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

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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 processes 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.

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References

  • Allen DR, Bevilacqua RM, Nedoluha GE, Randall CE, Manney GL (2003) Unusual stratospheric transport and mixing during the 2002 antarctic winter. Geophys Res Lett 30(12), 1599

    Article  Google Scholar 

  • Bowman KP (1990) Evolution of the total ozone field during the breakdown of the antarctic circumpolar vortex. J Geophys Res Atmos 95(D10):16529–16543

    Article  Google Scholar 

  • Bowman KP (1993) Large-scale isentropic mixing properties of the antarctic polar vortex from analyzed winds. J Geophys Res Atmos 98(D12):23013–23027

    Article  Google Scholar 

  • Charlton AJ, O’Neill A, Lahoz WA, Berrisford P (2005) The splitting of the stratospheric polar vortex in the southern hemisphere, september 2002: dynamical evolution. J Atmos Sci 66:590–602

    Article  Google Scholar 

  • Curbelo J, García-Garrido VJ, Mechoso CR, Mancho AM, Wiggins S, Niang C (2017) Insights into the three-dimensional Lagrangian geometry of the Antarctic polar vortex. Nonlinear Process Geophys 24(3):379–392

    Article  Google Scholar 

  • Dahlberg SP, Bowman KP (1994) Climatology of large-scale isentropic mixing in the Arctic winter stratosphere from analyzed winds. J Geophys Res Atmos 99(D10):20585–20599

    Article  Google Scholar 

  • de la Cámara A, Mancho AM, Ide K, Serrano E, Mechoso C (2012) Routes of transport across the Antarctic polar vortex in the southern spring. J Atmos Sci 69(2):753–767

    Article  Google Scholar 

  • de la Cámara A, Mechoso R, Mancho AM, Serrano E, Ide K (2013) Isentropic transport within the Antarctic polar night vortex: Rossby wave breaking evidence and Lagrangian structures. J Atmos Sci 70:2982–3001

    Article  Google Scholar 

  • Esler JG, Scott RK (2005) Excitation of transient Rossby waves on the stratospheric polar vortex and the barotropic sudden warming. Phys Rev E 62:3661–3681

    Google Scholar 

  • Fairlie TDA, O’Neill A (1988) The stratospheric major warming of winter 1984/85: observations and dynamical inferences. Q J R Meteorol Soc 114(481):557–577

    Article  Google Scholar 

  • García-Garrido VJ, Curbelo J, Mechoso CR, Mancho AM, Wiggins S (2017) A simple kinematic model for the Lagrangian description of relevant nonlinear processes in the stratospheric polar vortex. Nonlinear Process Geophys 24(2):265–278

    Article  Google Scholar 

  • Guha A, Mechoso CR, Konor CS, Heikes RP (2016) Modeling Rossby wave breaking in the southern spring stratosphere. J Atmos Sci 73(1):393–406

    Article  Google Scholar 

  • Haller G (2002) Lagrangian coherent structures from approximate velocity data. Phys Fluids 14:1851–1861

    Article  Google Scholar 

  • Juckes MN, McIntyre ME (1987) A high-resolution one-layer model of breaking planetary waves in the stratosphere. Nature 328:590–596

    Article  Google Scholar 

  • Konopka P, Grooß JU, Hoppel KW, Steinhorst HM, Müller R (2005) Mixing and chemical ozone loss during and after the Antarctic polar vortex major warming in September 2002. J Atmos Sci 62(3):848–859

    Article  Google Scholar 

  • Lopesino C, Balibrea-Iniesta F, García-Garrido VJ, Wiggins S, Mancho AM (2017) A theoretical framework for Lagrangian descriptors. Int J Bifurc Chaos 27(01):1730001

    Article  Google Scholar 

  • Madrid JAJ, Mancho AM (2009) Distinguished trajectories in time dependent vector fields. Chaos 19(013):111

    Google Scholar 

  • Mancho AM, Small D, Wiggins S (2006) A tutorial on dynamical systems concepts applied to Lagrangian transport in oceanic flows defined as finite time data sets: theoretical and computational issues. Phys Rep 237(3–4):55–124

    Article  Google Scholar 

  • Mancho AM, Wiggins S, Curbelo J, Mendoza C (2013) Lagrangian descriptors: a method for revealing phase space structures of general time dependent dynamical systems. Commun Nonlinear Sci Numer Simul 18(12):3530–3557

    Article  Google Scholar 

  • Manney GL, Lawrence ZD (2016) The major stratospheric final warming in 2016: dispersal of vortex air and termination of Arctic chemical ozone loss. Atmos Chem Phys Discuss 2016:1–40

    Article  Google Scholar 

  • Manney GL, Farrara JD, Mechoso CR (1991) The behavior of wave 2 in the southern hemisphere stratosphere during late winter and early spring. J Atmos Sci 48:976–998

    Article  Google Scholar 

  • Manney GL, Zurek RW, Gelman ME, Miller AJ, Nagatani R (1994) The anomalous arctic lower stratospheric polar vortex of 1992–1993. Geophys Res Lett 21:2405–2408

    Article  Google Scholar 

  • Manney GL, Sabutis JL, Alley DR, Lahoz WA, Scaife AA, Randall CE, Pawson S, Naujokat B, Swinbank R (2005) Simulations of dynamics and transport during the September 2002 Antarctic major warming. J Atmos Sci 66:690–707

    Article  Google Scholar 

  • McIntyre ME, Palmer TN (1984) The surf zone in the stratosphere. J Atmos Terr Phys 46(9):825–849

    Article  Google Scholar 

  • Mechoso CR, Hartmann DL (1982) An observational study of traveling planetary waves in the southern hemisphere. J Atmos Sci 39(9):1921–1935

    Article  Google Scholar 

  • Mechoso CR, O’Neill A, Pope VD, Farrara JD (1988) A study of the stratospheric final warming of 1982 in the Southern Hemisphere. Q J R Meteorol Soc 114:1365–1384

    Article  Google Scholar 

  • Mendoza C, Mancho AM (2010) The hidden geometry of ocean flows. Phys Rev Lett 105(3):038501

    Article  Google Scholar 

  • Mendoza C, Mancho AM (2012) The Lagrangian description of aperiodic flows: a case study of the Kuroshio Current. Nonlinear Proc Geophys 19(14):449–472

    Article  Google Scholar 

  • Mezic I, Wiggins S (1999) A method for visualization of invariant sets of dynamical systems based on the ergodic partition. Chaos 9(1):213–218

    Article  Google Scholar 

  • Nash ER, Newman PA, Rosenfield JE, Schoeberl MR (1996) An objective determination of the polar vortex using Ertel’s potential vorticity. J Geophys Res Atmos 101(D5):9471–9478

    Article  Google Scholar 

  • Öllers MC, van Velthoven PFJ, Kelder HM, Kamp LPJ (2002) A study of the leakage of the antarctic polar vortex in late austral winter and spring using isentropic and 3-D trajectories. J Geophys Res 107(D17):4328

    Article  Google Scholar 

  • Orsolini YJ, Randall CE, Manney GL, Allen DR (2005) An observational study of the final breakdown of the southern hemisphere stratospheric vortex in 2002. J Atmos Sci 62(3):735–747

    Article  Google Scholar 

  • Ottino JM (1989) The kinematics of mixing: stretching, chaos, and transport. Cambridge University Press, Cambridge (reprinted 2004)

    Google Scholar 

  • Rypina II, Brown MG, Beron-Vera FJ, Kocak H, Olascoaga MJ, Udovydchenkov IA (2007) On the lagrangian dynamics of atmospheric zonal jets and the permeability of the stratospheric polar vortex. J Atmos Sci 64:3595–3610

    Article  Google Scholar 

  • Samelson R, Wiggins S (2006) Lagrangian transport in geophysical jets and waves: the dynamical systems approach. Springer, New York

    Google Scholar 

  • Santitissadeekorn N, Froyland G, Monahan A (2010) Optimally coherent sets in geophysical flows: a transfer-operator approach to delimiting the stratospheric polar vortex. Phys Rev E 82(056):311

    Google Scholar 

  • Serra M, Sathe P, Beron-Vera F, Haller G (2017) Uncovering the edge of the polar vortex. J Atmos Sci 74:3871–3885

    Article  Google Scholar 

  • Simmons A, Uppala S, Dee D, Kobayashi S (2007) ERA-Interim: new ECMWF reanalysis products from 1989 onwards. ECMWF Newsl 110:25–35

    Google Scholar 

  • Smith ML, McDonald AJ (2014) A quantitative measure of polar vortex strength using the function M. J Geophys Res Atmos 119:5966–5985

    Article  Google Scholar 

  • Susuki Y, Mezić I (2009) Ergodic partition of phase space in continuous dynamical systems. In: Joint 48th IEEE conference on decision and control and 28th Chinese control conference, pp 7497–7502

  • Taguchi M (2014) Predictability of major stratospheric sudden warmings of the vortex split type: case study of the 2002 southern event and the 2009 and 1989 northern events. J Atmos Sci 71:2886–2904

    Article  Google Scholar 

  • Trounday B, Perthuis L, Strebelle S, Farrara JD, Mechoso CR (1995) Dispersion properties of the flow in the southern stratosphere during winter and spring. J Geophys Res 100:13901–13917

    Article  Google Scholar 

  • Varotsos C (2002) The southern hemisphere ozone hole split in 2002. Environ Sci Pollut Res Int 9(6):375–376

    Article  Google Scholar 

  • Varotsos C (2003) What is the lesson from the unprecedented event over Antarctica in 2002. Environ Sci Pollut Res Int 10(2):80–81

    Article  Google Scholar 

  • Varotsos C (2004) The extraordinary events of the major, sudden stratospheric warming, the diminutive Antarctic ozone hole, and its split in 2002. Environ Sci Pollut Res Int 11(6):405–411

    Article  Google Scholar 

  • Waugh DW, Randel WJ (1999) Climatology of Arctic and Antarctic polar vortices using elliptical diagnostics. J Atmos Sci 56:1594–1613

    Article  Google Scholar 

  • Wiggins S (2005) The dynamical systems approach to Lagrangian transport in oceanic flows. Annu Rev Fluid Mech 37:295–328

    Article  Google Scholar 

  • Wiggins S, Mancho AM (2014) Barriers to transport in aperiodically time-dependent two dimensional velocity fields: Nekhoroshev’s theorem and ‘nearly invariant’ tori. Nonlinear Proc Geophys 21:165–185

    Article  Google Scholar 

Download references

Acknowledgements

J. Curbelo and A. M. Mancho were supported by MINECO Grant MTM2014-56392-R. A. M. Mancho and J. Curbelo are supported by ONR. Grant No. N00014-17-1-3003. C. R. Mechoso was supported by the U.S. NSF Grant AGS-1245069. The research of S. Wiggins is supported by ONR Grant No. N00014-01-1-0769. This paper has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 777822.

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Authors and Affiliations

  1. Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049, Madrid, Spain

    Jezabel Curbelo

  2. Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, C/ Nicolás Cabrera 15, Campus de Cantoblanco UAM, 28049, Madrid, Spain

    Jezabel Curbelo & Ana M. Mancho

  3. Department of Atmospheric and Oceanic Sciences, University of California Los Angeles, Los Angeles, CA, USA

    Carlos R. Mechoso

  4. School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK

    Stephen Wiggins

Authors
  1. Jezabel Curbelo
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  2. Carlos R. Mechoso
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  3. Ana M. Mancho
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  4. Stephen Wiggins
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Correspondence to Jezabel Curbelo.

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Appendix

Appendix

There exist different dynamical objects that support the qualitative description of particle time evolution. This qualitative description is based on Poincaré’s ideas, and consist of determining geometrical structures that define regions where particle trajectories have qualitatively different behaviours. The boundaries between these regions are dynamical barriers. These geometrical structures provide a template for a specific velocity field and emphasize the essential transport features associated with it.

Hyperbolic trajectories are one type of recognisable dynamical features in flows. These are special trajectories, in the neighbourhood of which air masses are elongated along the unstable direction and compressed along the stable direction. An important feature here is that two parcels placed at nearby locations close to a hyperbolic trajectory may evolve in time quite differently, separating at exponential rates.

Trajectories of particles initially placed in the neighbourhood of a hyperbolic trajectory become aligned as time evolves forward with a curve called the unstable manifold; similarly, trajectories of particles in the neighbourhood of a hyperbolic trajectory as time evolves backwards become aligned with a curve called the stable manifold. Figure 11a illustrate this forwards and backwards alignment of the green blobs with the orange and cyan blobs. For time dependent flows, hyperbolic trajectories do not correspond to hyperbolic instantaneous stagnation points of the velocity field. Their positions can be rather different, thus being the behavior of particles in a time interval quite counter-intuitive from what is observed for a velocity field that is frozen in time.

Stable and unstable manifolds are aligned with singular features of M. Figure 11b shows two lines crossing in the middle of the yellowish region. These lines are aligned with the stable and unstable manifolds appearing in panel (a) and correspond, respectively, to the stable and unstable manifolds of the hyperbolic trajectory at the crossing point.

Unstable and stable manifolds are invariant curves. This means that as time evolves either forwards or backwards, respectively, particles stay on those curves. Particles do not cross these curves, therefore they are material curves, and are barriers to transport. Stable and unstable manifolds act as repelling and attracting material lines, respectively (Haller 2002).

Fig. 11
figure 11

a Sketch of a hyperbolic trajectory and its stable (blue line) and unstable (red line) manifolds. Particles in the green blob evolves forwards and backwards in time in time as the orange and cyan shades respectively. b The singular features of M are aligned with the stable and unstable manifolds

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Apart from hyperbolic trajectories and their stable and unstable manifolds, other types of dynamical flow structures exist, in which particles tend to stay together, coherently, without dispersing, such as vortices that keep fluid parcels inside them, or jets. Invariant tori are the dynamical objects related to that behaviour. These objects are invariant in the sense defined above, i.e. particles evolve in time staying on them. Further details on tori are given in Sect. 4.

Background for this appendix can be found in Ottino (1989), Wiggins (2005), Mancho et al. (2006) and Samelson and Wiggins (2006).

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Curbelo, J., Mechoso, C.R., Mancho, A.M. et al. Lagrangian study of the final warming in the southern stratosphere during 2002: Part I. The vortex splitting at upper levels. Clim Dyn 53, 2779–2792 (2019). https://doi.org/10.1007/s00382-019-04832-y

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