# Model help:WPHydResAMBL

## WPHydResAMBL

This model is an implementation of the Wright-Parker (2004) formulation for hydraulic resistance combined with the Ashida-Michiue (1972) bedload formulation.

## Model introduction

This model is a Depth-Discharge and Bedload Calculator, uses: 1. Wright-Parker formulation for flow resistance (without stratification correction) 2. Ashida-Michiue formulation for bedload transport.

## 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
Bed slope -
Submerged specific gravity of sediment -
Median sediment size (D50) mm
90% passing sediment size (D90) grain diameter such that 90% of the distribution is finer mm
factor such that ks = n * D90 -
low end value of Hs low end value of water depth due to skin friction m
step size for Hs step size for water depth due to skin friction m
number of steps to make for Hs -
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

 $\displaystyle{ \tau_{s} ^* = {\frac{H_{s} S}{R D_{50}}} }$ (1)
 $\displaystyle{ U = 8.32 \sqrt { g H_{s} S } \left ( {\frac{H_{s}}{k_{s}}} \right ) ^ \left ( {\frac{1}{6}} \right ) }$ (2)
 $\displaystyle{ \Gamma = \left ( {\frac{\tau _{s} ^* - 0.05 }{0.7}} \right ) ^ \left ( {\frac{5}{4}} \right ) }$ (3)
 $\displaystyle{ H = [ \Gamma {\frac{R D_{s50}}{S}} \left ( {\frac{\sqrt { g }}{U}} \right ) ^ \left ( 0.7 \right ) ] ^ \left ( {\frac{20}{13}} \right ) }$ (4)
 $\displaystyle{ q_{w} = U H }$ (5)
 $\displaystyle{ \tau ^* = {\frac{H S}{R D_{50}}} }$ (6)
 $\displaystyle{ Fr = {\frac{U}{\sqrt { g H }}} }$ (7)
 $\displaystyle{ u_{*} = \sqrt { g H S } }$ (8)
 $\displaystyle{ u_{*s} = \sqrt { g H_{s} S } }$ (9)
 $\displaystyle{ q_{b} = \sqrt { R g D_{50} } D_{50} \left ( \tau _{s} ^* - 0.05 \right ) \left ( \sqrt { \tau _{s} ^* } - \sqrt { 0.05 } \right ) }$ (10)

## Notes

This program uses the Wright-Parker formulation to calculate flow resistance, and the Ashida-Michiue formulation to calculate the water depth against water discharge and bedload transport, as well as calculating the flow velocity, shear velocities, shear stress, and several other parameters.

The program takes the inputs given above; the αstrat is an optional parameter that may be entered; if the user chooses not to include it, it will automatically be set to 1, and stratification will not be taken into account.

## 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: