Analytical solutions to a hillslope-storage kinematic wave equation for subsurface flow

Peter A Troch, Emiel Van Loon, Arno Hilberts

Research output: Contribution to journalArticle

81 Citations (Scopus)

Abstract

Hillslope response has traditionally been studied by means of the hydraulic groundwater theory. Subsurface flow from a one-dimensional hillslope with a sloping aquifer can be described by the Boussinesq equation [Mem. Acad. Sci. Inst. Fr. 23 (1) (1877) 252-260]. Analytical solutions to Boussinesq's equation are very useful to understand the dynamics of subsurface flow processes along a hillslope. In order to extend our understanding of hillslope functioning, however, simple models that nonetheless account for the three-dimensional soil mantle in which the flow processes take place are needed. This three-dimensional soil mantle can be described by its plan shape and by the profile curvatures of terrain and bedrock. This plan shape and profile curvature are dominant topographic controls on flow processes along hillslopes. Fan and Bras [Water Resour. Res. 34 (4) (1998) 921-927] proposed a method to map the three-dimensional soil mantle into a one-dimensional storage capacity function. Continuity and a kinematic form of Darcy's law lead to quasi-linear wave equations for subsurface flow solvable with the method of characteristics. Adopting a power function of the form proposed by Stefano et al. [Water Resour. Res. 36 (2) (2000) 607-617] to describe the bedrock slope, we derive more general solutions to the hillslope-storage kinematic wave equation for subsurface flow, applicable to a wide range of complex hillslopes. Characteristics drainage response functions for nine distinct hillslope types are computed. These nine hillslope types are obtained by combining three plan curvatures (converging, uniform, diverging) with three bedrock profile curvatures (concave, straight, convex). We demonstrate that these nine hillslopes show quite different dynamic behaviour during free drainage and rainfall recharge events.

Original languageEnglish (US)
Pages (from-to)637-649
Number of pages13
JournalAdvances in Water Resources
Volume25
Issue number6
DOIs
StatePublished - Jun 2002
Externally publishedYes

Fingerprint

subsurface flow
wave equation
hillslope
kinematics
curvature
Boussinesq equation
bedrock
mantle
drainage
Darcy law
soil
recharge
aquifer
hydraulics
water
rainfall
groundwater

Keywords

  • Hillslope hydrology
  • Kinematic wave approximation
  • Method of characteristics
  • Subsurface flow

ASJC Scopus subject areas

  • Earth-Surface Processes

Cite this

Analytical solutions to a hillslope-storage kinematic wave equation for subsurface flow. / Troch, Peter A; Van Loon, Emiel; Hilberts, Arno.

In: Advances in Water Resources, Vol. 25, No. 6, 06.2002, p. 637-649.

Research output: Contribution to journalArticle

@article{822628957c654359ab57064ccb5bbe1a,
title = "Analytical solutions to a hillslope-storage kinematic wave equation for subsurface flow",
abstract = "Hillslope response has traditionally been studied by means of the hydraulic groundwater theory. Subsurface flow from a one-dimensional hillslope with a sloping aquifer can be described by the Boussinesq equation [Mem. Acad. Sci. Inst. Fr. 23 (1) (1877) 252-260]. Analytical solutions to Boussinesq's equation are very useful to understand the dynamics of subsurface flow processes along a hillslope. In order to extend our understanding of hillslope functioning, however, simple models that nonetheless account for the three-dimensional soil mantle in which the flow processes take place are needed. This three-dimensional soil mantle can be described by its plan shape and by the profile curvatures of terrain and bedrock. This plan shape and profile curvature are dominant topographic controls on flow processes along hillslopes. Fan and Bras [Water Resour. Res. 34 (4) (1998) 921-927] proposed a method to map the three-dimensional soil mantle into a one-dimensional storage capacity function. Continuity and a kinematic form of Darcy's law lead to quasi-linear wave equations for subsurface flow solvable with the method of characteristics. Adopting a power function of the form proposed by Stefano et al. [Water Resour. Res. 36 (2) (2000) 607-617] to describe the bedrock slope, we derive more general solutions to the hillslope-storage kinematic wave equation for subsurface flow, applicable to a wide range of complex hillslopes. Characteristics drainage response functions for nine distinct hillslope types are computed. These nine hillslope types are obtained by combining three plan curvatures (converging, uniform, diverging) with three bedrock profile curvatures (concave, straight, convex). We demonstrate that these nine hillslopes show quite different dynamic behaviour during free drainage and rainfall recharge events.",
keywords = "Hillslope hydrology, Kinematic wave approximation, Method of characteristics, Subsurface flow",
author = "Troch, {Peter A} and {Van Loon}, Emiel and Arno Hilberts",
year = "2002",
month = "6",
doi = "10.1016/S0309-1708(02)00017-9",
language = "English (US)",
volume = "25",
pages = "637--649",
journal = "Advances in Water Resources",
issn = "0309-1708",
publisher = "Elsevier Limited",
number = "6",

}

TY - JOUR

T1 - Analytical solutions to a hillslope-storage kinematic wave equation for subsurface flow

AU - Troch, Peter A

AU - Van Loon, Emiel

AU - Hilberts, Arno

PY - 2002/6

Y1 - 2002/6

N2 - Hillslope response has traditionally been studied by means of the hydraulic groundwater theory. Subsurface flow from a one-dimensional hillslope with a sloping aquifer can be described by the Boussinesq equation [Mem. Acad. Sci. Inst. Fr. 23 (1) (1877) 252-260]. Analytical solutions to Boussinesq's equation are very useful to understand the dynamics of subsurface flow processes along a hillslope. In order to extend our understanding of hillslope functioning, however, simple models that nonetheless account for the three-dimensional soil mantle in which the flow processes take place are needed. This three-dimensional soil mantle can be described by its plan shape and by the profile curvatures of terrain and bedrock. This plan shape and profile curvature are dominant topographic controls on flow processes along hillslopes. Fan and Bras [Water Resour. Res. 34 (4) (1998) 921-927] proposed a method to map the three-dimensional soil mantle into a one-dimensional storage capacity function. Continuity and a kinematic form of Darcy's law lead to quasi-linear wave equations for subsurface flow solvable with the method of characteristics. Adopting a power function of the form proposed by Stefano et al. [Water Resour. Res. 36 (2) (2000) 607-617] to describe the bedrock slope, we derive more general solutions to the hillslope-storage kinematic wave equation for subsurface flow, applicable to a wide range of complex hillslopes. Characteristics drainage response functions for nine distinct hillslope types are computed. These nine hillslope types are obtained by combining three plan curvatures (converging, uniform, diverging) with three bedrock profile curvatures (concave, straight, convex). We demonstrate that these nine hillslopes show quite different dynamic behaviour during free drainage and rainfall recharge events.

AB - Hillslope response has traditionally been studied by means of the hydraulic groundwater theory. Subsurface flow from a one-dimensional hillslope with a sloping aquifer can be described by the Boussinesq equation [Mem. Acad. Sci. Inst. Fr. 23 (1) (1877) 252-260]. Analytical solutions to Boussinesq's equation are very useful to understand the dynamics of subsurface flow processes along a hillslope. In order to extend our understanding of hillslope functioning, however, simple models that nonetheless account for the three-dimensional soil mantle in which the flow processes take place are needed. This three-dimensional soil mantle can be described by its plan shape and by the profile curvatures of terrain and bedrock. This plan shape and profile curvature are dominant topographic controls on flow processes along hillslopes. Fan and Bras [Water Resour. Res. 34 (4) (1998) 921-927] proposed a method to map the three-dimensional soil mantle into a one-dimensional storage capacity function. Continuity and a kinematic form of Darcy's law lead to quasi-linear wave equations for subsurface flow solvable with the method of characteristics. Adopting a power function of the form proposed by Stefano et al. [Water Resour. Res. 36 (2) (2000) 607-617] to describe the bedrock slope, we derive more general solutions to the hillslope-storage kinematic wave equation for subsurface flow, applicable to a wide range of complex hillslopes. Characteristics drainage response functions for nine distinct hillslope types are computed. These nine hillslope types are obtained by combining three plan curvatures (converging, uniform, diverging) with three bedrock profile curvatures (concave, straight, convex). We demonstrate that these nine hillslopes show quite different dynamic behaviour during free drainage and rainfall recharge events.

KW - Hillslope hydrology

KW - Kinematic wave approximation

KW - Method of characteristics

KW - Subsurface flow

UR - http://www.scopus.com/inward/record.url?scp=0036620623&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036620623&partnerID=8YFLogxK

U2 - 10.1016/S0309-1708(02)00017-9

DO - 10.1016/S0309-1708(02)00017-9

M3 - Article

VL - 25

SP - 637

EP - 649

JO - Advances in Water Resources

JF - Advances in Water Resources

SN - 0309-1708

IS - 6

ER -