In the majority of lumped water balance models of river basins, groundwater is represented by a single reservoir, and groundwater discharge is described by a single-valued function of storage in the reservoir. It is demonstrated that single-valued storage-discharge functions are often incapable of representing the actual storage-discharge characteristics of a river basin. An alternative discharge function is proposed which is derived from a solution to the one-dimensional saturated flow equation for an idealized hillslope with spatially varying physical properties. The saturated flow in the whole river basin is, however, generally better described by a two-dimensional flow equation. Therefore, in order to apply the new discharge function to a whole basin, it is first necessary to show that the two-dimensional flow of groundwater can, in some way, be encapsulated in a conceptual model which can be represented by the one-dimensional flow equation. Two different methods for deriving such a conceptual model are developed and tested on an example river basin. The new discharge function, based on one of these conceptual models, successfully reproduces the discharge simulated by solving the two-dimensional flow equation. ¿ 2000 American Geophysical Union