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Knowledge of flow exchange between surface and groundwater is of great importance for use of water resources. The determination of seepage between a stream and an underlying aquifer requires an accurate estimation of the river stage and of the head in the aquifer. An approach is presented to estimate analytically river flow and stage while using the SAFE conductance to calculate the seepage. A major contribution of this article lies in the methodology for river routing with its use of a modified Linear Reservoir model. The parameter C is related to discharge based on Manning’s equation. That relation breathes into an empirical model a dynamic character. A second major contribution is to show that it is possible to simultaneously calculate river stage and aquifer head in the aquifer cell that contains the river. As a result iteration is not necessary to estimate that river cell head as river stage changes, as opposed to what is usually done in most numerical groundwater models. Iteration is still needed for the adjacent cells to the river cell. Because the influence of a change in the adjacent cell head on the river cell head is much delayed and attenuated the iteration is not sensitive to that change. A goal of this document is to show how that method can be used within a simple physically based routing procedure  to estimate the river stage that has a definite influence on seepage.
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