic groundwater flow", and Appendix V on "effective dispersion in a periodic flow field". Appendix U builds on similar periodic analyses published separately by Lloyd Townley. Appendix V improves an earlier solution by Okubo (1973), and was developed by Pierre Perrochet in collaboration with Lloyd Townley.

A slightly different compilation (784 pp.) has been prepared and archived by the University of Minnesota.

Even though the IAEA study relied on the geotechnical and hydrogeological simulations undertaken by the IGC, its report was published earlier. The IAEA main report (31.2 MB) is entitled "The Radiological Situation at the Atolls of Mururoa and Fangataufa". Lloyd Townley was a member of the IAEA's Working Group 4 (geosphere radionuclide transport) of Task Group B (on evaluation of the potential long term radiological situation), and contributed to preparation of Chapter 6 of the main report. Working Group 4 prepared a Technical Report entitled "Releases to the biosphere of radionuclides from underground nuclear weapon tests at the atolls" (270 pp.), being Volume 4 in a series of 6 reports supporting the main report.

For more information about the history of nuclear testing in French Polynesia, see www.mororua.org.