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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
https://doi.org/10.5194/hess-2017-580
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 4.0 License.
Opinion article
06 Oct 2017
Review status
This discussion paper is a preprint. A revision of the manuscript is under review for the journal Hydrology and Earth System Sciences (HESS).
Opinion paper: Linking Darcy's equation to the linear reservoir
Hubert H. G. Savenije Delft University of Technology, Delft, The Netherlands
Abstract. In groundwater hydrology, two simple linear equations exist describing the relation between groundwater flow and the gradient driving it: Darcy's equation and the linear reservoir. Both equations are empirical and straightforward, but work at different scales: Darcy's equation at the laboratory scale and the linear reservoir at the watershed scale. Although at first sight they appear similar, it is not trivial to upscale Darcy's equation to the watershed scale without detailed knowledge of the structure or shape of the underlying aquifers. This paper shows that these two equations, combined by the water balance, are indeed identical provided there is equal resistance in space for water entering the subsurface network. This implies that groundwater systems make use of an efficient drainage network, a mostly invisible pattern that has evolved over geological time scales. This drainage network provides equally distributed resistance for water to exit the system, connecting the active groundwater body to the stream, much like a leaf is organized to provide all stomata access to moisture at equal resistance. As a result, the residence time of the linear reservoir appears to be inversely proportional to Darcy's conductance, the proportionality being the product of the porosity and the resistance to entering the drainage network. The main question remaining is which physical law lies behind pattern formation in groundwater systems, evolving in a way that resistance to drainage is constant in space. But that is a physical question that is equally relevant for understanding the hydraulic properties of leaf veins in plants or of blood veins in animals.

Citation: Savenije, H. H. G.: Opinion paper: Linking Darcy's equation to the linear reservoir, Hydrol. Earth Syst. Sci. Discuss., https://doi.org/10.5194/hess-2017-580, in review, 2017.
Hubert H. G. Savenije
Hubert H. G. Savenije
Hubert H. G. Savenije

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This paper provides the connection between two simple equations describing groundwater flow at different scales: the Darcy equation describes groundwater flow at pore scale, the linear reservoir equation at catchment scale. The connection between the two appears to be very simple, although it took some time to find it. The two parameters of the equations are proportional, depending on the porosity of the subsoil and the resistance for the groundwater to enter the surface drainage network.
This paper provides the connection between two simple equations describing groundwater flow at...
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