Jana Ulrich EVA Talk Preview
From Anna Munro on May 19th, 2021
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Name: Jana Ulrich
Talk Title: Modeling seasonal variations of extreme rainfall on different time scales in Germany
Abstract: co-authors: Felix S. Fauer, Henning W. Rust. To estimate the properties of extreme precipitation events on different time scales, intensity-duration-frequency (IDF) curves are a well-known tool in hydrology. The idea of implementing the dependence of precipitation intensity on duration directly into the parameters of an extreme value distribution was proposed by Koutsoyiannis et al. (1998). Following this, we use a duration-dependent generalized extreme value distribution (d-GEV) in the framework of the block maxima approach.
When modeling precipitation extremes, this approach is typically used with an annual block size. Although large amounts of data are lost this way, choosing a smaller block size requires a more complex model that accounts for intra-annual variations. Yet, at least for planning or adaptation of hydrological structures, these variations are mostly not even relevant.
Nevertheless, it has been shown that within the block maxima approach monthly block sizes can be sufficient to model extreme precipitation in the mid-latitudes [e.g., Rust et al. 2009]. Likewise, several studies have demonstrated that it is possible to model the intra-annual variations using smooth periodic functions as covariates for the parameters of the GEV [e.g., Coles 2001, Rust et al. 2009, Fischer et al. 2019]. In addition, information on the occurrence probabilities in different months may well be needed by stakeholders in, for example, agriculture or water storage.
However, monthly block sizes have not yet been considered for modeling the IDF relationship. Still, particularly for this application, the use of monthly maxima may be relevant, because extreme precipitation events related to different time scales typically occur in different seasons due to different mechanisms causing them. In Germany, convective extreme events with a duration of minutes to a few hours occur almost exclusively in the summer months, while long-lasting extreme events are scattered throughout the year or even occur more frequently in autumn and winter months, depending on the location.
In this study, we model monthly precipitation maxima at different stations in Germany for a wide range of durations from one minute to 5 days using a d-GEV with seasonally varying parameters. On the one hand, this allows us to compare the characteristics of the IDF curves of different months: Since in summer months the curves are steeper and have higher intensities for short durations than in the rest of the year, at some stations the curves (for a given quantile) for different months cross. The meteorological interpretation of this crossing is that the season at which a certain extreme event is most likely to occur shifts for longer durations (usually towards autumn or winter). On the other hand, we can also investigate the influence of intra-annual variations on the distribution of annual maxima of different durations: We find that the annual IDF curves that result from modeling monthly maxima diverge from the assumtion of scale invariance, causing a flattening in the slope of the IDF curves for long durations.
Coles, S. An Introduction to Statistical Modeling of Extreme Values; Springer: New York, NY, USA, 2001.
Fischer, M.; Rust, H.; Ulbrich, U. A spatial and seasonal climatology of extreme precipitation return-levels: A case study. Spat. Stat. 2019, 34.
Koutsoyiannis, D.; Kozonis, D.; Manetas, A. A mathematical framework for studying rainfall Intensity-Duration-Frequency relationships. J. Hydrol. 1998, 206, 118–135.
Rust, H.; Maraun, D.; Osborn, T. Modelling seasonality in extreme precipitation. Eur. Phys. J. Spec. Top. 174, 99–111 (2009).
This talk is a contributed talk at EVA 2021. View the programme here.