# 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)