The fraction of suspended sediments is defined as:

1) r_{_{sk}} =\frac{q_{sk}}{q_{tk}}

where

r_{sk} : fraction of suspended sediments [-]

q_{sk} : suspended-load transport rate [M/L/T]

q_{tk} : total-load transport rate [M/L/T]

The fraction of suspended sediments is needed in the total-load transport model in order to separate the contributions from bed- and suspend-load to various parameters including the horizontal mixing coefficient and advection coefficients. The parameter is needed in order to close the system of equations. The fraction of suspended sediments is approximated by the transport mode parameter which is the ration of the suspended-load to total-load transport potential rates:

2) r_{sk}\approx f_{sk}=\frac{q_{sk}^{*}}{q_{tk}^{*}}

where

f_{sk} : transport mode parameter [-]

{q_{sk}}^{*} : suspended-load transport potential rate [M/L/T]

{t_{k}}^{*} : total-load transport potential rate [M/L/T]

There methods available to estimate the transport mode parameter:

1. Transport capacity method (Wu 2007)

2. Rouse parameter method of Greimann et al. (2008)

3. van Rijn (1984)

4. Jones and Lick (2001)

Figure 1. Representative transport mode parameter curves as a function of the Rouse number with d = 1 mm,  \rho_{w}= 1000 kg/m3, and \rho_{s} = 2650 kg/m3.

Transport Capacity Method

This is the simplest and preferred method.

3) f_{sk} =\frac{q_{sk}^{*}}{q_{tk}^{*}}

The default option is the transport capacity method. If the total-load transport capacity formula may be written in terms of bed and suspended capacities, the transport capacity method is utilized. This is the most consistent approach with the transport formulas. However, if the transport formula is a bed-material formula such as the Laursen formula, another approach must be used.

Greimann et al.

The transport mode parameter proposed by Greimann et al. (2008) is as follows

4) f_{sk} = \min[1, ~2.5\exp(−r_k)]

where

r_{k} = ω_{sk}/(κu_*) : Rouse parameter [-]

ω_{sk}: sediment settling velocity [L/T]

u_{*}: bed shear velocity [L/T]

van Rijn

An alternative formulation for estimating the fraction of suspended sediments was given by van Rijn (1984)

5) f_{sk} = 0.25 +0.325\ln(u_*/ω_{sk})

where

ω_{sk} : sediment settling velocity [L/T]

u_{*} : bed shear velocity [L/T]

Jones and Lick

Jones and Lick (2001) developed the following formula for the transport mode parameter

6) f_{sk}=\left\{\begin{array} 0\,\,\,\,\,\,\,\,\,\,\,\mathrm{for}\,\,\tau _{b}<\tau _{crk}\\ \frac{\ln \left(\frac{u_{*}}{\omega _{sk}}\right)-\ln \left(\frac{\sqrt{\tau _{cr}/\rho _{w}}}{\omega _{sk}}\right)}{\ln \left(4\right)-\ln \left(\frac{\sqrt{\tau _{cr}/\rho _{w}}}{\omega _{sk}}\right)}\,\,\,\mathrm{for}\,\,\tau _{b}>\tau _{crk}\,\,\mathrm{and}\,\,u_{*}<4\omega _{sk}\,\,\,\\ 1\,\,\,\,\,\,\,\,\,\,\,\,\text{otherwise} \end{array}\right.

where

ω_{sk} : sediment settling velocity [L/T]

u_{*} : bed shear velocity [L/T]