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Characterizing atmospheric surface layer turbulence using chaotic return map analysis

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Abstract

Nonlinear time series analysis methods are used to investigate the dynamics of mechanical and convective turbulences in the atmospheric surface layer flow. Using dynamical invariant analysis (e.g. correlation dimension, Lyapunov exponent and mutual information) along with recurrence quantification analysis (e.g. recurrent rate, determinism, average diagonal length of recurrence plot, etc.) of the vertical wind component data, it is confirmed that a convective turbulence is a lower order manifold in its phase space exhibiting higher degree of organization than a mechanical turbulence. Applying a quasi-one-dimensional chaotic return map technique, the topological differences between the mechanical and convective turbulences are explored. These quasi-one-dimensional return maps are produced using the local maxima of the first principal component of the reconstructed turbulence data. A comparison of the probability distribution of the local maxima of a forced Lorenz model with the turbulence data indicates the possible existence of a stable fixed point for both type of turbulences. Furthermore, dynamically the mechanical turbulence is found to resemble an unforced Lorenz model whereas the convective turbulence resembles a forced Lorenz model.

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Acknowledgments

This research is funded by the Ministry of Agriculture and Forestry, Govt. of New Zealand, and National Institute of Water and Atmospheric Research Ltd. (NIWA). Thanks to Justin Harrison and Nicholas Key of Department of Geography, University of Canterbury for providing the technical support and instrumentation. Thanks to Dr. Norbert Marwan, Potsdam University, Germany for providing us the CRPToolbox.

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  1. Sandipan Mukherjee

    Present address: G. B. Pant Institute of Himalayan Environment and Development, Kosi-Katarmal, Almora, Uttarakhand, India

Authors and Affiliations

  1. Centre for Atmospheric Research, University of Canterbury, Christchurch, New Zealand

    Sandipan Mukherjee, Peyman Zawar-Reza & Andrew Sturman

  2. Department of Physics, University of Allahabad, Allahabad, India

    Ashok Kumar Mittal

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  1. Sandipan Mukherjee
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  2. Peyman Zawar-Reza
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Correspondence to Sandipan Mukherjee.

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Responsible editor: S. Trini Castelli.

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Mukherjee, S., Zawar-Reza, P., Sturman, A. et al. Characterizing atmospheric surface layer turbulence using chaotic return map analysis. Meteorol Atmos Phys 122, 185–197 (2013). https://doi.org/10.1007/s00703-013-0286-0

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