Using numerical modeling to determine the transfer function for transport and dispersion problems in groundwater

The great interest in environmental issues has led to an attention to the quality of groundwater. Scienti…c e¤orts in groundwater ‡ow studies have primarily focused on the ‡ow and transport behavior and on the identi…cation of the corresponding parameters. Since ’90 increasing at- tention has been paid to the problem of recovering the release history of a pollutant because the knowledge of the pollution injection function gives information about the future pollution spread and allows a better planning of remediation action (Liu and Ball, 1999, Snodgrass and Kitanidis, 1997, Skaggs and Kabala, 1994, Butera and Tanda, 2003). Moreover, from a legal and regulatory point of view, it is also important to determine the release time period and the highest values of concentration released; in fact, an available release history can be a useful tool for sharing the costs of remediation of a polluted area among the actors . Some approaches developed in the literature to the inverse problem solution (geostatistical approach (Snodgrass and Kitanidis, 1997), Tichonov regularization method (Skaggs and Kabala, 1994)) require the computation of the function that describe the e¤ect, during time and in a certain location of the aquifer, due to an impulsive release of pollutant in the source. This function, named transfer or Kernell function can be analitically determined if the problem has a simple geometry and boundary conditions. In many cases the characteristic of the groundwater ‡ow …eld do not allow for the analytical transfer function formulation; this is the case, for instance, of non uniform in the mean ‡ow due to complicated boundary conditions, or to the existence of pumping wells, or high heterogeneity of the aquifer (Sudicky, 1986). With the available procedures the technician has to reduce the real problem to a very simpli…ed scheme to which the analytical transfer function can be applied. As a consequence a rough approximation of results can be expected. In this work, a procedure useful to determine the transfer function in case without analytical solution is developed. It is based on an analogy with the Instantaneous Unit Hydrograph theory used by the surface hydrologists to determine the ‡ood response of a basin to a rain event and it can be applied in groundwater problems nalyzed by numerical modeling.