Speaker
Description
Many real-world systems exhibit inherently nonlinear dynamics which can induce sudden, large and oftentimes irreversible changes when an external forcing parameter is varied. This phenomenon is known as tipping with Greenland Ice Sheet melting and the weakening of the Atlantic Meridional Overturning Circulation as prominent examples of climate tipping elements. We model these tipping phenomena via bifurcation theory and analyse these bifurcations in the realm of uncertainty [1]. In this talk, we will focus on parameter uncertainty. This arises naturally when model parameters need to be estimated from measurement data or cannot even be measured directly but need to be inferred from other observable quantities.
A natural question is how this parameter uncertainty propagates through the nonlinear dynamics and how it affects the bifurcation landscape, in particular the bifurcation curves. We use sensitivity analysis to tackle this question. In [2], the authors introduced a sensitivity analysis of uncertainty propagation for differential equations with random inputs subject to perturbations of the input measures. To build upon these results, we choose the Fréchet distance as a metric on the space of bifurcation curves. We transfer results from [2] to bifurcation theory. Thereby, we provide worst case estimates on the distance between bifurcation curves based on the distance of given model input parameter distributions contributing to a risk assessment of climate tipping phenomena.
[1] K. Lux, P. Ashwin, R. Wood, and C. Kuehn. Assessing the impact of parametric uncertainty on tipping points of the atlantic meridional overturning circulation. Environmental Research Letters, 17(7):075002, 2022.
[2] O. G. Ernst, A. Pichler, and B. Sprungk. Wasserstein Sensitivity of Risk and Uncertainty Propagation. SIAM/ASA Journal on Uncertainty Quantification, 10(3), 2022.
