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

Input Files and Directories

Run Parameters

Tectonics

Port

Grid

Output Grids

Output Cell Grids

About

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 > I_c)

[math]\displaystyle{ Q = \left (P - I_{c}\right ) A }[/math]

(25)

• Excess storage capacity runoff (T_rP > D_sr)

[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)

Nomenclature

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)

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

• Model:CHILD