The research, conducted by Muhammad Aslam Mohd Safari and Tosiyuki Nakaegawa, analyzed daily rainfall records from 51 synoptic weather stations spanning the Japanese archipelago from 1901 to 2020. Rather than simply pulling out the single wettest day of each year, as many traditional analyses do, the team employed a peaks-over-threshold framework, a cornerstone of modern extreme value theory. In this approach, every day on which rainfall exceeds a carefully chosen high threshold counts as an extreme event, which means the method extracts far more information from the historical record than annual maximum sampling alone. The trade-off is complexity: extreme events often arrive in clusters, as when a stalled rain band lingers over the same region for days, and treating those clustered days as independent observations can badly distort the statistics.

That clustering problem is precisely where the new study makes its most distinctive contribution. The researchers applied a dependence-adjusted framework in which the degree of temporal dependence in the extremes, summarized by a quantity known as the extremal index, guided how events were declustered at each station. Depending on what the data demanded, they either left the record unblocked or grouped consecutive days into blocks of five, seven, or nine days, retaining only the peak within each block. This station-specific strategy reduces the artificial inflation of event counts that arises when a single multi-day storm contributes multiple threshold exceedances, while avoiding the over-smoothing that aggressive declustering can introduce. The extremal index estimates, derived from established methods for inference on clusters of extreme values, effectively let each station tell the analysts how much independence its extremes actually possess.

Choosing the threshold itself is one of the most delicate steps in any peaks-over-threshold analysis. Set it too low, and the theoretical model that justifies the analysis breaks down because moderate, non-extreme rainfall contaminates the sample. Set it too high, and so few events remain that uncertainty explodes. The study combined three complementary diagnostics to navigate this dilemma: mean residual life plots, which look for the range where average excess rainfall becomes approximately linear in the threshold; shape-parameter stability plots, which identify thresholds where the estimated tail behavior stops drifting; and return-level stability checks, which confirm that the headline quantities of interest hold steady across plausible threshold choices. This triangulated approach, drawing on a substantial methodological literature on threshold selection for extreme values, was applied independently at every one of the 51 stations.

Once thresholds were fixed and events declustered, the team fitted generalized Pareto distributions, the mathematical workhorse for modeling exceedances over high thresholds, whose tail shape parameter determines whether extremes are bounded, exponentially decaying, or heavy-tailed. Crucially, the researchers did not commit to a single fitting method. They compared maximum likelihood estimation, the standard approach that performs well with ample data, against estimation via L-moments, a robust technique based on linear combinations of order statistics that is often more stable when samples are small or outliers are influential. They also tested a simpler exponential alternative, which assumes a lighter tail. Model performance was then judged honestly: the record was split so that 80 percent of the data trained the models and the held-out 20 percent tested them, and the winning model varied from station to station. The lesson, the authors argue, is that no one-size-fits-all model exists for Japanese rainfall extremes, and station-by-station validation should become standard practice.

Before trusting any of these fits, the team also interrogated the assumption of stationarity, the idea that the statistical behavior of extremes has not changed over the 120-year record. They examined trends in both the annual frequency of threshold exceedances and the magnitude of the largest events. This matters because a warming climate is expected to intensify heavy precipitation, and several prior studies using large-ensemble regional climate simulations have projected robust increases in extreme rainfall over Japan under future warming scenarios. If the historical record itself shows drift, the classical extreme value models would need modification. The study found that while the stationarity assumption was broadly workable, it warrants caution at some locations, a caveat the authors flag explicitly alongside residual dependence detected at eight stations where the declustering did not fully eliminate serial correlation.

The headline outputs of the analysis are return levels: the rainfall magnitudes expected to be exceeded once every 5, 10, 50, 100, or 200 years on average, each accompanied by a 95 percent confidence interval. These numbers are the currency of infrastructure design and hazard zoning, and the study’s maps of them reveal a striking geographic pattern. The highest return levels concentrate in Kyushu and the Okinawa-Amami region in the country’s southwest, where tropical cyclones and the seasonal rain front deliver some of the heaviest daily totals on record. Yet the pattern is far from smooth. In one of the study’s most vivid illustrations of local contrast, the 100-year return level at Kochi, on the island of Shikoku, came out at roughly twice the corresponding value at Matsuyama, a station not far to the northwest. Such sharp gradients underscore how topography, proximity to moisture sources, and storm tracks conspire to make rainfall hazard an intensely local phenomenon.

How do these estimates stack up against official figures? The researchers compared their results with probable precipitation estimates published by the Japan Meteorological Agency and with values reported in earlier studies. The comparison showed broad spatial agreement, which is reassuring for the coherence of the underlying data and methods, but also revealed station-specific discrepancies. Some of those differences are expected, since the agency’s procedures and the study’s dependence-adjusted, station-specific modeling differ in sampling and fitting choices. The authors present the comparison not as a verdict on either approach but as evidence that return-level estimation carries genuine methodological sensitivity, and that consumers of these numbers should always look at the accompanying uncertainty rather than treating a single figure as gospel.

Indeed, uncertainty is a central character in this story. The confidence intervals around return levels widen substantially as the return period lengthens, which is an inherent feature of extreme value statistics: the further one extrapolates beyond the observed record, the less the data can constrain the answer. A 200-year return level estimated from 120 years of data rests on the tail behavior of the fitted distribution in a region where observations are sparse by definition. By reporting intervals alongside point estimates at every station, the study gives planners a defensible range rather than a false promise of precision. That honesty is particularly valuable in a country where the 2018 and 2020 disasters demonstrated, in human terms, exactly what the upper tail of the rainfall distribution can do.

The practical payoff of this work lies in its consistency and its caution. By applying a single, transparent, dependence-aware protocol across 51 stations and 120 years, the study delivers a common yardstick for rainfall hazard that regional authorities can use to compare risk across the archipelago, while the station-specific modeling respects the reality that Kochi and Matsuyama, or Kyushu and Hokkaido, are not interchangeable. The authors position the results as a historical baseline for region-specific rainfall-hazard planning, a foundation against which future projections from climate models can be anchored. As warming continues to load the dice toward heavier downpours, knowing precisely where the historical extremes are worst, and how uncertain those estimates remain, is a quiet but consequential advance in the science of staying dry when the sky does its worst.

Subject of Research: Statistical modeling of extreme daily precipitation extremes in Japan using dependence-adjusted peaks-over-threshold methods

Article Title: Dependence-Adjusted Peaks over Threshold Modeling of Extreme Daily Precipitation in Japan

Article References: Safari, M. A. M., & Nakaegawa, T. (2026). Dependence-Adjusted Peaks over Threshold Modeling of Extreme Daily Precipitation in Japan. Water Resources Management, 40(13), Article 532. https://doi.org/10.1007/s11269-026-04897-5

Image Credits: AI Generated

DOI: 10.1007/s11269-026-04897-5

Keywords: extreme precipitation, peaks over threshold, generalized Pareto distribution, extremal dependence, return levels, Japan, flood risk, threshold selection, L-moments, climate extremes, Water Resources Management, rainfall hazard