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The increasing importance of catchment-scale and basin-scale models of the hydrological cycle makes it desirable to have a simple, yet physically realistic model for lateral subsurface water flow. As a first building block towards such a model, analytical solutions are presented for horizontal groundwater flow to surface waters held at prescribed water levels for aquifers with parallel and radial flow. The solutions are valid for a wide array of initial and boundary conditions and additions or withdrawals of water, and can handle discharge into as well as lateral infiltration from the surface water. Expressions for the average hydraulic head, the flux to or from the surface water, and the aquifer-scale hydraulic conductivity are developed to provide output at the scale of the modelled system rather than just point-scale values. The upscaled conductivity is time-variant. It does not depend on the magnitude of the flux but is determined by medium properties as well as the external forcings that drive the flow. For the systems studied, with lateral travel distances not exceeding 10 m, the circular aquifers respond very differently from the infinite-strip aquifers. The modelled fluxes are sensitive to the magnitude of the storage coefficient. For phreatic aquifers a value of 0.2 is argued to be representative, but considerable variations are likely. The effect of varying distributions over the day of recharge damps out rapidly; a soil water model that can provide accurate daily totals is preferable over a less accurate model hat correctly estimates the timing of recharge peaks

Transient flow between aquifers and surface water: analytically derived field-scale hydraulic heads and fluxes