A Cauchy boundary condition for the lumped interaction between an arbitrary number of surface waters and a regional aquifer

Abstract

A regional groundwater model may cover many surface waters and drains, which are difficult to include individually in a model. Large canals, rivers and other surface waters that are in direct contact with the upper regional aquifer may be included individually because their number is relatively small. The effects of the remaining drains and surface waters on the flow to or from that aquifer may be combined over some area. A method is presented to lump the interaction between an arbitrary number of surface waters and drains and the groundwater flow in a regional aquifer within an arbitrary area (e.g. cell or element). The effect of the saturated groundwater flow between the drains and surface waters and the regional aquifer is translated into a Cauchy boundary condition that is applied at the upper boundary of the regional groundwater model. The constants that feature in that boundary condition are derived from a closed-form solution of the governing differential equation and the boundary conditions. The present approach is applicable in any arbitrary area (and so in elements or cells of any shape) with any number of surface waters provided that, in the vicinity of the surface waters, the variation in the head in the regional aquifer is considerably smaller than the variation in the phreatic head. The approach has been tested and applied extensively in the Netherlands. (C) 1999 Elsevier Science B.V.