3.4.4. Water Age Submodel

The water age of the system is a surrogate metric for water quality [90]. Water age is calculated using water quality calculations in EPANET, which are executed at small time steps to reduce error. The weighted water age is calculated using Equation (14) at consumer nodes across the network.

$$WA\_S = \frac{\sum\_{c=1}^{C} \sum\_{t=1}^{T\_{\overline{\mathbb{M}}}} b\_{c,t} \times D\_{c,t} \times (WA\_{c,t} - WA\_{lim})}{\sum\_{c=1}^{C} \sum\_{t=1}^{T\_{\overline{\mathbb{M}}}} D\_{c,t}} \tag{14}$$

where *WAS* is the weighted average water age above the limit for the system (hours). The acceptable limit for water age (*WAlim*) is 48 h [90]. *WAc*,*<sup>t</sup>* represents the water age at consumer node *c* and time step *t*, reported in hours. The binary variable *bc*,*<sup>t</sup>* represents if the water age at node *c* and time step *t* exceeds the limit, where *kc*,*<sup>t</sup>* = 1 if the water age is greater than the limit, and *kc*,*<sup>t</sup>* = 0 otherwise. The time step for calculating water quality is 15 min, and the total number of time steps (*TWA*) is 2880 for simulation of a 30-day month.
