The average bed elevation and bed change over the wet and dry portions of the cell are
| 1) |
z_{b}=\frac{1}{A}\sum _{i}^{M}a_{i}z_{bi} |
| 2) |
\Delta z_{b}=\frac{1}{A}\sum _{i}^{M}a_{i}\Delta z_{bi} |
in which
i = subscript indicating sediment subregion
A = total cell horizontal area [L2]
{ϕ_{i}}^{W} = 1- {ϕ_{i}}^{D} = wetted fraction of subarea i (between 0 and 1) [-]
{ϕ_{i}}^{D} = dry fraction of subarea of subarea i (between 0 and 1) [-]
a_{i} = area corresponding to subarea i [L2]
The average wet bed change \Delta z_{b}^{W} is used for the bed change correction to sediment concentrations. \Delta z_{b}^{W} is also used to compute an average bed change rate for the bed slope term. The average dry bed change \Delta z_{b}^{D} is not used in any calculations except the average bed change rate which is a model output.
The cell averaged bed elevation and bed change are given by
| 3) |
z_{b}^{W}=\frac{1}{A^{W}}\sum _{i}a_{i}^{W}z_{bi}^{W} |
| 4) |
z_{b}^{D}=\frac{1}{A^{D}}\sum _{i}a_{i}^{D}z_{bi}^{D} |
| 5) |
\Delta z_{b}^{W}=\frac{1}{A^{W}}\sum _{i}a_{i}^{W}\Delta z_{bi}^{W} |
| 6) |
\Delta z_{b}^{D}=\frac{1}{A^{D}}\sum _{i}a_{i}^{D}\Delta z_{bi}^{D} |
in which
ℓ = subscript indicating sediment subregion
A=\sum _{i}^{M}a_{i} = cell area [L2]
\begin{aligned} a_{i}^{W}&=\phi _{i}^{W}a_{i} \\ a_{i}^{D}&=\phi _{i}^{D}a_{i} \end{aligned}
a_{i} = subregion i area [L2]
{A_{}}^{W} = wetted area determined from high-resolution elevate
{A_{}}^{D} = A−A^W = dry area of a cell [L2]
{ϕ_{i}}^{W} = 1-{\phi_{i}}^{D} = wetted fraction of subarea i (between 0 and 1) [-]
{ϕ_{i}}^{D} = dry fraction of subarea of subarea i (between 0 and 1) [-]