**3. Sample and Variables**

Chile is a long country whose extension is 4300 km. Hence, from a hydrometeorological point of view, Chile is a diverse country with significant precipitation variability throughout the country, increasing more than 500% from the North to the Austral region. Water runoff is also heterogeneous and varies from 510 m3/person/year to 2,300,000 m3/person/year. This diversity is expected to be accentuated by climate change, which will affect Chile in a complex fashion, with increased temperatures throughout the country and decreased precipitation in the Central and Southern areas of the country [21].

For empirical application, a sample of 146 Chilean DWTPs was used. All of the facilities were operated by private water companies, as the Chilean water industry was privatized between 1998 and 2004. The drinking water produced by all DWTPs must meet the quality standards of national norm NCh 409, which is based on the guidelines for drinking water quality published periodically by the World Health Organization (WHO) [22]. The quality of the drinking water supplied to citizens is monitored by water companies and the water regulation agency (Superintendencia de Servicios Sanitarios).

The energy consumed to treat raw water, expressed in kWh/year, was selected as the input; i.e., as the variable that DWTPs should minimize to improve energy performance. Following Molinos-Senante and Guzmán [10], the assessment of energy efficiency focused on DWTPs, without consideration of the energy used for groundwater pumping and raw water transport from the natural and artificial reservoirs to the DWTP.

In the assessment of water utility efficiency, the outputs selected should summarize the utilities' main function [23]. In this case study, the main function of DWTPs was considered to be the production of drinking water that met the NCh 409 quality standards. Moreover, the energy consumed by DWPTs (in kWh/year) depends not only on the volume of drinking water produced, but also on the pollutants removed, i.e., on the quality of the raw water and drinking water produced [12]. Hence, following the approach applied in previous studies [24,25] four quality-adjusted outputs (QAOs) were considered to assess DWTP energy efficiency, defined as follows:

$$QAO\_p = V \cdot \frac{(\mathbb{C}\_{pin} - \mathbb{C}\_{pcf})}{\mathbb{C}\_{pin}} \, ^\prime \tag{2}$$

where *V* is the volume of drinking water produced (in m3/year), *Cpin* is the concentration of pollutant *Cp* in the influent of the DWTP, and *Cpef* is the concentration of pollutant *Cp* in the effluent of the DWTP. Molinos-Senante and Sala-Garrido [7] defined energy intensity as the "energy consumed (kWh) per unit volume (m3) of drinking water produced". These authors developed energy intensity functions for DWTPs using parametric regression analysis to identify the main drivers of energy use in DWTPs. They concluded that energy intensity of DWTPs depended on the capacity of the facility and the removal efficiency of i) turbidity, ii) arsenic, iii) total dissolved solids, and iv) sulfates. Hence, these four pollutants were considered in this study as QAOs.

According to Sanders and Webber [26], the energy efficiency of a given water treatment technology correlates with the size, concentrations, and nature of the pollutants to be removed. Other factors, such as the water company operating the facility or the age of the DWTP, might also impact energy efficiency [9]. Based on previous studies [4,27], four variables were included as potential determinants of DWTP energy efficiency scores: i) DWTP age, ii) raw water source, iii) ownership of the company operating the DWTP, and iv) type of treatment.

Table 1 shows the main statistics for the variables (input, outputs, and factors underlying efficiency) used in this empirical application.


**Table 1.** Sample description. (Source: Water and Sewerage Management Reports by SISS).

SD: Standard Deviation; PF: Pressure filtration; RGF: Rapid gravity filtration.
