Richard M. Vogel | Heavy Tails are a Canary in the Coalmine
The prevalence of heavy tailed (HT) populations in hydrology is becoming increasingly commonplace due in part to the increasing need and use of high frequency and high-resolution data.?? In addition to the impact of HT on extremes, HT populations can have a profound impact on a wide range of other hydrologic statistics and methods associated with planning,?management and design for?extremes. ??We review the known impacts of HT populations on the instability and bias in a wide range of commonly used hydrologic statistics. Experiments reveal that HT distributions result in the degradation of many commonly used statistical methods including the bootstrap, probability plots, the central limit theorem, and the law of large numbers.?? ??We document the gross instability of perhaps the best-behaved statistic of all, the sample mean (SM) when computed from HT distributions.? The SM is ubiquitous because it is a component of and related to a myriad of statistical methods, thus its unstable behavior provides a window into future challenges faced by the hydrologic community.? We outline many challenges associated with HT data, for example, upper product moments are often infinite for HT populations, yet upper L-moment always exist, so that the theory of L-moments is uniquely suited to HT distributions and data.? We introduce a magnification factor for evaluating the impact of HT distributions on the behavior of extreme quantiles.
Francesco Marra | Estimating the probability of extreme precipitation with non-asymptotic statistics
The exceedance probability of extreme daily precipitation is usually quantified assuming asymptotic behaviours. Non-asymptotic statistics, however, would allow us to describe extremes with reduced uncertainty and to establish relations between physical processes and emerging extremes. These approaches are still mistrusted by part of the community as they rely on assumptions on the tail behaviour of the daily precipitation distribution. This paper addresses this gap. We use global quality-controlled long rain gauge records to show that daily precipitation annual maxima are samples likely emerging from Weibull tails in most of the stations worldwide. These non-asymptotic tails can explain the statistics of observed extremes better than asymptotic approximations from extreme value theory. We call for a renewed consideration of non-asymptotic statistics for the description of extremes.
Professor Richard M. Vogel is Professor Emeritus and Research Professor in the Department of Civil and Environmental Engineering in the Faculty at Tufts University. He is the former director of the interdisciplinary graduate program in Water: Systems, Science and Society. Professor Vogel’s research experience has covered a broad range of topics relating to hydrology, water resource engineering, natural hazards and environmental statistics. Most of his research involves the application of statistical and systems approaches to the solution of applied problems in the field of hydrology and water resources engineering. He has advanced the practice and science of hydrology and water resource planning and management by providing statistical foundations for solving problems relating to a range of problems relating to: reservoir operations, water supply, floods, droughts, water quality, watershed modeling, watershed management and environmental statistics. He has also extended and transferred basic innovations in the field of hydrology and water resource engineering to advance the state of practice for the frequency analysis of a range of related natural hazards including earthquakes, landslides, winds, sea levels as well as bird and plant extinctions. In 2020, he was elected Distinguished Member of American Society of Civil Engineers “for a lifetime of fundamental contributions to stochastic hydrology and its novel applications” and he received the Ven Te Chow Award from ASCE Environmental and Water Resources Institute for “his extensive contributions in the fields of probabilistic and stochastic methods in hydrology, environmental engineering and water resources.”
Francesco Marra is an Assistant Professor at the Department of Geosciences in the University of Padova and an Associate Researcher at the Institute of Atmospheric Sciences and Climate of the Italian National Research Council. His scientific interests span atmospheric sciences, climate change, hydrology, and geomorphology, with a particular focus on hydro-meteorological extremes and related hazards. He has authored 59 papers in top-ranked journals, 5 book chapters, and has made over 130 contributions to international conferences. Francesco received the Lady Davis Postdoctoral Fellowship and is an Associate Editor of the Journal of Hydrology and Guest Editor of Natural Hazards and Earth System Sciences. Before his current positions, Francesco worked as a researcher at the Institute of Atmospheric Sciences and Climate, National Research Council, Italy, and held various post-doctoral positions at the Hebrew University of Jerusalem, Israel.