Model help:AgDegNormGravMixSubPW

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
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

A list of the key equations. HTML format is supported; latex format will be supported in the future

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	-
O	channel sinuosity	-
s	subsidence rate	mm/yr
B	ratio of wash load deposited per unit bed material load deposited	-
V	ratio of wash load deposited per unit bed material load deposited	-
F_up	GSD at the upstream end	-
F_down	GSD at the downstream end	-
L_max	maximum reach length	-
S_l	the initial bed slope	-
D_i	diameter	-
x	downstream coordinate	m
Sl	slope of the bed surface	-
p_feed	GSD of the feed	tons / year
F_fs	GSD of the substrate	-
F_f	GSD of the final surface	-
Ω	channel sinuosity	-
r_B	ratio of depositional width to channel width
Λ	ratio of wash load depositional per unit bed material load dpeosited	-
σ	subsidence rate	mm/year
q_w	water discharge/width	m² / s
η_d	base level	m
I_f	flood intermittency	-
∆_t	time step	day
n_k	factor by which surface D_s90 is multiplied to obtain roughness height k_s
n_a	factor by which surface D_s90 is multiplied to obtain active layer thickness L_a	-
α_r	coefficient in Manning-Strickler resistance relation	-
R_r	submerged specific gravity of gravel	-
λ_p	bed porosity, gravel	m
I_f	flood intermittency	-
a_U	upwinding coefficient for load spatial derivatives in Exner equation (value > 0.5 suggested)	-
α	coefficient for material transferred to substrate as bed aggrades	-

Output

Symbol	Description	Unit
H	water depth	m
τ_sg	shear stress on the bed surface	N / m²
η	bed surface elevation	m
q_bT	bedload transport rate	m² / s
q_bTf	upstream feed rate	tons / year
D_sg	geometric mean grain size on the bed surface	mm
D_s90	the diameter such that 90% of the bed surface is finer	mm

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 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.

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.

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 η_d.

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 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.

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.

There is a maximum reach length equal to: L_max = I * (1+Λ) * σ * Ω * q_bTf / (rB * (1 – λ)), if the L value exceeds this critical value the program will exit and alert the user

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_c, 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:

Upload file: http://csdms.colorado.edu/wiki/Special:Upload
Create link to the file on your page: [[Image:<file name>]].

Developer(s)

Gary Parker

References

Key papers

Links

[Model:AgDegNormGravMixSubPW]