HESS Opinions: Linking Darcy's equation to the linear reservoir
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 labor...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2018-03-01
|
| Series: | Hydrology and Earth System Sciences |
| Online Access: | https://www.hydrol-earth-syst-sci.net/22/1911/2018/hess-22-1911-2018.pdf |
| _version_ | 1811262432802242560 |
|---|---|
| author | H. H. G. Savenije |
| author_facet | H. H. G. Savenije |
| author_sort | H. H. G. Savenije |
| collection | DOAJ |
| description | 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 timescales. This drainage network provides equally distributed resistance for water to access 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 timescale of the linear reservoir appears to be inversely proportional to Darcy's <q>conductance</q>, 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 fundamental question that is equally relevant for understanding the hydraulic properties of leaf veins in plants or of blood veins in animals. |
| first_indexed | 2024-04-12T19:25:11Z |
| format | Article |
| id | doaj.art-9073b40d98eb4c80bbcae5b96cb59a20 |
| institution | Directory Open Access Journal |
| issn | 1027-5606 1607-7938 |
| language | English |
| last_indexed | 2024-04-12T19:25:11Z |
| publishDate | 2018-03-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Hydrology and Earth System Sciences |
| spelling | doaj.art-9073b40d98eb4c80bbcae5b96cb59a202022-12-22T03:19:30ZengCopernicus PublicationsHydrology and Earth System Sciences1027-56061607-79382018-03-01221911191610.5194/hess-22-1911-2018HESS Opinions: Linking Darcy's equation to the linear reservoirH. H. G. Savenije0Delft University of Technology, Delft, the NetherlandsIn 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 timescales. This drainage network provides equally distributed resistance for water to access 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 timescale of the linear reservoir appears to be inversely proportional to Darcy's <q>conductance</q>, 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 fundamental question that is equally relevant for understanding the hydraulic properties of leaf veins in plants or of blood veins in animals.https://www.hydrol-earth-syst-sci.net/22/1911/2018/hess-22-1911-2018.pdf |
| spellingShingle | H. H. G. Savenije HESS Opinions: Linking Darcy's equation to the linear reservoir Hydrology and Earth System Sciences |
| title | HESS Opinions: Linking Darcy's equation to the linear reservoir |
| title_full | HESS Opinions: Linking Darcy's equation to the linear reservoir |
| title_fullStr | HESS Opinions: Linking Darcy's equation to the linear reservoir |
| title_full_unstemmed | HESS Opinions: Linking Darcy's equation to the linear reservoir |
| title_short | HESS Opinions: Linking Darcy's equation to the linear reservoir |
| title_sort | hess opinions linking darcy s equation to the linear reservoir |
| url | https://www.hydrol-earth-syst-sci.net/22/1911/2018/hess-22-1911-2018.pdf |
| work_keys_str_mv | AT hhgsavenije hessopinionslinkingdarcysequationtothelinearreservoir |