Model help:CHILD: Difference between revisions
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5) Water depth | 5) Water depth | ||
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|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 | ||
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|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 | ||
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|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 | ||
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|width=500px|<math> D _{c} = \left\{\begin{matrix} K_{br} \left ( \tau _{0} - \tau _{c} \right ) ^ \left (P_{b}\right ) & | |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) | ||
|} | |} | ||
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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"|(16) | ||
|} | |} | ||
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"|(17) | ||
|} | |} | ||
::::{| | ::::{| | ||
|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"|(18) | ||
|} | |} | ||
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|- | |- | ||
| k<sub>w</sub> | | k<sub>w</sub> | ||
| | | coefficient in bankfull width-discharge relation | ||
| - | | - | ||
|- | |- | ||
| ω<sub>b</sub> | | ω<sub>b</sub> | ||
| | | exponent in bankfull width-discharge relation | ||
| - | | - | ||
|- | |- | ||
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|- | |- | ||
| ω<sub>s</sub> | | ω<sub>s</sub> | ||
| | | exponent in at-a-station width-discharge relation | ||
| - | | - | ||
|- | |- | ||
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|- | |- | ||
| k<sub>d</sub> | | k<sub>d</sub> | ||
| | | coefficient in bankfull depth-discharge relation | ||
| - | | - | ||
|- | |- | ||
| δ<sub>b</sub> | | δ<sub>b</sub> | ||
| | | exponent in bankfull depth-discharge relation | ||
| - | | - | ||
|- | |- | ||
| δ<sub>s</sub> | | δ<sub>s</sub> | ||
| | | exponent in at-a-station depth-discharge relation | ||
| - | | - | ||
|- | |- | ||
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|- | |- | ||
| k<sub>N</sub> | | k<sub>N</sub> | ||
| | | coefficient in bankfull roughness-discharge relation | ||
| - | | - | ||
|- | |- | ||
| ν<sub>b</sub> | | ν<sub>b</sub> | ||
| | | exponent in bankfull roughness-discharge relation | ||
| - | | - | ||
|- | |- | ||
| ν<sub>s</sub> | | ν<sub>s</sub> | ||
| | | exponent in at-a-station roughness-discharge relation | ||
| - | | - | ||
|- | |- | ||
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|- | |- | ||
| k<sub>M</sub> | | k<sub>M</sub> | ||
| | | | ||
| - | | - | ||
|- | |- | ||
| μ<sub>b</sub> | | μ<sub>b</sub> | ||
| | | coefficient in bank roguhness-discharge relation | ||
| - | | - | ||
|- | |- | ||
| μ<sub>s</sub> | | μ<sub>s</sub> | ||
| | | exponent in bank roughness-discharge relation | ||
| - | | - | ||
|- | |- | ||
Line 461: | Line 461: | ||
|- | |- | ||
| P<sub>b</sub> | | P<sub>b</sub> | ||
| | | Excess power/shear exponent in detachment capacity equation | ||
| - | | - | ||
|- | |- | ||
| 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 | |||
| | |||
| m<sup>2</sup> / y / Pa<sup>-3/2</sup> | | m<sup>2</sup> / y / Pa<sup>-3/2</sup> | ||
|- | |- |
Revision as of 16:35, 13 May 2011
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
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 _{b} \right )}{Q_{b}}} }[/math] (3)
4) bankfull water depth
[math]\displaystyle{ d_{b} = k_{d} 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 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] (15)
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] (16)
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] (17)
[math]\displaystyle{ K_{f} = {\frac{a}{\rho ^ \left ({\frac{1}{2}}\right ) \left ( \delta - \rho \right ) g tan \Phi}} }[/math] (18)
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] (19)
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] (20)
- Soil Creep
1) volumetric sediment discharge per unit width (liner)
[math]\displaystyle{ q_{c} = K_{d} \nabla z }[/math] (21)
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] (22)
Symbol | Description | Unit |
---|---|---|
Rb | bankfull runoff rate | m / yr |
A | drainage area | km2 |
Qb | bankfull discharge | m3 / s |
Wb | bankfull channel width | m |
kw | coefficient in bankfull width-discharge relation | - |
ωb | exponent in bankfull width-discharge relation | - |
W | channel width | m |
ωs | exponent in at-a-station width-discharge relation | - |
db | bankfull water depth | m |
d | water depth | m |
kd | coefficient in bankfull depth-discharge relation | - |
δb | exponent in bankfull depth-discharge relation | - |
δs | exponent in at-a-station depth-discharge relation | - |
Nb | bankfull bed roughness | - |
N | bed roughness | - |
kN | coefficient in bankfull roughness-discharge relation | - |
νb | exponent in bankfull roughness-discharge relation | - |
νs | exponent in at-a-station roughness-discharge relation | - |
Mb | bankfull bank roughness | - |
M | bank roughness | - |
kM | - | |
μb | coefficient in bank roguhness-discharge relation | - |
μs | exponent in bank roughness-discharge relation | - |
zi | surface height at cell i | m |
Λi | cell's horizontal surface area | m |
QSi | volumetric water-borne sediment transport rate out of the cell | L3 / T |
QSj | the transport rate in from neighboring cell j | L3 / T |
Ni | the number of neighboring cells that drain to cell i | - |
Dci | potential detachment rate | L / T |
Φi | potential erosion/deposition rate | L / T |
τ0 | bed shear stress | - |
Q | discharge | L3 |
S | gradient from cell i to its downstream neighbor | - |
Kbr | rate coefficient (regolith for Detachment_Law = 0; bedrock for Detachment_Law = 1) | - |
τc | a threshold below which no detachment takes place | - |
Pb | Excess power/shear exponent in detachment capacity equation | - |
Kf | transport efficiency factor | m2 / y / Pa-3/2 |
ρ | m2 / y / Pa-3/2 |
Notes
Any notes, comments, you want to share with the user
Numerical scheme
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:
- Upload file: http://csdms.colorado.edu/wiki/Special:Upload
- Create link to the file on your page: [[Image:<file name>]].
See also: Help:Images or Help:Movies
Developer(s)
Name of the module developer(s)
References
Key papers
Links
Any link, eg. to the model questionnaire, etc.