Volume indicators

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).

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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.