**Giuseppe Del Giudice 1, Cristiana Di Cristo <sup>1</sup> and Roberta Padulano 2,\***


Received: 28 May 2020; Accepted: 14 July 2020; Published: 16 July 2020

**Abstract:** A methodological framework for the estimation of the expected value of hourly peak water demand factor and its dependence on the spatial aggregation level is presented. The proposed methodology is based on the analysis of volumetric water meter measurements with a 1-h time aggregation, preferred by water companies for monitoring purposes. Using a peculiar sampling design, both a theoretical and an empirical estimation of the expected value of the peak factor and of the related standard error (confidence bands) are obtained as a function of the number of aggregated households (or equivalently of the number of users). The proposed methodology accounts for the cross-correlation among consumption time series describing local water demand behaviours. The effects of considering a finite population is also discussed. The framework is tested on a pilot District Metering Area with more than 1000 households equipped with a telemetry system with 1-h time aggregation. Results show that the peak factor can be expressed as a power function tending to an asymptotic value greater than one for the increasing number of aggregated households. The obtained peak values, compared with several literature studies, provide useful indications for the design and management of secondary branched pipes of water distribution systems.

**Keywords:** cross-correlation; data spatial aggregation; finite population effect; metering; sample mean; sampling design; standard error; stochastic analysis; water demand peak factor; water distribution networks
