ABSTRACTGround water modeling has a rich history with four parallel streams of development. Groundwater theory and analytical models have evolved simultaneously over the last 200 years.Numerical models arose in response to the availability of scientific computing facilities fromthe 1950s onward, and user friendly commercial and public domain models followed thearrival of personal computers in the early 1980’s. The arrival of user friendly software doesnot reflect a maturation or stagnation of the discipline. Important new developments in groundwater modelling include a movement away from programming, toward using higher levelPDE solvers, with more focus on the problems and less on the development of new numericalmethods. New types of data, and integration of that data into models will continue to be afocus area. Finally, the boundaries of the discipline of ground water will continue to beextended and blurred as it becomes important to integrate groundwater into other dynamicsystems.INTRODUCTIONIn 2001 Schwartz and Ibaraki published a very provocative discussion paper in which theyhypothesized the maturation of the discipline of hydrogeology where most of the majordiscoveries have been made and the number of impactful publications is dwindling /1/. Hisanalysis was based on trends in citation and publications databases. This paper was followedby a strong rebuttal by Miller and Gray /2/, who provided a list of unresolved challenges inground water - a list worthy of the attention of a whole new generation of hydrogeologists.In this context it is worth reviewing the history and future perspectives for ground watermodeling. Is it a mature discipline or one that is vibrant and growing? Where are thechallenges in ground water modeling? There has been an explosion in the number ofpublications in groundwater over the last 2 centuries. Has the discipline reached a saturationpoint, or does there continue to be fundamental advances? What will our future groundwatermodels look like?Methodologically, this review presents considerable challenges. References and citations areprovided to important events in the history of the discipline. However, in the interest ofmaintaining a compact presentation, not all key authors and their papers are presented. Thereview attempts to identify some important issues and trends in the discipline withoutattempting to provide a comprehensive overview of the subject.HISTORYThe development of ground water modeling is occurring in four parallel streams, developmentof new theory, analytical solutions, solutions using numerical methods, and application inuser friendly modeling systems. Ground water theory has steadily developed over the last twocenturies (Table 1). New breakthroughs in our conceptual understanding have occurredregularly during that period and continue up to the present. Analytical modeling has occurredparallel to the theoretical development and continues to be important today. The potential ofnumerical models for ground water was recognized very early in the development ofcomputing with foundations of numerical modeling being laid in the 1950’s to 1970’s. With
that new numerical methods for the solution of Richards equation continue to be regularlypublished. Similar developments have occurred in all areas of numerical modeling.The advent of cheap and powerful personal computers has meant that research models arenow becoming widely available to practitioners. The 1980’s and 90’s have seen an explosionin the availability of commercial and public domain groundwater models. Such a developmentcould be interpreted as a sign of the maturity of the field of ground water research, with a longera of development in theory and solution techniques, now culminating in an array ofcommercial and public domain products. But, this is a misleading analysis. Rather, theappearance of widely available models reflects easy access to technology. As demonstratedabove, groundwater continues to be a very active area of research. With societal pressure forscientists to demonstrate applicability, it is likely that developments of new theory andnumerical models will continue to be closely followed by the release of commercial software.
these barriers are increasingly being overcome /49/. The launch of the Grace satellite meansthat sensitive gravimetric readings are now also available via remote sensing. The Gracesatellite has a bigger footprint (~300km) than earth based instruments, but is being used tocalibrate hydrological models at cm vertical resolution on the continental scale /50/. This isbut one example of the considerable advances that are being made in techniques forcharacterizing ground water systems.Parallel to improvements in data that can be used to calibrate groundwater models areimprovements to model calibration methods. Calibration tools are now available that can becoupled to any model /51/ and techniques for evaluating model uncertainty are becomingmore sophisticated /52/. Statistical methods are being developed to assist in model choice /53/and data assimilation techniques developed in meteorology allow for the dynamic calibrationof ground water models /54/. All these developments will enhance our ability to analyse andidentify new avenues of ground water research.WHERE ARE THE BOUNDARIES OF THE DISCIPLINE OF GROUND WATER?If a narrow view of groundwater is taken, for example, that the “groundwater hydrologist isprimarily concerned with the water contained in the zone of saturation” /55/, then it could beargued that ground water is a mature discipline, with the most important developments havingoccurred long ago. But as Freeze and Cherry /56/ so succinctly stated “We shall retain thisclassical definition, but we do so in full recognition that the study of groundwater must rest onan understanding of the subsurface water regime in a broader sense”. This viewpointcontinues to be as relevant today as it was 30 years ago. Much of the development of thediscipline is occurring at its fringes, where groundwater interfaces with other physical,chemical and biological systems. These could be new work on ecohydrology, theoreticaladvances in multiphase flow, applications to carbon dioxide sequestration, interfaces toclimate models and global carbon balances, or the coupling of groundwater into humanmanagement systems, to name a few areas of current research interest.Amongst the most important trends in the development of new numerical models is a trendtoward integration. In this regard, the development of groundwater models has an interestingparallel with climate models. Climate models have gradually increased in complexity, withincreasing numbers of processes and more sophisticated coupling between them (e.g. figure1.2, page 99 /57/). One of the challenges with this type of modeling is that it is highly interdisciplinaryand requires huge resources. Hence some of this development is occurring incollaboration with institutions like the USGS /58/, or in commercial software concerns likeDHI, with their MIKE series of products /38/. Researchers play an active role in thesedevelopments. One example of an integrated model that illustrated this trend is thedevelopment of a snow/ice/groundwater model designed to simulate hydrogeological systemsover geological time scales to study climatic impacts on groundwater /59/.CONCLUSIONIs groundwater research dead? No! It is looking up! Upward toward the land surface wherethere is intensive research being conducted on the interaction of the groundwater system withother components of the hydrological system. Future groundwater models will allow
increasing integration with other components of the hydrologic cycle. Contaminant massbalances and water quality will be part of this trend toward increased model integration. Thefuture promises new measurement methods, and techniques to integrate these measurementsinto models of increasing complexity. At the same time, our understanding of classicalgroundwater will continue to be challenged, for example as we come to grips with newtheories on multiphase flow. Our modeling tools will increasingly be built using advancedPDE solvers and commercial software as we move away from user designed and programmedsoftware solutions. The gap between research and practical products will become evensmaller, as technology allows the transfer of the latest research into new or improved userfriendly modeling systems.REFERENCES/1/ Hydrogeological research: Beginning of the end or end of the beginning?, Schwartz, F. W. and M.Ibaraki, 2001, Ground Water, 39(4): 492-498./2/ Hydrogeological research: Just getting started, Miller, C. T. and W. G. Gray, 2002, Ground Water,40(3): 224-231./3/ The public fountains of the city of dijon experience and application principles to follow and formulas tobe used in the question of the distribution of water. Work finishes with an appendix relating to the watersupplies of several cities the filtering of water and the manufacture of strong pipes of lead, sheet metaland bitumen, Darcy, H., 1856, The City of Dijon./4/ On the cause of fresh water springs, fountains etc, DuCommun, J., 1828, American Journal of Scienceand Arts, 14: 174-176./5/ Todd, D. K. (1980). Groundwater hydrology. New York, John Wiley and Sons./6/ Direct simulation of groundwater age, Goode, D. J., 1996, Water Resources Research, 32(2): 289-296./7/ Konikow, L. F., G. Z. Hornberger, et al. (2007). The use of groundwater age as a calibration target.Modelcare 2007, Copenhagen Denmark./8/ Averaging theorems and averaged equations for transport of interface properties in multiphase systems,Gray, W. G. and S. M. Hassanizadeh, 1989, International Journal of Multiphase Flow, 15(1): 81-95./9/ Bundle-of-tubes model for calculating dynamic effects in the capillary-pressure-saturation relationship,Dahle, H. K., M. A. Celia, et al., 2005, Transport in Porous Media, 58(1-2): 5-22./10/ A theoretical analysis of groundwater flow in small drainage baisins, Toth, J., 1963, J. GeophysicalResearch, 68(4795-4812)./11/ The relation between the lowering of a piezometric surface and the rate and duration of discharge of awell using groundwater storage, Theis, C. V., 1935, Transactions of the American Geophysical Union,2: 519-524./12/ Contaminant transport in fractured porous media: Analytical solution for a system of parallel fractures,Sudicky, E. A. and E. O. Frind, 1982, Water Resources Research, 18(6): 1634-1642./13/ Injection and storage of co 2 in deep saline aquifers: Analytical solution for co 2 plume evolution duringinjection, Nordbotten, J. M., M. A. Celia, et al., 2005, Transport in Porous Media, 58(3): 339-360./14/ A method for calculating multi-dimensional immiscible displacement, Peaceman, D. W., 1959,Petroleum Transactions, AIME, 216: 297-308./15/ A general mass-conservative numerical solution for the unsaturated flow equation, Celia, M. A., E. T.Bouloutas, et al., 1990, Water Resources Research, 26(7): 1483-1496./16/ Dupuit, J. (1863). Etudes theoretiques et pratiques sur le mouvement des eaux dans les canauxdecouverts et a travers les terrains permeables. Dunod, France./17/ Capillary conduction of liquids in porous media, Richards, L. A., 1931, Physics (New York), 1: pp. 318-333./18/ Studies on soil physics: 1. Flow of air and water through soils, Green, W. H. and G. A. Ampt, 1911,Journal of Agricultural Science, 4: 1-24./19/ Muskat, M. (1937). The flow of homogeneous fluids through prous media. New York, McGraw Hill./20/ Hubbert, M. K. (1987). Darcy's law: Its physical theory and application to entrapment of oil and gas.History of geophysics. E. R. Landau and S. Ince, AGU. 3: 1-26.
21/ Mechanism of fluid displacement in sands, Buckley, S. E. and M. C. Leverett, 1942, Trans. AIME, 146:107-116./22/ Statistical hydrodynamics in porous media, Schiedegger, A. E., 1954, Journal of Applied Physics, 25:994-1001./23/ Formule des minerais connexes Matheron, G., 1954, Ecole des Mines de Paris./24/ The network model of porous media, i, capillary pressure characteristics, Fatt, I., 1956, Pet. Trans.AIME, 207: 144-159./25/ Moisture movement in soils under temperature gradients with cold-side temperature below freezing,Hoekstra, P., 1966, Water Resources Research, 2(2): 241-./26/ A solution of the differential equation of longitudinal dispersion in porous media, Ogata, A. and R. B.Banks, 1961, USGS./27/ Numerical calculation of multidimensional miscible displacement, Peaceman, D. W. and H. H. J.Rachford, 1962, Soc. Pet. Eng. J., 2: 327-339./28/ Diffusion and dispersion in porous media, Whitaker, S., 1967, AIChE Journal, 13: 420./29/ Groundwater models solved by digital computer, Remson, I., C. A. Appel, et al., 1965, ASCE Journalof the Hydraulics Division, 91(HY3): 133-147./30/ Finite element analysis of land subsidence, Sanhu, R. S. and E. L. Wilson, 1969, Land SubsidenceProceedings, IAHS2: 393-400./31/ Numerical modelling of unsaturated groundwater flow and comparison to a field experiment, Green, D.W., H. Dabri, et al., 1970, Water Resources Research, 6: 862-874./32/ An investigation of laminar flow in fractures porous rockes, Wilson, C. R. and P. A. Witherspoon,1970, Department of Civil Engineering, University of California, Berkely./33/ A dispersion model for a quantitative study of a ground water pollution by salt, Fried, J. J. and P. O.Ungemach, 1971, Water Research, 5: 491-495./34/ Numerical approximation of cation exchange in miscible displacement through soil columns, Lai, S. H.and J. J. Jurinak, 1971, Soil Sci. Soc. Am. J., 35: 894-899./35/ Two phase, two dimensional simulation of a geothermal reservoir and the welbore system, Toronyi, R.M., 1974, Pennsylvania State University. PhD./36/ Simulation of microbial-growth dynamics coupled to nutrient and oxygen-transport in porous-media,Molz, F. J., M. A. Widdowson, et al., 1986, Water Resources Research, 22(8): 1207-1216./37/ A finite-element simulation model for saturated-unsaturated, fluid density-dependent groundwater flowwith energy transport or chemically reactive single-species solute transport, Voss, C. I., 1984, USGS./38/ An introduction to the european hydrological system - systeme hydrologique europeen, she .1. Historyand philosophy of a physically-based, distributed modeling system, Abbott, M. B., J. C. Bathurst, et al.,1986, Journal of Hydrology, 87(1-2): 45-59./39/ Geochemical calculations and observations on salt water intrusions. I: A combined geochemical/mixingcell model, Appelo, C. A. J. and A. Willemsen, 1987, Journal of Hydrology, 94: 313-330./40/ Tough user's guide, Pruess, K., 1987, U.S. Nuclear Regulatory Comission./41/ A modular three-dimensional finite-difference ground-water flow model, MacDonald, M. G. and A. W.Harbaugh, 1988, USGS: 576./42/ A critical review of data on field-scale dispersion in aquifers, Gelhar, L. W., C. Welty, et al., 1992,Water Resources Research, 28(7): 1955./43/ Eclipse 100, technological appendices, 94a release. , Intera Information Technologies Ltd., 1993./44/ Femlab v1.0 reference manual, COMSOL, A. B., 1998./45/ Long-term growth and water balance predictions for a mountain ash (eucalyptus regnans) forestcatchment subject to clear-felling and regeneration, Vertessy, R. A., T. J. Hatton, et al., 1996, TreePhysiology, 16(1-2): 221-232./46/ The hydrus code for simulating the one-dimensional movement of water, heat, and multiple solutes invariably-saturated media version 6.0, Simunek, J., K. Huang, et al., 1998. Riverside, California, U.S.Salinity Laboratory, USDA-ARS./47/ Fractran user’s guide. An efficient simulator for two-dimensional, saturated groundwater flow andsolute transport in porous or discretely-fractured porous formations., Sudicky, E. A. and R. G.McLaren, 1998. Ontario, Canada, Groundwater Simulations Group, Waterloo Centre for GroundwaterResearch, University of Waterloo.
48/ Determination of coefficient of storage by use of gravity measurements, Montgomery, E. L., 1971.Tucson, U.S.A., University of Arizona. Ph.D./49/ Measurements of aquifer-storage change and specific yield using gravity surveys, Pool, D. R. and J. H.Eychaner, 1995, Ground Water, 33(3): 425-432./50/ Global time variations of hydrological signals from grace satellite gravimetry, Ramillien, G., A.Cazenave, et al., 2004, Geophysical Journal International, 158(3): 813-826./51/ Methodologies for calibration and predictive analysis of a watershed model, Doherty, J. and J. M.Johnston, 2003, Journal of the American Water Resources Association, 39(2): 251-265./52/ Uncertainty in the environmental modelling process - a frameworkand guidance, Refsgaard, J. C., J. P. v. d. Sluijs, et al., 2007, Environmental Modelling and Software,22: 1543-1556./53/ Multimodel ranking and inference in ground water modeling, Poeter, E. and D. Anderson, 2005,Ground Water, 43(4): 597-605./54/ Kalman filtering in groundwater flow modelling: Problems and prospects, Eigbe, U., M. B. Beck, et al.,1998, Stochastic Hydrology and Hydraulics, 12(1): 15-32./55/ Bear, J. (1979). Hydraulics of groundwater. New York, McGraw-Hill Book Company./56/ Freeze, R. A. and J. A. Cherry (1979). Groundwater. London, Prentice Hall./57/ Ipcc, 2007: Climate change 2007: The physical science basis. Contribution of working group i to thefourth assessment report of the intergovernmental panel on climate change, Solomon, S., D. Qin, et al.,2007. Cambridge, United Kingdom and New York, NY, USA., Intergovernmental panel on climatechange./58/ Usgs directions in modflow development, Barlow, P. M. and A. W. Harbaugh, 2006, Ground Water,44(6): 771-774./59/ Flow and contaminant transport in integrated surface-subsurface flow systems: Model applications overmultiple spatial and tempopral scales, Sudicky, E. A., J.-M. Lemiuex, et al., 2007, Modelcare 2007. J.C. Refsgaard and E. Nygaard. Copenhagen Denmark: 304.