Response of aquifers to periodic forcing

This subject has been a topic of research in Perth, Western Australia, since 1984-85. Prior to and during the Perth Urban Water Balance Study (1983-87), there was tendency to believe that the magnitude of water table fluctuations could be interpreted to infer the annual fluctuations in recharge to the water table. While this is true in some circumstances, it is not always the case.

Townley (1985) presented a simple theory for one-dimensional situations, and referred to the use of AQUIFEM-P, which was developed in parallel in 1985.

Townley and Brooker (1990) extended the analytical results to multi-layered aquifers, but these results have not been published in a more formal form.

Townley (1993) prepared documentation for AQUIFEM-P. While the documentation was prepared at CSIRO, the model does not belong to CSIRO and any requests for information should be directed to me.

Townley (1995) published a suite of closed form analytical solutions, demonstrating a methodology based on complex algebra rather than time integration or separation of sine and cosine components. This paper forms the basis for Section 5.3.7 ("transient versus steady-state flow") in Section 5 ("Analytic Element Modeling") in a book by Henk Haitjema (1995) entitled "Analytic Element Modeling of Groundwater Flow". In 2023, an Addendum to the initial 1995 paper was published by Townley (2023a); the motivation for this Addendum was the fact that the version of the original paper available at Advances in Water Resources online contains 3D images that are almost black, so the solutions in space and time cannot be seen; a few minor errors in Figures had also been found. The Addendum contains 16 references, all of which (with the exception of the reference to Mathematica) were authored by a single author; of course there are other papers in this field with more than one author, but it does seem that this kind of analysis requires concentration and attention to detail, often easier alone than in a team. The Addendum is accompanied by Mathematica notebook .nb files, i.e. all the original 1995 solutions are now freely accessible at Mendeley Data. A good reference to the Mathematica notebooks would be Townley, L.R., 2023. Six Mathematica notebooks containing solutions for the response of aquifers to periodic forcing. Mendeley Data V1.

Tony Smith's PhD research combined our interests in surface water - groundwater interaction and periodic flows. His research focused on computation (using AQUIFEM-P) and visualisation of dynamic groundwater flow patterns beneath shallow lakes and wetlands, in response to periodic forcing. By "periodic", we mean a combination of steady (or average) climatic conditions, and harmonic (or sinusoidal) fluctuations in climate with a particular amplitude and phase. In general, our focus has been on annual or seasonal fluctuations, though the same techniques apply to tidal or diurnal fluctuations. Dynamic animations of streaklines have been prepared by Tony and made available via a standard web browser. One paper was published on the influence of regional setting on steady lake-aquifer interaction (Smith and Townley, 2002). Another describes the methods by which periodic fluctations can be visualised (Smith et al.,2005). After 14 years with CSIRO Land and Water in Perth, Tony now works in industry.

Additional analytical solutions have been developed and may be published soon. These include analysis of surface water - groundwater interaction in an idealised 1D horizontal system, and analysis of tidally induced transport between a lagoon in an atoll and the ocean beyond.


Copyright © 2024 by Lloyd Townley