An effective chaos-geometric computational approach to analysis and prediction of evolutionary dynamics of the environmental systems: Atmospheric pollution dynamics

Abstract

An effective chaos-geometric computational approach to analysis and prediction of evolutionary dynamics of the environmental systems: Atmospheric pollution dynamics Abstract. The present paper concerns the results of computational studying dynamics of the atmospheric pollutants (dioxide of nitrogen, sulphur etc) concentrations in an atmosphere of the industrial cities (Odessa) by using the dynamical systems and chaos theory methods. A chaotic behaviour in the nitrogen dioxide and sulphurous anhydride concentration time series at several sites of the Odessa city is numerically investigated. As usually, to reconstruct the corresponding attractor, the time delay and embedding dimension are needed. The former is determined by the methods of autocorrelation function and average mutual information, and the latter is calculated by means of a correlation dimension method and algorithm of false nearest neighbours. Further, the Lyapunov's exponents spectrum, Kaplan-Yorke dimension and Kolmogorov entropy are computed. It has been found an existence of a low-D chaos in the time series of the atmospheric pollutants concentrations. IntroductionThe last decades have seen a great progress in the understanding, analysis, modelling and evet prediction of the evolutionary dynamics of nonlinear complex systems. Various methods and algorithms of the modern theory of dynamical systems and a chaos theory became a powerful tool in computational studying complex non-linear statistical systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Many studies in different fields of science and technique have appeared, where the chaos theory methods were applied to a great number of dynamical systems. The studies concerning non-linear behaviour in the time series of atmospheric constituent concentrations are sparse, and their outcomes are ambiguous. In ref. [5] there is an analysis of the NO 2 , CO, O 3 concentrations time series and is not received an evidence of chaos. Also, it was shown that O 3 concentrations in Cincinnati (Ohio) and Istanbul are evidently chaotic, and non-linear approach provides satisfactory results [6]. In Ref.[14] it has been fulfilled the detailed analysis of the NO 2 , CO, CO 2 concentration time series in the Gdansk region (Polland) and it has been definitely obtained the evidence of a chaos. Moreover it has been given a short-range forecast of atmospheric pollutants time evolution using non-linear prediction method. These studies show that chaos theory methodology can be applied and the short-range forecast by the non-linear prediction method can be satisfactory. Time series of concentrations are however not always chaotic, and chaotic behaviour must be examined for each time series.In this work we study the temporal dynamics of the atmospheric constituents concentration in the Odessa region by using the non-linear prediction and chaos theory methods [3,4,[12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. A chaotic

Nonlinear Dynamics of the Industrial City’s Atmospheric Ventilation: New Differential Equations Model and Chaotic Ventilation

“…The physics of these processes in details is described in Refs. [2][3][4][5][6][7][8][9][10][11][12][13][14]). Here it is important to remind that turbulent vortices over the urban area should be in the interaction of resonant contact with turbulent vortices of cloud masses.…”

“…More details are in Refs. [2][3][4][5][6][7][8][9][10][14][15][16][17]. All computing is carried out with using the PC codes "Geomath", "Quantum Chaos", "ScanPoints" [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

“…Moreover, the application of modern methods of a chaos theory allows us to describe the most complex nonlinear and chaotic processes in many dynamical systems from a new point of view. The aim of our work is a quantitative study of nonlinear, chaotic phenomena in the nonequilibrium atmosphere of industrial cities based on the methods of the theory of dynamical systems, classical models with systems of hydrodynamic differential equations, generalized to the case of taking into account the chaos phenomenon, as well as the characteristics of chaotic (vortex) ventilation [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

“…In this chapter we present an elaborated advanced approach to the simulation of chaotic heat and air ventilation in atmosphere of an industrial region. It is based on the Arakawa-Schubert model of calculation of cloud convection, modified to calculate the current involvement of the ensemble of clouds, and hydrodynamical prediction model (with correct quantitative accounting for the turbulence in an atmosphere of the urban zone) [2][3][4][5][6][7][8][9][10][11][12][13][14]. The key moment of the total approach is linked with using complex geophysical plane field method.…”