The volume indicators refer to three kind of volumes:

• The demand volume (V_D), which is the target volume at the offtakes,

• The supply volume (V_S), which is the volume supplied at the offtakes,

• The effective volume (V_EF), which is the really usable part of the supply volume.

The definition of the effective volume depends on two coefficients: W and X (in %):

• if (1-W/100).Q_D <= Q_S <= (1+X/100).Q_D => Q_EF = Q_S
• if Q_S < (1-W/100).Q_D => Q_EF = 0
• if Q_S > (1+X/100).Q_D => Q_EF = (1+X/100).Q_D

All volumes are calculated with trapezoidlal rule:

$$V = \frac{t_d-t_f}{\Delta t} \left( \frac{f(t_d) + f(t_f)}{2} + \sum_{k=1}^{n-1} f \left( t_d+k \frac{t_d-t_f}{n} \right) \right)$$

Only the supply discharge close to the water demand is thus taken into account (see below).

Graph indices volumiques

In this figure the effective volume is shaded. We define three volume indicators:

• Indicator IND1 = V_S/V_D
• Indicator IND2 = V_EF/V_D
• Indicator IND3 = V_EF/V_S

These indicators can be defined for a single offtake or for a set of offtakes.