# 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 Dalg, σalg, Dal90, Dal70, Dal50 and Dal30 associated with the mean grain size distribution of the bedload are computed along with the corresponding values for the surface material, Dsg, σsg, Ds90, Ds70, Ds50 and Ds30. 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

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 (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)
• The geometric standard deviations
 $\displaystyle{ \sigma_{sg}= 2 ^\sigma }$ (6)
• the arithmetic standard deviations
 $\displaystyle{ \sigma ^2= \sum\limits_{i=1}^N \left (\Psi_{i} - \bar\Psi \right )^2 F_{i} }$ (7)
• The transport relation
 $\displaystyle{ W_{i}^*= {\frac{Rgq_{bi}}{F_{i}u_{*} ^3}}= 0.00218 G \left (\Phi \right ) }$ (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)
• Characteristic flow in the kth range (k=1...M)
 $\displaystyle{ Q_{wr,k}= {\frac{1}{2}} \left ( Q_{wd,k} + Q_{wd, k+1} \right ) }$ (23)
• Fraction of time the flow is in the kth range
 $\displaystyle{ P_{Q,k}= {\frac{p_{eQ,k+1} - p_{eQ,k}}{100}} }$ (24)

## Notes

• Note on the program

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

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

Ya = Sum(Yk pQ,k), k=1...M

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

pai = Sum(pk,i pQ,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: