A Backward probabilistic model to calculate well head protection areas

Delineation of Wellhead Protection Areas (WHPAs) is a basic tool for the protection of drinkable groundwater resources. At the present, WHPAs definition is usually carried out according to the backward particle tracking model, a deterministic model based on the concept of the time of travel (TOT); it accounts only of advective mechanism of transport ignoring the hydrodynamic dispersion. The aim of this study is to present a WHPAs method which accounts of dispersion phenomena without requiring too many additional computation, compared with the common backward particle tracking method. For this purpose a backward probabilistic (BP) method, based on the adjoint equation of the classical transport advective-dispersive equation (Neupauer and Wilson, 1999), has been implemented. With only one simulation, for every point of the model domain the probability that a solute particle located in that point will reach the well within the fixed TOT is computed. This result is obtained running a flow model (MODFLOW2000), whose output is opportunely modified, and then a transport model (e.g. MT3D); the transport model variable is not yet a concentration, but a capture probability, that moves backwards along the stream lines and spreads according to contaminant dispersion processes. The backward particle tracking method gives a deterministic perimeter of the WHPA, while the introduction of dispersion phenomena originates a probability map. In this paper the results of the BP model are discussed and compared with the particle tracking results. In particular, the 50% capture probability line and the particle tracking perimeter, which should match, are compared; the size, shape and surface of the areas held by different capture probabilities are calculated at the varying the TOT.