Topological Entropy: A Lagrangian Measure of the State of the Free Atmosphere

Tímea Haszpra MTA-ELTE Research Group in Theoretical Physics, Eötvös Loránd University, Budapest, Hungary

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Tamás Tél MTA-ELTE Research Group in Theoretical Physics, Eötvös Loránd University, Budapest, Hungary

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Abstract

Topological entropy is shown to be a useful characteristic of the state of the free atmosphere. It can be determined as the stretching rate of a line segment of tracer particles in the atmosphere over a time span of about 10 days. Besides case studies, the seasonal distribution of the average topological entropy is determined in several geographical locations. The largest topological entropies appear in the mid- and high latitudes, especially in winter, owing to the greater temperature gradient between the pole and the equator and the more intense stirring and shearing effects of cyclones. The smallest values can be found in the trade wind belt. The local value of the topological entropy is a measure of the chaoticity of the state of the atmosphere and of how rapidly pollutants and contaminants spread from a given location.

Corresponding author address: Tímea Haszpra, Institute of Theoretical Physics and MTA-ELTE Research Group in Theoretical Physics, Eötvös Loránd University, Pázmány P. s. 1/A, Budapest H-1117, Hungary. E-mail: hatimi@caesar.elte.hu

Abstract

Topological entropy is shown to be a useful characteristic of the state of the free atmosphere. It can be determined as the stretching rate of a line segment of tracer particles in the atmosphere over a time span of about 10 days. Besides case studies, the seasonal distribution of the average topological entropy is determined in several geographical locations. The largest topological entropies appear in the mid- and high latitudes, especially in winter, owing to the greater temperature gradient between the pole and the equator and the more intense stirring and shearing effects of cyclones. The smallest values can be found in the trade wind belt. The local value of the topological entropy is a measure of the chaoticity of the state of the atmosphere and of how rapidly pollutants and contaminants spread from a given location.

Corresponding author address: Tímea Haszpra, Institute of Theoretical Physics and MTA-ELTE Research Group in Theoretical Physics, Eötvös Loránd University, Pázmány P. s. 1/A, Budapest H-1117, Hungary. E-mail: hatimi@caesar.elte.hu
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  • Allshouse, M. R., and J.-L. Thiffeault, 2012: Detecting coherent structures using braids. Physica D, 241, 95105.

  • Aref, H., 1985: Stirring by chaotic advection. J. Fluid Mech., 143, 1–21.

  • Bowman, K. P., 1993: Large-scale isentropic mixing properties of the Antarctic polar vortex from analyzed winds. J. Geophys. Res., 98 (D12), 23 01323 027.

    • Search Google Scholar
    • Export Citation
  • Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597.

    • Search Google Scholar
    • Export Citation
  • Haszpra, T., and T. Tél, 2011: Volcanic ash in the free atmosphere: A dynamical systems approach. J. Phys., 333, 012008, doi:10.1088/1742-6596/333/1/012008.

    • Search Google Scholar
    • Export Citation
  • Haszpra, T., P. Kiss, T. Tél, and I. M. Jánosi, 2012: Advection of passive tracers in the atmosphere: Batchelor scaling. Int. J. Bifurcation Chaos, 22, 1250241, doi:10.1142/S0218127412502410.

    • Search Google Scholar
    • Export Citation
  • Holtstag, A. A. M., and B. A. Boville, 1993: Local versus nonlocal boundary-layer diffusion in a global climate model. J. Climate, 6, 18251842.

    • Search Google Scholar
    • Export Citation
  • Huber, M., J. C. McWilliams, and M. Ghil, 2001: A climatology of turbulent dispersion in the troposphere. J. Atmos. Sci., 58, 23772394.

    • Search Google Scholar
    • Export Citation
  • Kai, E., V. Rossi, J. Sudre, H. Weimerskirch, C. Lopez, E. Hernandez-Garcia, F. Marsac, and V. Garçon, 2009: Top marine predators track Lagrangian coherent structures. Proc. Natl. Acad. Sci. USA, 106, 82458250.

    • Search Google Scholar
    • Export Citation
  • Kalnay, E., 2003: Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press, 364 pp.

  • Lai, Y.-C., and T. Tél, 2011: Transient Chaos: Complex Dynamics on Finite Time Scales. Applied Mathematical Sciences, Vol. 173, Springer, 410 pp.

  • Mathur, M., G. Haller, T. Peacock, J. Ruppert-Felsot, and H. Swinney, 2007: Uncovering the Lagrangian skeleton of turbulence. Phys. Rev. Lett., 98, 144502, doi:10.1103/PhysRevLett.98.144502.

    • Search Google Scholar
    • Export Citation
  • Mizuta, R., and S. Yoden, 2001: Chaotic mixing and transport barriers in an idealized stratospheric polar vortex. J. Atmos. Sci., 58, 26162629.

    • Search Google Scholar
    • Export Citation
  • Newhouse, S., and T. Pignataro, 1993: On the estimation of topological entropy. J. Stat. Phys., 72, 13311351.

  • Ott, E., 1993: Chaos in Dynamical Systems. Cambridge University Press, 385 pp.

  • Ottino, J., 1989: The Kinematics of Mixing: Stretching, Chaos, and Transport. Cambridge Texts in Applied Mathematics, Vol. 3, Cambridge University Press, 396 pp.

  • Peacock, T., and G. Haller, 2013: Lagrangian coherent structures: The hidden skeleton of fluid flows. Phys. Today, 66, 4147.

  • Pierrehumbert, R. T., and H. Yang, 1993: Global chaotic mixing on isentropic surfaces. J. Atmos. Sci., 50, 24622480.

  • Ruppert-Felsot, J., O. Praud, E. Sharon, and H. Swinney, 2005: Extraction of coherent structures in a rotating turbulent flow experiment. Phys. Rev., 72E, 016311, doi:10.1103/PhysRevE.72.016311.

    • Search Google Scholar
    • Export Citation
  • Shadden, S., F. Lekien, and J. Marsden, 2005: Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D, 212, 271304.

    • Search Google Scholar
    • Export Citation
  • Shadden, S., F. Lekien, J. Paduan, F. Chavez, and J. Marsden, 2009: The correlation between surface drifters and coherent structures based on high-frequency radar data in Monterey Bay. Deep-Sea Res. II, 56, 161172.

    • Search Google Scholar
    • Export Citation
  • Sommerer, J. C., and E. Ott, 1993: Particles floating on a moving fluid: A dynamically comprehensible physical fractal. Science, 259, 335339.

    • Search Google Scholar
    • Export Citation
  • Sommerer, J. C., H.-C. Ku, and H. E. Gilreath, 1996: Experimental evidence for chaotic scattering in a fluid wake. Phys. Rev. Lett., 77, 50555058.

    • Search Google Scholar
    • Export Citation
  • Stohl, A., 1998: Computation, accurancy and applications of trajectories—A review and bibliography. Atmos. Environ., 32, 947966.

  • Tél, T., and M. Gruiz, 2006: Chaotic Dynamics: An Introduction Based on Classical Mechanics. Cambridge University Press, 412 pp.

  • Terada, H., and M. Chino, 2008: Development of an atmospheric dispersion model for accidental discharge of radionuclides with the function of simultaneous prediction for multiple domains and its evaluation by application to the Chernobyl nuclear accident. J. Nucl. Sci. Technol., 45, 920931.

    • Search Google Scholar
    • Export Citation
  • Thiffeault, J.-L., 2010: Braids of entangled particle trajectories. Chaos, 20, 017516, doi:10.1063/1.3262494.

  • von Hardenberg, J., K. Fraedrich, F. Lunkeit, and A. Provenzale, 2000: Transient chaotic mixing during baroclinic life cycle. Chaos, 10, 122134.

    • Search Google Scholar
    • Export Citation
  • Yang, H., and R. T. Pierrehumbert, 1994: Production of dry air by isentropic mixing. J. Atmos. Sci., 51, 34373454.

  • Ziemniak, E. M., C. Jung, and T. Tél, 1994: Tracer dynamics in open hydrodynamical flows as chaotic scattering. Physica D, 76, 123146.

    • Search Google Scholar
    • Export Citation
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