This is an illustration of calculation of depth-discharge relation, bed load transport, suspended load transport and total bed material load for a large, low-slope sand-bed river.

## Model introduction

This program calculates the same parameters as WPHydResAMBL, as well as calculating the Entrainment, Chézy coefficient, bedload ratios, and various other parameters.

This model is a Depth-Discharge and Total Load calculator, uses: 1. Wright-Parker formulation for flow resistance, 2. Ashida-Michiue formulation for bedload transport, 3. Wright-Parker formulation (without stratification) for suspended load.

## 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 (S) -
median sediment size (D50) mm
90% passing sediment size (D90) diameter such that 90% of the distribution is finer mm
factor such that ks = n*D90 -
submerged specific gravity of sediment (R) -
kinematic viscosity of water (v) m2 / s
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 m
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)
 $\displaystyle{ H = \left ( \Gamma {\frac{R D_{s50}}{S}} \left ( {\frac{\sqrt { g }}{U}} \right ) ^ \left ( 0.7 \right ) \right ) ^ \left ( {\frac{20}{13}} \right ) }$ (3)
 $\displaystyle{ \Gamma = \left ( {\frac{\tau_{s} ^* - 0.05}{0.7}} \right ) ^ \left ( {\frac{5}{4}} \right ) }$ (4)
 $\displaystyle{ \tau^* = {\frac {H S}{R D_{50}}} }$ (5)
 $\displaystyle{ F_{r}= {\frac{U}{\sqrt { g H }}} }$ (6)
 $\displaystyle{ u_{*} = \sqrt { g H S } }$ (7)
 $\displaystyle{ u_{*s} = \sqrt { g H_{s} S } }$ (8)
 $\displaystyle{ q_{b} = \sqrt { R g D_{50}} D_{50} \left ( \tau _{s} ^* -0.05 \right ) \left ( \sqrt { \tau _{s} ^* } - \sqrt { 0.05 } \right ) }$ (9)
 $\displaystyle{ C_{z} = {\frac{U}{u_{*}}} }$ (10)
 $\displaystyle{ k_{c} = {\frac{11H}{e^ \left ( \kappa C_{z} \right )}} }$ (11)
 $\displaystyle{ Z_{u} = {\frac{u_{*s}}{v_{s}}} Re_{p} ^ \left ( 0.6 \right ) S ^ \left ( 0.07 \right ) }$ (12)
 $\displaystyle{ E = {\frac{5.7 * 10^\left ( -7 \right ) Z_{u} ^5}{1 + {\frac{5.7 * 10^\left ( -7 \right )}{0.3}} Z_{u} ^5}} }$ (13)
 $\displaystyle{ q_{s} = {\frac{u_{*} E H}{\kappa}} I }$ (14)
 $\displaystyle{ q_{t} = q_{s} + q_{b} }$ (15)
 $\displaystyle{ I = \int _{\zeta _{b}} ^ 1 [ {\frac{\left ( 1 - \zeta \right ) / \zeta}{\left ( 1 - \zeta _{b} \right ) / \zeta_{b}}} ] ^ {\frac{V_{s}}{\kappa u_{*}}} ln \left ( 30 {\frac{H}{k_{c}}} \zeta \right ) d \zeta }$ (16)

## Notes

• Note on model running

The program shares the notes that are expressed in WPHydResAMBL.

The integration carried out in this program is performed with the trapezoidal rule.

## 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: