Model help:BedrockAlluvialTransition: Difference between revisions

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==Model introduction==
==Model introduction==
This program computes fluvial aggradation/degradation with a bedrock-alluvial transition. The bedrock-alluvial transition is located at a point sba(t) which is free to change in time. A bedrock basement channel with slope Sb is exposed from x = 0 to sba(t); it is covered with alluvium from x = s<sub>ba</sub>(t) to x = s<sub>d</sub>, where s<sub>d</sub> is fixed. Initially s<sub>ba</sub> = 0. The bedrock basement channel is assumed to undergo no incision on the time scales at which the alluvial reach responds to change. In computing bed level change on the alluvial reach, the normal (steady, uniform) flow approximation is used. Base level is maintained at x = s<sub>d</sub>, where bed elevation h = 0. The Engelund-Hansen relation is used to compute sediment transport rate, so the analysis is appropriate for sand-bed streams. Resistance is specified in terms of a constant Chezy coefficient C<sub>z</sub>.  
This program calculates the bed surface evolution at predefined nodes relative to moving boundary nodes for a transition from bedrock to allvium.


<div id=CMT_MODEL_PARAMETERS>
<div id=CMT_MODEL_PARAMETERS>
==Model parameters==
==Model parameters==
= First tab header =
= Input Files and Directories =
{|{{Prettytable}} class = "wikitable unsortable"  cellspacing="0" cellpadding="0" style="margin:0em 0em 0em 0;"
{|{{Prettytable}} class = "wikitable unsortable"  cellspacing="0" cellpadding="0" style="margin:0em 0em 0em 0;"
|-
|-
!Parameter!!Description!!Unit
!Parameter!!Description!!Unit
|-valign="top"
|-valign="top"
|width="20%"|<span class="remove_this_tag">First parameter</span>
|width="20%"|Input directory
|width="60%"|<span class="remove_this_tag">Description parameter</span>
|width="60%"|path to input files
|width="20%"|<span class="remove_this_tag">[Units]</span>
|width="20%"| -
|-
|Site prefix
|Site prefix for Input/Output files
| -
|-
|Case prefix
|Case prefix for Input/Output files
| -
|-
|}
|}


= Second tab header =
= Run Parameters =
{|{{Prettytable}} class = "wikitable unsortable"  cellspacing="0"  cellpadding="0" style="margin:0em 0em 0em 0;"
{|{{Prettytable}} class = "wikitable unsortable"  cellspacing="0"  cellpadding="0" style="margin:0em 0em 0em 0;"
|-
|-
!Parameter!!Description!!Unit
!Parameter!!Description!!Unit
|-valign="top"
|-valign="top"
|width="20%"|<span class="remove_this_tag">First parameter</span>
|width="20%"|Flood discharge (q)
|width="60%"|<span class="remove_this_tag">Description parameter</span>
|width="60%"|water discharge per unit width during floods
|width="20%"|<span class="remove_this_tag">[Units]</span>
|width="20%"| m<sup>2</sup> / s
|-
|Intermittency
|flood intermittency (I)
| -
|-
|Upstream bed material sediment fed rate during floods
|volume sediment feed rate per width at upstream end during flood
| m<sup>2</sup> / s
|-
|Grain size of bed material (D)
|
| mm
|-
|Chezy resistance coefficient (Cf)
| coefficient in Chezy relation
| -
|-
|Subaqueous basement slope (b)
|slope of bedrock basement
| -
|-
|Slope of forest face (S)
|initial slope of alluvial region
| -
|-
|Submerged specific gravity of sediment
|
| -
|-
|Bed porosity (L)
|
| -
|-
|Position of downstream end of the reach (d)
|
| m
|-
|Number of spatial steps (M)
|
| -
|-
|Time step (t)
|
| days
|-
|Number of iterations before printing (i)
|
| -
|-
|Number of printouts (p)
|
| -
|-
|}
|}


= Etc. tab header =
= About =
{|{{Prettytable}} class = "wikitable unsortable"  cellspacing="0"  cellpadding="0" style="margin:0em 0em 0em 0;"
|-
!Parameter!!Description!!Unit
|-valign="top"
|width="20%"|Model name
|width="60%"|name of the model
|width="20%"|
|-
|Author name
|name of the model author
| -
|-
|}
<headertabs/>
<headertabs/>
</div>


==Uses ports==
==Uses ports==
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==Main equations==
==Main equations==
<span class="remove_this_tag">A list of the key equations. HTML format is supported; latex format will be supported in the future</span>
* Continuity condition at the bedrock-alluvial transition
::::{|
|width=530px|<math> {\frac{\partial \eta}{\partial t}} | _{s_{ba}} - S | _{s_{ba}} \dot{s}_{ba} = - S_{b} | _{s_{ba}} \dot{s}_{ba}  </math>
|width=50p=x align="right"|(1)
|}
* coordinate transformation
::::{|
|width=530px|<math> \bar{x} = {\frac{x - s_{ba} \left ( t \right )}{s_{d} - s_{ba} \left ( t \right )}}  </math>
|width=50p=x align="right"|(2)
|}
::::{|
|width=530px|<math> \bar{t} = t  </math>
|width=50p=x align="right"|(3)
|}
* Bed slope
::::{|
|width=530px|<math> S = - {\frac{\partial \eta}{\partial x}} = - {\frac{1}{s_{d} - s_{ba}}} {\frac{\partial \eta}{\partial \bar{x}}}  </math>
|width=50p=x align="right"|(4)
|}
* Exner equation
::::{|
|width=530px|<math> \left ( 1 - \lambda_{p} \right ) {\frac{\partial \eta}{\partial t}} = - I_{f} {\frac{\partial q_{t}}{\partial x}}  </math>
|width=50p=x align="right"|(4)
|}
* Speed of migration of the bedrock-alluvial transition
::::{|
|width=530px|<math> \dot{s}_{ba} = - {\frac{1}{S_{b} |_{\bar{x} = 0}}} {\frac{\partial \eta}{\partial \bar{t}}} | _{\bar{x} = 0} </math>
|width=50p=x align="right"|(5)
|}


<div class="NavFrame collapsed" style="text-align:left">
<div class="NavFrame collapsed" style="text-align:left">
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{| {{Prettytable}} class="wikitable sortable"
{| {{Prettytable}} class="wikitable sortable"
!Symbol!!Description!!Unit
!Symbol!!Description!!Unit
|-
| x
| downstream coordinate (0 = initial bedrock - alluvial transition)
| L
|-
| Sl
| bed slope
| -
|-
| q<sub>b</sub>
| volume bedload transport per unit width
| L<sup>2</sup> / T
|-
| H
| water depth
| L
|-
|-
| q<sub>w</sub>
| q<sub>w</sub>
| water discharge per unit width during floods
| water discharge per unit width during floods
| m^2 / s
| L<sup>2</sup> / T
|-
|-
| I<sub>f</sub>
| I<sub>f</sub>
| intermittency factor for floods (0 < I <= 1)
| flood intermittency (0 < I <= 1)
| -
| -
|-
|-
| q<sub>tf</sub>
| Q
| volume sediment feed rate per width at upstream end during floods
| volume sediment feed rate per width at upstream and during flood
| -
| L<sup>2</sup> / T
|-
|-
| D
| D
| grain size of alluvium
| grain size of alluvium
| mm
| L
|-
|-
| C<sub>z</sub>
| Cz
| Chezy resistance coefficient
| coefficient in Chezy relation, Cf
| -
| -
|-
|-
| S<sub>b</sub>
| b
| slope of bedrock coefficient
| slope of bedrock basement
| -
| -
|-
|-
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| initial slope of alluvial region
| initial slope of alluvial region
| -
| -
|-
| L
| bed porosity
| -
|-
| k
| coefficient in Manning-Strickler relation
| -
|-
| a
| coefficient in Manning-Strickler relation
| -
|-
| d
| position of the downstream end of the reach
| L
|-
|-
| M
| M
| number of spatial intervals
| number of spatial intervals
| -
|-
| t
| time step
| T
|-
| i
| number of interations per print
| -
|-
| p
| number of prints
| -
|-
| s<sub>d</sub>
| position of the downstream end of the reach, equals to initial length of alluvial region
| -
|-
| q<sub>tf</sub>
| volume sediment feed rate per width at upstream end during floods
| L<sup>2</sup> / T
|-
| S<sub>b</sub>
| slope of bedrock basement
| -
| -
|-
|-
| dt
| dt
| time step
| time step
| yr
| T
|-
|-
| Mtoprint
| Mtoprint
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|-
|-
| Mprint
| Mprint
| number of printout
| number of printouts
| -
|-
| s<sub>ba</sub>
| position of the bedrock-alluvial transition, change with time
| -
|-
| S
| alluvial bed slope
| -
|-
| dot{s<sub>ba</sub>}
| speed of migration of the bedrock-alluvial transition
| -
|-
| S<sub>b</sub>
| slope of the bedrock channel
| -
| -
|-
|-
|}
| bar{x}
 
| dimensionless coordinate
'''Output'''
| -
{| {{Prettytable}} class="wikitable sortable"
|-
!Symbol!!Description!!Unit
| bar{t}
| dimensionless time
| -
|-
|-
| x
| x
|
| downstream coordinate
| L
|-
| η
| bed surface elevation
| L
|-
| λ<sub>p</sub>
| porosity of sediment
| -
| -
|-
| eta
|
|
|-
|-
|}
|}
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</div>
</div>
==Notes==
==Notes==
<span class="remove_this_tag">Any notes, comments, you want to share with the user</span>  
This program computes fluvial aggradation/degradation with a bedrock-alluvial transition. The bedrock-alluvial transition is located at a point s<sub>ba</sub>(t) which is free to change in time. A bedrock basement channel with slope S<sub>b</sub> is exposed from x = 0 to s<sub>ba</sub>(t); it is covered with alluvium from x = s<sub>ba</sub>(t) to x = s<sub>d</sub>, where S<sub>d</sub> is fixed. Initially s<sub>ba</sub> = 0. The bedrock basement channel is assumed to undergo no incision on the time scales at which the alluvial reach responds to change. In computing bed level change on the alluvial reach, the normal (steady, uniform) flow approximation is used. Base level is maintained at x = s<sub>d</sub>, where bed elevation h = 0. The Engelund-Hansen relation is used to compute sediment transport rate, so the analysis is appropriate for sand-bed streams. Resistance is specified in terms of a constant Chezy coefficient C<sub>z</sub>.


<span class="remove_this_tag">Numerical scheme</span>
From the continuity equation, it could be derived that If the bed aggrades, the transition moves upstream; if the bed degrades the transition moves downstream.


* Note on model running
The water depth is calculated using a Chézy formulation, when only the Chézy coefficient is present in the inputted file, and with the Manning-Strickler formulation, when only the roughness height, k<sub>c</sub>, value is present. When both are present the program will ask the user which formulation they would like to use.


==Examples==
==Examples==
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<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 140: Line 322:


==References==
==References==
<span class="remove_this_tag">Key papers</span>
Engelund, F. and E. Hansen, 1967, A Monograph on Sediment Transport in Alluvial Streams, Technisk Vorlag, Copenhagen, Denmark.
 
Parker, G. and Muto, T., 2003, 1D numerical model of delta response to rising sea level, Proc. 3rd IAHR Symposium, River, Coastal and Estuarine Morphodynamics, Barcelona, Spain, 1-5 September.
 
Sklar, L., and W. E. Dietrich, 1998, River longitudinal profiles and bedrock incision models: Stream power and the influence of sediment supply, in Rivers Over Rock: Fluvial Processes in Bedrock Channels, Geophys. Monogr. Ser., vol. 107, edited by K. J. Tinkler and E. E. Wohl, pp. 237–260, AGU, Washington, D. C.
 
Whipple, K. X., G. S. Hancock, and R. S. Anderson, 2000, River incision into bedrock: Mechanics and relative efficacy of plucking, abrasion, and cavitation, Geol. Soc. Am. Bull., 112, 490–503.
 
Wong, M. and Parker, G., submitted, The bedload transport relation of Meyer-Peter and Müller overpredicts by a factor of two, Journal of Hydraulic Engineering


==Links==
==Links==
* [[http://csdms.colorado.edu/wiki/Model:BedrockAlluvialTransition Model:BedrockAlluvialTransition]]
* [[Model:BedrockAlluvialTransition]]


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

Latest revision as of 17:15, 19 February 2018

The CSDMS Help System
The CSDMS Help System

BedrockAlluvialTransition

This is used to calculate aggradation and degradation with a migrating bedrock-alluvial transition at the upstream end.

Model introduction

This program calculates the bed surface evolution at predefined nodes relative to moving boundary nodes for a transition from bedrock to allvium.

Model parameters

Parameter Description Unit
Input directory path to input files -
Site prefix Site prefix for Input/Output files -
Case prefix Case prefix for Input/Output files -
Parameter Description Unit
Flood discharge (q) water discharge per unit width during floods m2 / s
Intermittency flood intermittency (I) -
Upstream bed material sediment fed rate during floods volume sediment feed rate per width at upstream end during flood m2 / s
Grain size of bed material (D) mm
Chezy resistance coefficient (Cf) coefficient in Chezy relation -
Subaqueous basement slope (b) slope of bedrock basement -
Slope of forest face (S) initial slope of alluvial region -
Submerged specific gravity of sediment -
Bed porosity (L) -
Position of downstream end of the reach (d) m
Number of spatial steps (M) -
Time step (t) days
Number of iterations before printing (i) -
Number of printouts (p) -
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

  • Continuity condition at the bedrock-alluvial transition
<math> {\frac{\partial \eta}{\partial t}} | _{s_{ba}} - S | _{s_{ba}} \dot{s}_{ba} = - S_{b} | _{s_{ba}} \dot{s}_{ba} </math> (1)
  • coordinate transformation
<math> \bar{x} = {\frac{x - s_{ba} \left ( t \right )}{s_{d} - s_{ba} \left ( t \right )}} </math> (2)
<math> \bar{t} = t </math> (3)
  • Bed slope
<math> S = - {\frac{\partial \eta}{\partial x}} = - {\frac{1}{s_{d} - s_{ba}}} {\frac{\partial \eta}{\partial \bar{x}}} </math> (4)
  • Exner equation
<math> \left ( 1 - \lambda_{p} \right ) {\frac{\partial \eta}{\partial t}} = - I_{f} {\frac{\partial q_{t}}{\partial x}} </math> (4)
  • Speed of migration of the bedrock-alluvial transition
<math> \dot{s}_{ba} = - {\frac{1}{S_{b} |_{\bar{x} = 0}}} {\frac{\partial \eta}{\partial \bar{t}}} | _{\bar{x} = 0} </math> (5)

Notes

This program computes fluvial aggradation/degradation with a bedrock-alluvial transition. The bedrock-alluvial transition is located at a point sba(t) which is free to change in time. A bedrock basement channel with slope Sb is exposed from x = 0 to sba(t); it is covered with alluvium from x = sba(t) to x = sd, where Sd is fixed. Initially sba = 0. The bedrock basement channel is assumed to undergo no incision on the time scales at which the alluvial reach responds to change. In computing bed level change on the alluvial reach, the normal (steady, uniform) flow approximation is used. Base level is maintained at x = sd, where bed elevation h = 0. The Engelund-Hansen relation is used to compute sediment transport rate, so the analysis is appropriate for sand-bed streams. Resistance is specified in terms of a constant Chezy coefficient Cz.

From the continuity equation, it could be derived that If the bed aggrades, the transition moves upstream; if the bed degrades the transition moves downstream.

  • Note on model running

The water depth is calculated using a Chézy formulation, when only the Chézy coefficient is present in the inputted file, and with the Manning-Strickler formulation, when only the roughness height, kc, value is present. When both are present the program will ask the user which formulation they would like to use.

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)

Gary Parker

References

Engelund, F. and E. Hansen, 1967, A Monograph on Sediment Transport in Alluvial Streams, Technisk Vorlag, Copenhagen, Denmark.

Parker, G. and Muto, T., 2003, 1D numerical model of delta response to rising sea level, Proc. 3rd IAHR Symposium, River, Coastal and Estuarine Morphodynamics, Barcelona, Spain, 1-5 September.

Sklar, L., and W. E. Dietrich, 1998, River longitudinal profiles and bedrock incision models: Stream power and the influence of sediment supply, in Rivers Over Rock: Fluvial Processes in Bedrock Channels, Geophys. Monogr. Ser., vol. 107, edited by K. J. Tinkler and E. E. Wohl, pp. 237–260, AGU, Washington, D. C.

Whipple, K. X., G. S. Hancock, and R. S. Anderson, 2000, River incision into bedrock: Mechanics and relative efficacy of plucking, abrasion, and cavitation, Geol. Soc. Am. Bull., 112, 490–503.

Wong, M. and Parker, G., submitted, The bedload transport relation of Meyer-Peter and Müller overpredicts by a factor of two, Journal of Hydraulic Engineering

Links

Retrieved from "https://csdms.colorado.edu/csdms_wiki/index.php?title=Model_help:BedrockAlluvialTransition&oldid=216354"