The concept of well catchment and time related capture zones has appeared in the ground water literature since the 60’s.  It allows (a) developing a rational planning in the management of existing groundwater resources; and (b) offering reliable criteria and guidelines for developments of future resources.  Following the pioneering work of Bear and Jacobs [1965], the concept of capture zone became popular after Javandel et al. [1984] developed the theory in their widely referenced monograph.  Since then, the practical utility of capture zones was actively promoted with a major impact on land use (i.e. definition criteria for a series of bans and limitations of human activities) and groundwater resources exploitation.  Geologic media are heterogeneous and exhibit both discrete and continuous spatial variations on a multiplicity of scales.  A series of analytical and numerical solutions for the determinations of well catchments in homogeneous or heterogeneous formations were presented in the literature.  Among others, we reference the works of Lerner [1992], Kinzelbach et al. [1992], Bakker and Strack [1996].  The computer programs MODFLOW and MODPATH or GWPATH are now available to calculate a variety of situations.  These techniques often require a great amount of field data to give accurate predictions, involve very high costs, and are site-specific.  Parameters entering in traditional predictive models have been traditionally viewed as well-defined local quantities that can be assigned unique values at each point in space-time and can be determined by suitable laboratory/field experiments.  This has encouraged (a) deterministic and reductionist attitudes toward hydrologic analysis and modeling; (b) overconfidence in the predictive powers of subsurface flow and transport models.  Yet experience shows that (a) models require continuous recalibration as flow and transport regimes and the data-base vary; (b) their predictability deteriorates as space-time hydrologic scales increase and complexity of the process increases.  In practice the needed parameters can be deduced from measurements only at selected locations where their values depend on the scale (support volume) and mode (instruments and procedure) of measurement.  All of this leads to uncertainty in the value of aquifers parameters and associated heads, fluxes and extent of well catchments.

It has become common [e.g. Dagan, 1989; Gelhar, 1993; Dagan and Neuman, 1997, and references therein] in groundwater models to quantify this uncertainty by treating all parameters and variable as random fields.  Therefore, the problem of solving flow quantities becomes the problem of determining their probability distribution.  Only a few applications of the stochastic approach to delineation of drinking wells protection zones and related topics have been reported in literature [e.g. Varljen and Shafer, 1991; Franzetti and Guadagnini, 1996; Vassolo et al., 1998; Van Leeuwen et al., 1999; Guadagnini and Franzetti, 1999].  All these applications are based on numerical (conditional) Monte Carlo simulation.  The latter is conceptually straight forward and can easily be applied to a broad range of both linear and nonlinear flow and transport problems.  Outputs include (a) mean system behaviour, which constitutes an optimum predictor (unbiased, with minimum variance) of the actual behaviour; and (b) second moments, which serve as measures of prediction errors.  This procedure is also computationally demanding and at the current stage of research lacks well-established convergence criteria.

An alternative to such simulation is provided by conditional moment equations, which yield corresponding predictions of flow and transport deterministically, together with quantification of the variance – covariance of the corresponding prediction errors.  These equations include nonlocal parameters that (a) depend on more than one point in space-time, and (b) are nonunique in that they depend not only on local medium properties but also on the information one has about these properties (scale, location, quantity, and quality of data).  Darcy's law and Fick's analogy are generally not obeyed by the flow and transport predictors except in special cases or as localized approximations.  Traditional deterministic equations are viewed at best as localised versions of nonlocal flow and transport equations: as localisation is not generally valid, neither are deterministic models based on such equations.  Like their conditional mean counterparts, deterministic models yield at best an estimate of actual system behaviour.  Whereas nonlocal equations contain information about predictive uncertainty, localised equations do not.  Therefore, predictions based on the latter are of undetermined quality.  This corresponds to the common groundwater modelling practice of taking the deterministic form of Darcy’s law (and Fick's analogy for transport) for granted, associating it with some effective or equivalent parameter, and estimating its spatial distribution by model calibration against measured heads and fluxes.

In a broad spectrum of international activities, the participants in the consortium have a major experience in dealing with a variety of conceptual, analytical, numerical (Monte Carlo, nonlocal moment equations), and field & laboratory (experiments, data analysis) work of drinking wells protection area.

List of References

Bakker, M. and Strack, O.D.L., Capture Zone Delineation in Two-Dimensional Groundwater Flow Models. Water Resources Research. v. 32, no. 5, pp. 1309-1315, 1996.

Bear, J. and Jacobs, M., On the Movement of Water Bodies Injected into Aquifers. Journal of Hydrology. v. 3, pp. 37-57, 1965.

Dagan, G., Flow and Transport in Porous Formations, Springer-Verlag, New York, 1989.

Dagan, G. and S.P. Neuman, Editors, Subsurface Flow and Transport: A Stochastic Approach, 241 pp., Cambridge University Press, 1997.

Franzetti S., and A. Guadagnini, Probabilistic Estimation of Well Catchments in Heterogeneous Aquifers, J. of Hydrology 174/1-2, 149-171, 1996

Gelhar, L. W., Stochastic Subsurface Hydrology, Prentice-Hall, Englewood Cliffs, N.J., 1993.

Guadagnini, A., and S. Franzetti, Contamination of Pumping Wells and Time-related Capture Zones in Heterogeneous Formations, Groundwater, 37(2), 253-260, 1999.

Javandel, I., C. Doughty, and C.F. Tsang, Groundwater transport: handbook of mathematical models, American geophysical Union, Water Resources Monograph 10, 1984.

Kinzelbach, W., Marburger, M. and Chiang, W.-H., Determination of groundwater catchment areas in two and three spatial dimensions. Journal of Hydrology. v. 134, pp. 221-246, 1992.

Lerner, D.N., Well Catchments and Time-of-Travel Zones in Aquifers with Recharge. Water Resources Research. v. 28, pp. 2621-2628, 1992.

Van Leeuwen, M., A.P. Butler, C.B.M. te Stroet, and J.A. Tompkins, Stochastic determination of the Wierden (Netherlands) capture zones, Ground Water, 37(1), 8-17, 1999.

Varljen, M.D and Shafer, J.M., Assessment of uncertainty in time-related capture zones using conditional simulation of hydraulic conductivity. Ground Water. v. 29, pp. 737-748, 1991

Vassolo, S., W. Kinzelbach, W. Schäfer, Determination of a well head protection zone by stochastic inverse modelling, Journal Of Hydrology, (206)3-4,  268-280, 1998.