Evaluating the uncertainty and reliability of standardized indices

Standardized indices are widely used in the spatio-temporal monitoring of several hydrological variables. The estimation of these indices is affected by uncertainty which depends on the methods adopted for their quantification and on the characteristics (i.e., size and variability) of the available sample of observations. In this paper various uncertainty measures, applicable to any kind of standardized index, are proposed. These measures derive from bootstrap-based confidence intervals expressed in years of return period and are effective for assessing both the uncertainty and the reliability of the index estimate. In the illustrative case study the indices considered are the Standardized Precipitation Index and the Standardized Precipitation Evapotranspiration Index. Their time series have been quantified by both nonparametric and parametric approaches, using the weather data of a single station in central Italy. For the parametric approach, two possible types of distributions have been assumed for each index. The results are discussed in order to analyze the behavior of the proposed uncertainty measures in relation to: sample size, type of approach (parametric or nonparametric), time scale, type of standardized index, and type of anomaly (excess or deficit).