Robust Method to Quantify the Risk of Shortage for Water Supply Systems

Conditions of shortage in a water supply system (WSS) occur when the available water resources are unable to satisfy the related demand (failure). The definition of risk of shortage conventionally relies on three indexes that capture the characteristics of possible failures in terms of probability of occurrence (reliability), duration (resiliency), and intensity (vulnerability). Although the conceptual bases for these definitions are largely acknowledged, the operative way to define them can largely affect the final value of the risk of shortage, making it difficult to compare among different WSSs when different formulations are applied. In this paper, a robust method to quantify the risk of shortage for WSSs that rely on surface water is proposed. The major novelties are to consider the extreme events in the risk analysis and to overcome the issue of the representativeness of the observed time series with respect to the characteristic return periods of drought events. To this aim, a stochastic approach based on a zero mean autoregressive (AR) model of standardized precipitation indexes (SPIs) is combined with a multilinear regressive model learning from observed SPI and associated inflow anomalies. This approach has been applied to the case study of the Ridracoli Reservoir in Central Italy, taking into account several climate scenarios, as well as several configurations of the WSS. Results show the ability of the proposed procedure to obtain convergence in the risk indexes and to distinguish among different levels of shortage risk, giving additional information for drought episodes with longer return periods. In particular, the standardized indexes focusing also on extreme events led to a quantification of the risk able to capture, at least in the proposed case study, the benefit of management options aiming to reduce the vulnerability (i.e., not fully meeting the demand in anticipation of a dry period), while those considering only the average features do not.