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

### Abstract

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/.The 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: oai:ir.library.oregonstate.edu:1957/33468
Provided by: ScholarsArchive@OSU

### Citations

1. (2005). A base flow separation algorithm based on the linearized Boussinesq equation for complex hillslopes,
2. (1997). A generalization of TOPMODEL for a power law transmissivity profile,
3. (1997). A generalized power function for the subsurface transmissivity profile in TOPMODEL,
4. (2004). A geological framework for interpreting the low-flow regimes of Cascade streams,
5. (2004). A hillslope-scale experiment to measure lateral saturated hydraulic conductivity, Water Resour.
6. (1992). A linear conceptual subsurface storm flow model,
7. (1979). A physically-based variable contributing-area model of catchment hydrology,
8. (1995). A review of baseflow recession analysis,
9. (1968). Base-flow recessions: A review,
10. (1999). Baseflow recession and recharge as nonlinear storage processes,
11. (1998). Baseflow separation based on analytical solutions of the Boussinesq equation,
12. (1998). Basin-scale geohydrologic drought flow features of riparian aquifers in the southern Great Plains, Water Resour.
13. (1999). Can we distinguish Richards’ and Boussinesq’s equations for hillslopes? The Coweeta experiment revisited,
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,
16. (2003). De Troch
17. (1966). Discussions of ‘‘Inflow hydrographs from large unconfined aquifers’’,
18. (1971). Drainage of groundwater resting on a sloping bed,
19. (2002). Drought flow from hillslope,
20. (2004). Drying front in a sloping aquifer: Nonlinear effects, Water Resour.
21. (1993). Effective water table depth to describe initial conditions prior to storm rainfall in humid regions,
22. Essai sur la the´orie des eaux courantes,
23. (2005). Evaluation of spring flow in the uplands of Matalom,
24. (1999). Generality of drought flow characteristics within the Arkansas River basin,
25. Hilberts (2004), Analytical solution of the linearized hillslope-storage Boussinesq equation for exponential hillslope width functions,
26. (1993). Hillslope drainage with sudden drawdown: Closed form solution and laboratory experiments,
27. (2003). Hillslope-storage Boussinesq model for subsurface flow and variable source areas along complex hillslopes: 1. Formulation and characteristic response,
28. (2003). Hillslope-storage Boussinesq model for subsurface flow and variable source areas along complex hillslopes: 2. Intercomparison with a threedimensional Richards equation model,
29. (2005). Hydrology: An Introduction,
30. (1984). Infiltration into a class of vertically non-uniform soils,
31. (1965). Inflow hydrographs from large unconfined aquifers,
32. (2006). Information, artifacts, and noise in dQ/ dt-Q recession analysis,
33. (1981). Kinematic subsurface stormflow,
34. (1982). On subsurface stormflow: An analysis of response times,
35. (1982). On subsurface stormflow: Predictions with simple kinematic theory for saturated and unsaturated flows,
36. (2005). Recession analysis of drought flow using Hele Shaw model,
37. (1988). Recession characteristics of groundwater outflow and base flow from mountainous watersheds,
38. (1998). Recession flow analysis for aquifer parameter determination,
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,
41. (1977). Regionalized drought flow hydrographs from a mature glaciated plateau,
42. (1998). Relating baseflow to catchment properties in south-eastern Australia,
43. (1997). Response of unconfined aquifer to sudden change in boundary head,
44. Selker (2004), Analytical methods for estimating saturated hydraulic conductivity in a tile-drained field,
45. Selker (2005), Drainage of a horizontal Boussinesq aquifer with a power law hydraulic conductivity profile, Water Resour.
46. (2005). Short- and long-time behavior of aquifer dainage after slow and sudden recharge according to the linearized Laplace equation,
47. (1981). Soil hydraulic properties and their effect on surface and subsurface water transfer in a tropical rainforest catchment,
48. (2001). Sudden drawdown and drainage of a horizontal aquifer,
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,
51. (1994). The unit response of groundwater outflow from a hillslope,
52. (1996). Toward a generalization of the TOPMODEL concepts: Topographic indices of hydrological similarity,
53. (2004). Troch
54. Troch (2000), Some analytical solutions of the linearized Boussinesq equation with recharge for a sloping aquifer,
55. (2004). Vadose zone influences on aquifer parameter estimates of saturated-zone hydraulic theory,
56. (1977). Water flux in soil and subsoil on a steep forested hillslope,
57. Wooding (1964), Overland flow and groundwater flow from a steady rainfall of finite duration,

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