# SMS:Lund Cirp and Watanabe Formula

The Lund Cirp and Watanabe formula can be found on page 16 of the Two-Dimensional Depth-Averaged Circulation Model CMS-M2D: Version 3.0, Report 2, Sediment Transport and Morphology Change TR.

The total load sediment transport rate of Watanabe is given by:

$q_{tot}=A{\biggl [}{\frac {(\tau _{b,max}-\tau _{cr})U_{c}}{p_{w}g}}{\biggr ]}$ where
τb,max = maximum shear stress at the bed
τcr = shear stress at incipient sediment motion
Uc = depth averaged current velocity
ρw = density of water
g = acceleration of gravity
A = empirical coefficient typically ranging from 0.1 to 2

## Transport Slope Coefficient

The Transport Slope Coefficient can be found on page 32 of the Two-Dimensional Depth-Averaged Circulation Model CMS-M2D: Version 3.0, Report 2, Sediment Transport and Morphology Change TR.

${\bar {q}}'_{tot,x}={\bar {q}}_{tot,x}+D_{s}\left\vert {\bar {q}}_{tot}\right\vert {\frac {\partial h}{\partial x}}$ ${\bar {q}}'_{tot,y}={\bar {q}}_{tot,y}+D_{s}\left\vert {\bar {q}}_{tot}\right\vert {\frac {\partial h}{\partial y}}$ Ds = empirical slope coefficient with typical range of 5 to 30.

The Transport Slope Coefficient can vary site by site and even within a single site domain in that some areas have constraints with naturally occurring steep bed slopes (e.g., channels) and other areas have gentle slopes (e.g. beach profiles, or tidal flats). It is a diffusion coefficent for increasing downhill transport or decreasing uphill transport (if D is >1) This is a good parameter to use as a morphology change calibration factor (along with the scalesus and scalebed coefficients). One thing to note is that what may calibrate well for one area will not calibrate well for another so an average value may be necessary.