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On the use of the Boussinesq equation for interpreting recession hydrographs from sloping aquifers



This is the publisher’s final pdf. The published article is copyrighted by American Geophysical Union and can be found at: method of recession analysis proposed by Brutsaert and Nieber (1977) remains one of the few analytical tools for estimating aquifer hydraulic parameters at the field scale and beyond. In the method, the recession hydrograph is examined as −dQ/dt = f(Q), where Q is aquifer discharge and f is an arbitrary function. The observed function f is parameterized through analytical solutions to the one-dimensional Boussinesq equation for unconfined flow in a homogeneous and horizontal aquifer. While attractive in its simplicity, as originally presented it is not applicable to settings where slope is an important driver of flow, or where hydraulic parameters vary greatly with depth. We compare analytical solutions to the linearized one-dimensional Boussinesq equation for a sloping aquifer to numerical solutions of the full nonlinear equation. The behavior of the nonlinear Boussinesq equation is also assessed when the aquifer is heterogeneous wherein the lateral saturated hydraulic conductivity k varies as a power law with height z above the impermeable layer (k ∼ z[superscript n] , n constant ≥ 0). All of the analytical solutions differ in key aspects from the nonlinear solution when plotted as −dQ/dt = f(Q) and thus are inappropriate for a Brutsaert and Nieber-type analysis. However, new analytical solutions for a sloping aquifer are derived “empirically” from the numerical simulations that are applicable during the late period of recession when the recession curve converges to −dQ/dt = aQ[superscript b] , where b = (2n + 1)/(n + 1) and a is a function of the dimensions and hydraulic properties of the aquifer

Topics: Boussinesq, Recession analysis, Sloping
Publisher: American Geophysical Union
Year: 2012
DOI identifier: 10.1029/2006WR005080
OAI identifier:
Provided by: ScholarsArchive@OSU

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  14. (1966). Closure to ‘‘Inflow hydrographs from large unconfined aquifers’’,
  15. (1995). Comment on ‘‘The unit response of groundwater outflow from a hillslope’’ by Wilfried Brutsaert, doi
  16. (2003). De Troch doi
  17. (1966). Discussions of ‘‘Inflow hydrographs from large unconfined aquifers’’,
  18. (1971). Drainage of groundwater resting on a sloping bed, doi
  19. (2002). Drought flow from hillslope, doi
  20. (2004). Drying front in a sloping aquifer: Nonlinear effects, Water Resour. doi
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  29. (2005). Hydrology: An Introduction, doi
  30. (1984). Infiltration into a class of vertically non-uniform soils, doi
  31. (1965). Inflow hydrographs from large unconfined aquifers,
  32. (2006). Information, artifacts, and noise in dQ/ dt-Q recession analysis, doi
  33. (1981). Kinematic subsurface stormflow, doi
  34. (1982). On subsurface stormflow: An analysis of response times, doi
  35. (1982). On subsurface stormflow: Predictions with simple kinematic theory for saturated and unsaturated flows, doi
  36. (2005). Recession analysis of drought flow using Hele Shaw model, doi
  37. (1988). Recession characteristics of groundwater outflow and base flow from mountainous watersheds, doi
  38. (1998). Recession flow analysis for aquifer parameter determination, doi
  39. (1904). Recherches the´oriques sur l’e´coulement des nappes d’eau infiltre´es dans le sol et sur de´bit de sources,
  40. (1992). Regional geohydrologic-geomorphic relationships for the estimation of low-flow statistics, doi
  41. (1977). Regionalized drought flow hydrographs from a mature glaciated plateau, doi
  42. (1998). Relating baseflow to catchment properties in south-eastern Australia, doi
  43. (1997). Response of unconfined aquifer to sudden change in boundary head, doi
  44. Selker (2004), Analytical methods for estimating saturated hydraulic conductivity in a tile-drained field, doi
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  49. (1903). Sur le de´bit, en temps de se´cheresse, d’une source alimente´e par une nappe d’eaux d’infiltration,
  50. (1988). The influence of basin morphology on groundwater outflow, doi
  51. (1994). The unit response of groundwater outflow from a hillslope, doi
  52. (1996). Toward a generalization of the TOPMODEL concepts: Topographic indices of hydrological similarity, doi
  53. (2004). Troch doi
  54. Troch (2000), Some analytical solutions of the linearized Boussinesq equation with recharge for a sloping aquifer, doi
  55. (2004). Vadose zone influences on aquifer parameter estimates of saturated-zone hydraulic theory, doi
  56. (1977). Water flux in soil and subsoil on a steep forested hillslope, doi
  57. Wooding (1964), Overland flow and groundwater flow from a steady rainfall of finite duration, doi

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