Detection Probability of Trends in Rare Events: Theory and Application to Heavy Precipitation in the Alpine Region

A statistical framework is presented for the assessment of climatological trends in the frequency of rare and extreme weather events. The methodology applies to long-term records of event counts and is based on the stochastic concept of binomial distributed counts. It embraces logistic regression for trend estimation and testing, and includes a quantification of the potential/limitation to discriminate a trend from the stochastic fluctuations in a record. This potential is expressed in terms of a detection probability, which is calculated from Monte Carlo–simulated surrogate records, and determined as a function of the record length, the magnitude of the trend and the average return period (i.e., the rarity) of events. Calculations of the detection probability for daily events reveal a strong sensitivity upon the rarity of events: in a 100-yr record of seasonal counts, a frequency change by a factor of 1.5 can be detected with a probability of 0.6 for events with an average return period of 30 days; however, this value drops to 0.2 for events with a return period of 100 days. For moderately rare events the detection probability decreases rapidly with shorter record length, but it does not significantly increase with longer record length when very rare events are considered. The results demonstrate the difficulty to determine trends of very rare events, underpin the need for long period data for trend analyses, and point toward a careful interpretation of statistically nonsignificant trend results. The statistical method is applied to examine seasonal trends of heavy daily precipitation at 113 rain gauge stations in the Alpine region of Switzerland (1901–94). For intense events (return period: 30 days) a statistically significant frequency increase was found in winter and autumn for a high number of stations. For strong precipitation events (return period larger than 100 days), trends are mostly statistically nonsignificant, which does not necessarily imply the absence of a trend.