Model help:AgDegNormalGravMixHyd

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 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.

Model parameters

Input Files and Directories

Run Parameters

About

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

[math]\displaystyle{ \Delta t_{w} = n_{step,w} \Delta t_{f} }[/math]

(1)

[math]\displaystyle{ P = \sum\limits_{w=1}^W n_{step,w} }[/math]

(2)

• Manning-Strickler formulation

[math]\displaystyle{ C_{f}^\left ( {\frac{-1}{2}} \right )=\alpha _{r}\left ( \frac{H}{K_{c}} \right )^{\frac{1}{6}} }[/math]

(3)

• Roughness height due to skin friction

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

(4)

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

(5)

Nomenclature

Symbol	Description	Unit
X	Streamwise coordinate	m
t	Temporal coordinate	seconds
Qw	Flood discharge	m3/s
Sl	Ambient bed slope	-
L	Length of reach	m
Δt	Time step	year
M	Number of spatial intervals	-
R	Submerged specific gravity	-
Cz	Non-dimensional Chézy friction coefficient	-
∆tf	flood time step, used to solve the Exner equation	-
nstep,w	an integer number of the flood time step	-
Qp	discharge for each time step p	-
ηd	downstream bed elevation	-
npp	input number of grain sizes defining distributions, npp must be between 2 and 9	-
Dbi		-
Dbnew		-
N	number of hydrograph entries	-
c	number of hydrograph cycles per year	-
e	downstream bed elevation	m
i	number of iterations per print	-
p	number of print	-
k	factor in roughness height calculation	-
n	factor in active layer calculation	-
r	coefficient in Manning-Strickler	-
l	bed porosity, gravel	-
u	upwinding coefficient for load spatial derivatives in Exner equation	-
a	coefficient for material transferred to substrate as bed aggrades	-
qbT	bedload transport rate	m2 / s
qbT / qbo	bedload transport rate relative to the feed rate	-
Dsg	geometric mean grain on the bed surface	mm
Dlg	geometric mean grain of the bedload	mm
D90s	grain size such that 90% of the sediment of the bed surface is finer	mm
qbo	feed rate	-
qbTf	bedload transport	-

Output

Symbol	Description	Unit
η	Bed surface elevation	m
S	Bed slope	-
H	Water depth	m
τb	Total (skin friction + form drag) Shields number	-
qt	total bed material load	m2/s

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 η_dI.

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 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: M = number of spatial intervals, so that the spatial step length = L/M. dt = time step length; Mtoprint = number of time steps to a printout; Mprint = number of printouts in the calculation.

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

References

Key papers

Links

• [Model:AgDegNormalGravMixHyd]