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Self-Organized Critical Behavior of Acid Deposition

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Abstract

By employing empirical probability distribution function and power spectrum analysis together with detrended fluctuation analysis (DFA), we show that acid deposition events are analogous to avalanches of granular piles displaying self-organized criticality (SOC). Under a wide variety of circumstances, frequency distributions of hydrogen ion concentration (HIC) and weekly hydrogen deposition (WHD) of precipitation are consistent with double power-law in two different regimes separated by a crossover HIC or a crossover WHD. WHD series can be depicted as 1/fβ noise (β = 0.3–1.3) with long-range correlations (LRC). And we argue that the critical state of atmospheric acid deposition refers to the normal acidity of water in atmosphere, or the environmental capacity. Therefore, acid deposition evolution is consistent with the three criteria of complex SOC systems. We thus suggest that SOC may be a possible mechanism underlying acid deposition evolution.

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References

  • Aegerter, C. M.: 2003, ‘A sandpile model for the distribution of rainfall?’, Physica A 319, 1.

    Google Scholar 

  • Ausloos, M.: 2000, ‘Statistical physics in foreign exchange currency and stock markets’, Physica A 285, 48.

    Google Scholar 

  • Axtell, R. L.: 2001, ‘Zipf distribution of U.S. firm sizes’, Science 293, 1818.

    Article  CAS  PubMed  Google Scholar 

  • Bak, P.: 1996, How Nature Works: The Science of Self-Organized Criticality, Copernicus, Springer, New York.

    Google Scholar 

  • Bak, P., Tang, C. and Wiesenfeld, K.: 1988, ‘Self-organized criticality’, Phys. Rev. A 38, 364.

    Article  PubMed  Google Scholar 

  • Bak, P. and Tang, C.: 1989, ‘Earthquakes as a self-organized critical phenomenon’, J. Geophys. Res. 94, 15635.

    Google Scholar 

  • Bak, P., Tang, C. and Wiesenfeld, K.: 1987, ‘Self-organized criticality: An explanation of 1/f noise’, Phys. Rev. Lett. 59, 381.

    Article  PubMed  Google Scholar 

  • Bernardo, A., Huberman, L. and Adamic, A.: 1999, ‘Growth dynamics of the World-Wide Web’, Nature 401, 131.

    PubMed  Google Scholar 

  • Beverland, I. J., Crowther, J. M. and Srinivas, M. S. N.: 1997, ‘Acid deposition during two contrasting frontal rainfall events’, Water Air Soil Pollut. 96, 93.

    Article  CAS  Google Scholar 

  • Butler, T. J. and Likens, G. E.: 1998, ‘Weekly and daily precipitation chemistry network comparisons in the Eastern U. S.: NADP/NTN vs MAP3S/AIRMoN’, Atmos. Environ. 32(21), 3749.

    Article  CAS  Google Scholar 

  • Canning, D., Amaral, L. A. N., Lee, Y., Meyer, M. and Stanley, H. E.: 1998, ‘Scaling the volatility of GDP growth rates’, Econ. Lett. 60, 335.

    Article  Google Scholar 

  • D’Odorico, P. and Rodríguez-Iturbe, I.: 2000, ‘Space-time self-organization of mesoscale rainfall and soil moisture’, Adv. Water Resour. 23, 349.

    Article  Google Scholar 

  • Dimri, V. P. and Ravi, P. M.: 2001, ‘Scaling of power spectrum of extinction events in the fossil record’, Earth Plan. 186, 363.

    Article  CAS  Google Scholar 

  • Driejana, Lee, D. S., Kingdon, R. D., Raper, D. W. and Gee, I. L.: 2001, ‘Modelling acidic deposition in the United Kingdom at a scale of 5 km by 5 km’, Water Air Soil Pollut. 130, 319.

    Article  Google Scholar 

  • Gopikrishnan, P., Plerou, V., Nunes, A. L. A., Meyer, M. and Stanley, H. E.: 1999, ‘Scaling of the distribution of fluctuations of financial market indices’, Phys. Rev. E 60, 5305.

    Article  CAS  Google Scholar 

  • Han, B., Kim, J. and Cho, S.: 2001, ‘A numerical simulation of acid deposition in East Asia’, Water Air Soil Pollut. 130, 487.

    Article  Google Scholar 

  • Harte, J., Kinzig, A. and Green, J.: 1999, ‘Self-similarity in the distribution and abundance of species’, Science 284, 334.

    Article  CAS  PubMed  Google Scholar 

  • Hedin, L. O. and Likens, G. E.: 1996, ‘Atmospheric dust and acid rain’, Sci. Am. 275, 88.

    CAS  Google Scholar 

  • Held, G. A.: 1990, ‘Experimental study of critical mass fluctuation in an evolving sand pile’, Phys. Rev. Lett. 65, 1120.

    Article  PubMed  Google Scholar 

  • Hergarten, S. and Neugebauer, H. J.: 1998, ‘Self-organized criticality in a landslide model’, Geophys. Res. Lett. 25, 801.

    Article  Google Scholar 

  • Klemm, O. and Lange, H.: 1999, ‘Trends of air pollution in the Fichtelgebirge Mountains, Bavaria’, Environ. Sci. Pollut. Res. 6, 193.

    CAS  Google Scholar 

  • Lovejoy, S. and Schertzer, D.: 1985, ‘Generalized scale invariance and fractal models of rain’, Water Resour. Res. 21, 1233.

    Google Scholar 

  • Lovejoy, S.: 1982, ‘Area-perimeter relation for rain and cloud areas’, Science 216(4542), 185.

    Google Scholar 

  • Malamud, B. D., Morein, G. and Turcotte, D. L.: 1998, ‘Forest fires: An example of self-organized critical behavior’, Science 281, 1840.

    Article  CAS  PubMed  Google Scholar 

  • Mantegna, R. N., Buldyrev, S. V., Goldberger, A. L., Havlin, S., Peng, C.-K., Simons, M. and Stanley, H. E.: 1994, ‘On long-range power-law correlations in DNA’, Phys. Rev. Lett. 73, 3169.

    Article  CAS  PubMed  Google Scholar 

  • Matsoukas, C., Islam, S. and Rodriguez-Iturbe, I.: 2000, ‘Detrended fluctuation analysis of rainfall and streamflow time series’. J. Geophys. Res. 105, 29165.

    Article  Google Scholar 

  • Nadim, F., Stapcinskaite, S., Trahiotis, M. M., Perkins, C., Carley, R., Liu, S. and Yang, X.: 2003, ‘The effect of precipitation amount and atmospheric concentrations on wet deposition fluxes of oxidized and reduced nitrogen species in Connecticut’, Water Air Soil Pollut. 143, 315.

    Article  CAS  Google Scholar 

  • National Atmospheric Deposition Program (NRSP-3)/National Trends Network, 2002. NADP Program Office, Illinois State Water Survey, 2204 Griffith Drive, Champaign, IL 61820.

  • Over, T. M. and Gupta, V.: 1996, ‘A space-time theory of mesoscale rainfall using random cascades’, J. Geophys. Res. 101, 26319.

    Article  Google Scholar 

  • Nunes Amaral, L. A., Buldyrev, S. V., Havlin, S., Salinger, M. A. and Stanley, H. E.: 1998, ‘Power-law scaling for a system of interacting units with complex internal structure’, Phys. Rev. Lett. 80, 1385.

    Article  Google Scholar 

  • Olsson, J., Niemczynowicz, J. and Berndtsson, R.: 1993, ‘Fractal analysis of high-resolution rainfall time series’, J. Geophys. Res. 98, 23265.

    Google Scholar 

  • Peng, C.-K., Havlin, S., Stanley, H. E. and Goldberger, A. L.: 1995, ‘Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series’, Chaos 5, 82.

    Article  CAS  PubMed  Google Scholar 

  • Peters, O., Hertlein, C. and Christensen, K.: 2002, ‘A complex view of rainfall’, Phys. Rev. Lett. 88, 018701.

    Article  PubMed  Google Scholar 

  • Peters-Lidard, C. D., Pan, F. and Wood, E. F.: 2001, ‘A re-examination of modeled and measured soil moisture spatial variability and its implications for land surface modeling’, Adv. Water Resour. 24, 1069.

    Article  Google Scholar 

  • Pelletier, J. D. and Turcotte, D. L.: 1997, ‘Long-range persistence in climatological and hydrological time series: Analysis, modeling and application to drought hazard assessment’, J. Hydrol. 203, 198.

    Article  Google Scholar 

  • Plotnick, R. E. and Sepkoski Jr., J. J.: 2001, ‘A multiplicative multifractal model for originations and extinctions’, Paleobiology 27(1), 126.

    Google Scholar 

  • Ricotta, C., Avena, G. C. and Marchetti, M.: 1999, ‘The flaming sandpile: Self-organized criticality and wildfires’, Ecol. Model. 119, 73.

    Article  Google Scholar 

  • Ricotta, C., Arianoutsou, M., Diaz-Delgado, R., Duguy, B., Lloret, F., Maroudi, E., Mazzoleni, S., Moreno, J. M., Rambal, S., Vallejo, R. and Vazquez, A.: 2001, ‘Self-organized criticality of wildfires ecologically revisited’, Ecol. Model. 141, 307.

    Article  Google Scholar 

  • Rodríguez-Iturbe, I., Marani, M., D’Odorico, P. and Rinaldo, A.: 1998a, ‘On space-time scaling of cumulated rainfall fields’, Water Resour. Res. 34(12), 3461.

    Article  Google Scholar 

  • Rodríguez-Iturbe, I., D’Odorico, P. and Rinaldo, A.: 1998b, ‘A possible self-organizing dynamics for land-atmosphere interaction’, J. Geophys. Res. 108 (D18), 23071.

    Article  Google Scholar 

  • Ruijgrok, W. and Romer, F. G.: 1993, ‘Aspects of wet acidifying deposition in Arnhem: Source regions, correlations and trends (1984–1991)’, Atmos. Environ. 27A, 637.

    CAS  Google Scholar 

  • Rybczynski, M., Wodarczyk, Z. and Wilk, G.: 2001, ‘Self-organized criticality in atmospheric cascades’, Nucl. Phys. B-P 97, 81.

    CAS  Google Scholar 

  • Sirois, A.: 1993, ‘Temporal variation of sulphate and nitrate concentrations in precipitation in Eastern North America: 1979–1990’, Atmos. Environ. 27A, 945.

    CAS  Google Scholar 

  • Stanley, H. E., Amaral, L. A. N., Gopikrishnan, P., Ivanov, P. Ch., Keitt, T. H. and Plerou, V.: 2000, ‘Scale invariance and universality: Organizing principles in complex systems’, Physica A 281, 60.

    Google Scholar 

  • Svensson, C., Olsson, J. and Berndtsson, R.: 1996, ‘Multifractal properties of daily rainfall in two different climates’, Water Resour. Res. 32, 2463.

    Article  Google Scholar 

  • Turcotte, D. L., Malamud, B. D., Guzzetti, F. and Reichenbach, P.: 2002, ‘Self-organization, the cascade model, and natural hazards’, Proc. Natl. Acad. Sci. USA 99, 2530.

    Article  PubMed  Google Scholar 

  • Ulrych, T. J. and Bishop, T. N.: 1975, ‘Maximum entropy spectral analysis and autoregressive decomposition’, Rev. Geophys. Space Phys. 13, 183.

    Google Scholar 

  • West, L. M. and Feaglwy, S. E.: 1995, ‘The chemical composition of the atmospheric deposition collected from six Louisiana sites from 1983 to 1992’, Atmos. Environ. 29, 1211.

    Article  CAS  Google Scholar 

  • Windsor, H. L. and Toumi, R.: 2001, ‘Scaling and persistence of UK pollution’, Atmos. Environ. 35, 4545.

    Article  CAS  Google Scholar 

  • Zhu, J. and Liu, Z.: 2003, ‘Power-law distribution of acid deposition’, Int. J. Environ. Pollut. 19, 11.

    CAS  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Environmental Science and Engineering, Hunan University, Changsha, 410082, P.R. China

    Jianlin Zhu, Guangming Zeng, Xing Zhao, Guohe Huang & Yimin Jiang

  2. Faculty of Architectural, Civil Engineering & Environment, Ningbo University, Ningbo, 315211, P.R. China

    Jianlin Zhu

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  1. Jianlin Zhu
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  2. Guangming Zeng
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  3. Xing Zhao
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  4. Guohe Huang
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Correspondence to Guangming Zeng.

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Zhu, J., Zeng, G., Zhao, X. et al. Self-Organized Critical Behavior of Acid Deposition. Water Air Soil Pollut 162, 295–313 (2005). https://doi.org/10.1007/s11270-005-2990-y

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