Model help:CHILD: Difference between revisions

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1) Log in to the wiki
1) Log in to the wiki
2) Create a new page for each model, by using the following URL:
2) Create a new page for each model, by using the following URL:
   * http://csdms.colorado.edu/wiki/Model help:<modelname>
   * https://csdms.colorado.edu/wiki/Model help:<modelname>
   * Replace <modelname> with the name of a model
   * Replace <modelname> with the name of a model
3) Than follow the link "edit this page"
3) Than follow the link "edit this page"
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2) bankfull channel width
2) bankfull channel width
::::{|
::::{|
|width=500px|<math> W_{b} = k_{w} Q_{b} ^ \left (\omega b\right ) </math>
|width=500px|<math> W_{b} = k_{w} Q_{b} ^ \left (\omega_{b} \right ) </math>
|width=50px align="right"|(2)
|width=50px align="right"|(2)
|}
|}
3) Channel width
3) Channel width
::::{|
::::{|
|width=500px|<math> {\frac{W}{W_{b}}} = {\frac{Q^ \left ( \omega _{b} \right )}{Q_{b}}}</math>
|width=500px|<math> {\frac{W}{W_{b}}} = {\frac{Q^ \left ( \omega _{s} \right )}{Q_{b}}}</math>
|width=50px align="right"|(3)
|width=50px align="right"|(3)
|}
|}
4) bankfull water depth
4) bankfull water depth
::::{|
::::{|
|width=500px|<math> d_{b} = k_{d} Q_{b} ^ \left (\delta _{b} \right )</math>
|width=500px|<math> d_{b} = k_{b} Q_{b} ^ \left (\delta _{b} \right )</math>
|width=50px align="right"|(4)
|width=50px align="right"|(4)
|}
|}
5) Water depth
5) Water depth
::::{|
::::{|
|width=500px|<math> {\frac{d}{d_{b}}} = {\frac{Q ^ \left ( \delta _{s}}{Q_{b}}}</math>
|width=500px|<math> {\frac{d}{d_{b}}} = {\frac{Q ^ \left ( \delta _{s}\right )}{Q_{b}}}</math>
|width=50px align="right"|(5)
|width=50px align="right"|(5)
|}
|}
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7) Bed roughness
7) Bed roughness
::::{|
::::{|
|width=500px|<math>  {\frac{N}{N_{b}}} = {\frac{Q ^ \left ( \nu _{s}}{Q_{b}}}</math>
|width=500px|<math>  {\frac{N}{N_{b}}} = {\frac{Q ^ \left ( \nu _{s}\right )}{Q_{b}}}</math>
|width=50px align="right"|(7)
|width=50px align="right"|(7)
|}
|}
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9) Bed roughness
9) Bed roughness
::::{|
::::{|
|width=500px|<math>  {\frac{M}{M_{b}}} = {\frac{Q ^ \left ( \mu _{s}}{Q_{b}}}</math>
|width=500px|<math>  {\frac{M}{M_{b}}} = {\frac{Q ^ \left ( \mu _{s}\right )}{Q_{b}}}</math>
|width=50px align="right"|(9)
|width=50px align="right"|(9)
|}
|}
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2) Detachment capacity
2) Detachment capacity
::::{|
::::{|
|width=500px|<math> D _{c} = \left\{\begin{matrix} K_{br} \left ( \tau _{0} - \tau _{c} \right ) ^ \left (P_{b}\right ) & Detachment_law = 0 \\ K_{br} \left ( \tau _{0} ^ \left (P_{b} \right ) - \tau _{c} ^ \left (P_{b}\right ) & Detachment_law = 1 </math>
|width=500px|<math> D _{c} = \left\{\begin{matrix} K_{br} \left ( \tau _{0} - \tau _{c} \right ) ^ \left (P_{b}\right ) & Detachmentlaw = 0 \\ K_{br} \left ( \tau _{0} ^ \left (P_{b} \right ) - \tau _{c} ^ \left (P_{b}\right ) \right ) & Detachmentlaw = 1 \end{matrix}\right.</math>
|width=50px align="right"|(14)
|width=50px align="right"|(14)
|}
* Transport capacity types
1) detachment-limited
::::{|
|width=500px|<math> {\frac{\partial z_{b}}{\partial t}} = - D_{c} </math>
|width=50px align="right"|(15)
|}
2) Transport limited
::::{|
|width=500px|<math> {\frac{\partial z_{b}}{\partial t}} = - {\frac{1}{\left ( 1 - \nu \right )}} {\frac{\partial C_{s} / W}{\partial x}} </math>
|width=50px align="right"|(16)
|}
|}
* Transport Capacity Laws
* Transport Capacity Laws
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::::{|
::::{|
|width=500px|<math> Q_{c} = K_{f} W \left ( \tau _{0} - \tau _{c} \right ) ^ \left (P_{f} \right ) </math>
|width=500px|<math> Q_{c} = K_{f} W \left ( \tau _{0} - \tau _{c} \right ) ^ \left (P_{f} \right ) </math>
|width=50px align="right"|(15)
|width=50px align="right"|(17)
|}
|}
2) Transport_Law = 1 (Power law formula, form 2)
2) Transport_Law = 1 (Power law formula, form 2)
::::{|
::::{|
|width=500px|<math> Q_{c} = K_{f} W \left ( \tau _{0} ^ \left (P_{f}\right ) - \tau _{c} ^ \left (P_{f} \right ) </math>
|width=500px|<math> Q_{c} = K_{f} W \left ( \tau _{0} ^ \left (P_{f}\right ) - \tau _{c} ^ \left (P_{f} \right )\right ) </math>
|width=50px align="right"|(16)
|width=50px align="right"|(18)
|}
|}
3) Transport_Law = 2 (Bridge-Dominic version of Bagnold formula)
3) Transport_Law = 2 (Bridge-Dominic version of Bagnold formula)
::::{|
::::{|
|width=500px|<math> Q_{c} = K_{f} W \left (\tau _{0} - \tau _{c} \right ) \left ( \sqrt{\tau _{0}} - \sqrt{\tau _{c}} </math>
|width=500px|<math> Q_{c} = K_{f} W \left (\tau _{0} - \tau _{c} \right ) \left ( \sqrt{\tau _{0}} - \sqrt{\tau _{c}} \right ) </math>
|width=50px align="right"|(17)
|width=50px align="right"|(19)
|}
|}
::::{|
::::{|
|width=500px|<math> K_{f} = {\frac{a}{\rho ^ \left ({\frac{1}{2}} \left ( \delta - \rho \right ) g tan \Phi}} </math>
|width=500px|<math> K_{f} = {\frac{a}{\rho ^ \left ({\frac{1}{2}}\right ) \left ( \delta - \rho \right ) g tan \Phi}} </math>
|width=50px align="right"|(18)
|width=50px align="right"|(20)
|}
|}
4) Transport_Law = 4 (Generic power-law formula for multiple size fractions)
4) Transport_Law = 4 (Generic power-law formula for multiple size fractions)
::::{|
::::{|
|width=500px|<math> Q_{ci} = f_{i} K_{f} W \left (\tau _{0} - \tau _{ci} \right ) ^\left ( P_{f} \right ) </math>
|width=500px|<math> Q_{ci} = f_{i} K_{f} W \left (\tau _{0} - \tau _{ci} \right ) ^\left ( P_{f} \right ) </math>
|width=50px align="right"|(19)
|width=50px align="right"|(21)
|}
|}
5) Transport_Law = 6 (Simple slope-discharge power law)
5) Transport_Law = 6 (Simple slope-discharge power law)
::::{|
::::{|
|width=500px|<math> Q_{c} = K_{f} Q^ \left (M_{f}\right ) S^\left (N_{f}\right ) </math>
|width=500px|<math> Q_{c} = K_{f} Q^ \left (M_{f}\right ) S^\left (N_{f}\right ) </math>
|width=50px align="right"|(20)
|width=50px align="right"|(22)
|}
|}
* Soil Creep
* Soil Creep
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::::{|
::::{|
|width=500px|<math> q_{c} = K_{d} \nabla z </math>
|width=500px|<math> q_{c} = K_{d} \nabla z </math>
|width=50px align="right"|(21)
|width=50px align="right"|(23)
|}
|}
2) volumetric sediment discharge per unit width (nonliner)
2) volumetric sediment discharge per unit width (nonliner)
::::{|
::::{|
|width=500px|<math> q_{c} = {\frac{K_{d}\nabla z}{1 - \left ( |\nabla z | / S_{c}\right )^2 }} </math>
|width=500px|<math> q_{c} = {\frac{K_{d}\nabla z}{1 - \left ( |\nabla z | / S_{c}\right )^2 }} </math>
|width=50px align="right"|(22)
|width=50px align="right"|(24)
|}
* Surface hydrology and runoff generation (P > I<sub>c</sub>)
::::{|
|width=500px|<math> Q = \left (P - I_{c}\right ) A </math>
|width=50px align="right"|(25)
|}
* Excess storage capacity runoff (T<sub>r</sub>P > D<sub>sr</sub>)
::::{|
|width=500px|<math> R = {\frac{T_{r} - D_{sr}}{T_{r}}} </math>
|width=50px align="right"|(26)
|}
* Saturation-excess runoff
1) Capacity for shallow subsurface flow per unit contour length
::::{|
|width=500px|<math> q_{sub} = {\frac{Q_{sub}}{w}} = T S </math>
|width=50px align="right"|(27)
|}
2) Surface discharge resulting from a combination of saturation-excess overland flow and return flow (P A > T S w)
::::{|
|width=500px|<math> Q = P A - T S w </math>
|width=50px align="right"|(28)
|}
* Lateral Stream Channel Migration (Meandering)
1) Migration vector of the outer bank
::::{|
|width=500px|<math> \hat{\zeta} = E_{eff} \tau_{w} \hat{n} </math>
|width=50px align="right"|(29)
|}
2) Effective bank erodibility
::::{|
|width=500px|<math> E_{eff} = \left\{\begin{matrix} E_{0} \left ({\frac{1 - P_{H}h_{B}}{H + h_{B}}}\right ) & h_{B} > 0 \\ E_{0} & h_{B} <= 0 \end{matrix}\right.</math>
|width=50px align="right"|(30)
|}
* Effective erodibility at node i of the bank on the eˆ -side
::::{|
|width=500px|<math> E_{eff,i}^ \left (hat{e}\right ) = {\frac{E_{eff,i1} d_{2} + E_{eff,i2} d_{1}}{d_{1} + d_{2}}} </math>
|width=50px align="right"|(31)
|}
* Floodplains: Overbank Sedimentation: Vertical deposition rate
::::{|
|width=500px|<math> D_{OB} = \left ( \eta - z \right ) \mu exp \left ( - d / \lambda \right ) </math>
|width=50px align="right"|(32)
|}
|}
<div class="NavFrame collapsed" style="text-align:left">
<div class="NavFrame collapsed" style="text-align:left">
   <div class="NavHead">Nomenclature</div>
   <div class="NavHead">Nomenclature</div>
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| R<sub>b</sub>
| R<sub>b</sub>
| bankfull runoff rate
| bankfull runoff rate
| m / yr
| L / T
|-
|-
|A
|A
| drainage area
| drainage area
| km<sup>2</sup>
| L<sup>2</sup>
|-
|-
| Q<sub>b</sub>
| Q<sub>b</sub>
| bankfull discharge
| bankfull discharge
| m<sup>3</sup> / s
| L<sup>3</sup> / T
|-
|-
| W<sub>b</sub>
| W<sub>b</sub>
| bankfull channel width
| bankfull channel width
| m
| L
|-
|-
| k<sub>w</sub>
| k<sub>w</sub>
| hydro_wid_coefficient_Ds
| coefficient in bankfull width-discharge relation
| -
| -
|-
|-
| ω<sub>b</sub>
| ω<sub>b</sub>
| hydro_wid_exp_Ds
| exponent in bankfull width-discharge relation
| -
| -
|-
|-
| W
| W
| channel width
| channel width
| m
| L
|-
|-
| ω<sub>s</sub>
| ω<sub>s</sub>
| hydro_wid_exp_stn
| exponent in at-a-station width-discharge relation
| -
| -
|-
|-
| d<sub>b</sub>
| d<sub>b</sub>
| bankfull water depth
| bankfull water depth
| m
| L
|-
|-
| d
| d
| water depth
| water depth
| m
| L
|-
|-
| k<sub>d</sub>
| k<sub>d</sub>
| hydro_dep_coeff_ds
| coefficient in bankfull depth-discharge relation
| -
| -
|-
|-
| δ<sub>b</sub>
| δ<sub>b</sub>
| hydro_dep_exp_ds
| exponent in bankfull depth-discharge relation
| -
| -
|-
|-
| δ<sub>s</sub>
| δ<sub>s</sub>
| hydro_dep_exp_stn
| exponent in at-a-station depth-discharge relation
| -
| -
|-
|-
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|-
|-
| k<sub>N</sub>
| k<sub>N</sub>
| hydro_rough_coeff_ds
| coefficient in bankfull roughness-discharge relation
| -
| -
|-
|-
| ν<sub>b</sub>
| ν<sub>b</sub>
| hydro_rough_exp_ds
| exponent in bankfull roughness-discharge relation
| -
| -
|-
|-
| ν<sub>s</sub>
| ν<sub>s</sub>
| hydro_rough_exp_stn
| exponent in at-a-station roughness-discharge relation
| -
| -
|-
|-
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|-
|-
| k<sub>M</sub>
| k<sub>M</sub>
| bank_rough_coeff
|  
| -
| -
|-
|-
| μ<sub>b</sub>
| μ<sub>b</sub>
| bank_rough_coeff
| coefficient in bank roguhness-discharge relation
| -
| -
|-
|-
| μ<sub>s</sub>
| μ<sub>s</sub>
| bank_rough_exp
| exponent in bank roughness-discharge relation
| -
| -
|-
|-
| z<sub>i</sub>
| z<sub>i</sub>
| surface height at cell i
| surface height at cell i
| m
| L
|-
|-
| Λ<sub>i</sub>
| Λ<sub>i</sub>
| cell's horizontal surface area
| cell's horizontal surface area
| m
| L
|-
|-
| Q<sub>Si</sub>
| Q<sub>Si</sub>
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|-
|-
| P<sub>b</sub>
| P<sub>b</sub>
| a parameter
| Excess power/shear exponent in detachment capacity equation
| -
|-
| Q<sub>c</sub>
| transport capacity
| -
| -
|-
|-
| K<sub>f</sub>
| K<sub>f</sub>
| transport efficiency factor
| transport efficiency factor
| m<sup>2</sup> / y / Pa<sup>-3/2</sup>
| -
|-
| ρ
| water density
| M / L<sup>3</sup>
|-
| δ
| sediment density
| M / L<sup>3</sup>
|-
| a / tan φ
| dimensionless transport-capacity coefficient
| M / L<sup>3</sup>
|-
| g
| acceleration due to gravity
| L / T<sup>2</sup>
|-
| f<sub>i</sub>
| proportion of size i on the bed
| -
|-
| τ<sub>ci</sub>
| effective critical shear stress for the ith size fraction
| -
|-
| q<sub>c</sub>
| volumetric sediment discharge per unit width
| L<sup>2</sup> / T
|-
| K<sub>d</sub>
| transport coefficient
| -
|-
| S<sub>c</sub>
| threshold slope gradient at which transport rate tends to infinity
| -
|-
| Q
| surface discharge
| L<sup>3</sup> / T
|-
| P
| rainfall intensity
| L / T
|-
| I<sub>c</sub>
| infiltration capacity
| L / T
|-
| R
| local runoff rate
| L / T
|-
| D<sub>sr</sub>
| soil-canopy-surface retention depth
| L
|-
| T<sub>r</sub>
| rainfall duration
| T
|-
| q<sub>sub</sub>
| capacity for shallow subsurface flow per unit contour length
| -
|-
| S
| local slope
| -
|-
| T
| soil transmissivity
| L<sup>2</sup> / T
|-
| w
| width of adjoining Voronoi cell edges
| -
|-
| z<sub>b</sub>
| elevation of the channel bed above a datum within the underlying rock column
| L
|-
| D<sub>c</sub>
| maximum detachment (erosion) capacity
| L / T
|-
| ν
| bed sediment porosity
| -
|-
| x
| a vector oriented in the direction of flow
| -
|-
| C<sub>s</sub>
| transport capacity
| L<sup>3</sup> / T
|-
| ζˆ
| migration vector of the outer bank
| -
|-
| τ<sub>w</sub>
| bank shear stress
| -
|-
| E<sub>eff</sub>
| effective bank erodibility
| -
|-
| nˆ
| unit vector perpendicular to the downstream direction
| -
|-
| E<sub>0</sub>
| nominal bank erodibility
| -
|-
| H
| water depth
| L
|-
| h<sub>B</sub>
| bank height above the water surface
| L
|-
| P<sub>H</sub>
| degree to which the effective bank erodibility is dependent on bank height, 0<= P<sub>H</sub> <= 1
| -
|-
| eˆ
| unit vector in the direction of either the left (nˆ) or the right (− nˆ ) bank
| -
|-
| E<sub>eff,i1</sub>, E<sub>eff,i2</sub>
| effective erodibility of the bank nodes with respect to node i
| -
|-
| d<sub>1</sub>, d<sub>2</sub>
| distances of the bank nodes from the line parallel to the unit vector
| L
|-
| D<sub>OB</sub>
| vertical deposition rate
| L / T
|-
| z
| local elevation
| L
|-
| d
| distance between the point in question and the nearest point on the main channel
| L
|-
| η
| water surface height at the nearest point on the main channel
| L
|-
| μ
| deposition rate constant
| 1 / T
|-
| λ
| distance-decay constant
| -
|-
| K<sub>t</sub>
| Coefficient relating shear stress to discharge and slope, can be calculated from water density, gravitational acceleration, and roughness (See Tucker and Slingerland (1997)).
| -
|-
|-
|}
|}
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</div>
</div>
==Notes==
==Notes==
<span class="remove_this_tag">Any notes, comments, you want to share with the user</span>
See reference: Tucker, G.E. et al. (2001) and Tucker, G.E. (2010).
 
<span class="remove_this_tag">Numerical scheme</span>
 


==Examples==
==Examples==
Line 481: Line 704:


<span class="remove_this_tag">Follow the next steps to include images / movies of simulations:</span>
<span class="remove_this_tag">Follow the next steps to include images / movies of simulations:</span>
* <span class="remove_this_tag">Upload file: http://csdms.colorado.edu/wiki/Special:Upload</span>
* <span class="remove_this_tag">Upload file: https://csdms.colorado.edu/wiki/Special:Upload</span>
* <span class="remove_this_tag">Create link to the file on your page: <nowiki>[[Image:<file name>]]</nowiki>.</span>
* <span class="remove_this_tag">Create link to the file on your page: <nowiki>[[Image:<file name>]]</nowiki>.</span>


Line 487: Line 710:


==Developer(s)==
==Developer(s)==
<span class="remove_this_tag">Name of the module developer(s)</span>
[[User:Gtucker|Gregory Tucker]]


==References==
==References==
<span class="remove_this_tag">Key papers</span>
* Tucker, G.E., Lancaster, S.T., Gasparini, N.M., Bras, R.L., 2001. The Channel-Hillslope Integrated Landscape Development Model (CHILD) in Landscape erosion and evolution modeling. R. S. Harmon and W. W. Doe (ed.). Kluwer Press, Dordrecht, pages 349–388.
 
* Tucker, G.E., 2010. CHILD User Guide for version R9.4.1. University of Colorado, Boulder, USA


==Links==
==Links==
<span class="remove_this_tag">Any link, eg. to the model questionnaire, etc.</span>
* [[Model:CHILD]]


[[Category:Modules]] [[Category:Utility components]]
[[Category:Modules]]

Latest revision as of 16:18, 19 February 2018

The CSDMS Help System

CHILD

The CHILD model simulates the evolution of a topographic surface and its subjacent stratigraphy under a set of driving erosion and sedimentation processes and with a prescribed set of initial and boundary conditions.

Model introduction

Designed to serve as a computational framework for investigating a wide range of problems in catchment geomorphology, CHILD is both a model, in the sense that it com¬prises a set of hypotheses about how nature works, and a software tool, in the sense that it provides a simulation environment for exploring the conse¬quences of different hypotheses, parameters, and boundary conditions. The model provides a general and extensible computational framework for exploring research questions related to landscape evolution. It simulates the interaction of two general types of process: “fluvial” processes, a category which encompasses erosion or deposition by runoff cascading across the landscape, and “hillslope” processes, which includes weathering, soil creep, and other slope transport processes.

Model parameters

Parameter Description Unit
Input directory Paths to input files -
Site prefix Site prefix for input/output files -
Case prefix Case prefix for input/output files -
Parameter Description Unit
Run duraction simulation run time years
Parameter Description Unit
Type of uplift 0 = none; 1 = uniform; 2 = block -
Duration of uplift years
Uplift rate m / yr
Subsidence rate m / yr
Position of fault m
Parameter Description Unit
SubaqueousErosion port use the SubaqueousErosion provides port -
Parameter Description Unit
Width of grid in x-direction m
Width of grid in y-direction m
Mean distance between grid nodes m
Parameter Description Unit
Output directory path to output grid files -
Interval between output files -
File format format for output files -
elevation file output file prefix for variable -
erosion file output file prefix for variable -
discharge file output file prefix for variable -
sediment file output file prefix for variable -
Parameter Description Unit
Output directory path to output grid files -
Interval between output files -
File format format for output files -
Cellelevation file output file prefix for variable -
Cellerosion file output file prefix for variable -
Celldischarge file output file prefix for variable -
Cellsediment file output file prefix for variable -
Parameter Description Unit
Model name name of the model -
Author name name of the model author -

Uses ports

This will be something that the CSDMS facility will add

Provides ports

This will be something that the CSDMS facility will add

Main equations

  • Hydraulic Geometry

1) bankfull discharbge

[math]\displaystyle{ Q_{b} = R_{b} A }[/math] (1)

2) bankfull channel width

[math]\displaystyle{ W_{b} = k_{w} Q_{b} ^ \left (\omega_{b} \right ) }[/math] (2)

3) Channel width

[math]\displaystyle{ {\frac{W}{W_{b}}} = {\frac{Q^ \left ( \omega _{s} \right )}{Q_{b}}} }[/math] (3)

4) bankfull water depth

[math]\displaystyle{ d_{b} = k_{b} Q_{b} ^ \left (\delta _{b} \right ) }[/math] (4)

5) Water depth

[math]\displaystyle{ {\frac{d}{d_{b}}} = {\frac{Q ^ \left ( \delta _{s}\right )}{Q_{b}}} }[/math] (5)

6) Bankfull bed roughness

[math]\displaystyle{ N_{b} = k_{N} Q_{b} ^ \left (\nu _{b} \right ) }[/math] (6)

7) Bed roughness

[math]\displaystyle{ {\frac{N}{N_{b}}} = {\frac{Q ^ \left ( \nu _{s}\right )}{Q_{b}}} }[/math] (7)

8) Bankfull bank roughness

[math]\displaystyle{ M_{b} = k_{M} Q_{b} ^ \left (\mu _{b} \right ) }[/math] (8)

9) Bed roughness

[math]\displaystyle{ {\frac{M}{M_{b}}} = {\frac{Q ^ \left ( \mu _{s}\right )}{Q_{b}}} }[/math] (9)
  • Overview of Transport, Erosion, and Deposition by Running water

1) Continuity of mass equation for the time rate of change of height at a cell

[math]\displaystyle{ {\frac{dz_{i}}{dt}} = {\frac{1}{\Lambda _{i}}} \left ( -Q_{Si} + \sum\limits_{i=1}^\left (N_{i} \right ) Q_{Sj} \right ) }[/math] (10)

2) Potential erosion/deposition rate

[math]\displaystyle{ \Phi _{i} = {\frac{1}{\Lambda _{i}}} \left ( -Q_{Ci} + \sum\limits_{i=1}^\left (N_{i} \right ) Q_{Sj} \right ) }[/math] (11)

3) Volumetric water-borne sediment transport rate out of the cell

[math]\displaystyle{ Q_{Si} = \left\{\begin{matrix} \lambda _{i} D_{ci} & if \Phi _{i} \gt D_{c} \\ Q_{Ci} & otherwise \end{matrix}\right. }[/math] (12)
  • Detachment-Capacity Laws

1) bed shear stress

[math]\displaystyle{ \tau _{0} = K_{t} \left ({\frac{Q}{W}}\right ) ^ \left (M_{b}\right ) S^ \left (N_{b}\right ) }[/math] (13)

2) Detachment capacity

[math]\displaystyle{ D _{c} = \left\{\begin{matrix} K_{br} \left ( \tau _{0} - \tau _{c} \right ) ^ \left (P_{b}\right ) & Detachmentlaw = 0 \\ K_{br} \left ( \tau _{0} ^ \left (P_{b} \right ) - \tau _{c} ^ \left (P_{b}\right ) \right ) & Detachmentlaw = 1 \end{matrix}\right. }[/math] (14)
  • Transport capacity types

1) detachment-limited

[math]\displaystyle{ {\frac{\partial z_{b}}{\partial t}} = - D_{c} }[/math] (15)

2) Transport limited

[math]\displaystyle{ {\frac{\partial z_{b}}{\partial t}} = - {\frac{1}{\left ( 1 - \nu \right )}} {\frac{\partial C_{s} / W}{\partial x}} }[/math] (16)
  • Transport Capacity Laws

1) Transport_Law = 0 (Power law formula, form 1)

[math]\displaystyle{ Q_{c} = K_{f} W \left ( \tau _{0} - \tau _{c} \right ) ^ \left (P_{f} \right ) }[/math] (17)

2) Transport_Law = 1 (Power law formula, form 2)

[math]\displaystyle{ Q_{c} = K_{f} W \left ( \tau _{0} ^ \left (P_{f}\right ) - \tau _{c} ^ \left (P_{f} \right )\right ) }[/math] (18)

3) Transport_Law = 2 (Bridge-Dominic version of Bagnold formula)

[math]\displaystyle{ Q_{c} = K_{f} W \left (\tau _{0} - \tau _{c} \right ) \left ( \sqrt{\tau _{0}} - \sqrt{\tau _{c}} \right ) }[/math] (19)
[math]\displaystyle{ K_{f} = {\frac{a}{\rho ^ \left ({\frac{1}{2}}\right ) \left ( \delta - \rho \right ) g tan \Phi}} }[/math] (20)

4) Transport_Law = 4 (Generic power-law formula for multiple size fractions)

[math]\displaystyle{ Q_{ci} = f_{i} K_{f} W \left (\tau _{0} - \tau _{ci} \right ) ^\left ( P_{f} \right ) }[/math] (21)

5) Transport_Law = 6 (Simple slope-discharge power law)

[math]\displaystyle{ Q_{c} = K_{f} Q^ \left (M_{f}\right ) S^\left (N_{f}\right ) }[/math] (22)
  • Soil Creep

1) volumetric sediment discharge per unit width (liner)

[math]\displaystyle{ q_{c} = K_{d} \nabla z }[/math] (23)

2) volumetric sediment discharge per unit width (nonliner)

[math]\displaystyle{ q_{c} = {\frac{K_{d}\nabla z}{1 - \left ( |\nabla z | / S_{c}\right )^2 }} }[/math] (24)
  • Surface hydrology and runoff generation (P > Ic)
[math]\displaystyle{ Q = \left (P - I_{c}\right ) A }[/math] (25)
  • Excess storage capacity runoff (TrP > Dsr)
[math]\displaystyle{ R = {\frac{T_{r} - D_{sr}}{T_{r}}} }[/math] (26)
  • Saturation-excess runoff

1) Capacity for shallow subsurface flow per unit contour length

[math]\displaystyle{ q_{sub} = {\frac{Q_{sub}}{w}} = T S }[/math] (27)

2) Surface discharge resulting from a combination of saturation-excess overland flow and return flow (P A > T S w)

[math]\displaystyle{ Q = P A - T S w }[/math] (28)
  • Lateral Stream Channel Migration (Meandering)

1) Migration vector of the outer bank

[math]\displaystyle{ \hat{\zeta} = E_{eff} \tau_{w} \hat{n} }[/math] (29)

2) Effective bank erodibility

[math]\displaystyle{ E_{eff} = \left\{\begin{matrix} E_{0} \left ({\frac{1 - P_{H}h_{B}}{H + h_{B}}}\right ) & h_{B} \gt 0 \\ E_{0} & h_{B} \lt = 0 \end{matrix}\right. }[/math] (30)
  • Effective erodibility at node i of the bank on the eˆ -side
[math]\displaystyle{ E_{eff,i}^ \left (hat{e}\right ) = {\frac{E_{eff,i1} d_{2} + E_{eff,i2} d_{1}}{d_{1} + d_{2}}} }[/math] (31)
  • Floodplains: Overbank Sedimentation: Vertical deposition rate
[math]\displaystyle{ D_{OB} = \left ( \eta - z \right ) \mu exp \left ( - d / \lambda \right ) }[/math] (32)

Notes

See reference: Tucker, G.E. et al. (2001) and Tucker, G.E. (2010).

Examples

An example run with input parameters, BLD files, as well as a figure / movie of the output

Follow the next steps to include images / movies of simulations:

See also: Help:Images or Help:Movies

Developer(s)

Gregory Tucker

References

  • Tucker, G.E., Lancaster, S.T., Gasparini, N.M., Bras, R.L., 2001. The Channel-Hillslope Integrated Landscape Development Model (CHILD) in Landscape erosion and evolution modeling. R. S. Harmon and W. W. Doe (ed.). Kluwer Press, Dordrecht, pages 349–388.
  • Tucker, G.E., 2010. CHILD User Guide for version R9.4.1. University of Colorado, Boulder, USA

Links