Abstract
The multifractal properties and scaling behaviors of the long-term and recent 2000-year δ 18 O records of NGRIP ice core are investigated by the multifractal detrended fluctuation analysis method. The generalized Hurst exponents, multifractal scaling exponents, and singularity spectrums of two δ 18 O records are derived to verify the multifractiality of two records. And the multifractal behaviors of two records are obviously different, which may reflect the climate change of the recent 2000-year time is quite different from one of the long-term time. In addition, the probability distribution analysis of two δ 18 O records is presented to manifest the different multifractality between two δ 18 O records of NGRIP ice core. Our results will be helpful to research the climate change.
Similar content being viewed by others
References
Alley RB (2000) Ice-core evidence of abrupt climate changes. Proc Natl Acad Sci USA 97(4):1331–1334
Arzel O, England MH (2013) Wind-stress feedback amplification of abrupt millennial-scale climate changes. Clim Dyn 40:983–995
Ashkenazy Y, Baker DR, Gildor H, Havlin S (2003) Nonlinearity and multifractality of climate change in the past 420,000 years. Geophys Res Lett 30:2146
Ditlevsen PD (1999) Observation of alpha-stable noise and a bistable climate potential in an ice-core record. Geophys Res Lett 26:1441–1444
Ditlevsen PD, Ditlevsen OD (2009) On the stochastic nature of the rapid climate shifts during the last ice age. J Clim 22:446–457
Ditlevsen PD, Svensmark H, Johnsen S (1996) Contrasting atmospheric and climatic dynamics of last-glacial and Holocene periods. Nature 379:810–812
GRIP Project Members (1993) Climate instability during the last interglacial period recorded in the GRIP ice core. Nature 364(6434):203–207
Ihlen EAF (2012) Introduction to multifractal detrended fluctuation analysis in matlab. Front Physiol 3:141
Johnsen SJ, Dansgaard W, Clausen HB, Langway Jun CC (1972) Oxygen isotope profiles through Antarctic and Greenland ice sheets. Nature 235:429–434
Jouzel J et al (1997) Validity of the temperature reconstruction from water isotopes in ice cores. J Geophys Res 102(C12):26471–26487
Jouzel J et al (2007) Orbital and millennial Antarctic climate variability over the past 800,000 years. Science 317(5839):793–796
Kantelhardt JW, Zschiegner SA, Koscielny-Bunde E, Havlin S, Bunde A, Stanley HE (2002) Multifractal detrended fluctuation analysis of nonstationary time series. Phys A 316:87–114
Kantelhardt JW, Koscielny-Bunde E, Rybski D, Braun P, Bunde A, Havli S (2006) Long-term persistence and multifractality of precipitation and river runoff records. J Geophys Res 111:D01106
Kaufman DS, Schneider DP, McKay NP, Ammann CM, Bradley RS, Briffa KR, Miller GH, Otto-Bliesner BL, Overpeck JT, Vinther BM (2009) Recent warming reverses long-term Arctic cooling. Science 325(5945):1236–1239
Kavasseri RG, Nagarajan R (2005) A multifractal description of wind speed records. Chaos Soliton Fract 24:165–173
Knudsen MF, Seidenkrantz M-S, Jacobsen BH, Kuijpers A (2011) Tracking the Atlantic multidecadal oscillation through the last 8,000 years. Nat Commun 2:178
Kobashi T, Kawamura K, Severinghaus JP, Barnola J-M, Nakaegawa T, Vinther BM, Box JE (2011) High variability of Greenland surface temperature over the past 4000 years estimated from trapped air in an ice core. Geophys Res Lett 38:L21501
Landais A, Masson-Delmotte V, Jouzel J, Raynaud D, Johnsen S, Huber C, Leuenberger M, Schwander J, Minster B (2006) The glacial inception as recorded in the NorthGRIP Greenland ice core: timing, structure and associated abrupt temperature changes. Clim Dyn 26:273–284
Lin M, Yan SX, Zhao G, Wang G (2013) Multifractal detrended fluctuation analysis of interevent time series in a modified OFC model. Commun Theor Phys 59:1
Livina VN, Kwasniok F, Lohmann G, Kantelhardt JW, Lenton TM (2011) Changing climate states and stability: from Pliocene to present. Clim Dyn 37:2437–2453
Lovejoy S (1981) Analysis of rain areas in terms of fractals. In 20th conference on radar meteorology, AMS Boston, pp 476–484
Lovejoy S, Mandelbrot B (1985) Fractal properties of rain and a fractal model. Tellus 37:209–232
Lovejoy S, Schertzer D (1986a) Scale invariance in climatological temperatures and the spectral plateau. Ann Geophys 4B:01–410
Lovejoy S, Schertzer D (1986b) Scale invariance, symmetries, fractals and stochastic simulations of atmospheric phenomena. Bull AMS 67:21–32
Lovejoy S, Schertzer D (2012a) Haar wavelets, fluctuations and structure functions: convenient choices for geophysics. Nonlinear Proc Geophys 19:513–527
Lovejoy S, Schertzer D (2012b) Low frquency weather and the emergence of the climate. In: Sharma AS, Bunde A, Baker D, Dimiri VP (eds) Extreme events and natural hazards: the complexity perspective. AGU monographs, pp 231–254
Lovejoy S, Schertzer D (2013) The weather and climate: emergent laws and multifractal cascades. Cambridge University Press, Cambridge, 496 pp
Marsh ND, Ditlevsen PD (1997) Observation of atmospheric and climate dynamics from a high resolution ice core record of a passive tracer over the last glaciation. J Geophys Res 102:D11219–11224
North Greenland Ice Core Project members (2004) High-resolution record of Northern Hemisphere climate extending into the last interglacial period. Nature 431:147–151
Norouzzadeh P, Rahmani B (2006) A multifractal detrended fluctuation description of Iranian rial–US dollar exchange rate. Phys A 367:328–336
Oświecimka P, Kwapień J, Drożdż S (2005) Multifractality in the stock market: price increments versus waiting times. Phys A 347:626–638
Roe GH, Steig EJ (2004) Characterization of millennial-scale climate variability. J Clim 17:1929–1944
Ruan YP, Zhou WX (2011) Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant, Phys A 390:1646–1654
Schertzer D, Lovejoy S (1985) The dimension and intermittency of atmospheric dynamics. In: Launder B (ed) Turbulent shear flow, vol 4. Springer, Berliin, pp 7–33
Schmitt F, Lovejoy S, Schertzer D (1995) Multifractal analysis of the greenland ice-core project climate data. Geophys Res Lett 22:1689–1692
Steig EJ, Alley RB (2002) Phase relationships between Antarctic and Greenland climate records. Ann Glaciol 35:451–456
Telesca L, Lapenna V (2006) Measuring multifractality in seismic sequences. Tectonophysics 423:115–123
Vinther BM, Clausen HB, Johnsen SJ, Rasmussen SO, Andersen KK, Buchardt SL, Dahl-Jensen D, Seierstad IK, Siggaard-Andersen M-L, Steffensen JP, Svensson AM, Olsen J, Heinemeier J (2006) A synchronized dating of three Greenland ice cores throughout the Holocene. J Geophys Res 111:D13102
Wunsch C (2003) Greenland-Antarctic phase relations and millennial time-scale climate fluctuations in the Greenland ice-cores. Quat Sci Rev 22:1631–1646
Acknowledgments
This work was supported by the Foundation for Distinguished Young Talents in Higher Education of Guangdong, China (Grant No. LYM10065) and the National Natural Science Foundation of China (Grant No. 11105054) and PCSIRT (Grant No. IRT1243).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shao, ZG., Wang, HH. Multifractal detrended fluctuation analysis of the δ 18 O record of NGRIP ice core. Clim Dyn 43, 2105–2109 (2014). https://doi.org/10.1007/s00382-013-2037-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00382-013-2037-9