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

The gravel is divided into N grain size ranges bounded by N+1 sizes D_b,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 (D_b,i, F_f,i), i = 1..N+1, where F_f,i denotes the percent finer in the surface layer. Here D_b,1 must be the coarsest size, such that F_f,1 = 100, and D_b,N+1 must be the finest size, such that F_f,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 renormalized, in determining the surface grain size distribution to be input into Acronym1.

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

Grain Size:

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

(1)

[math]\displaystyle{ \Psi_{i}= LN_{2}\left ( D_{i}\right) = {\frac{log_{10}\left (D_{i}\right)}{log_{10}\left (2\right)}} }[/math]

(2)

[math]\displaystyle{ D_{i}= Sqrt \left (D_{b, i} D_{b, i+1} \right ) }[/math]

(3)

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

(4)

[math]\displaystyle{ D_{sg}=2^\Psi_{s} }[/math]

(5)

[math]\displaystyle{ \Psi_{s}= \Sigma \Psi_{i} F{i} }[/math]

(6)

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

(7)

[math]\displaystyle{ \sigma ^2= \Sigma \left (\Psi_{i} - \Psi \right )^2 F_{i} }[/math]

(8)

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

(9)

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

(10)

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

(11)

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

(12)

φ> 1.59

[math]\displaystyle{ G \left ( \Phi \right )= 5474 \left ( 1 - {\frac{0.853}{\Phi}} \right ) ^ \left (4.5 \right ) }[/math]

(13)

1<=φ<=1.59

[math]\displaystyle{ G\left (\Phi \right )= exp\left ( 14.2\left ( \Phi - 1\right ) - 9.28 \left ( \Phi - 1 \right )^2 \right ) }[/math]

(14)

φ< 1

[math]\displaystyle{ G\left (\Phi \right )= \Phi ^\left (14.2 \right ) }[/math]

(15)

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

(16)

[math]\displaystyle{ q_{bT}= \Sigma q_{bi} }[/math]

(17)

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

(18)

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

(19)

[math]\displaystyle{ \Psi_{l}= \Sigma \Psi_{i} p_{i} }[/math]

(20)

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

(21)

[math]\displaystyle{ \delta_{l} ^2= \Sigma \left ( \Psi_{i} - \Psi_{l} \right )^2 p_{i} }[/math]

(22)

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

(23)

[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]

(24)

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

(25)

Notes

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Numerical scheme

Examples

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References

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