Model help:Acronym1D

Acronym1D

This program acts the same way as the Acronym1 do, with the addition of a “flow duration curve;” the program calculates the same values (though taken as a mean annual) as well as the mean annual water discharge, and the characteristics of the flow duration curve.

Model introduction

“Acronym1_D” simply adds a flow duration curve to the algorithm of “Acronym1_R” in order to compute the average volume gravel bedload transport rate per unit width, as well as the average bedload grain size distribution. In addition, it computes the annual mean values of the water discharge, depth, shear velocity and Shields stress based on surface geometric mean size. The values D_alg, σ_alg, D_al90, D_al70, D_al50 and D_al30 associated with the mean grain size distribution of the bedload are computed along with the corresponding values for the surface material, D_sg, σ_sg, D_s90, D_s70, D_s50 and D_s30. Finally, the program computes the volume gravel bedload transport rate per unit width, the water discharge, flow depth, the shear velocity and the Shields stress associated with each range in the flow duration curve, along with the fraction of time that the flow is in that range.

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
Submerged Specific Gravity		-
Bed Slope		-
Channel Width		m
Roughness Factor		-

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

• Characteristic grain size for the ith grain size range (spans (D_b,i, D_b,i+1)) (for i=1...N)

[math]\displaystyle{ D_{i}= \sqrt{ D_{b, i} D_{b, i+1} } }[/math]

(1)

• Fraction in the surface layer F_i for the ith grain size range (for i=1...N)

[math]\displaystyle{ F_{i}= \left ( F_{f, i} - F_{f, i+1} \right ) / 100 }[/math]

(2)

• Grain Size on the base-2 logarithmic scale:

[math]\displaystyle{ \Psi= LN_{2}\left (D\right) = {\frac{log_{10}\left (D\right)}{log_{10}\left (2\right)}} }[/math]

(3)

• Geometric mean size of the surface material

[math]\displaystyle{ D_{sg}=2^\left (\bar\Psi_{s} \right ) }[/math]

(4)

[math]\displaystyle{ \bar\Psi_{s}= \sum\limits_{i=1}^N \Psi_{i} F{i} }[/math]

(5)

• The geometric standard deviations

[math]\displaystyle{ \sigma_{sg}= 2 ^\sigma }[/math]

(6)

• the arithmetic standard deviations

[math]\displaystyle{ \sigma ^2= \sum\limits_{i=1}^N \left (\Psi_{i} - \bar\Psi \right )^2 F_{i} }[/math]

(7)

• The transport relation

[math]\displaystyle{ W_{i}^*= {\frac{Rgq_{bi}}{F_{i}u_{*} ^3}}= 0.00218 G \left (\Phi \right ) }[/math]

(8)

[math]\displaystyle{ \phi= \omega \phi_{sgo} \left ( {\frac{D_{i}} {D_{sg}}} \right )^ \left (-0.0951 \right ) }[/math]

(9)

[math]\displaystyle{ \phi_{sgo}= {\frac{\tau_{sg} ^*}{\tau_{ssrg} ^*}} }[/math]

(10)

[math]\displaystyle{ \tau_{sg} ^*={\frac{u_{*} ^2}{R g D_{sg}}} }[/math]

(11)

[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]

(12)

[math]\displaystyle{ \omega= 1 + {\frac{\sigma}{\sigma_{O} \left ( \phi_{sgo} \right ) }} [ \omega_{O} \left ( \phi_{sgo} \right ) - 1 ] }[/math]

(13)

• total volume gravel bedload transport rate per unit width summed over all sizes

[math]\displaystyle{ q_{bT}= \sum\limits_{i=1}^N q_{bi} }[/math]

(14)

• fraction of gravel bedload in the ith grain size range

[math]\displaystyle{ p_{i}= {\frac{q_{bi}}{q_{bT}}} }[/math]

(15)

• Geometric mean of the bedload

[math]\displaystyle{ D_{lg}= 2 ^\left (\bar\psi_{l} \right ) }[/math]

(16)

[math]\displaystyle{ \Psi_{l}= \sum\limits_{i=1}^\left (Np \right ) \Psi_{i} p_{i} }[/math]

(17)

• Geometric standard deviation of the bedload

[math]\displaystyle{ \delta_{lg}= 2 ^\left ( \delta_{l} \right ) }[/math]

(18)

[math]\displaystyle{ \delta_{l} ^2= \sum\limits_{i=1}^\left (Np \right ) \left ( \Psi_{i} - \bar\Psi_{l} \right )^2 p_{i} }[/math]

(19)

• Grain sizes in the bedload material

[math]\displaystyle{ D_{lx}= 2 ^\left (\Psi_{lx} \right ) }[/math]

(20)

[math]\displaystyle{ \Psi_{lx}= \Psi_{b, i+1} + {\frac{\Psi_{b, j} - \Psi_{b, i+1}}{p_{f, i} - p_{f, i+1}}}\left ( x - p_{f, i+1} \right ) }[/math]

(21)

[math]\displaystyle{ \Psi_{b, i}= Ln_{2} \left ( D_{b, j} \right ) }[/math]

(22)

• Characteristic flow in the kth range (k=1...M)

[math]\displaystyle{ Q_{wr,k}= {\frac{1}{2}} \left ( Q_{wd,k} + Q_{wd, k+1} \right ) }[/math]

(23)

• Fraction of time the flow is in the kth range

[math]\displaystyle{ P_{Q,k}= {\frac{p_{eQ,k+1} - p_{eQ,k}}{100}} }[/math]

(24)

Nomenclature

Symbol	Description	Unit
D	grain size	L
Di	characteristic grain size for the ith grain size range (i=1...N)	L
Fi	fraction in surface layer for the ith grain size range(for i =1...N)	-
τssrg *	equals to 0.0386	-
ψ	grain sizes on the base-2 logarithmic ψ scale
ρ	density of water	M / L3
ρs	density of sediment	M / L3
R	submerged specific density of sediment, equals to (ρs /ρ-1)	-
u	shear velocity of flow	L / T
g	acceleration of gravity	L / T2
τb	boundary shear stress on the bed	M / (L T)
u*	shear velocity on the bed, equals to sqrt(τb / ρ )	L / T
pi	fraction of gravel bedload in the ith grain size range	L
ψs	equals to τbs / τb
Wi *	dimensionless bedload transport rate for ith grain size	-
qbi	volume gravel bedload transport per unit width of grains in the ith size range	L 2 / T
ω	straining relation in Parker (1990a,b) bedload relation for mixtures
G(Φ)	function in Parker (1990a, b) and Wilcock and Crowe (2003) bedload relation for gravel mixture
ω0	function relation in Parker (1990a, b) bedload relation for mixture	-
Φ	parameter in Parker (1990a, b) bedload relation for mixures
Φsgo	equals to τsg * / τssrg *	-
ψl	grain sizes on the base-2 logarithmic ψ scale for bedload	-
ψlx	grain sizes on the base-2 logarithmic ψ scale for bedload such that x percent of the material is finer	-
Dg	geometric mean size	L
σg	geometric standard deviation	-
Dx	diameter such that x% of the distribution is finer	L
Qwd,k	The kth discharge	L3 / T
Qwr,k	Characteristic flow in the kth range	L3 / T
peQ,k	the percentage of time the kth flow is exceeded	-
pQ,k	fraction of time that the flow is in the kth range	-

Output

Symbol	Description	Unit
qbT	total volume gravel bedload transport rate per unit width summed over all sizes	L2 / T
τsg *	Shields number based on surface geometric mean size	-
Dsg	geometric mean size of the surface material	L
σsg	geometric standard deviations of the surface material	-
Dlg	geometric mean of the bedload material	L
σlg	geometric standard deviations of the bedload material	-
Dalg	geometric mean size of the bedload	L
σalg	geometric standard deviations of the bedload	-
σ	arithmetic standard deviations of the surface materials	-
σlg	geometric standard deviation of the bedload	-
Dsx	grain size in the surface material, such that x percentage of the material is finer	L
Dlx	grain size in the bedload material, such that x percentage of the material is finer	L
Dalx	mean grain size in the bedload material, such that x percentage of the material is finer	L
σl	arithmetic standard deviations of bedload materials	-
Qa	mean water discharge	L3 / T
Ha	mean water depth	L
u*a	mean shear velocity	L / T
τga	mean Shields stress	-

Notes

• Note on the program

The flow duration curve is specified in terms of the pairs (Q_wd,k, p_eQ,k), k = 1..M+1. Here k = 1 corresponds to the highest flow in the curve, with an exceedance percentage p_eQ of zero, and k = M+1 corresponds to the lowest flow in the curve, with an exceedance percentage p_eQ of 100. The lowest flow on the curve Q_wd,M must exceed zero.

Let Y_k be any parameter defined for each of the flow ranges k = 1..M. The mean value Y_a averaged over the flow duration curve is then given as

Y_a = Sum(Y_k p_Q,k), k=1...M

For example, if the fractions in the bedload in each grain size range within flow range k are given as p_k,i then the average fractions of the bedload p_ai are given as

p_ai = Sum(p_k,i p_Q,k)

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: https://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

• Parker, G., 1990a. Surface based bedload transport relation for gravel rivers. Journal of Hydraulic Research, 28(4), 417~436.(DOI:10.1080/00221689009499058)

• Parker, G.,1990b. The "ACRONYM" series of Pascal programs for computing bedload transport in gravel rivers. External Memorandum M 220, St. Anthony Falls Hydraulic Laboratory, University of Minnesota.

Links

• Model:Acronym1D