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.