Environmental SystemsNo Access

NONLINEAR DETERMINISTIC ANALYSIS OF AIR POLLUTION DYNAMICS IN A RURAL AND AGRICULTURAL SETTING

Department of Land, Air and Water Resources, University of California, Davis, California 95616, USA

Corresponding author.

Departments of Land, Air and Water Resources, and Biological and Agricultural Engineering, University of California, Davis, California 95616, USA

Search for more papers by this author

WILLIAM R. HORWATH

Department of Land, Air and Water Resources, University of California, Davis, California 95616, USA

Search for more papers by this author

, and

JEFFREY P. MITCHELL

Department of Vegetable Crops and Weed Science, University of California, Davis, California 95616, USA

Search for more papers by this author

https://doi.org/10.1142/S0219525907001288Cited by:11 (Source: Crossref)

Abstract

Applications of nonlinear dynamic tools for studying air pollution are gaining attention. Studies on ozone concentration in urban areas have reported the presence of low-dimensional deterministic natures and thus the possibility of good predictions of air pollution dynamics. In light of these encouraging results, a nonlinear deterministic approach is employed herein to study air pollution dynamics in a rural, and largely agricultural, setting in California. Specifically, air quality index (AQI) data observed at the University of California, Davis/National Oceanic and Atmospheric Administration (UCD/NOAA) climate station are studied. Four different daily AQI types of data are analyzed: maximum, minimum, difference (between maximum and minimum), and average. The correlation dimension method, a nonlinear dynamic technique that uses phase–space reconstruction and nearest neighbor concepts, is employed to identify the nature of the underlying dynamics, whether high-dimensional or low-dimensional. Correlation dimensions of 5.12, 6.20, 6.68, and 5.84 obtained for the above four series, respectively, indicate the presence of low-dimensional deterministic behavior, with six or seven dominant governing variables in the underlying dynamics. The dimension results and number of variables are in reasonable agreement with those reported by past studies, even though the studied data are different: rural versus urban, and AQI versus ozone concentration. Future efforts will focus on strengthening the present results on the nature of air pollution dynamics, identifying the actual governing variables, and predictions of air pollution dynamics.

Keywords:

References

S. Khan, A. R. Ganguly and S. Saigal, Nonlinear Proc. Geophys. 12, 41 (2005). Web of Science, Google Scholar
T. Y. Chang and M. J. Suzio, J. Air Waste Manage. Assoc. 45, 20 (1995). Web of Science, Google Scholar
E. N. Lorenz, Nature 353, 241 (1991), DOI: 10.1038/353241a0. Web of Science, Google Scholar
K. Fraedrich, J. Atmos. Sci. 43, 419 (1986). Web of Science, Google Scholar
R. Berndtssonet al., Trends Hydrol. 1, 291 (1994). Google Scholar
J. L. Chen, S. Islam and P. Biswas, Atmos. Environ. 32, 1839 (1998), DOI: 10.1016/S1352-2310(97)00399-3. Web of Science, Google Scholar
W. W. Heck , O. C. Taylor and D. T. Tingey , Assessment of Crop Loss from Air Pollutants ( Elsevier , London , 1988 ) . Google Scholar
S. R. Templeet al., Am. J. Alternative Agr. 9, 64 (1994). Google Scholar
G. Sugihara and R. M. May, Nature 344, 734 (1990), DOI: 10.1038/344734a0. Web of Science, Google Scholar
C. Nicolis and G. Nicolis, Nature 311, 529 (1984), DOI: 10.1038/311529a0. Web of Science, Google Scholar
L. A. Smith, Phys. Lett. A 133, 283 (1988), DOI: 10.1016/0375-9601(88)90445-8. Web of Science, Google Scholar
J. Olsson, J. Niemczynowicz and R. Berndtsson, J. Geophys. Res. D 98, 23265 (1993), DOI: 10.1029/93JD02658. Web of Science, Google Scholar
A. R. Osborne and A. Provenzale, Physica D 35, 357 (1989), DOI: 10.1016/0167-2789(89)90075-4. Web of Science, Google Scholar
N. H. Packardet al., Phys. Rev. Lett. 45, 712 (1980), DOI: 10.1103/PhysRevLett.45.712. Web of Science, Google Scholar
F. Takens, Dynamical Systems and Turbulence, Lecture Notes in Mathematics 898, eds. D. A. Rand and L. S. Young (Springer-Verlag, Berlin, 1981) pp. 366–381. Google Scholar
S. Islam, R. L. Bras and I. Rodriguez-Iturbe, J. Appl. Meteorol. 32, 203 (1993). Web of Science, Google Scholar
B. Sivakumaret al., Water Resour. Res. 38(2), (2002), DOI: 10.1029/2001WR000333. Google Scholar
L. C. Murray and R. J. Farber, Atmos. Environ. 16, 2299 (1982). Web of Science, Google Scholar
A. A. Tsonis , Chaos: From Theory to Applications ( Plenum Press , New York , 1992 ) . Google Scholar
I. F. Li, P. Biswas and S. Islam, Atmos. Environ. 28, 1701 (1994). Google Scholar
J. W. Havstad and C. L. Ehlers, Phys. Rev. A 39, 845 (1989), DOI: 10.1103/PhysRevA.39.845. Web of Science, Google Scholar
B. Sivakumar, J. Hydrol. 227, 1 (2000), DOI: 10.1016/S0022-1694(99)00186-9. Web of Science, Google Scholar
A. M. Frazer and H. L. Swinney, Phys. Rev. A 33, 1134 (1986). Web of Science, Google Scholar
A. S. Heagle, Annu. Rev. Phytopathol. 27, 397 (1989). Web of Science, Google Scholar
A. A. Tsonis, J. B. Elsner and K. P. Georgakakos, J. Atmos. Sci. 50, 2549 (1993). Web of Science, Google Scholar
D. Schertzeret al., Hydrol. Sci. J. 47, 139 (2002). Web of Science, Google Scholar
S. T. Rao and I. G. Zurbenko, J. Air Waste Manage. Assoc. 44, 1089 (1994). Web of Science, Google Scholar
E. N. Lorenz, J. Atmos. Sci. 20, 130 (1963). Web of Science, Google Scholar
M. C. Dodge, J. Geophys. Res. D 94, 5121 (1989), DOI: 10.1029/JD094iD04p05121. Web of Science, Google Scholar
P. Grassberger and I. Procaccia, Physica D 9, 189 (1983), DOI: 10.1016/0167-2789(83)90298-1. Web of Science, Google Scholar
J. Holzfuss and G. Mayer-Kress, Dimensions and Entropies in Chaotic Systems, ed. G. Mayer-Kress (Springer, New York, 1986) pp. 114–122. Google Scholar
R. W. Simpson and A. P. Layton, Atmos. Environ. 17, 1649 (1983). Web of Science, Google Scholar
T. Schreiber and H. Kantz, Predictability of Complex Dynamical Systems, Springer Series in Synergetics, eds. Yu. A. Kravtsov and J. B. Kadtke (Springer, Berlin, 1996) pp. 43–65. Google Scholar
T. L. Clark and T. T. Karl, J. Appl. Meteorol. 21, 1662 (1982). Web of Science, Google Scholar
T. Frison, Trading on the Edge: Neural, Genetic, and Fuzzy Systems for Chaotic Financial Markets, ed. G. J. Deboeck (Wiley, New York, 1994) pp. 280–296. Google Scholar
B. Sivakumaret al., Hydrol. Sci. J. 47, 149 (2002). Web of Science, Google Scholar
J. H. Seinfeld, J. Atmos. Pollut. Control Assoc. 38, 616 (1988). Google Scholar
K. Koçak, L. Şaylan and O. Şen, Atmos. Environ. 34, 1267 (2000). Web of Science, Google Scholar
G. T. Wolff and P. J. Lioy, J. Atmos. Pollut. Control Assoc. 28, 1034 (1978). Google Scholar
B. Sivakumar, Chaos Soliton Fract. 19, 441 (2004), DOI: 10.1016/S0960-0779(03)00055-9. Web of Science, Google Scholar
B. Sivakumar, Hydrol. Process. 18, 2349 (2004), DOI: 10.1002/hyp.5606. Web of Science, Google Scholar
B. Sivakumar, Hydrol. Sci. J. 50, 591 (2005), DOI: 10.1623/hysj.2005.50.4.591. Google Scholar
B. Sivakumaret al., J. Hydrol. 219, 103 (1999), DOI: 10.1016/S0022-1694(99)00051-7. Web of Science, Google Scholar
I. Iturbeet al., Water Resour. Res. 25, 1667 (1989), DOI: 10.1029/WR025i007p01667. Web of Science, Google Scholar
W. Leibert and H. G. Schuster, Phys. Lett. A 141, 386 (1989). Web of Science, Google Scholar
S. M. Robeson and D. G. Steyn, Atmos. Environ. B 24, 303 (1990), DOI: 10.1016/0957-1272(90)90036-T. Web of Science, Google Scholar
G. B. Raga and L. Le Moyne, Atmos. Environ. 30, 3987 (1996), DOI: 10.1016/1352-2310(96)00122-7. Web of Science, Google Scholar
A. A. Tsonis and J. B. Elsner, Nature 333, 545 (1988), DOI: 10.1038/333545a0. Web of Science, Google Scholar
U. Hertstein, L. Grünhage and H. J. Jäger, Atmos. Environ. 26, 2031 (1995). Web of Science, Google Scholar
B. Sivakumar, Hydrol. Earth Syst. Sci. 5, 645 (2001). Web of Science, Google Scholar
J. D. Farmer and J. J. Sidorowich, Phys. Rev. Lett. 59, 845 (1987), DOI: 10.1103/PhysRevLett.59.845. Web of Science, Google Scholar