# Model help:Acronym1

## Acronym1

The Acronym1 programs implement the Parker (1990a) surface-based bedload transport relation in order to compute gravel bedload transport rates.

## Model introduction

This program calculates the volume bedload transport per unit width and the Shields number, based on the surface geometric mean diameter and the bedload GSD with its various derivatives (mean, stand. dev., interpolations), given the surface GSD.

## 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
Sediment Specific Gravity -
Shear velocity of flow m / s
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)
 $\displaystyle{ G \left ( \phi \right )= \left\{\begin{matrix} 5474 \left ( 1 - {\frac{0.853}{\phi}} \right ) ^ \left (4.5 \right ) & \phi \gt 1.59 \\ exp[ 14.2\left ( \phi - 1\right ) - 9.28 \left ( \phi - 1 \right )^2 ] & 1 \lt = \phi \lt = 1.59 \\ \phi ^\left (14.2 \right ) & \phi \lt 1 \end{matrix}\right. }$ (12)
 $\displaystyle{ \omega= 1 + {\frac{\sigma}{\sigma_{O} \left ( \phi_{sgo} \right ) }} [ \omega_{O} \left ( \phi_{sgo} \right ) - 1 ] }$ (13)
• total volume gravel bedload transport rate per unit width summed over all sizes
 $\displaystyle{ q_{bT}= \sum\limits_{i=1}^N q_{bi} }$ (14)
• fraction of gravel bedload in the ith grain size range
 $\displaystyle{ p_{i}= {\frac{q_{bi}}{q_{bT}}} }$ (15)
• Geometric mean of the bedload
 $\displaystyle{ D_{lg}= 2 ^\left (\bar\psi_{l} \right ) }$ (16)
 $\displaystyle{ \Psi_{l}= \sum\limits_{i=1}^\left (Np \right ) \Psi_{i} p_{i} }$ (17)
• Geometric standard deviation of the bedload
 $\displaystyle{ \delta_{lg}= 2 ^\left ( \delta_{l} \right ) }$ (18)
 $\displaystyle{ \delta_{l} ^2= \sum\limits_{i=1}^\left (Np \right ) \left ( \Psi_{i} - \bar\Psi_{l} \right )^2 p_{i} }$ (19)
• Grain sizes in the bedload material
 $\displaystyle{ D_{lx}= 2 ^\left (\Psi_{lx} \right ) }$ (20)
 $\displaystyle{ \Psi_{lx}= \Psi_{b, i+1} + {\frac{\Psi_{b, j} - \Psi_{b, i+1}}{p_{f, i} - p_{f, i+1}}}\left ( x - p_{f, i+1} \right ) }$ (21)
 $\displaystyle{ \Psi_{b, i}= Ln_{2} \left ( D_{b, j} \right ) }$ (22)

## Notes

• Note on equations

The gravel is divided into N grain size ranges bounded by N+1 sizes Db,i, i = 1 to N+1. The grain size distribution of the surface (active) layer of the bed is specified in terms of the N+1 pairs (Db,i, Ff,i), i = 1..N+1, where Ff,i denotes the percent finer in the surface layer. Here Db,1 must be the coarsest size, such that Ff,1 = 100, and Db,N+1 must be the finest size, such that Ff,N+1 = 0.

The finest size must equal or exceed 2 mm. That is, the sand must be removed from the surface size distribution, and the fractions appropriately re-normalized, in determining the surface grain size distribution to be input into Acronym1.

If the boundary shear stress at the bed includes a component of form drag, the component must be removed before computing u.

Once the parameters qbi are known, the total volume bed load transport rate per unit width qbT and the fractions pi in the bedload can be calculated as equations 14.

The results are presented in terms of qbT and the grain size distribution of the bed load, which is computed from the values of pi. These same fractions pi are used to compute the geometric mean and geometric standard deviation of the bedload, from the relations of equations 16, 17, 18, 19.

The percent finer in the bedload pf,i for the grain size Df,i is obtained from the fractions pi as follows: pf,1 = 100 pf,i = pf,i-1 - 100 pi-1 (i=2~N+1)

Once Ff,i is specified (pf,i is computed) the value Dsx (Dlx) can be computed by interpolation. The interpolation should be done using a logarithmic scale for grain size. For example, consider the computation of Dlx where pf,i ≤ x ≤ pf,i+1. Then we got equation 20, 21, using equation 22.

In order to carry out the above calculation it is necessary to specify specific gravity of the sediment R + 1, the shear velocity of the flow u, and the grain size distribution of the material in excess of 2 mm in the surface layer (Db,i, Ff,i), i = 1 to N+1. The relation then predicts the total volume bed load transport rate per unit width qbT of material in excess of 2 mm, as well as the grain size distribution of this load (Db,i, pf,i).

• Note on running the program

User may enter GSD on either a 0.00-1.00 scale or a 0%-100% scale, and the program will automatically convert it to a 0% -100% scale.

In the case of a uniform diameter, the user should simply enter the diameter in the diameter column, and 0 in the % passing column.

This formulation does not work for sand, so if sand is present and the border value of 2mm is present the program cuts off all sand (<2mm) and re-normalizes the remaining distribution; if sand is present and the border value of 2mm is not present the program alerts the user and exits.

This formulation requires endpoints at 0% and 100%, so if these boundary values are not present the program will automatically interpolate them.

The program automatically organizes the data, so the user may enter the distribution in whatever order they desire.

Note, the Acronym family of functions do not have a GetData function, because there is no time loop, and all the data is being outputted already.

## 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: