Abstracts
Mark Holland
Recurrence and hitting time laws for dynamical systems
For a time series of observations on a dynamical system, the statistics of extremes (maxima) are governed by the corresponding statistics of hitting and recurrence times to certain regions of the phase space. We consider the possible limit laws that arise, and the properties of the dynamical system that lead to such laws (or non-existence thereof). We also consider performance of statistical schemes used in the estimation of the limit law parameters. The theory will be illustrated using examples from low dimensional dynamical systems. This talk is based on joint work with I. del Amo, and G. Datseris.
Valerio Lucarini
Metastability Properties of the Earth's Climate: a Multiscale Viewpoint
The ultralow frequency variability of the Earth's climate features an interplay of typically long periods of stasis accompanied by critical transitions between qualitatively different regimes associated with metastable states. Such transitions have often been accompanied by massive and rapid changes in the biosphere. Multiple transitions between the coexisting warm and snowball climates occurred more than 500 Mya and eventually led to conditions favourable to the development of multicellular life. The coexistence of such states is due to the instability associated with the positive ice-albedo feedback, Yet, this behaviour repeats itself across a wide range of timescales, spatial domains, and physical processes. Building on Hasselmann's program, we propose here to interpret the time-evolution of the Earth system as a trajectory taking place in a dynamical landscape, whose multiscale features describe a hierarchy of metastable states and associated tipping points. We introduce the concept of climatic Melancholia states, saddle embedded in the boundary between the basins of attraction of the stable climates and explain under which conditions they act as gateways of noise-induced transitions. Using a hierarchy of numerical models, we discuss in detail the dichotomy between warm and snowball climate by bringing together the deterministic and stochastic viewpoint on the related global stability properties. We then discuss the paleoclimatically-relevant case where multiple competing climatic states are present and show the relevance of our angle for interpreting proxy data. Finally, if time allows, we will present some very recent results suggesting that our viewpoint might explain some intriguing aspects of the dynamical features of the tipping points of the Atlantic Meridional Overturning Circulation.
References
V. Lucarini and T. Bodai, Transitions across Melancholia States in a Climate Model: Reconciling the Deterministic and Stochastic Points of View, Phys. Rev. Lett. 122, 158701 (2019)
G. Margazoglou et al., Dynamical landscape and multistability of a climate model, Proc. R. Soc. A.477 210019 (2021)
D. D. Rousseau et al., A punctuated equilibrium analysis of the climate evolution of cenozoic exhibits a hierarchy of abrupt transitions. Sci Rep 13, 11290 (2023)
J. Lohmann et al., Multistability and Intermediate Tipping of the Atlantic Ocean Circulation, Sci. Advances 10 DOI: 10.1126/sciadv.adi4253 (2024)
Matt Patterson
Developing targeted climate storylines using a particle filter: application to abrupt AMOC declines
A severe weakening of the Atlantic Meridional Overturning Circulation (AMOC) with climate change would have catastrophic consequences for Europe and other regions. However, climate model simulations, dynamical systems analyses and paleoproxy records give conflicting answers on the likelihood of such an event. While no state-of-the-art climate models exhibit a collapse of the AMOC during the 21st century, they generally do show a weakening and there is concern that the AMOC in such models may be too stable.
In this study we seek to explore the role that internal variability might play in future AMOC declines, employing a particle filter method, sometimes referred to as a rare-event algorithm. I will present some preliminary analyses from applying this to an idealised coupled model, FORTE2.0 with the eventual goal of applying this method in a comprehensive GCM.
Paul Ritchie
The role of coupling in interacting tipping elements
Sudden and abrupt changes known as tipping points are of importance in many fields of science where nonlinear dynamics can lead to rapid changes relative to slow changes in an external forcing. These occur where inputs force the system past a critical threshold and self-perpetuating positive feedbacks that cause tipping. If an upstream system loses stability in this way, this may also cause a downstream system to tip. Here we study conditions on the coupling and timescales of the systems that lead to various types of tipping response.
Christian Rohrbeck
A clustering framework for conditional extremes models
Many devastating weather events are characterised by two or more weather variables being extreme at the same time. Conditional extreme value models describe the distribution of the components of a random vector conditional on one of them exceeding a suitably high threshold and they have proven useful in many applications. However, model estimates tend to be highly uncertain due to the natural scarcity of data on weather extremes. This motivates the development of clustering methods for this class of models; pooling similar within-cluster data drastically reduces parameter estimation uncertainty.
We consider a framework where multiple variables (e.g. precipitation and wind speed) are observed at several spatial sites, and interest lies in identifying groups of sites for which the variables exhibit a similar joint tail behaviour. In a first step, we define a dissimilarity measure for conditional extremes models which can be applied in arbitrary dimensions. Clustering is then performed by applying the k-medoids algorithm to our novel dissimilarity matrix, which collects the dissimilarity between all pairs of spatial sites. Performance of our framework is demonstrated using simulation studies and by applying it to precipitation and wind speed data from Ireland.
Reinhard Schiemann
The CANARI HadGEM3 Large Ensemble: Production and first applications
Emma Simpson
Spatial extremal modelling: A case study on the interplay between margins and dependence under non-stationarity
As with many statistical approaches, spatial analysis of extreme events often requires that we make simplifying assumptions when choosing a model. One of the most common such assumptions is temporal stationarity in the marginal and/or dependence features. If non-stationarity is detected in the marginal distributions, it is tempting to try to model this while assuming stationarity in the dependence, without necessarily putting the latter assumption through thorough testing. However, margins and dependence are often intricately connected and the detection of non-stationarity in one feature might affect the detection of non-stationarity in the other. We present a case study on this interrelationship, focusing on a dataset of sea surface temperatures from the Red Sea, which has well-documented marginal non-stationarity. Specifically, we compare four different marginal detrending approaches in terms of our post-detrending ability to detect temporal non-stationarity in the spatial extremal dependence structure. The key message is that different marginal detrending techniques can lead to very different conclusions about temporal (non-)stationarity in the dependence features, and care should be taken when performing this delicate task.
Kirstin Strokorb
Modelling of extreme excursions of stochastic processes in space and time: Foundations for a new tail process
Extreme excursions of stochastic processes in space and time often appear to be more localized the more extreme they are. While classical stochastic processes in extreme value theory cannot model this effect, we introduce an adapted version, where a suitable domain-scaling can be incorporated to accommodate this behaviour. Our theory is inspired by the triangular array convergence of maxima of Gaussian processes to a Brown–Resnick process and turns out to be natural in this context. We study key properties of the resulting tail process and demonstrate its ability to approximate conditional exceedance probabilities of a range of stochastic processes. Joint work with Marco Oesting and Raphael de Fondeville (based on the preprint https://publications.mfo.de/handle/mfo/4206).