Save hydrological observations! Return period estimation without data decimation

The concept of return period and its estimation are pivotal in risk management for many geophysical applications. Return period is usually estimated by inferring a probability distribution from an observed series of the random process of interest and then applying the classical equation, i.e. the inverse of the exceedance probability. Traditionally, we form a statistical sample by selecting, from the ”complete” time series (e.g. at the daily scale), those values that can reasonably be considered as realizations of independent extremes, e.g. annual maxima or peaks over a certain high threshold. Such a selection procedure entails that a large number of observations are discarded; this wastage of information could have important consequences in practical problems, where the reduction of the already small size of common hydrological records significantly affects the reliability of the estimates. Under such circumstances, it is crucial to exploit all the available information. To this end, we investigate the advantages of estimating the return period without any data decimation, by using the full data-set. The proposed procedure, denoted as Complete Time-series Analysis (CTA), exploits the property that the average interarrival time (i.e. return period) of potentially damaging events is not affected by the dependence structure of the underlying process, even for cyclo-stationary (e.g. seasonal) processes. For the sake of illustration, the CTA is compared to that based on annual maxima selection, through a simple non-parametric approach, discussing advantages and limitations of the method. Results suggest that the proposed CTA approach provides a more conservative return period estimation in an holistic implementation framework within a broader range of return period values than that pertaining to other methods, which means not only the largest extremes that are the focus of extreme value theory.