Minimal dynamical systems model of the Northern Hemisphere jet stream via embedding of climate data

We derive a minimal dynamical systems model for the Northern Hemisphere midlatitude jet dynamics by embedding atmospheric data and by investigating its properties (bifurcation structure, stability, local dimensions) for different atmospheric flow regimes. The derivation is a three-step process: first, we obtain a 1-D description of the midlatitude jet stream by computing the position of the jet at each longitude using ERA-Interim. Next, we use the embedding procedure to derive a map of the local jet position dynamics. Finally, we introduce the coupling and stochastic effects deriving from both atmospheric turbulence and topographic disturbances to the jet. We then analyze the dynamical properties of the model in different regimes: one that gives the closest representation of the properties extracted from real data; one featuring a stronger jet (strong coupling); one featuring a weaker jet (weak coupling); and one with modified topography. Our model, notwithstanding its simplicity, provides an instructive description of the dynamical properties of the atmospheric jet.

Minimal dynamical systems model of the northern hemisphere jet stream via embedding of climate data

We derive a minimal dynamical model for the northern hemisphere mid-latitude jet dynamics by embedding atmospheric data, and investigate its properties (bifurcation structure, stability, local dimensions) for different atmospheric flow regimes. We derive our model according to the following steps: i) obtain a 1-D description of the mid-latitude jet-stream by computing the position of the jet at each longitude using the ERA-Interim reanalysis, ii) use the embedding procedure to derive a map of the local jet position dynamics, iii) introduce the coupling and stochastic effects deriving from both atmospheric turbulence and topographic disturbances to the jet. We then analyze the dynamical properties of the model in different regimes: i) one that gives the closest representation of the properties extracted from real data, ii) one featuring a stronger jet (strong coupling), iii) one featuring a weaker jet (low coupling), iv) modified topography. We argue that such a simple model provides a useful description of the dynamical properties of the atmospheric jet.

Crossed products and minimal dynamical systems

Let [Formula: see text] be an infinite compact metric space with finite covering dimension and let [Formula: see text] be two minimal homeomorphisms. We prove that the crossed product [Formula: see text]-algebras [Formula: see text] and [Formula: see text] are isomorphic if and only if they have isomorphic Elliott invariant. In a more general setting, we show that if [Formula: see text] is an infinite compact metric space and if [Formula: see text] is a minimal homeomorphism such that [Formula: see text] has mean dimension zero, then the tensor product of the crossed product with a UHF-algebra of infinite type has generalized tracial rank at most one. This implies that the crossed product is in a classifiable class of amenable simple [Formula: see text]-algebras.