Within the 1D river reach segments, only a single water surface and therefore a single mean energy are computed at each cross section. For a given water surface elevation, the mean energy is obtained by computing a flow weighted energy from the three subsections of a cross section (left overbank, main channel, and right overbank). The figure below shows how the mean energy would be obtained for a cross section with a main channel and a right overbank (no left overbank area).
Example of How Mean Energy is Obtained

To compute the mean kinetic energy it is necessary to obtain the velocity head weighting coefficient alpha. Alpha is calculated as follows:
Mean Kinetic Energy Head = Discharge-Weighted Velocity Head

1) \alpha \frac{\overline{V}^2}{2g}=\frac{Q_1 \frac{V_1^2}{2g}+Q_2 \frac{V_2^2}{2g}}{Q_1+Q_2}
2) \alpha=\frac{2g\ \left(\ Q_1\ \frac{V_1^2}{2g}+Q_2\ \frac{V_2^2}{2g}\ \right)}{\left(\ Q_1+Q_2\ \right)\ \overline{V}^2}
3) \alpha=\frac{Q_1V_1^2+Q_2V_2^2}{\left(\ Q_1+Q_2)\ \overline{V}^2}

In General:

4) \alpha=\frac{\left[\ Q_1V_1^2+Q_2V_2^2+\cdots\ Q_NV_N^2 \right]}{Q\ \overline{V}^2}

The velocity coefficient, α, is computed based on the conveyance in the three flow elements: left overbank, right overbank, and channel. It can also be written in terms of conveyance and area as in the following equation

5) \alpha=\frac{\left( A_t \right)^2 \left[ \frac{K_{lob}^3}{A_{lob}^2} +\frac{K_{ch}^3}{A_{ch}^2} + \frac{K_{rob}^3}{A_{rob}^2 } \right]}{K_t^3}
SymbolDescriptionUnits

A_t

total flow area of cross section

A_{lob}, A_{ch}, A_{rob}

flow areas of left overbank, main channel and right overbank, respectively

K_t

total conveyance of cross section

K_{lob}, K_{ch}, K_{rob}

conveyances of left overbank, main channel and right overbank