Lagrangian study of the final warming in the southern stratosphere during 2002: Part I. The vortex splitting at upper levels

Abstract

The present two-part paper provides a Lagrangian perspective of the final southern warming in 2002, during which the stratospheric polar vortex (SPV) experienced a unique splitting. Part I focuses on the understanding of fundamental processes for filamentation and ultimately for vortex splitting on a selected isentropic surface in the middle stratosphere. Part II discusses the three-dimensional evolution of the selected sudden warming event. We approach the subject from a dynamical systems viewpoint and search for Lagrangian coherent structures using a Lagrangian descriptor as a tool. In this Part I we work in the idealized framework of a kinematic model that allows for an understanding of the contributing elements of the flow in late September during the splitting. We introduce a definition of kinematic SPV boundary based on a criterion for binning parcels inside and outside the vortex according to their values of the Lagrangian descriptor and associated PDF. This definition is justified by using arguments that go beyond heuristic considerations based on the potential vorticity. Next, we turn to the filamentation proceses along this kinematic boundary, and the role of Lagrangian structures in the SPV splitting. We determine a criterion for splitting based on the structure of the evolving unstable and unstable manifolds.

Lagrangian Analysis of the Northern Stratospheric Polar Vortex Split in April 2020

“…Of primary importance to our study is that M provides a visualization of the (kinematic) vortex boundary that is helpful in transport studies. Curbelo et al (2019b) employed arguments of ergodic theory to conjecture that, on either a horizontal or an isentropic surface, a region where the values of M computed with sufficiently large τ has values that are very close to their maximum on the surface (M max ) would, (i) materially divide the Stratospheric Polar Vortex (SPV) core from its surroundings, and (ii) be free of hyperbolic trajectories and hence tend to not produce filaments during a certain time interval. In a nutshell, such regions represent kinematic barriers of the flow.…”

“…In a nutshell, such regions represent kinematic barriers of the flow. Based on results from numerical experiments Curbelo et al (2019b) suggested that on an isentropic surface in the stratosphere the threshold for M can be taken as the lower limit of the fat tail in its probability density function (PDF), which is approximately 0.93 M max . In the present paper, therefore, we define the kinematic vortex boundary at an isentropic level as the region bounded by the contour where M = 0.93M max .…”

Lagrangian transport across the upper Arctic waters in the Canada Basin

“…Recent work in the context of the stratospheric polar vortex (SPV) by (Curbelo et al ), who present similar jet‐like features as those under discussion, has introduced a heuristic procedure for determining from the M function the boundaries of the SPV, which act as limits for the jet barrier, and has linked these results to ergodic partition theory (Mezić and Wiggins, ; Lopesino et al ). (Curbelo et al ) have applied this methodology to determine the boundaries of the SPV on the ERA‐Interim reanalysis.…”

Transport pathways across the West African Monsoon as revealed by Lagrangian Coherent Structures

“…In particular, the “singular features” just discussed are related to dynamical structures linked to highly contracting or expanding regions (connected to mathematical objects called hyperbolic trajectories), while regions with smooth patterns are linked to non-dispersive regions (connected to mathematical objects called tori) that hold matter together. This two-fold capacity has been exploited in the stratospheric polar vortex context in 52 , 53 . In contrast, other approaches based on tools such as Finite Time Lyapunov Exponents (FTLE), also used in 3D stratospheric studies 65 , highlight only structures related to highly contracting or expanding regions.…”

“…The methodology used in this study focuses on a Lagrangian method based on the Lagrangian descriptor (LD) known as the M function 54 – 56 . This function has been used to visualise the three-dimensional Lagrangian structures in idealised 3D flows 51 , 56 , 57 and also in atmospheric flows, in the stratospheric polar vortex above Antarctica 49 , 52 , 53 . More recently in the context of the Transition State Theory in Chemistry, LDs have been successfully used to picture phase space structures in high dimensional dynamical systems 58 – 60 .…”