Closing horizontal groundwater fluxes with pipe network analysis: An application of the REW approach to an aquifer

The Representative Elementary Watershed (REW) approach for modeling the hydrologic response of watersheds is based on the discretization of a catchment into hydrologically sensitive control volumes. Global balance laws for mass, momentum (and energy) are formulated for the volumes. An implementation of the approach requires closing unknown REW-scale mass fluxes and forces exchanged across the REW-internal control volume boundaries and between REWs. In the present paper we focus exclusively on the horizontal groundwater flow, while neglecting other hydrological processes such as surface runoff, subsurface stormflow and surface-groundwater interaction. Here we describe a simplified groundwater modeling approach, which is based on the parsimonious estimation of mass fluxes exchanged laterally between REWs. The procedure employs principles of mass and energy conservation as stated by the Kirchhoff laws. The problem is reduced to the solution of a coupled system of linear equations in terms of inter-REW groundwater fluxes and a dimensionless ratio Θ between the local saturated zone depths ys and spatial length scales Λ over which piezometric head gaps are dissipated. The equation system is solved by successive approximation, as suggested by the Cross method, which is used in engineering practice for resolving resistor networks under steady state conditions. The procedure converges rapidly for complex network configurations. It is shown that for given boundary fluxes imposed at the watershed edges, mass fluxes exchanged in-between REWs can be calculated in an unique and consistent fashion. The paper briefly reviews the essential governing equations, introduces the formulation of the problem in terms of the Kirchoff laws and shows the numerical solution of the network. Simulation results for an application to the Hesbaye groundwater system in Belgium are presented.