AN APPLIED VIEW: THE ANALYTIC ELEMENT METHOD 1988-2011

Starting with a 1980s short-course, the Analytic Element (AE) Method has been a robust tool in my hydrogeology toolbox. Although conveyed unadorned on rolling transparencies in Otto Strack’s basement, the power and elegance of the applied mathematics was easy to see. The model runtimes were short (<10 minutes) when run with a co-processing board, and results were immediately assessed using integrated graphics.

This initial rollout was followed by the 1994 1^st International Conference on the AE Method, where a wide-ranging discussion involved AE and non-AE model developers and practitioners. Our University of Wisconsin presentation focused on strengths and weaknesses of methods, which, in turn, resulted in close collaboration with Indiana University on telescopic mesh refinement: an extract utility that allowed MODFLOW models to be automatically derived from AE screening models. Work presented at the 2000 International Conference centered on extending some of the University of Minnesota’s pioneering work of combining AE and parameter estimation methods. Subsequent work focused on applied enhancements, including lake elements, larger models with higher numbers of equations, and integration of parameter estimation into the graphical user interface. Work presented at the 2006 International Conference pointed out a limitation of AE methods, the inability to handle highly parameterized problems. Sufficiently high levels of parameterization are needed to reduce structural error and provide the minimum error variance prediction. Current work focuses on coupling AE and MODFLOW models, and data handling methods to link insight and reduce redundancy in areas with multiple existing AE models.

Due to the ease of model construction, relatively fast solution times, and easy visualization of results, AE models are ideal for educating students and stakeholders on the concepts of groundwater flow, groundwater-surface water interaction, and effects of pumping.They allow efficient testing and visualization of “what if” scenarios – capabilities important for the speed of decision making. Moreover, early AE screening models are easily extended to other modeling techniques. These characteristics, although not as unique as in the past, are still well-suited for 21^st Century water-resources management.