Temperature time series analysis at Yucatan using natural and horizontal visibility algorithms

Autoři: J. Alberto Rosales-Pérez aff001;  Efrain Canto-Lugo aff001;  David Valdés-Lozano aff002;  Rodrigo Huerta-Quintanilla aff001
Působiště autorů: Departamento de Física Aplicada, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional. Unidad Mérida, Mérida, Yucatán 97310, México aff001;  Departamento de Recursos del Mar, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional. Unidad Mérida, Mérida, Yucatán 97310, México aff002
Vyšlo v časopise: PLoS ONE 14(12)
Kategorie: Research Article
doi: https://doi.org/10.1371/journal.pone.0226598


Several methods to quantify the complexity of a time series have been proposed in the literature, which can be classified into three categories: structure/self-affinity, attractor in the phase space, and randomness. In 2009, Lacasa et al. proposed a new method for characterizing a time series called the natural visibility algorithm, which maps the data into a network. To further investigate the capabilities of this technique, in this work, we analyzed the monthly ambient temperature of 4 cities located in different climatic zones on the Peninsula of Yucatan, Mexico, using detrended fluctuation analysis (structure complexity), approximate entropy (randomness complexity) and the network approach. It was found that by measuring the complexity of the dynamics by structure or randomness, the magnitude was very similar between the cities in different climatic zones; however, by analyzing topological indices such as Laplacian energy and Shannon entropy to characterize networks, we found differences between those cities. With these results, we show that analysis using networks has considerable potential as a fourth way to quantify complexity and that it may be applied to more subtle complex systems such as physiological signals and their high impact on early warnings.

Klíčová slova:

Algorithms – Bodies of water – Dynamical systems – Entropy – Equipment – Network analysis – Temperature analysis – Time series analysis


1. Shuangcheng L, Qiaofu Z, Shaohong W, Erfu D. Measurement Of Climate Complexity Using Sample Entropy. Int. J. Climatol. 2006;26: 2131–2139. doi: 10.1002/joc.1357

2. Veleva L, Pérez G, Acosta M. Statistical analysis of the temperature-humidity complex and time of wetness of a tropical climate in the Yucat´an Peninsula in Mexico. Atmos Environ 1997;31: 773–776. doi: 10.1016/S1352-2310(96)00232-4

3. Castro P, Weva L, Balancim M. Corrosion of reinforced concrete in a tropical marine environment and in accelerated tests. Constr Build Mater. 1997;112: 75–81. doi: 10.1016/S0950-0618(97)00009-3

4. Maldonado L, Veleva L. Corrosivity category maps of a humid tropical atmosphere: the Yucatan Peninsula, Mexico. Werkst. Korros. 1999;503: 261–266. doi: 10.1002/(SICI)1521-4176(199905)50:5%3C261::AID-MACO261%3E3.0.CO;2-G

5. Castro P, Moreno EI, Genescá J. Influence of marine micro-climates on carbonation of reinforced concrete buildings. Cem Concr Res. 2000;30: 1565–1571. doi: 10.1016/S0008-8846(00)00344-6

6. Sosa M, Pérez T, Reyes J, Corvo F, Camacho R, Quintana P, et al. Influence of the Marine Environment on Reinforced Concrete Degradation Depending on Exposure Conditions. Int. J. Electrochem. Sci. 2011;6: 6300–6318.

7. Donner R, Barbosa S, Kurths J, Marwan N. Understanding the Earth as a Complex System—recent advances in data analysis and modelling in Earth sciences. Eur. Phys. J. Special Topics. 2009;174: 1–9 doi: 10.1140/epjst/e2009-01086-6

8. Mudelsee M. Climate time series analysis, classical statistical and bootstram methods. 1st ed. Springer; 2010.

9. Bradley E, Kantz H. Nonlinear time-series analysis revisited. Chaos. 2015; 25: 9. doi: 10.1063/1.4917289

10. Kantz H, Schreiber T. Nonlinear Time Series Analysis. 1st ed. Cambridge University Press; 2003.

11. Rypdal k, Østvand L, Rypdal M. Long range memory in Earth’s surface temperature on time scales from months to centuries. J Geophys Res Atmos. 2013;118: 7046–7042. doi: 10.1002/jgrd.50399

12. Orun M, Ko K. Applicatıon of detrended fluctuation analysis to temperature data from Turkey. Int. J. Climatol. 2009;29:2130–2136. doi: 10.1002/joc.1853

13. Lopes AM, Tenreiro JA. Complexity Analysis of Global Temperature Time Series. Entropy 2018;20: 437. doi: 10.3390/e20060437

14. Zhang J, Small M. Complex network from pseudoperiodic time series: Topology versus dynamics. Phys Rev Lett. 2006; 96: 238701. doi: 10.1103/PhysRevLett.96.238701 16803415

15. Xu XK, Zhang J, Small M. Superfamily phenomena and motifs of networks induced from time series. Proc Natl Acad Sci USA. 2008;105:601–605. doi: 10.1073/pnas.0806082105

16. Donner RV, Small M, Donges JF, Marwan N Zou Y., Xiang R, Kurths J. Recurrence-based time series analysis by means of complex network methods. International Int J Bifurcat Chaos. 2011;21:1019–1046. doi: 10.1142/S0218127411029021

17. Lacasa L, Luque B, Ballesteros F, Luque J, Nuño JC. From time series to complex networks: the visibility graph. PNAS. 2008;105: 4972–4975. doi: 10.1073/pnas.0709247105 18362361

18. Campanharo ASLO, Irmak M, Dean R, Ramos FM, Nunes LA. Duality between Time Series and Networks. PLoS ONE. 2011;6:pp 1–12. doi: 10.1371/journal.pone.0023378

19. Liu J, Li Q. Planar Visibility Graph Network Algorithm For Two Dimensional Timeseries. 29th Chinese Control And Decision Conference (CCDC). 2017.

20. Zou Y, Small M, Liu Z, Kurths J. Complex network approach to characterize the statistical features of the sunspot series. New J. Phys. 2014;16.

21. Elsner JB, Jagger TH, Fogarty EA. Visibility network of United States hurricanes. Geophys Res Lett, 2009; 36. doi: 10.1029/2009GL039129

22. Donner RV, Donges JF. Visibility graph analysis of geophysical time series: Potentials and possible pitfalls. Acta Geophys. 2012;60:589–623. doi: 10.2478/s11600-012-0032-x

23. Telescaa L, Lovallob M, Aggarwalc SK, Khand PK. Precursory signatures in the visibility graph analysis of seismicity: An application to the Kachchh (Western India) seismicity. J. Phys. Chem. Earth. 2015;85:195–200. doi: 10.1016/j.pce.2015.02.008

24. Telesca L, Lovallo M, Toth L. Visibility graph analysis of 2002–2011 Pannonian seismicity. Physica A. 2014;416:219–224. doi: 10.1016/j.physa.2014.08.048

25. Zhuang E, Small M, Feng G Time series analysis of the developed financial markets’ integration using visibility graphs. Physica A. 2014; 410:483–495. doi: 10.1016/j.physa.2014.05.058

26. Yu L. Visibility graph network analysis of gold price time series. Physica A. 2013;392:3374–3384. doi: 10.1016/j.physa.2013.03.063

27. Costa LF, Rodrigues FA, Travieso G, Villas PR. Characterization of complex networks: A survey of measurements. Adv Phys. 2007;56:167–242. doi: 10.1080/00018730601170527

28. Vega-Redondo F. Complex Social Networks. 1st ed. Cambridge University Press, 2007.

29. Luque B, Lacasa L, Ballesteros FJ, Robledo A. Analytical properties of horizontal visibility graphs in the Feigenbaum scenario. Chaos. 2012;

30. Kragujevac ML. On the Laplacian Energy of a graph. Czech Math J. 2006;56:1207–1213. doi: 10.1007/s10587-006-0089-2

31. Stevanovica D, Stankovicb I, Milosevicb M. More on the relation between energy and Laplacian Energy of graphs. Commun. Math. Comput. Chem., 2009;61:395–401.

32. Davis Instruments. Davis Instruments [accessed 15 March 2019]. In: Davids Instruments web site. http://www.davisnet.com/product_documents/weather/manuals/07395-234_IM_06312.pdf

33. Garcia E. Modifications to Köpen’s Climate Classification System (Modificaciones al Sistema de Clasificación Climática de Köpen). Instituto de Geografía Univeridad Nacional Autónoma de México, 1998

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2019 Číslo 12
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