Model help:AgDegNormGravMixPW

AgDegNormGravMixPW

This is the calculator for aggradation and degradation of sediment mixtures in gravel-bed streams.

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. 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 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. 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 hdI.

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.

Model parameters

First tab header

Second tab header

Etc. tab header

Parameter	Description	Unit
First parameter	Description parameter	[Units]

Parameter	Description	Unit
First parameter	Description parameter	[Units]

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

• Exner equation of conservation of channel bed sediment

[math]\displaystyle{ \left ( 1 - \lambda _{p} \right ) {\frac{\partial \eta}{\partial t}} = - I_{f} {\frac{\partial q_{bT}}{\partial x}} }[/math]

(1)

• Characteristic diameter

[math]\displaystyle{ D_{i} = \left ( D_{b,i} \ast D_{b,i+1} \right ) ^ \left ( {\frac{1}{2}} \right ) }[/math]

(2)

[math]\displaystyle{ f_{i} = f_{f,i+1} - f_{f,i} }[/math]

(3)

• The conservation of sediment in each grain size range

[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_{i}}{\partial x}} + I_{f} f_{li} {\frac{\partial q_{bT}}{\partial x}} }[/math]

(4)

• Fraction of sediment in the ith grain size range at the active-layer substrate interface (if ∂η / ∂t > 0)

[math]\displaystyle{ f_{li} = \alpha F_{i} + \left ( 1 - \alpha \right ) p_{i} }[/math]

(5)

• Fraction of sediment in the ith grain size range at the active-layer substrate interface (if ∂η / ∂t < 0)

[math]\displaystyle{ f_{li} = f_{sub,i} }[/math]

(6)

• Roughness height due to skin friction

[math]\displaystyle{ k_{s} = n_{k} D_{s90} }[/math]

(7)

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

(8)

• Non-dimensional bed shear stress

[math]\displaystyle{ \tau _{sg} ^* = {\frac{\tau_{b}}{\left ( \rho _{s} - \rho \right ) g D_{sg}}} }[/math]

(9)

Nomenclature

Symbol	Description	Unit
q	water discharge / width	m2 / s
T	gravel input	m2 / s
I	intermittency	-
e	base level	m
S	initial bed slope	-
L	reach length	m
t	time step	days
M	no. of intervals	-
p	no. of prints	-
i	no. of iterations per print	-
k	factor by which Ds90 is multiplied for roughness height	-
n	factor by which Ds90 is multiplied for active layer thickness	-
r	coefficient in Manning-Strickler relation	-
R	submerged specific gravity of gravel	-
l	bed porosity, gravel	-
u	upwinding coefficient for load spatial deviations in Exner equation (> 0.5 suggested)	-
a	coefficient for material transferred to substrate as bed aggrades	-
C	coefficient, Cf, in the Chezy formulation	-
qw	the characteristic flood discharge per unit channel width	-
If	flood intermittency	-
qbTf	the volumetric gravel input rate per unit channel width	-
ηd	the downstream bed elevation	m
λp	the bed porosity	-
Sl	the initial bed slope	-
Dbi	the bound diameter	-
nk	dimensionless coefficient typically between 2 and 5	-
Δt	time step	year
Ntoprint	number of time steps to printout	-
Nprint	number of printouts	-
aU	upwinding coefficient (1=full upwind, 0.5=central difference)	-
αr	coefficient to compute the roughness height	-
na	coefficient to compute the thickness of the active layer	-
α	the parameter that governs the grain size distribution of the sediment at the active layer-substrate interface during bed aggradation	-
x	downstream coordinate	m
Sl	slope of the bed surface	-
u*	shear velocity	m / s
pfeed	GSD of the feed	tons / year
Ffs	GSD of the substrate	-
Ff	GSD of the final surface	-
η	bed elevation	m
ffi	the mass fraction of the sample that is finer than Dbi	-
fi	the fraction of sample in the ith size range	-
pi	the fraction of sediment in the ith grain size range in the bedload	-
α	a user specified parameter	-
fsub,i	the fraction of substrate material in the ith range	-
ψs	boundary shear stress due to skin friction	-
kc	composite roughness height for the Manning-Strickler formulation	-
ks	roughness height due to skin friction	-
Ffi	grain size distributions of the active layer	-

Output

Symbol	Description	Unit
H	water depth	m
τsg	shear stress on the bed surface	N / m2
η	bed surface elevation	m
qbT	bedload transport rate	m2 / s
qbTf	upstream feed rate	tons / year
Dsg	geometric mean grain size on the bed surface	mm
Ds90	the diameter such that 90% of the bed surface is finer	mm

Notes

The program AgDegNormGravMixPW is an extension of AgDegNormal for sediment mixtures in gravel bed rivers where the channel bed material is transported as bedload only. Gravel-bed rivers tend to be poorly-sorted. During floods, bed material load consists almost exclusively of bedload. (Sand is often transported in copious quantities as washload during floods.) The surface material (armor or pavement) tends to be coarser than the substrate. By definition the median size D_sub50 or geometric mean size D_subg of the substrate is in the gravel range, but the substrate may contain up to 30% sand in the interstices of an otherwise clast-supported deposit.

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 program does not store the vertical and streamwise structure of the new substrate created as the bed aggrades. 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 notvary in the vertical. These constraints are easy to relax.

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.

The river is assumed to be morphologically active only intermittently (during floods); this condition is specified in terms of an intermittency If < 1 expressing the fraction of time the river is in flood.

In performing the calculation, the following control parameters must be specified: M = number of spatial intervals, so that the spatial step length = L/M; dt = time step length; Ntoprint = number of time steps to a printout; Nprint = number of printouts in the calculation.

• Note on model running

In the case of the load relation due to Parker (1990), the grain size distributions are automatically renormalized 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 user will be prompted by the program as to which bedload relation he would like to use.

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 D_bU and D_bL such that f_fU = 100 (1.00) and f_fL = 0

The water depth is calculated using a Chézy formulation, when only the Chézy coefficient is specified in the input text file. The Manning-Strickler formulation is implemented, when only the coefficients αr and nk are given in the inputfile. When all the three parameters 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:

• Upload file: http://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)

Gary Parker

Links

• [Model:AgDegNormGravMixPW]