Channel Reaches

For channel units the form of the sediment continuity equation used is:

                    (1)

Where

λ = bed porosity

W = water surface width

z = bed elevation

t = time

G = sediment transport rate (m/s)

x = distance in flow direction

Equation (1) assumes that the rate of change of sediment entrained in the flow is negligible in comparison with the terms expressing rate of change in bed elevation and change in transport rate.

Equation (1) is discretised in the following form:

                    (2)

Where

k = position index, which increases in the downstream direction

i = time index

Δ z = change in bed elevation over timestep Δ t

Equation (2) can be solved explicitly for Δ z as is calculated by the sediment transport capacity equation and will have been determined previously.