The traditional approach to extreme event analysis treats the occurrence of a flood, storm, or drought as a random variable described by a probability distribution fitted to historical observations. Design values for infrastructure are extrapolated from the tail of that distribution, often corresponding to magnitudes that have never actually been recorded. A 100-year event, for instance, is expected on average to occur once every 100 years, carrying an annual exceedance probability of 0.01. But as the authors emphasize, this framework rests on the natural variability of the climate and on assumptions of stationarity that are increasingly strained in a warming world, where hazards such as flooding, storms, and droughts are becoming more frequent and severe while urban exposure continues to grow.

The core of the new analysis is a simple but powerful reframing. In engineering, reliability is defined as the probability that a system remains in a satisfactory state over its lifetime. For a system designed around a T-year event over a lifespan of N years, the reliability is calculated as the probability that the design event never occurs during that period. The authors invert this familiar formula: instead of asking whether a structure will survive, they ask whether the T-year event itself is likely to appear in a dataset of observations or simulations spanning N years. The complement of the engineering reliability—the probability of observing the event of interest at least once—becomes a quantitative measure of confidence in the data itself.

Expressed as a function of the ratio between the return period T and the dataset length N, this observation probability converges, as the dataset grows large, to a Poisson distribution. The elegance of the Poisson approximation is that it is independent of the underlying distribution used to model the phenomenon, making it a broadly applicable yardstick. The authors caution, however, that the approximation breaks down for very small datasets, those shorter than roughly 30 years, and for return periods vastly exceeding the record length. Within its valid range, the metric delivers strikingly counterintuitive results that challenge how the rarity of extremes is commonly interpreted.

The most arresting finding concerns the case where the return period equals the length of the record. When N equals T, the probability of having observed the event of interest is always 0.63, regardless of the absolute magnitudes involved. The chance of seeing a 30-year event in 30 years of data is identical to the chance of seeing a 1000-year event in 1000 years of data. This invariance means that the extreme character of an event should be judged not in absolute terms but relative to the length of the observations or simulations used to derive it. A 100-year event estimated from 50 years of observations carries only about a 0.40 probability of having been captured in the record at all, and that figure drops to 0.26 when only 30 years of data are available—precisely the range of most instrumental records worldwide.

These numbers matter because recorded observations typically span only 30 to 50 years, meaning that inferences about 100-year or rarer events almost always lie outside the range of the data and depend heavily on the chosen statistical model. History shows how unprepared societies can be for events beyond their records: the 1953 storm surge flood in the Netherlands reshaped that country’s entire flood management system precisely because it exceeded what past experience had suggested was possible. The authors argue that preparedness must go beyond historical events, accepting that the past may not be a reliable guide to the future in a nonstationary climate, and that unexpected events are intrinsic to nonlinear, dynamic systems.

One promising response to the scarcity of observations is the use of large ensembles—many climate model simulations run under identical forcing conditions, each producing a different physically plausible realization of weather. Large ensembles allow researchers to sample internal climate variability far beyond what the observational record permits, and they have already demonstrated their value. Ensemble boosting techniques generated plausible storylines of a heatwave hotter than the unprecedented Pacific Northwest event of late June 2021, an event that was essentially unpredictable from observations alone. Conditional probability approaches have since shown promise in assigning return periods to such extreme simulated events, and studies using large ensembles have flagged high risks of unprecedented rainfall in the current climate.

Yet the authors issue a clear warning against overconfidence in these tools. Ensemble members are generated by climate models validated against observations, meaning their credibility derives from matching the statistical properties of the very records whose limitations the ensembles are meant to overcome. The apparent reduction in uncertainty comes simply from having more events to count, not necessarily from better estimates. Capturing internal variability in climate models is harder than capturing their response to external forcings, the computational demands of large ensembles are substantial, and validating their representativeness is not always feasible. Crucially, the reliability framework shows that the probability of simulating an event whose return period equals the dataset length remains 0.63 no matter how large the ensemble grows—more data does not dissolve this fundamental constraint.

The authors also dismantle the hope that large ensembles could eliminate statistical extrapolation altogether. Because the severity of an event is defined by its frequency of exceedance, some form of extrapolation—parametric or nonparametric—is unavoidable. Nonparametric plotting positions involve empirical interpolation whose results vary depending on the method chosen, while order statistics reveal that the return period of the single largest event in a dataset is formally undefined, tending to infinity. The link between event frequency and the definition of an extreme cannot be severed. Under nonstationarity, the classical formulas no longer hold because exceedance probabilities change from year to year; some researchers have proposed time-varying return periods, while others recommend abandoning return periods in favor of reliability-based design, fixing a desired reliability level within a project horizon and deriving design values numerically.

The broader message is one of calibrated humility. Return periods are often perceived as certain estimates, but attaching a reliability level to every inferred extreme would give decision-makers an honest measure of confidence and encourage critical use of available resources, whether observational or model-based. Large ensembles remain extremely valuable for compensating for limited observations, but they should be deployed with caution to avoid a false sense of security rooted in modeling assumptions and biases. As climate extremes intensify and exposure grows, the study suggests that the most dangerous illusion in disaster risk science may be the belief that our numbers about rare events are more solid than the data behind them.

Subject of Research: Reliability of estimated return periods for climate extremes based on observational and simulated dataset length

Article Title: On the Reliability of Estimated Return Periods for Climate Extremes

Article References: Ragno, E., & AghaKouchak, A. (2026). On the Reliability of Estimated Return Periods for Climate Extremes. International Journal of Disaster Risk Science. https://doi.org/10.1007/s13753-026-00764-4

Image Credits: AI Generated

DOI: 10.1007/s13753-026-00764-4

Keywords: return period, climate extremes, reliability, large ensembles, Poisson distribution, nonstationarity, risk assessment, statistical extrapolation, climate adaptation, disaster risk science, Estimated, Return