Model help:CHILD
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
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Provides ports
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Main equations
- Hydraulic Geometry
1) bankfull discharbge
<math> Q_{b} = R_{b} A </math> (1)
2) bankfull channel width
<math> W_{b} = k_{w} Q_{b} ^ \left (\omega_{b} \right ) </math> (2)
3) Channel width
<math> {\frac{W}{W_{b}}} = {\frac{Q^ \left ( \omega _{s} \right )}{Q_{b}}}</math> (3)
4) bankfull water depth
<math> d_{b} = k_{b} Q_{b} ^ \left (\delta _{b} \right )</math> (4)
5) Water depth
<math> {\frac{d}{d_{b}}} = {\frac{Q ^ \left ( \delta _{s}\right )}{Q_{b}}}</math> (5)
6) Bankfull bed roughness
<math> N_{b} = k_{N} Q_{b} ^ \left (\nu _{b} \right )</math> (6)
7) Bed roughness
<math> {\frac{N}{N_{b}}} = {\frac{Q ^ \left ( \nu _{s}\right )}{Q_{b}}}</math> (7)
8) Bankfull bank roughness
<math> M_{b} = k_{M} Q_{b} ^ \left (\mu _{b} \right )</math> (8)
9) Bed roughness
<math> {\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> {\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> \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> Q_{Si} = \left\{\begin{matrix} \lambda _{i} D_{ci} & if \Phi _{i} > D_{c} \\ Q_{Ci} & otherwise \end{matrix}\right. </math> (12)
- Detachment-Capacity Laws
1) bed shear stress
<math> \tau _{0} = K_{t} \left ({\frac{Q}{W}}\right ) ^ \left (M_{b}\right ) S^ \left (N_{b}\right ) </math> (13)
2) Detachment capacity
<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> (14)
- Transport capacity types
1) detachment-limited
<math> {\frac{\partial z_{b}}{\partial t}} = - D_{c} </math> (15)
2) Transport limited
<math> {\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> 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> 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> Q_{c} = K_{f} W \left (\tau _{0} - \tau _{c} \right ) \left ( \sqrt{\tau _{0}} - \sqrt{\tau _{c}} \right ) </math> (19)
<math> 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> 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> 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> q_{c} = K_{d} \nabla z </math> (23)
2) volumetric sediment discharge per unit width (nonliner)
<math> 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> Q = \left (P - I_{c}\right ) A </math> (25)
- Excess storage capacity runoff (TrP > Dsr)
<math> R = {\frac{T_{r} - D_{sr}}{T_{r}}} </math> (26)
- Saturation-excess runoff
1) Capacity for shallow subsurface flow per unit contour length
<math> 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> Q = P A - T S w </math> (28)
- Lateral Stream Channel Migration (Meandering)
1) Migration vector of the outer bank
<math> \hat{\zeta} = E_{eff} \tau_{w} \hat{n} </math> (29)
2) Effective bank erodibility
<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> (30)
- Effective erodibility at node i of the bank on the eˆ -side
<math> 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> D_{OB} = \left ( \eta - z \right ) \mu exp \left ( - d / \lambda \right ) </math> (32)
| Symbol | Description | Unit |
|---|---|---|
| Rb | bankfull runoff rate | L / T |
| A | drainage area | L2 |
| Qb | bankfull discharge | L3 / T |
| Wb | bankfull channel width | L |
| kw | coefficient in bankfull width-discharge relation | - |
| ωb | exponent in bankfull width-discharge relation | - |
| W | channel width | L |
| ωs | exponent in at-a-station width-discharge relation | - |
| db | bankfull water depth | L |
| d | water depth | L |
| 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 | L |
| Λi | cell's horizontal surface area | L |
| 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 | - |
| Qc | transport capacity | - |
| Kf | transport efficiency factor | - |
| ρ | water density | M / L3 |
| δ | sediment density | M / L3 |
| a / tan φ | dimensionless transport-capacity coefficient | M / L3 |
| g | acceleration due to gravity | L / T2 |
| fi | proportion of size i on the bed | - |
| τci | effective critical shear stress for the ith size fraction | - |
| qc | volumetric sediment discharge per unit width | L2 / T |
| Kd | transport coefficient | - |
| Sc | threshold slope gradient at which transport rate tends to infinity | - |
| Q | surface discharge | L3 / T |
| P | rainfall intensity | L / T |
| Ic | infiltration capacity | L / T |
| R | local runoff rate | L / T |
| Dsr | soil-canopy-surface retention depth | L |
| Tr | rainfall duration | T |
| qsub | capacity for shallow subsurface flow per unit contour length | - |
| S | local slope | - |
| T | soil transmissivity | L2 / T |
| w | width of adjoining Voronoi cell edges | - |
| zb | elevation of the channel bed above a datum within the underlying rock column | L |
| Dc | maximum detachment (erosion) capacity | L / T |
| ν | bed sediment porosity | - |
| x | a vector oriented in the direction of flow | - |
| Cs | transport capacity | L3 / T |
| ζˆ | migration vector of the outer bank | - |
| τw | bank shear stress | - |
| Eeff | effective bank erodibility | - |
| nˆ | unit vector perpendicular to the downstream direction | - |
| E0 | nominal bank erodibility | - |
| H | water depth | L |
| hB | bank height above the water surface | L |
| PH | degree to which the effective bank erodibility is dependent on bank height, 0<= PH <= 1 | - |
| eˆ | unit vector in the direction of either the left (nˆ) or the right (− nˆ ) bank | - |
| Eeff,i1, Eeff,i2 | effective erodibility of the bank nodes with respect to node i | - |
| d1, d2 | distances of the bank nodes from the line parallel to the unit vector | L |
| DOB | 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 | - |
| Kt | Coefficient relating shear stress to discharge and slope, can be calculated from water density, gravitational acceleration, and roughness (See Tucker and Slingerland (1997)). | - |
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:
- Upload file: https://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)
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
