Analysis and forecast of the environmental radioactivity dynamics based on methods of chaos theory: general scheme and some application

  • A.V. Glushkov
  • E.R. Gubanova
  • O.Yu. Khetselius
  • G.P. Prepelitsa
  • A.A. Svinarenko
  • Yu.Ya. Bunyakova
  • V.V. Buyadzhi
Keywords: environmental radioactivity dynamics, the ecological state, time series of concentrations, pollutants, analysis and prediction methods of the theory of chaos

Abstract

We present firstly a new whole technique of analysis, processing and forecasting environmental radioactivity dynamics, which has been earlier developed for the atmospheric pollution dynamics analysis and investigation of chaotic feature sin dynamics of the typical hydroecological systems. The general formalism include: a) A general qualitative analysis of dynamical problem of the environmental radioactivity dynamics (including a qualitative analysis from the viewpoint of ordinary differential equations, the “Arnold-analysis”); b) checking for the presence of a chaotic (stochastic) features and regimes (the Gottwald-Melbourne’s test; the method of correlation dimension); c) Reducing the phase space (choice of the time delay, the definition of the embedding space by methods of correlation dimension algorithm and false nearest neighbor points); d) Determination of the dynamic invariants of a chaotic system (Computation of the global Lyapunov dimension λa; determination of the Kaplan-York dimension dLand average limits of predictability Prmax on the basis of the advanced algorithms; e) A non-linear prediction (forecasting) of an dynamical evolution of the system. The last block indeed includes new (in a theory of environmental radioactivity dynamics) methods and algorithms of nonlinear prediction such as methods of predicted trajectories, stochastic propagators and neural networks modelling, renorm-analysis with blocks of the polynomial approximations, wavelet-expansions etc.

References

Bunyakova Yu.Ya., Glushkov A.V. Analysis and forecast of the impact of anthropogenic factors on air basin of an industrial city. Odessa: Ecology, 2010. 256 p. (In Russian).

Glushkov A.V., Khokhlov V.N., Serbov N.G., Bunyakova Yu.Ya., Balan A.K., Balanyuk E.P. Low-dimensional chaos in the time series of concentrations of pollutants in an atmosphere and hydrosphere. Vìsn. Odes. derž. ekol. unìv. – Bulletin of Odessa state environmental university, 2007, vol. 4, pp.337-348. (In Russian)

Glushkov A.V. Analysis and forecast of the anthropogenic impact on industrial city’s atmosphere based on methods of chaos theory: new general scheme. Ukr. gìdrometeorol. ž. – Ukranian hydrometeorological journal, 2014, no. 15, pp. 32-36.

Khokhlov V.N., Glushkov A.V., Loboda N.S., Bunyakova Yu.Ya. Short-range forecast of atmospheric pollutants using non-linear prediction method. Atmospheric Environment. The Netherlands: Elsevier, 2008, vol.42, pp.7284–7292.

Glushkov A.V., Khokhlov V.N., Prepelitsa G.P., Tsenenko I.A. Temporal variability of the atmosphere ozone content: Effect of North-Atlantic oscillation. Optics of atmosphere and ocean, 2004, vol.14, no.7, pp.219-223.

Glushkov A.V., Loboda N.S., Khokhlov V.N. Using meteorological data for reconstruction of annual runoff series over an ungauged area: Empirical orthogonal functions approach to Moldova-Southwest Ukraine region. Atmospheric Research. Elseiver, 2005, vol.77, pp.100-113.

Glushkov A.V., Kuzakon’ V.M., Khetselius O.Yu., Bunyakova Yu.Ya., Zaichko P.A. Geometry of Chaos: Consistent com-bined approach to treating chaotic dynamics atmospheric pollutants and its forecasting. Proceedings of International Geometry Center, 2013, vol.6, no.3, pp.6-13.

Glushkov A.V., Rusov V.N., Loboda N.S., Khetselius O.Yu., Khokhlov V.N., Svinarenko A.A., Prepelitsa G.P. On possible genesis of fractal dimensions in the turbulent pulsations of cosmic plasma – galactic-origin rays – turbulent pulsation in planetary atmosphere system. Adv. in Space Research. Elsevier, 2008, vol.42(9), pp.1614-1617.

Glushkov A.V., Loboda N.S., Khokhlov V.N., Lovett L. Using non-decimated wavelet decomposition to analyse time variations of North Atlantic Oscillation, eddy kinetic energy, and Ukrainian precipitation. Journal of Hydrology. Elseiver, 2006, vol.322, no. 1-4, pp.14-24.

Glushkov A.V., Khetselius O.Yu., Brusentseva S.V., Zaichko P.A., Ternovsky V.B. Adv. in Neural Networks, Fuzzy Systems and Artificial Intelligence. Series: Recent Adv. in Computer Engineering. Gdansk: WSEAS, 2014, vol.21, pp.69-75. (Ed.: J. Balicki).

Glushkov A.V., Svinarenko A.A., Buyadzhi V.V., Zaichko P.A., Ternovsky V.B. Adv.in Neural Networks, Fuzzy Systems and Artificial Intelligence, Series: Recent Adv. in Computer Engineering. Gdansk: WSEAS, 2014, vol.21, pp. 143-150 (Ed.: J. Balicki).

Rusov V.D., Glushkov A.V., Vaschenko V.N., Myhalus O.T., Bondartchuk Yu.A. etal. Galactic cosmic rays - clouds effect and bifurcation model of the earth global climate. Part 1. Theory. Journal of Atmospheric and Solar-Terrestrial Physics. Elsevier, 2010, vol.72, pp.498-508.

Sivakumar B. Chaos theory in geophysics: past, present and future. Chaos, Solitons & Fractals, 2004, vol.19, № 2, pp.441-462.

Chelani A.B. Predicting chaotic time series of PM10 concentration using artificial neural network. Int. J. Environ. Stud, 2005, vol. 62. № 2, pp. 181-191.

Gottwald G.A., Melbourne I. A new test for chaos in deterministic systems. Proc. Roy. Soc. London. Ser. A. Mathemat. Phys. Sci., 2004, vol.460, pp.603-611.

Packard N.H., Crutchfield J.P., Farmer J.D., Shaw R.S. Geometry from a time series. Phys. Rev. Lett., 1980, vol.45, pp.712-716.

Kennel M., Brown R., Abarbanel H. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A., 1992, vol.45, pp.3403-3411.

Abarbanel H.D.I., Brown R., Sidorowich J.J., Tsimring L.Sh. The analysis of observed chaotic data in physical systems. Rev. Mod. Phys, 1993, vol.65, pp.1331-1392.

Schreiber T. Interdisciplinary application of nonlinear time series methods. Phys. Rep., 1999, vol.308, pp.1-64.

Fraser A.M., Swinney H. Independent coordinates for strange attractors from mutual information. Phys. Rev. A., 1986, vol.33, pp.1134-1140.

Grassberger P., Procaccia I. Measuring the strangeness of strange attractors. Physica D, 1983, vol.9, pp.189-208.

Gallager R.G. Information theory and reliable communication. NY: Wiley, 1968. 608 p.

Mañé R. On the dimensions of the compact invariant sets of certain non-linear maps. Dynamical systems and turbulence, Warwick 1980. Lecture Notes in Mathematics no.898. Berlin: Springer, 1981, pp.230-242. (Eds: D.A. Rand, L.S. Young).

Takens F. Detecting strange attractors in turbulence. Dynamical systems and turbulence, Warwick 1980. Lecture Notes in Mathematics no.898. Berlin: Springer, 1981, pp.366-381. (Eds: D.A. Rand, L.S. Young).

Prepelitsa G.P., Glushkov A.V., Lepikh Ya.I., Buyadzhi V.V., Ternovsky V.B., Zaichko P.A. Chaotic dynamics of non-linear processes in atomic and molecular systems in electromagnetic field and semiconductor and fiber laser devices: new approaches, uniformity and charm of chaos. Sensor Electronics and Microsystems Techn., 2014, vol.11, no.4, pp.43-57.

Hayashi K., Yasuoka Y., Nagahama H. et al. Normal seasonal variations for atmospheric radon concentration: a sinusoidal model. Journ. of Env. Radiact., 2015, vol.139, pp.149-153.

Bossew P., Dubois G., Tollefsen T. Investigations on indoor radon in Austria, part 2: Geological classes as categorical external drift for spatial modelling of the radon potential. J. Environ. Radioact., 2008, vol.99, pp.81-97.

Chambers S., Zahorowski W., Matsumoto K., Uematsu M. Seasonal variability of radon-derived fetch regions for Sado Island, Japan, based on 3 years of observations: 2002-2004. Atmos. Environ., 2009, vol.43, pp.271-279.

Published
2017-10-29
How to Cite
Glushkov, A., Gubanova, E., Khetselius, O., Prepelitsa, G., Svinarenko, A., Bunyakova, Y., & Buyadzhi, V. (2017). Analysis and forecast of the environmental radioactivity dynamics based on methods of chaos theory: general scheme and some application. Ukrainian Hydrometeorological Journal, (16), 40-45. https://doi.org/10.31481/uhmj.16.2015.05
Section
Hydrometeorological Aspects of Environmental Monitoring