Model help:CHILD: Difference between revisions

From CSDMS
No edit summary
mNo edit summary
Line 376: Line 376:
| 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>
Line 400: Line 400:
| W
| W
| channel width
| channel width
| m
| L
|-
|-
| ω<sub>s</sub>
| ω<sub>s</sub>
Line 408: Line 408:
| 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>
Line 468: Line 468:
| 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>
Line 524: Line 524:
| 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
| ρ
Line 552: Line 552:
| q<sub>c</sub>
| q<sub>c</sub>
| volumetric sediment discharge per unit width
| volumetric sediment discharge per unit width
| -
| L<sup>2</sup> / T
|-
|-
| K<sub>d</sub>
| K<sub>d</sub>
| transport coefficient
| transport coefficient
| L<sup>2</sup> / T
| -
|-
|-
| S<sub>c</sub>
| S<sub>c</sub>
Line 695: Line 695:
==Notes==
==Notes==
See reference: Tucker, G.E. et al. (2001) and Tucker, G.E. (2010).
See reference: Tucker, G.E. et al. (2001) and Tucker, G.E. (2010).


==Examples==
==Examples==

Revision as of 13:29, 26 May 2011

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 _{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 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