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Fractional State Space Analysis of Temperature Time Series

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Abstract

Atmospheric temperatures characterize Earth as a slow dynamics spatiotemporal system, revealing long-memory and complex behavior. Temperature time series of 54 worldwide geographic locations are considered as representative of the Earth weather dynamics. These data are then interpreted as the time evolution of a set of state space variables describing a complex system. The data are analyzed by means of multidimensional scaling (MDS), and the fractional state space portrait (fSSP). A centennial perspective covering the period from 1910 to 2012 allows MDS to identify similarities among different Earth’s locations. The multivariate mutual information is proposed to determine the “optimal” order of the time derivative for the fSSP representation. The fSSP emerges as a valuable alternative for visualizing system dynamics.

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Authors and Affiliations

  1. Institute of Engineering, Polytechnic of Porto Dept. of Electrical Engineering Rua Dr. Ant´onio Bernardino de Almeida, 431 4249–015, Porto, Portugal

    J. A. Tenreiro Machado

  2. Institute of Mechanical Engineering Faculty of Engineering, University of Porto Rua Dr. Roberto Frias, 4200–465, Porto, Portugal

    António M. Lopes

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  1. J. A. Tenreiro Machado
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  2. António M. Lopes
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Correspondence to J. A. Tenreiro Machado.

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Machado, J.A.T., Lopes, A.M. Fractional State Space Analysis of Temperature Time Series. FCAA 18, 1518–1536 (2015). https://doi.org/10.1515/fca-2015-0088

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  • DOI: https://doi.org/10.1515/fca-2015-0088

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