Of Extreme Events and Climate Catastrophes
The Research Project
Extreme weather events, like devastating floods, hurricanes or wildfires, demand precise understanding and prediction of rare natural phenomena. The mathematical tools to tackle those challenges emerge from the field extreme value theory. As the events of interest, e.g. a 500-year flooding at a dike, may not have been observed so far, parametric models are applied to extrapolate beyond the limits of observation.
A key challenge within extreme value statistics is making efficient use of limited available data. The two major paradigms study either exceedances over a large threshold (‘Peaks over Threshold’ approach) or annual maximal events (‘Block Maxima’ method). By considering just annual maxima, the information of more than 99% of data is not leveraged while estimating the parameters of suitable models. In a first project, we therefore investigate the question of using more than just the largest value in each block, but more than one order statistic. In a proof-of-concept study, we demonstrate how to construct a suitable (maximum-likelihood) estimator based on blockwise Top-Two order statistics under the presence of temporal dependence. By naively applying the already available theory for independent data, we demonstrate that the resulting estimators will be inconsistent in general; but we discuss a procedure to re-establish its consistency. Our proposed estimator indeed shows favorable properties over the already existing estimators. These promising results open pathways
into generalizing the findings to exploiting the information from an arbitrary number of large order statistics.
The further projects are less theoretical and in closer collaboration with meteorologists and climate scientists. One aspect of this collaboration will contribute to the field of Extreme Event Attribution, asking the question, whether a particular extreme weather event has become more likely under the influence of climate change. We will try to combine evidence from observational data and climate models into a joint prediction, increasing confidence in climatologically relevant statements.
Related publications:
• Bücher, A., and Haufs, E. (2025). Extreme Value Analysis based on Blockwise Top-Two Order Statistics. arXiv preprint submitted to Bernoulli. arxiv.org/abs/2502.15036
What I need the IRB for
Extreme weather events are a global problem of increasing importance. Accordingly high is the demand for global collaboration between scientists from different fields. The IRB grant enables me to contribute to this scientific discourse. By visiting climatologists, I will learn first-hand about the needs and practical aspects of extreme weather attribution. With my mathematical background, I can contribute to the development and improvement of statistical tools. This interdisciplinary approach may arguably give rise to mathematical tools precisely tailored to climatological needs.
IRB funded activities
Extreme Value Analysis Conference (21–28 June 2025)
My first IRB-funded activity was the participation in the Extreme Value Analysis (EVA) Conference 2025 in Chapel Hill, North Carolina (21–28 June 2025). The EVA is the leading international conference in the field of extreme value statistics, bringing together renowned researchers from all over the world. Prior to the main conference, I attended a one-day workshop on Statistical Modeling of Extremes and Statistical Learning and Extreme Value Analysis, which provided an excellent overview of recent theoretical and methodological advancements. During the conference week, I had the opportunity to connect with many experts in extreme value analysis and to follow a broad range of stimulating talks. I contributed with a presentation in the session Recent Advances on Stationary and Nonstationary Time Series, where I presented results from our paper Extreme Value Analysis based on Blockwise Top-Two Order Statistics. In addition, I took part in the conference Data Challenge together with my colleague Dr. Alexis Boulin (RUB). Our approach is currently being written up as
a working paper, titled Extrapolating into the Extremes with Minimum Distance Estimation. These contributions allowed me to receive valuable feedback and foster new collaborations.
Research Visits in Canada
University of Toronto
Immediately after EVA 2025, I spent five weeks at the Department of Statistical Sciences, University of Toronto. Under the supervision of Prof. Stanislav Volgushev, we initiated a research project extending the idea of blockwise top-two order statistics to a higher-dimensional setting. Our goal was to explore how to jointly estimate the dependence structure of extreme events occurring at multiple locations, making use of more than just blockwise maxima. The stay provided the perfect environment for developing these ideas and exchanging with leading scholars.
Université du Québec à Montréal
The project was continued during a four-week research stay at the Faculty of Mathematics, Université du Québec à Montréal. Together with Michael Lalancette, I worked on laying the theoretical foundations for a suitable estimator of extremal dependence based on blockwise top-two order statistics. This collaboration will be pursued further from Bochum through remote exchange.
Beyond the scientific progress, the IRB funding was crucial in enabling these research stays and in fostering long-term collaborations and personal contacts. Spending ten weeks in North America was also a highly enriching personal experience: it allowed me to engage with different research cultures and gain valuable international exposure.