Model help:AgDegNormalGravMixHyd: Difference between revisions

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==Model introduction==
==Model introduction==
This program is a close relative of AgDegNormGravMixP. It computes aggradation and degradation in gravel-bed river subject to a repeated hydrograph. The sediment is modeled as mixture of different grain sizes and the bedload formulation is that of Parker (1990) that was derived to compute the transport of gravel only.   
This program is a close relative of AgDegNormGravMixPW. It computes aggradation and degradation in gravel-bed river subject to a repeated hydrograph. The sediment is modeled as mixture of different grain sizes and the bedload formulation is that of Parker (1990) that was derived to compute the transport of gravel only.   


<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%"|number of hydrograph entries
|width="60%"|<span class="remove_this_tag">Description parameter</span>
|width="60%"| between 2 and 16 values
|width="20%"|<span class="remove_this_tag">[Units]</span>
|width="20%"|  
|-
|number of cycles per year
|
| -
|-
|bed elevation at downstream end
|
| m
|-
|initial bed slope
|
| -
|-
|reach length
|
| m
|-
|Time step
|
| days
|-
|Number of intervals
|
|
|-
|Number of printouts
|
| -
|-
|Iterations per each printout
|
| -
|-
|factor by which Ds90 is multiplied for roughness height
|
| -
|-
|factor by which Ds90 is multiplied for active layer thickness
|
| -
|-
|Manning-Strickler cofficient r
|
|
|-
|Submerged specific gravity of sediment
|
|
|-
|bed porosity, gravel
|
|
|-
|upwinding coefficient for load spatial derivatives in Exner equation (> 0.5 suggested)
|
|
|-
|Coefficient for material transferred to substrate as bed aggrades
|
|
|-
|}
|}


= 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==
* time duration of a short flood
::::{|
::::{|
|width=500px|<math> \Delta t_{w} = n_{step,w} \Delta t_{f} </math>
|width=500px|<math> \Delta t_{w} = n_{step,w} \Delta t_{f} </math>
|width=50px align="right"|(1)
|width=50px align="right"|(1)
|}
|}
* Total time for flood
::::{|
::::{|
|width=500px|<math> P = \sum\limits_{w=1}^W n_{step,w} </math>
|width=500px|<math> P = \sum\limits_{w=1}^W n_{step,w} </math>
|width=50px align="right"|(2)
|width=50px align="right"|(2)
|}
* Manning-Strickler formulation
::::{|
|width=500px|<math>C_{f}^\left ( {\frac{-1}{2}} \right )=\alpha _{r}\left ( \frac{H}{K_{c}} \right )^{\frac{1}{6}}</math>
|width=50px align="right"|(3)
|}
* Roughness height due to skin friction
::::{|
|width=500px|<math> k_{s} = n_{k} D_{s90} </math>
|width=50px align="right"|(4)
|}
::::{|
|width=500px|<math> L_{a} = n_{a} D_{s90} </math>
|width=50px align="right"|(5)
|}
|}


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!Symbol!!Description!!Unit
!Symbol!!Description!!Unit
|-
|-
| X
| Q<sub>w</sub>
| Streamwise coordinate
| constant water discharge for the Wth flood
| m
| L <sup>3</sup> / T
|-
| Q<sub>p</sub>
| discharge for each time step p (p =1...P)
| L <sup>3</sup> / T
|-
| p
| time step in the hydrograph
|
|-
| P
| Total time for flood
|
|-
| Δt<sub>w</sub>
| time duration of a short flood
| T
|-
| Δt<sub>f</sub>
| a short flood time step
| T
|-
| n<sub>step,w</sub>
| an integer number of the flood time step
| T
|-
| η
| river bed elevation
| L
|-
|-
| t
| t
| Temporal coordinate
| time step
| seconds
| T
|-
|-
| Q<sub>w</sub>
| B
| Flood discharge
| river width
| m<sup>3</sup>/s
| L
|-
|-
| S<sub>l</sub>
| D
| Ambient bed slope
| grain size of the bed sediment
| -
| L
|-
|-
| D<sub>bi</sub>
| bound diameter
| L
| L
| Length of reach
| m
|-
|-
| Δt
| λ<sub>p</sub>
| Time step
| bed porosity
| year
| -
|-
|-
| M
| α
| Number of spatial intervals
| the parameter that governs the grain size distribution of the sediment at the active layer-substrate interface during bed aggredation
| -
| -
|-
|-
| R
| F<sub>fi</sub>
| Submerged specific gravity
| grain size distribution of the active layer for initial condition
| -
| -
|-
|-
| Cz
| F<sub>i</sub>
| Non-dimensional Chézy friction coefficient
| fraction of sediment in the ith grain size range in the active layer
| -
| -
|-
|-
| ∆t<sub>f</sub>
| f<sub>subfi</sub>
| flood time step, used to solve the Exner equation
| fraction of sediment in the ith grain size range in the substrate layer for initial condition
| -
| -
|-
|-
| n<sub>step,w</sub>
| n<sub>pp</sub>
| an integer number of the flood time step
| number of grain sizes for which a percent finer is specified, it must have the value between 2 and 9
| -
| -
|-
|-
| Q<sub>p</sub>
| D<sub>bnew</sub>
| discharge for each time step p
| bound of the distribution such that the fraction of sediment finer than D<sub>bnew</sub> is equal to 0
| L
|-
| F<sub>subfli</sub>
| percent finer than ith grain size range for the substrate layer for initial condition
| -
| -
|-
|-
| η<sub>d</sub>
| f<sub>li</sub>
| downstream bed elevation
| fraction of sediment in the ith grain size range in the active-layer substrate interface
| -
| -
|-
|-
| npp
| p<sub>i</sub>
| input number of grain sizes defining distributions, npp must be between 2 and 9
| fraction of sediment in the ith grain size range in the bedload
| -
| -
|-
|-
| D<sub>bi</sub>
| F<sub>sub,i</sub>
|  
| fraction of substrate material in the ith size range
| -
| -
|-
|-
| D<sub>bnew</sub>
| D<sub>s90</sub>
|  
| the diameter of the bed surface such that the 90% of the sediment is finer
| L
|-
| n<sub>a</sub>
| user specified order-one non dimensional constant
| -
| -
|-
|-
| N
| p<sub>ffi</sub>
| number of hydrograph entries
| the percent that is finer than the ith size range for upstream boundary conditon
| -
| -
|-
|-
| c
| η<sub>d</sub>
| number of hydrograph cycles per year
| fixed bed elevation at the downstream end of the modeled reach
| L
|-
| k<sub>c</sub>
| composite roughness height
| L
|-
| G
| imposed annual sediment transfer rate from upstream
| M / T
|-
| G<sub>tf</sub>
| upstream sediment feed rate
| -
| -
|-
|-
| e
| ξ<sub>d</sub>
| downstream bed elevation
| downstream water surface elevation
| m
| L
|-
| L
| length of reach under consideration
| L
|-
| q<sub>w</sub>
| water discharge per unit width
| L<sup>2</sup> / T
|-
|-
| i
| i
| number of iterations per print
| number of time steps per printout
| -
| -
|-
|-
| p
| p
| number of print
| number of printouts desired
| -
| -
|-
|-
| k
| M
| factor in roughness height calculation
| number of spatial intervals
| -
| -
|-
|-
| n
| R
| factor in active layer calculation
| submerged specific gravity of sediment
| -
| -
|-
|-
| r
| S<sub>f</sub>
| coefficient in Manning-Strickler
| friction slope
| -
| -
|-
|-
| l
| F<sub>r</sub>
| bed porosity, gravel
| Froude number
| -
| -
|-
|-
| u
| U
| upwinding coefficient for load spatial derivatives in Exner equation
| flow velocity
| L / T
|-
| g
| acceleration of gravity
| L / T<sup>2</sup>
|-
| α<sub>r</sub>
| coefficient in Manning-Stricker, dimensionless coefficient between 8 and 9
| -
| -
|-
|-
| a
| k<sub>s</sub>
| coefficient for material transferred to substrate as bed aggrades
| grain roughness
| L
|- 
| n<sub>k</sub>
| dimensionless coefficient typically between 2 and 5
| -
| -
|- 
| τ<sup>*</sup>
| Shield number
| -
|-
| ρ
| fluid density
| M / L<sup>3</sup>
|-
| ρ<sub>s</sub>
| sediment density
| M / L<sup>3</sup>
|-
|-
| q<sub>bT</sub>
| τ<sub>c</sub>
| bedload transport rate
| critical Shields number for the onset of sediment motion
| m<sup>2</sup> / s
| -
|-
|-
| q<sub>bT</sub> / q<sub>bo</sub>
| ψ<sub>s</sub>
| bedload transport rate relative to the feed rate
| the fraction of bed shear stress
| -
| -
|-
|-
| D<sub>sg</sub>
| q<sub>t</sub> <sup>*</sup>
| geometric mean grain on the bed surface
| Einstein number
| mm
| -
|-
|-
| D<sub>lg</sub>
| I<sub>f</sub>
| geometric mean grain of the bedload
| flood intermittency
| mm
| -
|-
|-
| D<sub>90s</sub>
| t<sub>f</sub>
| grain size such that 90% of the sediment of the bed surface is finer
| cumulative time the river has been in flood
| mm
| T
|-
|-
| q<sub>bo</sub>
| G<sub>t</sub>
| feed rate
| the annual sediment yield
| M / T
|-
| t<sub>a</sub>
| the number of seconds in a year
| -
| -
|-
|-
| q<sub>bTf</sub>
| Q<sub>f</sub>
| bedload transport
| sediment transport rate during flood discharge
| L<sup>2</sup> / T
|-
| α<sub>t</sub>
| dimensionless coefficient in the sediment transport equation, equals to 8
| -
|-
| n<sub>t</sub>
| exponent in sediment transport relation, equals to 1.5
| -
|-
| τ<sub>c</sub> <sup>*</sup>
| reference Shields number in sediment transport relation, equals to 0.047
|-
| C<sub>f</sub>
| bed friction coefficient, equals to τ<sub>b</sub> / (ρ U<sup>2</sup> )
| -
|-
| C<sub>Z</sub>
| dimensionless Chezy resistance coefficient.
| -
|-
| S<sub>l</sub>
| initial bed slope of the river
| -
|-
| η<sub>i</sub>
| initial bed elevation
| L
|-
| D<sub>sub50</sub>
| median size of the substrate layer
| L
|-
| D<sub>subg</sub>
| geometric mean size of the substrate layer
| L
|-
| L<sub>a</sub>
| thickness of the active layer
| L
|-
| x
| downstream coordinate
| L
|-
| τ
| shear stress on bed surface
| -
|-
| q<sub>b</sub>
| bed material load
| M / T
|-
| Δx
| spatial step length, equals to L / M
| L
|-
| Q<sub>w</sub>
| flood discharge
| L<sup>3</sup> / T
|-
| Δt
| time step
| T
|-
| Ntoprint
| number of time steps to printout
| -
|-
| Nprint
| number of printouts
| -
|-
| a<sub>U</sub>
| upwinding coefficient (1=full upwind, 0.5=central difference)
| -
|-
| α<sub>s</sub>
| coefficient in sediment transport relation
| -
| -
|-
|-
|}
|}


'''Output'''
'''Output'''
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!Symbol!!Description!!Unit
!Symbol!!Description!!Unit
|-
|-
| η
| H
| Bed surface elevation
| water depth
| m
| L
|-
|-
| S
| ξ
| Bed slope
| water surface elevation
| -
| L
|-
|-
| H
| τ<sub>b</sub>
| Water depth
| bed shear stress
| m
| M / (T<sup>2</sup> L)
|-
|-
| τ<sub>b</sub>
| S
| Total (skin friction + form drag) Shields number
| bed slope
| -
| -
|-
|-
| q<sub>t</sub>
| q<sub>t</sub>
| total bed material load
| total bed material load
| m<sup>2</sup>/s
| L<sup>2</sup> / T
|-
|-
|}
|}
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Gravel bedload transport of mixtures is computed using the Parker (1990) surface-based formulation. Sand and finer material must be excluded from the grain size distributions before implementing this relation.
Gravel bedload transport of mixtures is computed using the Parker (1990) surface-based formulation. Sand and finer material must be excluded from the grain size distributions before implementing this relation.


The grain size distributions of the sediment feed, initial surface material and substrate material must be specified. It is assumed that the grain size distribution of the sediment feed rate does not change in time, the initial grain size distribution of the surface material is the same at every node, the grain size distribution of the substrate is the same at every node and does not vary in the vertical.  These constraints are easy to relax.
The grain size distributions of the sediment feed, initial surface material and substrate material must be specified. It is assumed that the grain size distribution of the sediment feed rate does not change in time, the initial grain size distribution of the surface material is the same at every node, the grain size distribution of the substrate is the same at every node and does not vary in the vertical.  


The program does not store the vertical and streamwise structure of the new substrate created as the bed aggrades. As a result, is cannot capture the case of aggradation followed by degradation.  Again, the constraint is easy to relax, but at the price of increased memory requirements for storing the newly-created substrate.
The program does not store the vertical and streamwise structure of the new substrate created as the bed aggrades. As a result, is cannot capture the case of aggradation followed by degradation.  Again, the constraint is easy to relax, but at the price of increased memory requirements for storing the newly-created substrate.


In performing the calculation, the following control parameters must be specified:
To perform a numerical calculation with a flow hydrograph, the actual hydrograph must be specified in terms of W constant water discharges Q<sub>w</sub>, where w = 1 … W, each extending for time duration Δt<sub>w</sub>.  The river is assumed to be morphologically inactive when it is not in flood.
M = number of spatial intervals, so that the spatial step length = L/M.
The morphodynamic evolution is computed solving the equation of sediment continuity (i.e. Exner equation).
dt = time step length;
 
Mtoprint = number of time steps to a printout;
*Note on model running
Mprint = number of printouts in the calculation.
The program may take a few seconds to calculate, depending on the user’s inputs—this is a calculation intensive program—please give the program some time to make the calculations.
 
There are no output values at time=0 for the geometric mean diameter of the load and the ration between the total bedload transport rate and the feed rate, because these are calculated in the time loop; they are not initial values.
 
Due to the many variables that are dependent upon user inputted values in this function the “ReadIn” function is called in the main, instead of in the Initialize portion of the code.


==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>


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==References==
==References==
<span class="remove_this_tag">Key papers</span>
* Parker, G., 1990, Surface-based bedload transport relation for gravel rivers, Journal of Hydraulic Research, 28(4): 417-436.
 
* Wilcock, P. R., and Crowe, J. C., 2003, Surface-based transport model for mixed-size sediment, Journal of Hydraulic Engineering, 129(2), 120-128.
 


==Links==
==Links==
* [[http://csdms.colorado.edu/wiki/Model:AgDegNormalGravMixHyd Model:AgDegNormalGravMixHyd]]
* [[Model:AgDegNormalGravMixHyd]]
* [[Model_help:AgDegNormGravMixPW]]
* [[Model_help:AgDegNormal]]


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

Latest revision as of 17:18, 19 February 2018

The CSDMS Help System

AgDegNormalGravMixHyd

This is a module that calculates the evolution of a gravel bed river under an imposed cycled hydrograph.

Model introduction

This program is a close relative of AgDegNormGravMixPW. It computes aggradation and degradation in gravel-bed river subject to a repeated hydrograph. The sediment is modeled as mixture of different grain sizes and the bedload formulation is that of Parker (1990) that was derived to compute the transport of gravel only.

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
number of hydrograph entries between 2 and 16 values
number of cycles per year -
bed elevation at downstream end m
initial bed slope -
reach length m
Time step days
Number of intervals
Number of printouts -
Iterations per each printout -
factor by which Ds90 is multiplied for roughness height -
factor by which Ds90 is multiplied for active layer thickness -
Manning-Strickler cofficient r
Submerged specific gravity of sediment
bed porosity, gravel
upwinding coefficient for load spatial derivatives in Exner equation (> 0.5 suggested)
Coefficient for material transferred to substrate as bed aggrades
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

  • time duration of a short flood
[math]\displaystyle{ \Delta t_{w} = n_{step,w} \Delta t_{f} }[/math] (1)
  • Total time for flood
[math]\displaystyle{ P = \sum\limits_{w=1}^W n_{step,w} }[/math] (2)

Notes

This program computes the time evolution of the long profile of a river of constant width carrying a mixture of gravel sizes, the downstream end of which has a prescribed elevation. In particular, the program computes the time evolution of the spatial profiles of bed elevation, total gravel bedload transport rate and grain size distribution of the surface (active) layer of the bed.

The flow is specified in terms of a hydrograph repeated a specified number of times annually, rather than a constant flood discharge and an intermittency.

The river has constant width. The upstream point, at which sediment is fed, is fixed in the horizontal to be at x = 0. The vertical elevation of the upstream point may change freely as the bed aggrades or degrades.In the program it is assumed that all gravel reaching the topset-foreset break is captured in the delta.

The reach has constant length L, so that the downstream point is fixed in the horizontal at x = L. This downstream point has a user-specified initial elevation ηdI.

Gravel bedload transport of mixtures is computed using the Parker (1990) surface-based formulation. Sand and finer material must be excluded from the grain size distributions before implementing this relation.

The grain size distributions of the sediment feed, initial surface material and substrate material must be specified. It is assumed that the grain size distribution of the sediment feed rate does not change in time, the initial grain size distribution of the surface material is the same at every node, the grain size distribution of the substrate is the same at every node and does not vary in the vertical.

The program does not store the vertical and streamwise structure of the new substrate created as the bed aggrades. As a result, is cannot capture the case of aggradation followed by degradation. Again, the constraint is easy to relax, but at the price of increased memory requirements for storing the newly-created substrate.

To perform a numerical calculation with a flow hydrograph, the actual hydrograph must be specified in terms of W constant water discharges Qw, where w = 1 … W, each extending for time duration Δtw. The river is assumed to be morphologically inactive when it is not in flood. The morphodynamic evolution is computed solving the equation of sediment continuity (i.e. Exner equation).

  • Note on model running

The program may take a few seconds to calculate, depending on the user’s inputs—this is a calculation intensive program—please give the program some time to make the calculations.

There are no output values at time=0 for the geometric mean diameter of the load and the ration between the total bedload transport rate and the feed rate, because these are calculated in the time loop; they are not initial values.

Due to the many variables that are dependent upon user inputted values in this function the “ReadIn” function is called in the main, instead of in the Initialize portion of the code.

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

  • Parker, G., 1990, Surface-based bedload transport relation for gravel rivers, Journal of Hydraulic Research, 28(4): 417-436.
  • Wilcock, P. R., and Crowe, J. C., 2003, Surface-based transport model for mixed-size sediment, Journal of Hydraulic Engineering, 129(2), 120-128.


Links

Retrieved from "https://csdms.colorado.edu/csdms_wiki/index.php?title=Model_help:AgDegNormalGravMixHyd&oldid=216519"