The hydraulic curves must also be modified at the cell faces for deposition and erosion. Since bed elevations at faces may have very different characteristics from the neighboring cells, it is not possible to simply interpolate the bed elevations at faces. Instead, the bed change as a function of elevation is interpolated from neighboring cells and applied on the face bed elevations. The first step is to interpolate the neighboring cell bed changes to the same elevation points as the face:

1) \Delta z_{b,L}(z_{L})\Rightarrow \Delta z_{b,L}(z_{f})
2) \Delta z_{b,R}(z_{R})\Rightarrow \Delta z_{b,R}(z_{f})

where is the face bed elevations above the face invert, and and are the elevations above the inverts for the left and right cells respectively. The face bed elevations are then computed as a simple weighted average of the neirghboring cell bed changes:

3) \Delta z_{b,f}(z_{f})=w_{L}\Delta z_{b,L}(z_{f})+w_{R}\Delta z_{b,R}(z_{f})

where and are interpolation weights. Many interpolation schemes are possible including inverse area weighting, however here for simplicity a simple arithmetic average is utilized. Further testing with other interpolation schemes will be done in the future.

It is noted that the face property tables are the same resolution for both hydrodynamics and sediment transport. This means that they can be very high resolution with more than 30 or 40 elevations per face. This is one of the reasons for utilizing a simple scheme for updating the face bed elevations. An alternative scheme could be invisioned in which the bed elevations are updated by computing face erosion and deposition rates similar to how the cell bed elevations are computed. However, it would also be very computationally expensive since it would require storing, interpolating, and computing many additional variables at faces. It is expected that different approaches will perform better than others in different situations and more testing will be done on this in the future.