Atmospheric Chemistry and Physics www.atmos-chem-phys.net 1680-7316 1680-7324 7 3 2007 10.5194/acp-7-629-2007 http://www.atmos-chem-phys.net/7/629/2007/ http://www.atmos-chem-phys.net/7/629/2007/acp-7-629-2007.html http://www.atmos-chem-phys.net/7/629/2007/acp-7-629-2007.pdf 629 634 2007-02-09 Technical Note: Long-term memory effect in the atmospheric CO₂ concentration at Mauna Loa C. Varotsos covar@phys.uoa.gr M.-N. Assimakopoulos M. Efstathiou Department of Applied Physics, University of Athens, Athens, Greece The monthly mean values of the atmospheric carbon dioxide concentration derived from in-situ air samples collected at Mauna Loa Observatory, Hawaii, USA during 1958–2004 (the longest continuous record available in the world) are analyzed by employing the detrended fluctuation analysis to detect scaling behavior in this time series. The main result is that the fluctuations of carbon dioxide concentrations exhibit long-range power-law correlations (long memory) with lag times ranging from four months to eleven years, which correspond to 1/f noise. This result indicates that random perturbations in the carbon dioxide concentrations give rise to noise, characterized by a frequency spectrum following a power-law with exponent that approaches to one; the latter shows that the correlation times grow strongly. This feature is pointing out that a correctly rescaled subset of the original time series of the carbon dioxide concentrations resembles the original time series. Finally, the power-law relationship derived from the real measurements of the carbon dioxide concentrations could also serve as a tool to improve the confidence of the atmospheric chemistry-transport and global climate models. Asher, W. E., Jessup, A. T., and Atmane, M. A.: Oceanic application of the active controlled flux technique for measuring air-sea transfer velocities of heat and gases, J. Geophys. Res.-Oceans, 109(C8), C08S12, doi:10.1029/2003JC001862, 2004. Audit, B., Bacry, E., Muzy, J. F., and Arneodo, A.: Wavelets based estimators of scaling behaviour IEEE, Trans. Information Theory 48, 11, 2938–2954, 2002. Aziz, M. A., Reising, S. C., Asher, W. E., Rose, L. A., Gaiser, P. W., and Horgan, K. A.: Effects of air-sea interaction parameters on ocean surface microwave emission at 10 and 37 GHz,~IEEE Trans. Geosci. Rem. Sens., 43(8), 1763–1774, 2005. Berger, U. and Dameris, M.: Cooling of the upper-atmosphere due to CO₂ increases – a model study, Ann. Geophys., 11(9), 809–819, 1993. Cartalis, C. and Varotsos, C.: Surface ozone in Athens, Greece, at the beginning and at the end of the 20th-century, Atmos. Environ., 28(1), 3–8, 1994. Chen, Z., Hu, K., Carpena, P., Bernaola-Galvan, P., Stanley, H. E., and Ivanov, P.: Effect of nonlinearities on detrended fluctuation analysis, Phys. Rev. E, 71, 011104, doi:10.1103/PhysRevE.71.011104, 2005. Chen, Z., Ivanov, P., Hu, K., and Stanley, H.: Effect of nonstationarities on detrended fluctuation analysis, Phys. Rev. E, 65(4), 041107, doi:10.1103/PhysRevE.65.041107, 2002. Crutzen, P. J., Lawrence, M. G., and Poschl, U.: On the background photochemistry of tropospheric ozone, Tellus A, 51(1), 123–146, 1999. Dameris, M., Grewe, V., Ponater, M., Deckert, R., Eyring, V., Mager, F., Matthes, S., Schnadt, C., Stenke, A., Steil, B., Bruhl, C. and Giorgetta, M. A.: Long-term changes and variability in a transient simulation with a chemistry-climate model employing realistic forcing, Atmos. Chem. Phys., 5, 2121–2145, 2005. Ebel, A.: Evaluation and reliability of meso-scale air pollution simulations, Lect. Notes Comput. Sc., 2179, 255–263, 2001. Govindan, R. B., Vyushin, D., Bunde, A., Brenner, S., Havlin, S., and Schellnhuber, H. J.: Global climate models violate scaling of the observed atmospheric variability, Phys. Rev. Lett., 89(1), 028501, doi:10.1103/PhysRev.Lett.89.028501, 2002. Grytsai, A., Grytsai, Z., Evtushevsky, A., and Milinevsky, G.: Interannual variability of planetary waves in the ozone layer at 65 degrees S, Int. J. Remote Sens., 26(16), 3377–3387, 2005. Hu, K., Ivanov, P. C., Chen, Z., Carpena, P., and Stanley, H. E.: Effect of trends on detrended fluctuation analysis, Physi. Rev. E, 64(1), 011114, doi:10.1103/PhysRevE.64.011114, 2001. Jacovides, C. P., Varotsos, C., Kaltsounides, N. A., Petrakis, M., and Lalas, D. P.: Atmospheric turbidity parameters in the highly polluted site of Athens basin, Renewable Energy, 4(5), 465–470, 1994. Kantelhardt, J. W., Zschiegner, S. A., Koscielny-Bunde, E., Havlin, S., Bunde, A. and Stanley, H. E.: Multifractal detrended fluctuation analysis of nonstationary time series, Physica A 316 (1–4), 87–114, 2002. Keeling, C. D. and Whorf, T.P.: Atmospheric CO₂ records from sites in the SIO air sampling network. In Trends: A Compendium of Data on Global Change. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Dept. of Energy, Oak Ridge, Tenn., USA, (http://cdiac.esd.ornl.gov/trends/co2/sio-mlo.htm), 2005. Kondratyev, K. Y. and Varotsos C.: Atmospheric greenhouse effect in the context of global climate-change, Nuovo Cimento della Societa Italiana di Fisica C-Geophysics and Space Physics, 18(2), 123–151, 1995. Kondratyev, K. Y. and Varotsos, C.: Global tropospheric ozone dynamics – Part I: Tropospheric ozone precursors - Part II: Numerical modelling of tropospheric ozone variability, Environmental Science and Pollution Research, 8(1), 57–62, 2001a. Kondratyev, K. Y. and Varotsos, C.: Global tropospheric ozone dynamics – Part II: Numerical modelling of tropospheric ozone variability – Part I: Tropospheric ozone precursors [ESPR 8 (1) 57-62 (2001)] Environmental Science and Pollution Research, 8(2), 113–119, 2001b. Koscielny-Bunde, E., Bunde, A., Havlin, S., Roman, H.E., Goldreich, Y., and Schellnhuber, H.J.: Indication of a universal persistence law governing atmospheric variability, Phys. Rev. Lett., 81(3), 729–732, 1998. Lovejoy, S.: Area-perimeter relation for rain and cloud areas, Science, 216(4542), 185–187, 1982. Peng, C. K., Buldyrev, S. V., Havlin, S., Simons, M., Stanley, H. E., and Goldberger, A. L.: Mosaic organization of DNA nucleotides, Phys. Rev. E, 49(1), 1685–1689, 1994. Reid, S. J., Rex, M., Von der Gathen, P., et al.: A study of ozone laminae using diabatic trajectories, contour advection and photochemical trajectory model simulations, J. Atmos. Chem., 30(1), 187–207, 1998. Sarlis, N. and Skordas, E.:Interactive comment on "Technical Note: Long-term memory effect in the atmospheric CO₂ concentration at Mauna Loa" by Varotsos, C. et al., Atmos. Chem. Phys. Discuss., 6, S5095–S5098, 2006a. Sarlis N. and Skordas E.: Interactive comment on "Technical Note: Long-term memory effect in the atmospheric CO₂, concentration at Mauna Loa" by Varotsos, C. et al., Atmos. Chem. Phys. Discuss., 6, S5324–S5328, 2006b. Schertzer, D. and Lovejoy, S.: The dimension and intermittency of atmospheric dynamics, in Turbulent Shear Flows, Vol. 4, Springer, New York, 7–33, 1985. Schulz, A., Rex, M., Harris, N. R. P., et al.: Arctic ozone loss in threshold conditions: Match observations in 1997/1998 and 1998/1999, J. Geophys. Res.-Atmos., 106(D7), 7495–7503, 2001. Stanley, E.: Scaling, universality, and renormalization: three pillars of modern critical phenomena, Rev. Modern Phys., 71(1), S358–S366, 1999. Syroka, J. and Toumi, R.: Scaling and persistence in observed and modelled surface temperature, Geophys. Res. Lett., 28(17), 3255–3258, 2001. Talkner, P. and Weber, R. O.: Power spectrum and detrended fluctuation analysis: application to daily temperatures, Phys. Rev.E, 62(1), 150–160 Part A, 2000. Tuck, A. F. and Hovde, S. J.: Fractal behavior of ozone, wind and temperature in the lower stratosphere, Geophys. Res. Lett., 26, 1271–1274, 1999. Tuck, A. F., Hovde, S. J., Gao, R. S., and Richard, E. C.: Law of mass action in the Arctic lower stratospheric polar vortex January–March 2000: ClO scaling and the calculation of ozone loss rates in a turbulent fractal medium. J. Geophys. Res.-Atmos., 108(D15), 4451, doi:10.1029/2002JD002832, 2003. Varotsos, C.: Climate change problems and carbon dioxide emissions: Expecting "Rio+10" – Global summit on sustainable development in Johannesburg (26th August–6th September 2002), Environmental Science and Pollution Research, 9(2), 97–98, 2002a. Varotsos, C.: The southern hemisphere ozone hole split in 2002, Environ. Sci. Pollut. Res., 9(6), 375–376, 2002b. Varotsos, C.: Power-law correlations in column ozone over Antarctica, Int. J. Remote Sens., 26(16), 3333–3342, 2005a. Varotsos, C.: Modern computational techniques for environmental data; Application to the global ozone layer, (Proceedings of the ICCS 2005) Lecture Notes in Computer Science, 3516, 504–510, 2005b. Varotsos, C. and Kirk-Davidoff, D.: Long-memory processes in ozone and temperature variations at the region 60 degrees S–60 degrees N, Atmos. Chem. Phys., 6, 4093–4100, 2006. Varotsos, C., Kondratyev, K. Y., and Efstathiou, M.: On the seasonal variation of the surface ozone in Athens, Greece, Atmos. Environ., 35(2), 315–320, 2001. Varotsos, C., Assimakopoulos, M.-N., and Efstathiou, M.: Technical Note: Long-term memory effect in the atmospheric CO₂ concentration at Mauna Loa", Atmos. Chem. Phys. Discuss., 6, 11 957–11 970, 2006a. Varotsos, C. A., Ondov, J. M., Cracknell, A. P., Efstathiou, M. N., and Assimakopoulos M. N.: Long-range persistence in global Aerosol Index dynamics,~Int. J. Remote Sens., 27(16), 3593–3603, 2006b. Varotsos, C., Ondov, J., and Efstathiou, M.: Scaling properties of air pollution in Athens, Greece and Baltimore, Maryland, Atmos. Environ., 39(22), 4041–4047, 2005. Varotsos, P. A., Sarlis, N. V., and Skordas, E. S.: Long-range correlations in the electric signals that precede rupture, Phys. Rev. E, 66, 011902, doi:10.1103/PhysRevE.66.011902, 2002. Varotsos, P. A., Sarlis, N. V., and Skordas, E. S.: Long-range correlations in the electric signals that precede rupture: Further investigations, Phys. Rev. E, 67, 021109, doi:10.1103/PhysRevE.67.021109, 2003a. Varotsos, P. A., Sarlis, N. V., and Skordas, E. S.: Attempt to distinguish electric signals of a dichotomous nature, Phys. Rev. E, 68(3), 031106, doi:10.1103/PhysRevE.68.031106, 2003b. Varotsos, P. A., Sarlis, N. V., Skordas, E. S., Tanaka, H. K., and Lazaridou, M. S: Entropy of Seismic Electric Signals: Analysis in natural time under time reversal, Phys. Rev. E, 73, 031114, doi:10.1103/PhysRevE.73.031114, 2006c. Varotsos, P. A., Sarlis, N. V., Skordas, E. S., Tanaka, H. K., and Lazaridou, M. S.: Attempt to distinguish long-range temporal correlations from the statistics of the increments by natural time analysis, Phys. Rev. E, 74, 021123, doi:10.1103/PhysRevE.74.021123, 2006d. Zhu, J. and Liu, Z.: Long-range persistence of acid deposition, Atmos. Environ., 37, 2605–2613, 2003.