Related papers: A topological perspective on weather regimes

Topological data analysis is a powerful framework for extracting useful topological information from complex datasets. Recent work has shown its application for the dynamical analysis of classical dissipative systems through a…

There is growing evidence that the atmospheric dynamics of the Euro-Atlantic sector during winter is driven in part by the presence of quasi-persistent regimes. However, general circulation models typically struggle to simulate these, with…

We characterize the geometrical and topological aspects of a dynamical system by associating a geometric phase with a phase space trajectory. Using the example of a nonlinear driven damped oscillator, we show that this phase is resilient to…

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…

Irreversible processes play a major role in the description and prediction of atmospheric dynamics. In this paper, we present a variational derivation of the evolution equations for a moist atmosphere with rain process and subject to the…

Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of networks flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and…

We write a nonlinear model that predicts the climate (temperature and humidity) on the surface of a small region on Earth, perform numerical investigations using the model, and compare the results to real climate on a variety of regions on…

In meteorology the analysis of motions of the atmosphere on the Earth has been done using various mathematical models and using various approximations. In this article as the simplest model the compressible Euler equations with barotropic…

Remote observing of exoplanetary atmospheres is now possible, offering us access to circulation regimes unlike any of the familiar Solar System cases. Atmospheric circulation models are being developed to study these new regimes but model…

Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…

The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…

Terrestrial planets in the Habitable Zone of Sun-like stars are priority targets for detection and observation by the next generation of space telescopes. Earth's long-term habitability may have been tied to the geological carbon cycle, a…

Time series are ubiquitous in our data rich world. In what follows I will describe how ideas from dynamical systems and topological data analysis can be combined to gain insights from time-varying data. We will see several applications to…

Relatively long-period nonsynchronized planets---such as warm Jupiters---potentially retain the primordial rotation, eccentricity, and obliquity that might encapsulate information on planetary climate and formation processes. To date, there…

Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…

We propose a topological framework for the detection of Hopf bifurcations directly from time series, based on persistent homology applied to phase space reconstructions via Takens embedding within the framework of Topological Data Analysis.…

Unstable Periodic Orbits (UPOs) were used to identify regimes, and transitions between regimes, in a reduced-order coupled atmosphere-land spectral model. In this paper we describe how the chaotic attractor of this model was clustered using…

We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been…

Atmospheric flows, an example of turbulent fluid flows, exhibit fractal fluctuations of all space-time scales ranging from turbulence scale of mm -sec to climate scales of thousands of kilometers - years and may be visualized as a nested…

We use a simple yet Earth-like atmospheric model to propose a new framework for understanding the mathematics of blocking events. Analysing error growth rates along a very long model trajectory, we show that blockings are associated with…