Relationship between selected percentiles and return periods of extreme events

This paper investigates the relationship between selected percentiles, return periods and the concepts of rare and extreme events in climate and hydrological series, considering both regular and irregular datasets, and discusses the IPCC and WMO indications. IPCC (Annex II: Glossary. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. IPCC, Geneva, 2014) establishes that an extreme event should be rare and exceed selected upper and lower thresholds (10th and 90th percentiles); WMO (Guidelines on the definition and monitoring of extreme weather and climate events--TT-DEWCE WMO 4/14/2016. World Meteorological Organization, Geneva, 2016) suggests thresholds near the ends of the range, but leaves them undetermined. The concept of "rare" relates the extreme events to the time domain and is typically expressed in terms of return period (RP). The key is to find the combination between "rare", percentile and return period. In particular, two crucial items are analysed: (1) how the return period may vary in response to the choice of the threshold, in particular when it is expressed in terms of percentiles; (2) how the choice of producing a regular or irregular dataset may affect the yearly frequency and the related return periods. Some weather variables (e.g. temperature) are regular and recorded at fixed time intervals, while other phenomena (e.g. tornadoes) occur at times. Precipitation may be considered either regular, all-days being characterized by a precipitation amount from 0 (no precipitation) to the top of the range, or irregular (rainy-days only) considering a precipitation day over a selected instrumental or percentile threshold. These two modes of interpreting precipitation include a different number of events per year (365 or less) and generate different return periods. Any Every climatic information may be affected by this definition. The 90th percentile applied to observations with daily frequency produces 10-day return period and the percentiles necessary to get 1 year, 10 years or other return periods are calculated. The general case of events with selected or variable frequencies, and selected percentiles, is also considered with an example of a precipitation series, two-century long.