THE POTENTIAL ENERGY PROFILE

To define the trend of potential energy values along the elevation, i.e., to construct the POTENTIAL ENERGY PROFILE, the classic relation is used:

Ep​=m×g×H

This can be developed by considering that mass (m) is a variable that increases from upstream to downstream. The relationship can be expressed as:

Ep​=γ×V×H

Where the volume (Vi​) at a given point is a function of the cumulative basin AREA (Ai​) at elevation Hi​ and the precipitation height (pi​). The general relation used in the model is therefore:

Epi​=γ×(Ai​×pi​)×Hi​

Since the calculated Ep​ values are too large for direct comparison with other data on a graph, they are normalized by dividing them by the maximum observed value.

The resulting values (epi​), ranging from 0 to 1, can be plotted on a graph along with the hypsometric curve and the profile generally takes on a classic bell shape.

At the highest point of the basin, the flowing mass is zero, so the potential energy is zero. At the outlet (e.g., at sea level), the elevation H is zero, and again the potential energy is zero.

FIG_1: TYPICAL ENERGY PROFILE OF BASINS POSTED ALONG THE COAST.