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
i : 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) [-]