# Model help:Acronym1R

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## Acronym1R

"Acronym1_R” combines Acronym1 scheme with a Manning-Strickler relation for flow resistance.

## Model introduction

Acronym1_R is used for computing the volume bedload transport rate per unit width and bedload grain size distribution from a specified surface grain size distribution (with sand removed) (Db,i, Ff,i), i = 1..N+1, a specific gravity of the sediment (here equal to R + 1), a water discharge Q, a channel width B and a streamwise bed slope S.

## 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
Submerged Specific Gravity -
Water discharge m3 / s
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 (Db,i, Db,i+1)) (for i=1...N)
 $\displaystyle{ D_{i}= \sqrt{ D_{b, i} D_{b, i+1} } }$ (1)
• Fraction in the surface layer Fi for the ith grain size range (for i=1...N)
 $\displaystyle{ F_{i}= \left ( F_{f, i} - F_{f, i+1} \right ) / 100 }$ (2)
• Grain Size on the base-2 logarithmic scale:
 $\displaystyle{ \Psi= LN_{2}\left (D\right) = {\frac{log_{10}\left (D\right)}{log_{10}\left (2\right)}} }$ (3)
• Geometric mean size of the surface material
 $\displaystyle{ D_{sg}=2^\left (\bar\Psi_{s} \right ) }$ (4)
 $\displaystyle{ \bar\Psi_{s}= \sum\limits_{i=1}^N \Psi_{i} F{i} }$ (5)
• Geometric standard deviations of the surface material
 $\displaystyle{ \sigma_{sg}= 2 ^\sigma }$ (6)
• Arithmetic standard deviations of the surface material
 $\displaystyle{ \sigma ^2= \sum\limits_{i=1}^N \left (\Psi_{i} - \bar\Psi \right )^2 F_{i} }$ (7)
 $\displaystyle{ W_{i}^*= {\frac{Rgq_{bi}}{F_{i}u_{*} ^3}}= 0.00218 G \left (\Phi \right ) }$ (8)
 $\displaystyle{ \phi= \omega \Phi_{sgo} \left ( {\frac{D_{i}} {D_{sg}}} \right )^ \left (-0.0951 \right ) }$ (9)
 $\displaystyle{ \Phi_{sgo}= {\frac{\tau_{sg} ^*}{\tau_{ssrg} ^*}} }$ (10)
 $\displaystyle{ \tau_{sg} ^*={\frac{u_{*} ^2}{R g D_{sg}}} }$ (11)
• Φ> 1.59
 $\displaystyle{ G \left ( \Phi \right )= 5474 \left ( 1 - {\frac{0.853}{\Phi}} \right ) ^ \left (4.5 \right ) }$ (12)
• 1<=Φ<=1.59
 $\displaystyle{ G\left (\Phi \right )= exp[ 14.2\left ( \Phi - 1\right ) - 9.28 \left ( \Phi - 1 \right )^2 ] }$ (13)
• Φ< 1
 $\displaystyle{ G\left (\Phi \right )= \Phi ^\left (14.2 \right ) }$ (14)
 $\displaystyle{ \omega= 1 + {\frac{\sigma}{\sigma_{O} \left ( \Phi_{sgo} \right ) }} [ \omega_{O} \left ( \Phi_{sgo} \right ) - 1 ] }$ (15)
• total volume gravel bedload transport rate per unit width summed over all sizes
 $\displaystyle{ q_{bT}= \sum\limits_{i=1}^N q_{bi} }$ (16)
• fraction of gravel bedload in the ith grain size range
 $\displaystyle{ p_{i}= {\frac{q_{bi}}{q_{bT}}} }$ (17)
• Geometric mean of the bedload
 $\displaystyle{ D_{lg}= 2 ^\left (\bar\psi_{l} \right ) }$ (18)
 $\displaystyle{ \Psi_{l}= \sum\limits_{i=1}^\left (Np \right ) \Psi_{i} p_{i} }$ (19)
• Geometric standard deviation of the bedload
 $\displaystyle{ \delta_{lg}= 2 ^\left ( \delta_{l} \right ) }$ (20)
 $\displaystyle{ \delta_{l} ^2= \sum\limits_{i=1}^\left (Np \right ) \left ( \Psi_{i} - \bar\Psi_{l} \right )^2 p_{i} }$ (21)
• Grain sizes in the bedload material
 $\displaystyle{ D_{lx}= 2 ^\left (\Psi_{lx} \right ) }$ (22)
 $\displaystyle{ \Psi_{lx}= \Psi_{b, i+1} + {\frac{\Psi_{b, j} - \Psi_{b, i+1}}{p_{f, i} - p_{f, i+1}}}\left ( x - p_{f, i+1} \right ) }$ (23)
 $\displaystyle{ \Psi_{b, i}= Ln_{2} \left ( D_{b, j} \right ) }$ (24)
• Roughness height of the channel (including bed and vertical sidewalls)
 $\displaystyle{ k_{s} = n_{k} D_{s90} }$ (25)
 $\displaystyle{ \tau_{b} B = \rho u_{*} ^2 B = \rho g S \left ( H B - H ^2 \right ) }$ (26)
 $\displaystyle{ {\frac{U}{u_{*}}} = \alpha _{r} \left ( {\frac{H}{k_{s}}} \right )^ {\frac{1}{6}} }$ (27)
 $\displaystyle{ U = {\frac{Q}{BH}} }$ (28)
 $\displaystyle{ H = \left ({\frac{k_{s} ^ {\frac{1}{3}} Q ^2}{\alpha_{r} ^2 g B^2 S}} \right )^ {\frac{3}{10}} c_{1} }$ (29)
 $\displaystyle{ c_{1}= \left ( 1 - {\frac{H}{B}} \right ) ^ \left ({\frac{-3}{10}}\right ) }$ (30)

## Notes

• Note on the program

The channel is assumed to be rectangular, with the vertical sidewalls having the same roughness as the bed.

Depth is computed according to the relation for momentum balance in the bed region using equation 26 applicable to normal (steady, streamwise uniform) flow. Flow resistance on the bed region is computed using a Manning-Strickler resistance relation.

Equation 29, 30 is solved iteratively for H in the code. Once H is known, the shear velocity u is computed from equation 26, and the calculation proceeds using the same algorithm as “Acronym1”. It is implicitly assumed in the calculation that all of the boundary shear stress consists of skin friction, with form drag neglected.

## 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: