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Drainage of a horizontal Boussinesq aquifer with a power law hydraulic conductivity profile

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dc.creator Rupp, David E.
dc.creator Selker, John S.
dc.date.accessioned 2012-10-03T20:42:09Z
dc.date.available 2012-10-03T20:42:09Z
dc.date.issued 2005
dc.identifier.citation Rupp, D. E. and J. S. Selker (2005), Drainage of a horizontal Boussinesq aquifer with a power law hydraulic conductivity profile, Water Resources Res.earch, 41, W11422, doi:10.1029/2005WR004241. en_US
dc.identifier.uri http://hdl.handle.net/1957/34106
dc.description This is the publisher’s final pdf. The published article is copyrighted by American Geophysical Union and can be found at: http://sites.agu.org/. en_US
dc.description.abstract Solutions to the Boussinesq equation describing drainage into a fully penetrating channel have been used for aquifer characterization. Two analytical solutions exist for early- and late-time drainage from a saturated, homogeneous, and horizontal aquifer following instantaneous drawdown. The solutions for discharge Q can be expressed as dQ/dt = −aQ [superscript b] , where a is constant and b takes on the value 3 and 3/2 for early and late time, respectively. Though many factors can contribute to departures from the two predictions, we explore the effect of having permeability decrease with depth, as it is known that many natural soils exhibit this characteristic. We derive a new set of analytical solutions to the Boussinesq equation for k ∝ z [superscript n] , where k is the saturated hydraulic conductivity, z is the height above an impermeable base, and n is a constant. The solutions reveal that in early time, b retains the value of 3 regardless of the value of n, while in late time, b ranges from 3/2 to 2 as n varies from 0 to ∞. Similar to discharge, water table height h in late time can be expressed as dh/dt = −ch [superscript d] , where d = 2 for constant k and d → ∞ as n → ∞. In theory, inclusion of a power law k profile does not complicate aquifer parameter estimation because n can be solved for when fitting b to the late-time data, whereas previously b was assumed to be 3/2. However, if either early- or late-time data are missing, there is an additional unknown. Under appropriate conditions, water table height measurements can be used to solve for an unknown parameter. en_US
dc.description.sponsorship This work was supported in part by National Science Foundation grant INT-0203787. en_US
dc.language.iso en_US en_US
dc.publisher American Geophysical Union en_US
dc.relation.ispartofseries Water Resources Research en_US
dc.relation.ispartofseries Vol. 41 no. W11422 en_US
dc.subject analytical solution en_US
dc.subject aquifer drainage en_US
dc.subject Boussinesq equation en_US
dc.title Drainage of a horizontal Boussinesq aquifer with a power law hydraulic conductivity profile en_US
dc.type Article en_US
dc.description.peerreview yes en_US
dc.identifier.doi 10.1029/2005WR004241

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