Sediment Concentration Correction due to Bed Change

After the bed elevation is adjusted the sediment concentration should be corrected to preserve local sediment mass balance. This correction is done using the following simple formula

1)	$\begin{array}{l}\displaystyle C'_{tk}=\frac{C_{tk}^{n+1}h^{n+1}}{h^{n+1}-\Delta z_{b}^{W}}\end{array}$

where

$\begin{array}{l}{C_{tk}}^{n+1}\end{array}$ = uncorrected cell-averaged total-load sediment concentration [M/L³]

$\begin{array}{l}{C_{tk}}^{′n+1}\end{array}$ = corrected cell-averaged total-load sediment concentration [M/L³]

$\begin{array}{l}h^{n + 1}\end{array}$ = cell hydraulic (average) water depth [L]

$\begin{array}{l}{\Delta z_{b}^{W}}\end{array}$ = average bed change for wetted portion of a cell [L]

It is noted that the sediment concentration is not resolved at a subgrid level which is why the water depth in the above equation corresponds to the hydraulic water depth.