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Minisymposium at the XLIII Dynamics Days Europe
2023 (3-8 September 2023):
Nonautonomous dynamical systems in the climate sciences
Organizers:
Michael Ghil, Ecole Normale Supérieure, Paris, and
University of California at Los Angeles
Stefano Pierini, Parthenope University of Naples, Naples
Tamás Tél, Eötvös University, Budapest
Climate change is one of the greatest challenges of
our times. The problem is nonautonomous, since the forcing of the climate
system and some of its basic parameters change in time. Changes in
atmospheric concentration of greenhouse gases lead to a monotonic increase
in the radiation balance and hence to increasing globally averaged surface
temperatures. Furthermore, atmospheric and oceanic turbulence and many
other nonlinearities lead to complex and unpredictable behavior as well.
Overall, climate has therefore deterministically chaotic as well as random
features. In contrast to traditional chaos, the very high dimension of the
climate system renders a description of the ''climatic attractor'' and of
its predictability rather difficult.
Qualitatively, one can imagine
a multitude of possible instantaneous climatic states, a concept that helps
interpret the climate's ''internal variability'', whether chaotic or not.
Even if a single state is observed at a given time instant, many others are
also permitted due to the dynamics' chaotic nature. Individual states
are not predictable; the full plethora of permitted states, along with
their associated weights, is, however, predictable. In mathematical terms,
the climatic attractor is time dependent: it is a so-called snapshot or
pullback attractor, which possesses a unique natural measure at any instant
of time. This measure can, in principle, be determined with arbitrary
accuracy, and the averages and momenta taken with respect to it form the base
of probabilistic climate predictions.
A basic difference between
climate behavior and low-dimensional chaos is the presence of a wide range
of time and space scales. These arise from the nature of the different
subsystems - e.g., atmosphere, oceans and ice masses - and basic components
of the climate system, such as greenhouse gases and aerosols. In addition,
spatial patterns and strong spatio-temporal correlations giving rise to
so-called teleconnections are observed to evolve in time.
In this context, the aim of
this Minisymposium is to present the most recent developments in the
numerical simulation of nonautonomous and random dynamical systems, as
applied to the climate sciences, to show examples of the complex behavior
that arises in specific applications, and to describe basic mathematical
tools for their analysis.
Session 1: Extremes, tippings,
teleconnections (Tuesday September 5,
10:15-12:00)
Michael Ghil. Dynamical Systems Meet Algebraic Topology in the
Climate Sciences
Ulrike Feudel. Rate-induced Tipping in Predator-Prey Systems
Stefano Galatolo. Rare Events and Hitting Time Distribution for
Discrete Time Samplings of Stochastic Differential Equations
Juergen Kurths. Forcing of Teleconnections among Tipping Elements
in the Climate System
Camille Hankel. An Approach for Projecting the Timing of Abrupt
Winter Arctic Sea Ice Loss
Session 2: General nonautonomous aspects (Wednesday September 6, 15:15-17:00)
Mickaël D. Chekroun. Stochastically Augmented Realism and Stochastic
Smale's Horseshoes from Time Delay Systems
Dan Crisan. Asymptotic Behaviour of the Forecast-Assimilation
Process with Unstable Dynamics
Bernardo
Maraldi.
Changes in intraseasonal atmospheric variability under climate trends
Thierry Penduff. The OCCIPUT Ensemble Simulation: Describing the
Ocean Variability as an Atmospherically-Modulated Oceanic "Chaos"
Session 3: Pullback and snapshot approaches (Thursday September 7, 10:15-12:00)
Gábor Drótos. In
Search of the Definition of Climate as a Conditional Probability Measure
Stefano Pierini. The Pullback Attractors of an Excitable Low-Order
Ocean Model with Periodic, Aperiodic and Monotonically Drifting Forcing
Denisse
Sciamarella. A Templex for a Reduced-Dimension Ocean Model
Dániel Jánosi. Quantitative and Qualitative
Methods to Describe Chaos in Nonautonomous Systems As Models For Climate
Change
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