Skip to main content

Advertisement

SpringerLink
Log in

A chaotic analysis on air pollution index change over past 10 years in Lanzhou, northwest China

  • Original Paper
  • Published:
Stochastic Environmental Research and Risk Assessment Aims and scope Submit manuscript

Abstract

In terms of the chaos theory, the phase-space-reconstruction method has been employed to describe the multi-dimensional phase space for the time series of air pollution index (API) during the past 10 years in Lanzhou, northwest China. The mutual information and Cao method were used to determine the reconstruction parameters, and the characteristic quantities including the Lyapunov exponent and the correlation dimension were calculated respectively. As a result, the correlation dimensions were fractioned, and the maximum Lyapunov exponent (λ 1) > 0. It shows that these presented the obvious chaotic characteristics that resulted from the evolution of non-linear chaotic dynamic system in the time series of air pollution index over the past 10 years. In the meanwhile, three or even four main dynamic variables were discussed here that could effectively interpret the changes of air pollution index time series and their causes. Some reasonable preventive countermeasures were thus put forward. These findings might provide a scientific basis for probing further into the regional complexity and evolution of the time series of air pollution index.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • An XQ, Zuo HC, Chen LJ (2007) Atmospheric environmental capacity of SO2 in winter over Lanzhou in China: a case study. Adv Atmos Sci 24:688–699

    Article  CAS  Google Scholar 

  • Anh V, Duc H, Azzi M (1997) Modeling anthropogenic trends in air quality data. J Air Waste Manage Assoc 47:66–71

    CAS  Google Scholar 

  • Ardalani-Farsa M, Zolfaghari S (2010) Chaotic time series prediction with residual analysis method using hybrid Elman–NARX neural networks. Neurocomputing 73:2540–2553

    Article  Google Scholar 

  • Cao LY (1997) Practical method for determining the minimum embedding dimension of a scalar time series. Phys D 110:43–50

    Article  Google Scholar 

  • Chen JL, Islam S, Biswas P (1998) Nonlinear dynamics of hourly ozone concentrations: nonparametric short term prediction. Atmos Environ 32:1839–1848

    Article  CAS  Google Scholar 

  • Chen L, Omaye ST, Yang W (2001) A comparison of two statistical models for analyzing the association between PM10 and hospital admissions for chronic obstructive pulmonary disease. Toxicol Mech Method 11:233–246

    CAS  Google Scholar 

  • Chu PC, Chen YC, Lu SH (2008a) Atmospheric effects on winter SO2 pollution in Lanzhou, China. Atmos Res 89:365–373

    Article  CAS  Google Scholar 

  • Chu PC, Chen YC, Lu SH, Li ZC, Lu YQ (2008b) Particulate air pollution in Lanzhou China. Environ Int 34:698–713

    Article  CAS  Google Scholar 

  • Dong ZL, He HG, Yu T, Li HY (2009) Correlation analysis on influencing factors of the atmospheric environmental quality in Lanzhou City. J Arid Land Resour Environ 23(12):49–53 (in Chinese with English abstract)

    Google Scholar 

  • Fraser AM, Swinney HL (1986) Independent coordinates for strange attractors from mutual information. Phys Rev A 33:1134–1140

    Article  Google Scholar 

  • Frazier C, Kockelman KM (2004) Chaos theory & transportation systems: an instructive example. Transp Res Rec 1897:9–17

    Article  Google Scholar 

  • Gomez-Sanchis J, Martin-Guerrero J, Soria-Olivas E, Vila-Frances J, Carrasco J, del Valle-Tascon S (2006) Neural networks for analysing the relevance of input variables in the prediction of tropospheric ozone concentration. Atmos Environ 40:6173–6180

    Article  CAS  Google Scholar 

  • Grassberger P, Procaccia I (1983a) Measuring the strangeness of strange attractor. Phys D 9:189–208

    Article  Google Scholar 

  • Grassberger P, Procaccia I (1983b) Estimation of the Kolmogorov entropy from a chaotic signal. Phys Rev A 28:2591–2593

    Article  Google Scholar 

  • Harvey AC (1989) Forecasting, structural time series models and the Kalman filter. Cambridge University Press, Cambridge

    Google Scholar 

  • Ho DS, Juang LC, Liao YY, Wang CC, Lee CK, Hsu TC, Yang YS (2004) The temporal variations of PM10 concentration in Taipei: Fractal Approach. Aerosol Air Qual Res 4:37–54

    Google Scholar 

  • Horowitz J, Barakat S (1979) Statistical analysis of the maximum concentration of an air pollutant: effects of autocorrelation and non-stationarity. Atmos Environ 13:811–818

    Article  Google Scholar 

  • Hu YQ, Zhang Q (1999) Atmospheric pollution mechanism and prevention countermeasure of the Lanzhou. China Environ Sci 19(2):119–122 (in Chinese with English abstract)

    Google Scholar 

  • Ibarra-Berastegi G, Elias A, Barona A, Saenz J, Ezcurra A, Argadona JD (2008) From diagnosis to prognosis for forecasting air pollution using neural networks: air pollution monitoring in Bilbao. Environ Modell Softw 23:622–637

    Google Scholar 

  • Jazwinski AH (1970) Stochastic processes and filtering theory. Academic Press, New York

    Google Scholar 

  • Jiang JH, Peng XD (2002) Numerical study on air pollution concentration over Lanzhou in winter under complex terrain. Plateau Meteorol 21(1):1–7 (in Chinese with English abstract)

    Google Scholar 

  • Jiang JH, Chen YC, Peng XD, Hu F, Li L (2001) Contributions of industrial and residential sources to atmospheric SO2 concentration in winter over Lanzhou. Plateau Meteorol 20(Suppl):15–21 (in Chinese with English abstract)

    Google Scholar 

  • Kin HS, Eykholt R, Salas JD (1999) Nonlinear dynamics, delay time, and embedding window. Phys D 127:48–60

    Article  Google Scholar 

  • Kocak K, Saylan L, Sen O (2000) Nonlinear time series prediction of O3 concentration in Istanbul. Atmos Environ 34:1267–1271

    Article  CAS  Google Scholar 

  • Kugiumtzis D (1996) State space reconstruction parameters in the analysis of chaotic time series: the role of the time window length. Phys D 95:13–28

    Article  Google Scholar 

  • Kukkonen J, Partanen L, Karppinen A, Ruuskanen J, Junninen H, Kolehmainen M, Niska H, Dorling S, Chatterton T, Foxall R, Cawley G (2003) Extensive evaluation of neural network models for the prediction of NO2 and PM10 concentrations, compared with a deterministic modelling system and measurements in central Helsinki. Atmos Environ 37:4539–4550

    Article  CAS  Google Scholar 

  • Kumar U, Prakash A, Jain VK (2008) Characterization of chaos in air pollutants: a Volterra–Wiener–Korenberg series and numerical Titration approach. Atmos Environ 42:1537–1551

    Article  CAS  Google Scholar 

  • Kurt A, Gulbagci B, Karaca F (2008) An online air pollution forecasting system using neural networks. Environ Int 34:592–598

    Article  CAS  Google Scholar 

  • Lee CK (2002) Multifractal characteristics in air pollutant concentration time series. Water Air Soil Pollut 135:389–409

    Article  CAS  Google Scholar 

  • Lee CK, Lin SH (2008) Chaos in air pollutant concentration (APC) time series. Aerosol Air Qual Res 8(4):381–391

    CAS  Google Scholar 

  • Lee CK, Ho DS, Yu CC, Wang CC (2003) Fractal analysis of temporal variation of air pollutant concentration by box counting. Environ Modell Softw 18:243–251

    Article  Google Scholar 

  • Lee IF, Biswas P, Islam S (1994) Estimation of the dominant degrees of freedom for air pollutant concentration data: applications to ozone measurements. Atmos Environ 28:1707–1714

    Article  Google Scholar 

  • Li J, Tang H (1998) Model for predicting the acidity of precipitation in China. China Environ Sci 18(1):8–11 (in Chinese with English abstract)

    CAS  Google Scholar 

  • Li IF, Biswas P, Islam S (1994) Estimation of the dominant degrees of freedom for air pollutant concentration data: applications to ozone measurements. Atmos Environ 28:1707–1714

    Article  CAS  Google Scholar 

  • Liang SX, Wu H, Li ZC, Zheng J, Dong ZM (2010) Fuzzy mathematics-based comprehensive evaluation of dynamics of atmospheric environmental quality. J Arid Land Resour Environ 24(6):77–81 (in Chinese with English abstract)

    Google Scholar 

  • Liu LC, Fan Y, Wu G, Wei YM (2007) Using LMDI method to analyze the change of China’s industrial CO2 emissions from final fuel use: an empirical analysis. Energy Policy 35:5892–5900

    Article  Google Scholar 

  • Lorenz EN (1963) Detemministic nonperiodic flow. J Atmos Sci 20:130–141

    Article  Google Scholar 

  • Lorenz EN (1993) The essence of chaos. UCL Press, Los Angeles

  • Ma JH, Liu LX (2007) Testing for nonlinearity in time series of monthly rainfall in Yunnan Province. J Syst Eng 22(6):561–567 (in Chinese with English abstract)

    Google Scholar 

  • Martinerie JM, Albano AM, Mees AI, Rapp PE (1992) Mutual information, strange attractors, and the optimal estimation of dimension. Phys Rev A 45:7058–7064

    Article  Google Scholar 

  • Millán H, Ghanbarian-Alavijeh B, García-Fornaris I (2010) Nonlinear dynamics of mean daily temperature and dewpoint time series at Babolsar, Iran, 1961–2005. Atmos Res 98:89–101

    Article  Google Scholar 

  • OECD (2007) OECD Annual Report 2007: Environmental Performance Review of China. The Public Affairs Division, Public Affairs and Communications Directorate, Paris

  • Ott E, Sauer T, Yorke JA (1994) Coping with Chaos. Wiley, New York

    Google Scholar 

  • Packard NH, Crutchfield JP, Farmers JD, Shaw RS (1980) Geometry from a time series. Phys Rev Lett 45:712–716

    Article  Google Scholar 

  • Poon C, Barahona M (2001) Titration of chaos with added noise. Proc Natl Acad Sci USA 98:7107–7112

    Article  CAS  Google Scholar 

  • Raga GB, Le Moyne L (1996) On the nature of air pollution dynamics in Mexico City—I, nonlinear analysis. Atmos Environ 30:3987–3993

    Article  CAS  Google Scholar 

  • Rosenstein MT, Collins JJ, De Luca CJ (1993) A practical method for calculating largest Lyapunov exponents from small data sets. Phys D 65:117–134

    Article  Google Scholar 

  • Saarikoski S, Sillanpää M, Sofiev M, Timonen H, Saarnio K, Teinilä K, Karppinen A, Kukkonen J, Hillamo R (2007) Chemical composition of aerosols during a major biomass burning episode over northern Europe in spring 2006: experimental and modelling assessments. Atmos Environ 41:3577–3589

    Article  CAS  Google Scholar 

  • Sannasiraj SA, Zhang H, Vladan Babovic, Chan ES (2004) Enhancing tidal prediction accuracy in a deterministic model using chaos theory. Adv Water Resour 27:761–772

    Article  Google Scholar 

  • Schlink U, Stephen D, Emil P, Giuseppe N, Gavin C, Heikki J, Alison G, Rob F, Krystof E (2003) A rigorous inter-comparison of ground-level ozone predictions. Atmos Environ 37:3237–3253

    Article  CAS  Google Scholar 

  • Schlink U, Herbarth O, Richter M, Dorling S, Nunnari G, Cawley G, Pelikan E (2006) Statistical models to assess the health effects and to forecast ground-level ozone. Environ Modell Softw 21:547–558

    Article  Google Scholar 

  • Shang KZ, Da CY, Fu YZ, Wang SG, Yang DB (2001) The stable energy in Lanzhou city and the relations between air pollution and it. Plateau Meteorol 20(1):76–81 (in Chinese with English abstract)

    Google Scholar 

  • Shi K, Liu CQ, Ai NS, Zhang XH (2008) Using three methods to investigate time-scaling properties in air pollution indexes time series. Nonlinear Anal Real World Appl 9:693–707

    Article  Google Scholar 

  • Sivakumar B (2000) Chaos theory in hydrology: important issues interpretations. J Hydrol 227:1–20

    Article  Google Scholar 

  • Sivakumar B (2004) Chaos theory in geophysics: past, present and future. Chaos Solitons Fract 19:441–462

    Article  Google Scholar 

  • Sivakumar B, Wallender WW, Horwath WR, Mitchell JP (2007) Nonlinear deterministic analysis of air pollution dynamics. Adv Complex Syst 10:581–597

    Article  Google Scholar 

  • Slini T, Kaprara A, Karatzas K, Moussiopoulos N (2006) PM10 forecasting for Thessaloniki, Greece. Environ Modell Softw 21:559–565

    Article  Google Scholar 

  • Song HJ, Miao CY, Shen ZQ, Roel W, Maja DH, Franck C (2010) Design of fuzzy cognitive maps using neural networks for predicting chaotic time series. Neural Netw 23:1264–1275

    Article  CAS  Google Scholar 

  • Sun YB, Piyamarn S, Vladan B, Chan ES (2009) Efficient data assimilation method based on chaos theory and Kalman filter with an application in Singapore Regional Model. J Hydro Environ Res 3:85–95

    Article  CAS  Google Scholar 

  • Ta WQ, Wang T, Xiao HL, Zhu XY, Xiao Z (2004) Gaseous and particulate air pollution in the Lanzhou Valley, China. Sci Total Environ 320:163–176

    Article  CAS  Google Scholar 

  • Takens F (1981) Detecting strange attractors in fluid turbulence. Lect Notes Math 898:366–381

    Article  Google Scholar 

  • Tao JH, Huang YX, Lu DR (2007) Influence of sand-dust activities in Hexi Corridor on PM10 concentration in Lanzhou and its assessment. J Desert Res 27(4):272–276 (in Chinese with English abstract)

    Google Scholar 

  • Tao ZN, Geoffrey H, Kieran D (2010) An economic analysis of Midwestern US criteria pollutant emissions trends from 1970 to 2000. Ecol Econ 691:666–1674

    Google Scholar 

  • Tian QX, Zhou LZ, Wang R, Tian ZM (2001) The pollution law of the metal and nonmetal elements in the aerosol in Lanzhou. Environ Monitor China 17(7):18–22 (in Chinese with English abstract)

    Google Scholar 

  • Tunç GI, Türüt-Aşik S, Akbostancı E (2009) A decomposition analysis of CO2 emissions from energy use: Turkish case. Energy Policy 37:4689–4699

    Article  Google Scholar 

  • Wang JM (1992) Turbulence characteristics in an urban atmosphere of complex terrain. Atmos Environ 26:2717–2724

    Google Scholar 

  • Wang XK, Lu WZ (2006) Seasonal variation of air pollution index: Hong Kong case study. Chemosphere 63:1261–1272

    Article  CAS  Google Scholar 

  • Wang SG, Yang M, Qi B, Xin CL, Yang MF (1999) Influence of sand-dust storms occurring over the Gansu Hexi district on the air pollution in Lanzhou city. J Desert Res 19(4):354–358 (in Chinese with English abstract)

    Google Scholar 

  • Wang SG, Jiang DB, Yang DB, Shang KZ, Qi B (2000) A study on characteristics of change of maximum mixing depths in Lanzhou. Plateau Meteorol 19(3):363–370 (in Chinese with English abstract)

    Google Scholar 

  • Wang SG, Yuan W, Shang KZ (2006) The impacts of different kinds of dust events on PM10 pollution in northern China. Atmos Environ 40:7975–7982

    Article  CAS  Google Scholar 

  • Wang SG, Feng XY, Zeng XQ, Ma YX, Shang KZ (2009) A study on variations of concentrations of particulate matter with different sizes in Lanzhou, China. Atmos Environ 43:2823–2828

    Article  CAS  Google Scholar 

  • Windsor HL, Toumi R (2001) Scaling and persistence of UK pollution. Atmos Environ 35:4545–4556

    Article  CAS  Google Scholar 

  • Wolf A, Swift JB, Swinny HL et al (1985) Determining Lyapunov exponents from a time serises. Phys D 16:285–317

    Article  Google Scholar 

  • Xia DS, Yang LP, Ma JY, Yu Y, Wang G, Chen FH (2007) Magnetic characteristics of dustfall in urban area of north China and its environmental significance. Sci China Ser D Earth Sci 50:1724–1732

    Article  CAS  Google Scholar 

  • Xie XJ, Li J, Wang ZF (2010) Numerical simulation of diurnal variations of the air pollutants in winter of Lanzhou city. Clim Environ Res 15(5):695–703 (in Chinese with English abstract)

    Google Scholar 

  • Xu H, Zhai J, Liu ZQ, Zhang JQ (2003) Effect of energy structure on atmospheric environment of Lanzhou. Urban Environ Urban Ecol 16(1):73–75 (in Chinese with English abstract)

    CAS  Google Scholar 

  • Zhang Q (2003) A study of the interaction between pollutants concentration and the climatic and environmental factors of Lanzhou. J Lanzhou Univ (Nat Sci) 39(1):99–106 (in Chinese with English abstract)

    CAS  Google Scholar 

  • Zhang W, Hu B, Chen CH, Du P, Zhang L, Feng GH (2004) Scattering properties of atmospheric aerosols over Lanzhou city and applications using an integrating nephelometer. Adv Atmos Sci 21:848–856

    Article  Google Scholar 

  • Zhang N, Li LP, Wang SG, Wang D, Wang Z (2008) The composition characteristics of main inorganic ions in atmospheric aerosol of the urban and atmospheric background in Lanzhou city in winter. Environ Chem 27(4):494–498 (in Chinese with English abstract)

    CAS  Google Scholar 

  • Zhu JL, Liu ZG (2003) Long-range persistence of acid deposition. Atmos Environ 37:2605–2613

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The authors are grateful to Professor Yong Li of Institute of Mountain Hazards and Environment, Chinese Academy of Sciences and two anonymous reviewers for their insightful comments and valuable advice. This study is financially supported by the Program for New Century Excellent Talents in University of China (Grant No. NCET-08-0379).

Author information

Authors and Affiliations

  1. College of Architecture and Environment, Sichuan University, No. 24, South Sect. 1, First Ring Road, Chengdu, 610065, Sichuan, China

    Bo Yu & Chengmin Huang

  2. Land and Resources College, China West Normal University, Nanchong, 637009, China

    Zuhan Liu & Haipeng Wang

  3. Information Management College, Chengdu University of Technology, Chengdu, 610059, China

    Lili Wang

Authors
  1. Bo Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chengmin Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zuhan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Haipeng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Lili Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chengmin Huang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yu, B., Huang, C., Liu, Z. et al. A chaotic analysis on air pollution index change over past 10 years in Lanzhou, northwest China. Stoch Environ Res Risk Assess 25, 643–653 (2011). https://doi.org/10.1007/s00477-011-0471-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-011-0471-y

Keywords

Search

Navigation