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Analysis of Climate Dynamics Across a European Transect Using a Multifractal Method

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Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

Abstract

Climate dynamics were assessed using multifractal detrended fluctuation analysis (MF-DFA) for sites in Finland, Germany and Spain across a latitudinal transect. Meteorological time series were divided into the two subsets (1980–2001 and 2002–2010) and respective spectra of these subsets were compared to check whether changes in climate dynamics can be observed using MF-DFA. Additionally, corresponding shuffled and surrogate time series were investigated to evaluate the type of multifractality. All time series indicated underlying multifractal structures with considerable differences in dynamics and development between the studied locations. The source of multifractality of precipitation time series was two-fold, coming from the width of the probability function to a greater extent than for other time series. The multifractality of other analyzed meteorological series was mainly due to long-range correlations for small and large fluctuations. These results may be especially valuable for assessing the change of climate dynamics, as we found that larger changes in asymmetry and width parameters of multifractal spectra for divided datasets were observed for precipitation than for other time series. This suggests that precipitation is the most vulnerable meteorological quantity to change of climate dynamics.

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References

  1. Balling, R.C., Vose, R.S., Weber, G.R.: Analysis of long-term European temperature records: 1751–1995. Clim. Res. 10, 193–200 (1998)

    Article  Google Scholar 

  2. Kantelhardt, J.W., Zschiegner, S.A., Koscielny-Bunde, E., Havlin, S., Bunde, A., Stanley, H.E.: Multifractal detrended fluctuation analysis of nonstationary time series. Phys. A 316(1–4), 87–114 (2002)

    Article  MATH  Google Scholar 

  3. Higuchi, T.: Approach to an irregular time series on the basis of the fractal theory. Physica D 31, 277–283 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  4. Kalauzi, A., Spasić, S., Ćulić, M., Grbić, G., Martać, Lj: Consecutive differences as a method of signal fractal analysis. Fractals 13(4), 283–292 (2005)

    Article  Google Scholar 

  5. Schertzer, D., Lovejoy, S.: Multifractal simulation and analysis of clouds by multiplicative process. Atmos. Res. 21, 337–361 (1988)

    Article  Google Scholar 

  6. Kavasseri, R.G., Nagarajan, R.: A multifractal description of wind speed records. Chaos Solitons Fractals 24, 165–173 (2005)

    Article  MATH  Google Scholar 

  7. Feng, T., Fu, Z., Deng, X., Mao, J.: A brief description to different multi-fractal behaviors of daily wind speed records over China. Phys. Lett. A 45, 4134–4141 (2009)

    Article  Google Scholar 

  8. Koscielny-Bunde, E., Roman, H.E., Bunde, A., Havlin, S., Schellnhuber, H.J.: Long-range power-law correlations in local daily temperature fluctuations. Philos. Mag. B 77(5), 1331–1340 (1998)

    Article  Google Scholar 

  9. Király, A., Jánosi, I.M.: Detrended fluctuation analysis of daily temperature records: Geographic dependence over Australia. Meteorol. Atmos. Phys. 88, 119–128 (2005)

    Article  Google Scholar 

  10. Bartos, I., Jánosi, I.M.: Nonlinear correlations of daily temperature records over land. Nonlinear Process. Geophys. 13, 571–576 (2006)

    Article  Google Scholar 

  11. Lin, G., Fu, Z.: A universal model to characterize different multi-fractal behaviors of daily temperature records over China. Phys. A 387, 573–579 (2008)

    Article  Google Scholar 

  12. Yuan, N., Fu, Z., Mao, J.: Different multifractal behaviors of diurnal temperature range over the north and the south of China. Theor. Appl. Climatol. 112, 673–682 (2013)

    Article  Google Scholar 

  13. Fraedrich, K., Blender, R.: Scaling of atmosphere and ocean temperature correlations in observations and climate models. Phys. Rev. Lett. 90, 108501 (2003)

    Article  Google Scholar 

  14. Jiang, L., Zhao, J., Li, N., Li, F., Guo, Z.: Different multifractal scaling of the 0 cm average ground surface temperature of four representative weather stations over China. Adv. Meteorol. 2013, Article ID 341934 (2013)

    Google Scholar 

  15. Deidda, R.: Rainfall downscaling in a space-time multifractal framework. Water Resour. Res. 36, 1779–1794 (2000)

    Article  Google Scholar 

  16. García-Marín, A.P., Jiménez-Hornero, F.J., Ayuso, J.L.: Applying multifractality and the self-organised criticality theory to describe the temporal rainfall regimes in Andalusia (southern Spain). Hydrol. Process. 22, 295–308 (2008)

    Article  Google Scholar 

  17. De Lima, M.I.P., de Lima, J.L.M.P.: Investigating the multifractality of point precipitation in the Madeira archipelago. Nonlinear Process. Geophys. 16, 299–311 (2009)

    Article  Google Scholar 

  18. Gemmer, M., Fischer, T., Su, B., Liu, L.L.: Trends of precipitation extremes in the Zhujiang River Basin. South China J. Clim. 24, 750–761 (2011)

    Google Scholar 

  19. Lovejoy, S., Pinel, J., Schertzer, D.: The global space—time cascade structure of precipitation: satellites, gridded gauges and reanalyses. Adv. Water Resour. 45, 37–50 (2012)

    Article  Google Scholar 

  20. Jimenez-Hornero, F.J., Jimenez-Hornero, J.E., de Rave, E.G., Pavon-Dominguez, P.: Exploring the relationship between nitrogen dioxide and ground-level ozone by applying the joint multifractal analysis. Environ. Monit. Assess. 167, 675–684 (2010)

    Article  Google Scholar 

  21. Murcio, R., Masucci, A.P., Arcaute, E., Batty, M.: Multifractal to monofractal evolution of the London street network. Phys. Rev. E 92, 062130 (2015)

    Article  Google Scholar 

  22. Yu, Z.-G., Leung, Y., Chen, Y.D., Zhang, Q., Anh, V., Zhou, Y.: Multifractal analyses of daily rainfall time series in Pearl River basin of China. Phys. A 405, 193–202 (2014)

    Article  Google Scholar 

  23. Valencia, J.L., Requejo, A.S., Gasco, J.M., Tarquis, A.M.: A universal multifractal description applied to precipitation patterns of the Ebro River Basin. Spain. Clim. Res. 44, 17–25 (2010)

    Article  Google Scholar 

  24. Veneziano, D., Langousis, A., Furcolo, P.: Multifractality and rainfall extremes: a review. Water Resour. Res.42, W06D15 (2006)

    Google Scholar 

  25. Venugopal, V., Roux, S.G., Foufoula-Georgiou, E., Arneodo, A.: Revisiting multifractality of high-resolution temporal rainfall using a wavelet-based formalism. Water Resour. Res. 42, W06D14 (2006)

    Google Scholar 

  26. Yonghe, L., Kexin, Z., Wanchang, Z., Yuehong, S., Hongqin, P., Jinming, F.: Multifractal analysis of 1 min summer rainfall time series from a monsoonal watershed in eastern China. Theor. Appl. Climatol. 111, 37–50 (2013)

    Article  Google Scholar 

  27. Rodríguez, R., Casas, M.C., Redaño, A.: Multifractal analysis of the rainfall time distribution on the metropolitan area of Barcelona (Spain). Meteorol. Atmos. Phys. 121, 181–187 (2013)

    Article  Google Scholar 

  28. Huntingford, C., Jones, P.D., Livinia, V.N., Lenton, T.M., Cox, P.M.: No increase in global temperature variability despite changing regional patterns. Nature 500, 327–330 (2013)

    Article  Google Scholar 

  29. Swanson, K.L., Tsonis, A.A.: Has the climate recently shifted? Geophys. Res. Lett. 36, L06711 (2009)

    Article  Google Scholar 

  30. Dee, D., Uppala, S., et al.: The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q. J. R. Meteorol. Soc. 137, 553–597 (2011)

    Article  Google Scholar 

  31. Telesca, L., Lovallo, M.: Analysis of the time dynamics in wind records by means of multifractal detrended fluctuation analysis and the Fisher-Shannon information plane. J. Stat. Mech., P07001 (2011)

    Google Scholar 

  32. Theiler, J., Galdrikian, B., Longtin, A., Eubank, S., Farmer, D.J.: Using surrogate data to detect nonlinearity in time series. In: Nonlinear Modeling and Forecasting, pp. 163–188. Addison-Wesley (1992)

    Google Scholar 

  33. Min, L., Shuang-Xi, Y., Gang, Z., Gang, W.: Multifractal detrended fluctuation analysis of interevent time series in a modified OFC model. Commun. Theor. Phys. 59, 1–6 (2013)

    Article  MATH  Google Scholar 

  34. Mali, P.: Multifractal characterization of global temperature anomalies. Theor. Appl. Climatol. 121(3), 641–648 (2014)

    Google Scholar 

  35. Kantelhardt, J.W., Koscielny-Bunde, E., Rybski, D., Braun, P., Bunde, A., Havlin, S.: Long-term persistence and multifractality of precipitation and river runoff records. J. Geophys. Res. 111, D01106 (2006)

    Article  MATH  Google Scholar 

  36. Baranowski, P., Krzyszczak, J., Slawinski, C., Hoffmann, H., Kozyra, J., Nierobca, A., Siwek, K., Gluza, A.: Multifractal analysis of meteorological time series to assess climate impacts. Clim. Res. 65, 39–52 (2015)

    Article  Google Scholar 

  37. Venäläinen, A., Tuomenvirta, H., Pirinen, P., Drebs, A.: A basic finnish climate data set 1961–2000—description and illustration. Finnish Meteorological Institute Reports, vol. 5. Finnish Meteorological Institute, Helsinki, Finland (2005)

    Google Scholar 

  38. Krzyszczak, J., Baranowski, P., Zubik, M., Hoffmann, H.: Temporal scale influence on multifractal properties of agro-meteorological time series. Agric. For. Meteorol. 239, 223–235 (2017)

    Google Scholar 

  39. Hoffmann, H., Baranowski, P., Krzyszczak, J., Zubik, M., Sławiński, C., Gaiser, T., Ewert, F.: Temporal properties of spatially aggregated meteorological time series. Agric. For. Meteorol. 234–235, 247–257 (2017)

    Google Scholar 

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Acknowledgements

This paper has been partly financed from the funds of the Polish National Centre for Research and Development in frame of the projects: LCAgri, contract number: BIOSTRATEG1/271322/3/NCBR/2015 and GyroScan, contract number: BIOSTRATEG2/298782/11/NCBR/2016. We acknowledge Finnish Meteorological Institute (FMI) for delivering us data for Jokioinen site [37]. HH was financially supported by the German Federal Ministry of Food and Agriculture (BMEL) through the Federal Office for Agriculture and Food (BLE), (2851ERA01J).

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Correspondence to Jaromir Krzyszczak .

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Krzyszczak, J., Baranowski, P., Hoffmann, H., Zubik, M., Sławiński, C. (2017). Analysis of Climate Dynamics Across a European Transect Using a Multifractal Method. In: Rojas, I., Pomares, H., Valenzuela, O. (eds) Advances in Time Series Analysis and Forecasting. ITISE 2016. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-55789-2_8

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