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A Class of Exact Solutions of the Boussinesq Equation for Horizontal and Sloping Aquifers

Publication ,  Journal Article
Bartlett, MS; Porporato, A
Published in: Water Resources Research
February 1, 2018

The nonlinear equation of Boussinesq (1877) is a foundational approach for studying groundwater flow through an unconfined aquifer, but solving the full nonlinear version of the Boussinesq equation remains a challenge. Here, we present an exact solution to the full nonlinear Boussinesq equation that not only applies to sloping aquifers but also accounts for source and sink terms such as bedrock seepage, an often significant flux in headwater catchments. This new solution captures the hysteretic relationship (a loop rating curve) between the groundwater flow rate and the water table height, which may be used to provide a more realistic representation of streamflow and groundwater dynamics in hillslopes. In addition, the solution provides an expression where the flow recession varies based on hillslope parameters such as bedrock slope, bedrock seepage, aquifer recharge, plant transpiration, and other factors that vary across landscape types.

Duke Scholars

Published In

Water Resources Research

DOI

EISSN

1944-7973

ISSN

0043-1397

Publication Date

February 1, 2018

Volume

54

Issue

2

Start / End Page

767 / 778

Related Subject Headings

  • Environmental Engineering
  • 4011 Environmental engineering
  • 4005 Civil engineering
  • 3707 Hydrology
  • 0907 Environmental Engineering
  • 0905 Civil Engineering
  • 0406 Physical Geography and Environmental Geoscience
 

Citation

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Bartlett, M. S., & Porporato, A. (2018). A Class of Exact Solutions of the Boussinesq Equation for Horizontal and Sloping Aquifers. Water Resources Research, 54(2), 767–778. https://doi.org/10.1002/2017WR022056
Bartlett, M. S., and A. Porporato. “A Class of Exact Solutions of the Boussinesq Equation for Horizontal and Sloping Aquifers.” Water Resources Research 54, no. 2 (February 1, 2018): 767–78. https://doi.org/10.1002/2017WR022056.
Bartlett MS, Porporato A. A Class of Exact Solutions of the Boussinesq Equation for Horizontal and Sloping Aquifers. Water Resources Research. 2018 Feb 1;54(2):767–78.
Bartlett, M. S., and A. Porporato. “A Class of Exact Solutions of the Boussinesq Equation for Horizontal and Sloping Aquifers.” Water Resources Research, vol. 54, no. 2, Feb. 2018, pp. 767–78. Scopus, doi:10.1002/2017WR022056.
Bartlett MS, Porporato A. A Class of Exact Solutions of the Boussinesq Equation for Horizontal and Sloping Aquifers. Water Resources Research. 2018 Feb 1;54(2):767–778.
Journal cover image

Published In

Water Resources Research

DOI

EISSN

1944-7973

ISSN

0043-1397

Publication Date

February 1, 2018

Volume

54

Issue

2

Start / End Page

767 / 778

Related Subject Headings

  • Environmental Engineering
  • 4011 Environmental engineering
  • 4005 Civil engineering
  • 3707 Hydrology
  • 0907 Environmental Engineering
  • 0905 Civil Engineering
  • 0406 Physical Geography and Environmental Geoscience