Model help:AgDegNormGravMixSubPW: Difference between revisions

From CSDMS
No edit summary
m (Text replacement - "http://csdms.colorado.edu/wiki/" to "https://csdms.colorado.edu/wiki/")
 
(18 intermediate revisions by 2 users not shown)
Line 3: Line 3:
1) Log in to the wiki
1) Log in to the wiki
2) Create a new page for each model, by using the following URL:
2) Create a new page for each model, by using the following URL:
   * http://csdms.colorado.edu/wiki/Model help:<modelname>
   * https://csdms.colorado.edu/wiki/Model help:<modelname>
   * Replace <modelname> with the name of a model
   * Replace <modelname> with the name of a model
3) Than follow the link "edit this page"
3) Than follow the link "edit this page"
Line 17: Line 17:


==Model introduction==
==Model introduction==
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.  
This program calculates the bed surface evolution for a river of constant width with a mixture of gravel sizes with a load computed either by the Parker relation or the Wilcock-Crowe relation, as in the case of AgDegNormGravMixPW, but this program also takes into effect the subsidence.


<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 options =
{|{{Prettytable}} class = "wikitable unsortable"  cellspacing="0" cellpadding="0" style="margin:0em 0em 0em 0;"
|-
!Parameter!!Description!!Unit
|-valign="top"
|width="20%"|Chezy Or Manning, Chezy-1 or Manning-2
|width="60%"|
|width="20%"|
|-
|Bedload relation, Parker or Wilock, Parker-1 or Wilock-2
|
|
|-
|}
 
= 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
|width="60%"|<span class="remove_this_tag">Description parameter</span>
|width="60%"|
|width="20%"|<span class="remove_this_tag">[Units]</span>
|width="20%"| m<sup>3</sup> / s
|-
|gravel input
|
| m<sup>2</sup> / s
|-
|Intermittency
|
| -
|-
|base level
|
| m
|-
|initial bed slope
|
| -
|-
|reach length
|
| m
|-
|Time step
|
| days
|-
|no. of intervals(100 or less)
|
| -
|-
|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 coefficient 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
|
|
|-
|channel sinuosity
|
|
|-
|ratio of depositional width to channel width
|
|
|-
|ratio of wash load deposited per unit bed material load deposited
|
|
|-
|Chezy resistance coefficient
|
| -
|-
|}
|}


= 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==
Line 52: Line 169:


==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>
* Total bedload transport over all grain sizes
::::{|
|width=530px|<math>  q_{bT} = \sum\limits_{i=1}^N q_{bi} </math>
|width=50p=x align="right"|(1)
|}
* Fraction of bedload in the ith grain size range
::::{|
|width=530px|<math>  p_{bi} = {\frac{q_{bi}}{q_{bT}}} </math>
|width=50p=x align="right"|(2)
|}
* Exner equation describing the evolution of grain size distribution of the active layer
::::{|
|width=530px|<math>  \left ( 1 - \lambda_{p} \right ) [L_{a}{\frac{\partial F_{i}}{\partial t}} + \left (F_{i} - f_{li}\right ) {\frac{\partial L_{a}}{\partial t}}] = - I_{f} {\frac{\partial q_{bT} p_{bi}}{\partial x}} + I_{f} f_{li} {\frac{\partial q_{bT}}{\partial x}} </math>
|width=50p=x align="right"|(3)
|}
* Fraction in the ith grain size range of materials exchanged between the surface and substrate as the bed aggrades or degrades
::::{|
|width=530px|<math> f_{li} = \left\{\begin{matrix} f_{i}|_{Z = \eta - L_{a}} & {\frac{\partial \eta}{\partial t}} < 0 \\ \lambda F_{i} + \left ( 1 - \lambda \right ) p_{bi} & {\frac{\partial \eta}{\partial t}} > 0 \end{matrix}\right.  </math>
|width=50p=x align="right"|(4)
|}
* Surface-based bedload transport formulation for mixtures
1) Thickness of the active (surface) layer of the bed
::::{|
|width=530px|<math> L_{a} = n_{a} D_{s90}  </math>
|width=50p=x align="right"|(5)
|}
2) Dimensionless grain size specific Shields number
::::{|
|width=530px|<math> \tau_{i}^* \equiv {\frac{\tau_{b}}{\rho R g D_{i}}} = {\frac{u_{*}^2}{R g D_{i}}} </math>
|width=50p=x align="right"|(6)
|}
3) Grain size specific Einstein number
::::{|
|width=530px|<math> q_{bi}^* = {\frac{q_{bi}}{\sqrt{R g D_{i}}D_{i} F_{i}}} </math>
|width=50p=x align="right"|(7)
|}
4) Dimensionless grain size specific bedload transport rate
::::{|
|width=530px|<math> W_{i}^* \equiv {\frac{q_{bi}^*}{\left ( \tau_{i}^* \right )^ \left ({\frac{3}{2}}\right )}} = {\frac{R g q_{bi}}{\left (u_{*}\right )^3 F_{i} }} </math>
|width=50p=x align="right"|(8)
|}
* Bedload relation for mixtures due to Parker (1990a, b)
::::{|
|width=530px|<math> W_{i}^* = 0.00218 G\left (\phi_{i} \right ) </math>
|width=50p=x align="right"|(9)
|}
::::{|
|width=530px|<math>\phi_{i}= \omega \phi_{sgo} \left ( {\frac{D_{i}} {D_{sg}}} \right )^ \left (-0.0951 \right )  </math>
|width=50p=x align="right"|(10)
|}
::::{|
|width=530px|<math> \phi_{sgo}= {\frac{\tau_{sg} ^*}{\tau_{ssrg} ^*}}  </math>
|width=50p=x align="right"|(11)
|}
::::{|
|width=530px|<math>\tau_{sg} ^*={\frac{u_{*} ^2}{R g D_{sg}}}  </math>
|width=50p=x align="right"|(12)
|}
::::{|
|width=530px|<math> G \left ( \phi \right )= \left\{\begin{matrix} 5474 \left ( 1 - {\frac{0.853}{\phi}} \right ) ^ \left (4.5 \right ) & \phi > 1.59 \\ exp[ 14.2\left ( \phi - 1\right ) - 9.28 \left ( \phi - 1 \right )^2  ] & 1 <= \phi <= 1.59 \\  \phi ^\left (14.2 \right ) & \phi < 1 \end{matrix}\right. </math>
|width=50p=x align="right"|(13)
|}
::::{|
|width=530px|<math>\omega= 1 + {\frac{\sigma}{\sigma_{O} \left ( \phi_{sgo} \right ) }} [ \omega_{O} \left ( \phi_{sgo} \right ) - 1 ]  </math>
|width=50p=x align="right"|(14)
|}
::::{|
|width=510px|<math>D_{sg}=2^\left (\bar\Psi_{s} \right ) </math>
|width=50px align="right"|(15)
|}
::::{|
|width=510px|<math>\bar\Psi_{s}= \sum\limits_{i=1}^N \Psi_{i} F{i} </math>
|width=50px align="right"|(16)
|}
::::{|
|width=510px|<math> \delta_{s} ^2 = \sum\limits_{i=1}^N \left (\Psi_{i} - \bar{\Psi}_{s} \right )^2 F_{i} </math>
|width=50px align="right"|(17)
|}
* Bedload relation for mixture due to Wilcock and Crowe (2003)
::::{|
|width=510px|<math> W_{i}^* = G \left (\phi_{i}\right ) </math>
|width=50px align="right"|(18)
|}
::::{|
|width=510px|<math> G = \left\{\begin{matrix} 0.002 \phi^ \left (7.5 \right ) & for \phi < 1.35 \\ 14 \left (1 - {\frac{0.894}{\phi_{0.5}}}\right )^ \left (4.5 \right ) & \phi >= 1.35 \end{matrix}\right. </math>
|width=50px align="right"|(19)
|}
::::{|
|width=510px|<math> \phi_{i} = {\frac{\tau_{sg}^*}{\tau_{ssrg}^*}} \left ( {\frac{D_{i}}{D_{sg}}}\right )^ \left (-b \right ) </math>
|width=50px align="right"|(20)
|}
::::{|
|width=510px|<math> \tau_{sg}^* = {\frac{u_{*}^2}{R g D_{sg}}} </math>
|width=50px align="right"|(21)
|}
::::{|
|width=510px|<math> \tau_{ssrg}^* = 0.021 + 0.015 exp \left (-14 F_{s}\right ) </math>
|width=50px align="right"|(22)
|}
::::{|
|width=510px|<math> b = {\frac{0.69}{1 + exp \left (1.5 - {\frac{D_{i}}{D_{sg}}}\right )}} </math>
|width=50px align="right"|(23)
|}
* Roughness hight
::::{|
|width=510px|<math> k_{s} = n_{k} D_{s90} </math>
|width=50px align="right"|(24)
|}
* Boundary shear stress
::::{|
|width=510px|<math> \tau_{b,k} = \rho u_{*}^2 = \left ({\frac{k_{s,k}^\left ({\frac{1}{3}} \right ) q_{w}^*}{\alpha_{r}^2}} \right )^ \left ({\frac{3}{10}}\right ) g^\left ({\frac{7}{10}}\right ) S_{k}^ \left ({\frac{7}{10}}\right )  </math>
|width=50px align="right"|(25)
|}
* Bed slope
::::{|
|width=510px|<math> S_{k} = \left\{\begin{matrix} {\frac{\eta_{1} - \eta_{2}}{\Delta x}} & k = 1 \\ {\frac{\eta_{k-1} - \eta_{k+1}}{2 \Delta x}} & k = 2...M \end{matrix}\right.  </math>
|width=50px align="right"|(26)
|}
* Shields number based on the  geometric mean size
::::{|
|width=510px|<math> \tau_{sg}^* = \left ({\frac{k_{s}^ \left ({\frac{1}{3}}\right ) q_{w}^2}{\alpha_{r}^2 g}}\right ) ^ \left ({\frac{3}{10}}\right ) {\frac{S^ \left ({\frac{7}{10}}\right )}{R D_{sg}}}  </math>
|width=50px align="right"|(27)
|}
* Shear velocity based on the surface geometric mean size
::::{|
|width=510px|<math> u_{*} = \left ({\frac{k_{s}^ \left ({\frac{1}{3}}\right ) q_{w}^2}{\alpha_{r}^2}}\right )^ \left ({\frac{3}{20}}\right ) g^ \left ({\frac{7}{20}}\right ) S^ \left ({\frac{7}{20}}\right ) </math>
|width=50px align="right"|(28)
|}
* Volume bedload transport rate per unit width in the ith grain size
::::{|
|width=510px|<math> q_{bi} = F_{i}{\frac{u_{*}^3}{R g}}W_{i}^* </math>
|width=50px align="right"|(29)
|}
 
<div class="NavFrame collapsed" style="text-align:left">
  <div class="NavHead">Nomenclature</div>
  <div class="NavContent">
{| {{Prettytable}} class="wikitable sortable"
!Symbol!!Description!!Unit
|-
| x
| streamwise coordinate
| L
|-
| t
| time step
| T
|-
| Z
| boundary-attached upward normal coordinate
| L
|-
| D<sub>bi</sub>
| ith bounding size specifying percents or fractions finer of grain size distribution
| L
|-
| λ<sub>p</sub>
| bed porosity
| -
|-
| α
| the parameter that governs the grain size distribution of the sediment at the active layer-substrate interface during bed aggredation (0 <= α <= 1)
| -
|-
| F<sub>fi</sub>
| grain size distribution of the active layer for initial condition
| -
|-
| F<sub>i</sub>
| fraction of material in the surface layer in the ith grain size range, i = 1...N
| -
|-
| D<sub>i</sub>
| characteristic size of the ith grain size range
| L
|-
| f<sub>subfi</sub>
| fraction of sediment in the ith grain size range in the substrate layer for initial condition
| -
|-
| F<sub>fli</sub>
| percent finer than ith grain size range for the bed surface for initial condition
| -
|-
| F<sub>subfli</sub>
| percent finer than ith grain size range for the substrate layer for initial condition
| -
|-
| f<sub>li</sub>
| fraction of sediment in the ith grain size range in the active-layer substrate interface
| -
|-
| p<sub>i</sub>
| fraction of sediment in the ith grain size range in the bedload
| -
|-
| F<sub>sub,i</sub>
| fraction of substrate material in the ith size range
| -
|-
| 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
| -
|-
| p<sub>ffi</sub>
| the percent that is finer than the ith size range for upstream boundary conditon
| -
|-
| η<sub>d</sub>
| fixed bed elevation at the downstream end of the modeled reach
| L
|-
| k<sub>c</sub>
| composite roughness height
| L
|-
| G
| function in Parker (1990a, b) and Wilcock and Crowe (2003) bedload relation for gravel mixture
|
|-
| L
| length of reach under consideration
| L
|-
| i
| number of time steps per printout
| -
|-
| p
| number of printouts desired
| -
|-
| M
| number of spatial intervals
| -
|-
| R
| submerged specific gravity of sediment
| -
|-
| g
| acceleration of gravity
| L / T<sup>2</sup>
|-
| α<sub>r</sub>
| coefficient in Manning-Stricker, dimensionless coefficient between 8 and 9
| -
|-
| k<sub>s</sub>
| grain roughness
| L
|- 
| n<sub>k</sub>
| dimensionless coefficient typically between 2 and 5
| -
|- 
| τ<sub>i</sub> <sup>*</sup>
| dimensionless grain size specific Shields number
| -
|-
| τ<sub>b</sub>
| bed shear stress
| -
|-
| u<sub>*</sub>
| shear velocity
| L / T
|-
| q<sub>bi</sub> <sup>*</sup>
| Einstein bedload number for ith grain size
| L / T
|-
| W<sub>i</sub> <sup>*</sup>
| dimensionless grain size specific bedload transport rate
| -
|-
| φ<sub>i</sub>
| parameter in Parker (1990a,b) bedload relation for mixtures
| -
|-
| ω
| straining parameter in Parker (1990a,b) bedload relation for
mixtures
| -
|-
| φ<sub>sg</sub> <sup>*</sup>
| Shields number based on surface geometric mean size
| -
|-
| φ<sub>ssrg</sub> <sup>*</sup>
| reference Shields number close to (but above) the threshold of motion, equals to 0.0386 for Parker (1990a,b)
| -
|-
| ω<sub>O</sub>
| function relation in Parker (1990a, b) bedload relation for mixture
| -
|-
| δ<sub>O</sub>
| function relation in Parker (1990a, b) bedload relation for mixture
| -
|-
| D<sub>sg</sub>
| geometric mean size of surface layer sediment
| L
|-
| δ<sub>s</sub>
| arithmetic standard deviation of surface size distribution
| -
|-
| ρ
| fluid density
| M / L<sup>3</sup>
|-
| ρ<sub>s</sub>
| sediment density
| M / L<sup>3</sup>
|-
| τ<sub>c</sub>
| critical Shields number for the onset of sediment motion
| -
|-
| ψ<sub>s</sub>
| the fraction of bed shear stress
| -
|-
| q<sub>t</sub> <sup>*</sup>
| Einstein number
| -
|-
| I<sub>f</sub>
| flood intermittency
| -
|-
| t<sub>f</sub>
| cumulative time the river has been in flood
| T
|-
| α<sub>t</sub>
| dimensionless coefficient in the sediment transport equation, equals to 8
| -
|-
| b
| reference distance above the bed where sediment entrainment is specified
| -
|-
| n<sub>k</sub>
| an order-one dimensionless number
| -
|-
| F<sub>s</sub>
| mass fraction of the surface sediment that is sand
| -
|-
| 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
| -
|-
| 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
|-
| σ
| subsidence rate
| L / T
|-
| r<sub>B</sub>
| the ratio of depositional width to channel width
| -
|-
| Ω
| channel sinuosity
| -
|-
| Λ
| units of wash load deposited in the system per unit of bed material load
| -
|-
| τ
| shear stress on bed surface
| -
|-
| q<sub>bi</sub>
| volume bedload transport rate per unit width of material in the ith grain size range
| L<sup>2</sup> / T
|-
| q<sub>bT</sub>
| total volume bedload transport rate per unit width
| L<sup>2</sup> / 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
| -
|-
| φ
| transverse angle of inclination of bed
| -
|-
| λ
| wavelength of bedform
| -
|-
| φ<sub>sgo</sub>
| equals to τ<sub>sg</sub> <sup>*</sup> / τ<sub>ssrg</sub> <sup>*</sup>
| -
|-
|}
 
'''Output'''
{| {{Prettytable}} class="wikitable sortable"
!Symbol!!Description!!Unit
|-
| η
| bed surface elevatioon
| L
|-
| H
| water depth
| L
|-
| ξ
| water surface elevation
| L
|-
| τ<sub>b</sub>
| bed shear stress
| M / (T<sup>2</sup> L)
|-
| S
| bed slope
| -
|-
| L<sub>max</sub>
| maximum length of basin that the sediment supply can fill
| L
|-
|}
  </div>
</div>


==Notes==
==Notes==
The river is assumed to be morphologically active for If fraction of time, during which the flow is approximated as constant.  Otherwise, the river is assumed to be morphologically dead.
The river is assumed to be morphologically active for If fraction of time, during which the flow is approximated as constant.  Otherwise, the river is assumed to be morphologically dead.


The river flows into a basin that is subsiding with rate s.  The basin has constant width; the ratio of basin width to river width is rB.  The river has sinuosity W.  For each unit of bedload deposited, L units of washload (typically sand transported in suspension) is deposited across the depositional basin.
The river flows into a basin that is subsiding with rate σ.  The basin has constant width.  For each unit of bedload deposited, L units of washload (typically sand transported in suspension) is deposited across the depositional basin.
 
In particular, the program computes the time evolution of the spatial profiles of bed elevation, bed slope, total bedload transport rate and grain size distribution of the surface (active) layer of the bed.


If run for a sufficient length of time, the river profile approaches a steady-state balance between subsidence. At this steady state the profile displays both an upward-concave elevation profile and downstream fining of the surface material.
If run for a sufficient length of time, the river profile approaches a steady-state balance between subsidence. At this steady state the profile displays both an upward-concave elevation profile and downstream fining of the surface material.
Line 69: Line 675:
Gravel bedload transport of mixtures is computed with a user-specified selection of the Parker (1990), or Wilcock-Crowe (2003)  surface-based formulations for gravel transport.Sand and finer material must first be excluded from the grain size distributions, which then must be renormalized for gravel content only, in the case of the Parker (1990) relation. In the case of the Wilcock-Crowe (2003) relation, the sand is retained in the computation.
Gravel bedload transport of mixtures is computed with a user-specified selection of the Parker (1990), or Wilcock-Crowe (2003)  surface-based formulations for gravel transport.Sand and finer material must first be excluded from the grain size distributions, which then must be renormalized for gravel content only, in the case of the Parker (1990) relation. In the case of the Wilcock-Crowe (2003) relation, the sand is retained in the computation.


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.
Line 75: Line 681:
The flow is calculated using the normal flow (local equilibrium) approximation.  
The flow is calculated using the normal flow (local equilibrium) approximation.  


In performing the calculation, the following control parameters must be specified:
* Note on model running
M = number of spatial intervals, so that the spatial step length = L/M;
In the case of the load relation due to Parker (1990), the grain size distributions are automatically re-normalized because the relation is for the transport of gravel only in the case of the load relation due to Wilcock-Crowe (2003), the sand and the fine sediment are retained for the computation.
dt = time step length;
 
Ntoprint = number of time steps to a printout;
The input grain size distributions may be on a 0-100% or a 0.00-1.00 scale, and the program will automatically scale.
Nprint = number of printouts in the calculation.
 
The input grain size distributions must have bounds at 0% and 100% (1.00) to properly perform the calculation. If the user does not input the bounds the program will automatically interpolate upper and lower bounds D<sub>bU</sub> and D<sub>bL</sub> such that f<sub>fU</sub> = 100 (1.00) and f<sub>fL</sub> = 0
 
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==
Line 85: Line 694:


<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 94: Line 703:


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


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

Latest revision as of 17:18, 19 February 2018

The CSDMS Help System

AgDegNormGravMixSubPW

It is the calculator for evolution of upward-concave bed profiles in rivers carrying sediment mixtures in subsiding basins.

Model introduction

This program calculates the bed surface evolution for a river of constant width with a mixture of gravel sizes with a load computed either by the Parker relation or the Wilcock-Crowe relation, as in the case of AgDegNormGravMixPW, but this program also takes into effect the subsidence.

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
Chezy Or Manning, Chezy-1 or Manning-2
Bedload relation, Parker or Wilock, Parker-1 or Wilock-2
Parameter Description Unit
Flood discharge m3 / s
gravel input m2 / s
Intermittency -
base level m
initial bed slope -
reach length m
Time step days
no. of intervals(100 or less) -
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 coefficient 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
channel sinuosity
ratio of depositional width to channel width
ratio of wash load deposited per unit bed material load deposited
Chezy resistance coefficient -
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

  • Total bedload transport over all grain sizes
[math]\displaystyle{ q_{bT} = \sum\limits_{i=1}^N q_{bi} }[/math] (1)
  • Fraction of bedload in the ith grain size range
[math]\displaystyle{ p_{bi} = {\frac{q_{bi}}{q_{bT}}} }[/math] (2)
  • Exner equation describing the evolution of grain size distribution of the active layer
[math]\displaystyle{ \left ( 1 - \lambda_{p} \right ) [L_{a}{\frac{\partial F_{i}}{\partial t}} + \left (F_{i} - f_{li}\right ) {\frac{\partial L_{a}}{\partial t}}] = - I_{f} {\frac{\partial q_{bT} p_{bi}}{\partial x}} + I_{f} f_{li} {\frac{\partial q_{bT}}{\partial x}} }[/math] (3)
  • Fraction in the ith grain size range of materials exchanged between the surface and substrate as the bed aggrades or degrades
[math]\displaystyle{ f_{li} = \left\{\begin{matrix} f_{i}|_{Z = \eta - L_{a}} & {\frac{\partial \eta}{\partial t}} \lt 0 \\ \lambda F_{i} + \left ( 1 - \lambda \right ) p_{bi} & {\frac{\partial \eta}{\partial t}} \gt 0 \end{matrix}\right. }[/math] (4)
  • Surface-based bedload transport formulation for mixtures

1) Thickness of the active (surface) layer of the bed

[math]\displaystyle{ L_{a} = n_{a} D_{s90} }[/math] (5)

2) Dimensionless grain size specific Shields number

[math]\displaystyle{ \tau_{i}^* \equiv {\frac{\tau_{b}}{\rho R g D_{i}}} = {\frac{u_{*}^2}{R g D_{i}}} }[/math] (6)

3) Grain size specific Einstein number

[math]\displaystyle{ q_{bi}^* = {\frac{q_{bi}}{\sqrt{R g D_{i}}D_{i} F_{i}}} }[/math] (7)

4) Dimensionless grain size specific bedload transport rate

[math]\displaystyle{ W_{i}^* \equiv {\frac{q_{bi}^*}{\left ( \tau_{i}^* \right )^ \left ({\frac{3}{2}}\right )}} = {\frac{R g q_{bi}}{\left (u_{*}\right )^3 F_{i} }} }[/math] (8)
  • Bedload relation for mixtures due to Parker (1990a, b)
[math]\displaystyle{ W_{i}^* = 0.00218 G\left (\phi_{i} \right ) }[/math] (9)
[math]\displaystyle{ \phi_{i}= \omega \phi_{sgo} \left ( {\frac{D_{i}} {D_{sg}}} \right )^ \left (-0.0951 \right ) }[/math] (10)
[math]\displaystyle{ \phi_{sgo}= {\frac{\tau_{sg} ^*}{\tau_{ssrg} ^*}} }[/math] (11)
[math]\displaystyle{ \tau_{sg} ^*={\frac{u_{*} ^2}{R g D_{sg}}} }[/math] (12)
[math]\displaystyle{ G \left ( \phi \right )= \left\{\begin{matrix} 5474 \left ( 1 - {\frac{0.853}{\phi}} \right ) ^ \left (4.5 \right ) & \phi \gt 1.59 \\ exp[ 14.2\left ( \phi - 1\right ) - 9.28 \left ( \phi - 1 \right )^2 ] & 1 \lt = \phi \lt = 1.59 \\ \phi ^\left (14.2 \right ) & \phi \lt 1 \end{matrix}\right. }[/math] (13)
[math]\displaystyle{ \omega= 1 + {\frac{\sigma}{\sigma_{O} \left ( \phi_{sgo} \right ) }} [ \omega_{O} \left ( \phi_{sgo} \right ) - 1 ] }[/math] (14)
[math]\displaystyle{ D_{sg}=2^\left (\bar\Psi_{s} \right ) }[/math] (15)
[math]\displaystyle{ \bar\Psi_{s}= \sum\limits_{i=1}^N \Psi_{i} F{i} }[/math] (16)
[math]\displaystyle{ \delta_{s} ^2 = \sum\limits_{i=1}^N \left (\Psi_{i} - \bar{\Psi}_{s} \right )^2 F_{i} }[/math] (17)
  • Bedload relation for mixture due to Wilcock and Crowe (2003)
[math]\displaystyle{ W_{i}^* = G \left (\phi_{i}\right ) }[/math] (18)
[math]\displaystyle{ G = \left\{\begin{matrix} 0.002 \phi^ \left (7.5 \right ) & for \phi \lt 1.35 \\ 14 \left (1 - {\frac{0.894}{\phi_{0.5}}}\right )^ \left (4.5 \right ) & \phi \gt = 1.35 \end{matrix}\right. }[/math] (19)
[math]\displaystyle{ \phi_{i} = {\frac{\tau_{sg}^*}{\tau_{ssrg}^*}} \left ( {\frac{D_{i}}{D_{sg}}}\right )^ \left (-b \right ) }[/math] (20)
[math]\displaystyle{ \tau_{sg}^* = {\frac{u_{*}^2}{R g D_{sg}}} }[/math] (21)
[math]\displaystyle{ \tau_{ssrg}^* = 0.021 + 0.015 exp \left (-14 F_{s}\right ) }[/math] (22)
[math]\displaystyle{ b = {\frac{0.69}{1 + exp \left (1.5 - {\frac{D_{i}}{D_{sg}}}\right )}} }[/math] (23)
  • Roughness hight
[math]\displaystyle{ k_{s} = n_{k} D_{s90} }[/math] (24)
  • Boundary shear stress
[math]\displaystyle{ \tau_{b,k} = \rho u_{*}^2 = \left ({\frac{k_{s,k}^\left ({\frac{1}{3}} \right ) q_{w}^*}{\alpha_{r}^2}} \right )^ \left ({\frac{3}{10}}\right ) g^\left ({\frac{7}{10}}\right ) S_{k}^ \left ({\frac{7}{10}}\right ) }[/math] (25)
  • Bed slope
[math]\displaystyle{ S_{k} = \left\{\begin{matrix} {\frac{\eta_{1} - \eta_{2}}{\Delta x}} & k = 1 \\ {\frac{\eta_{k-1} - \eta_{k+1}}{2 \Delta x}} & k = 2...M \end{matrix}\right. }[/math] (26)
  • Shields number based on the geometric mean size
[math]\displaystyle{ \tau_{sg}^* = \left ({\frac{k_{s}^ \left ({\frac{1}{3}}\right ) q_{w}^2}{\alpha_{r}^2 g}}\right ) ^ \left ({\frac{3}{10}}\right ) {\frac{S^ \left ({\frac{7}{10}}\right )}{R D_{sg}}} }[/math] (27)
  • Shear velocity based on the surface geometric mean size
[math]\displaystyle{ u_{*} = \left ({\frac{k_{s}^ \left ({\frac{1}{3}}\right ) q_{w}^2}{\alpha_{r}^2}}\right )^ \left ({\frac{3}{20}}\right ) g^ \left ({\frac{7}{20}}\right ) S^ \left ({\frac{7}{20}}\right ) }[/math] (28)
  • Volume bedload transport rate per unit width in the ith grain size
[math]\displaystyle{ q_{bi} = F_{i}{\frac{u_{*}^3}{R g}}W_{i}^* }[/math] (29)

Notes

The river is assumed to be morphologically active for If fraction of time, during which the flow is approximated as constant. Otherwise, the river is assumed to be morphologically dead.

The river flows into a basin that is subsiding with rate σ. The basin has constant width. For each unit of bedload deposited, L units of washload (typically sand transported in suspension) is deposited across the depositional basin.

If run for a sufficient length of time, the river profile approaches a steady-state balance between subsidence. At this steady state the profile displays both an upward-concave elevation profile and downstream fining of the surface material.

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.

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 ηd.

Gravel bedload transport of mixtures is computed with a user-specified selection of the Parker (1990), or Wilcock-Crowe (2003) surface-based formulations for gravel transport.Sand and finer material must first be excluded from the grain size distributions, which then must be renormalized for gravel content only, in the case of the Parker (1990) relation. In the case of the Wilcock-Crowe (2003) relation, the sand is retained in the computation.

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 flow is calculated using the normal flow (local equilibrium) approximation.

  • Note on model running

In the case of the load relation due to Parker (1990), the grain size distributions are automatically re-normalized because the relation is for the transport of gravel only in the case of the load relation due to Wilcock-Crowe (2003), the sand and the fine sediment are retained for the computation.

The input grain size distributions may be on a 0-100% or a 0.00-1.00 scale, and the program will automatically scale.

The input grain size distributions must have bounds at 0% and 100% (1.00) to properly perform the calculation. If the user does not input the bounds the program will automatically interpolate upper and lower bounds DbU and DbL such that ffU = 100 (1.00) and ffL = 0

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

  • 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