T.E. Danova a*, B.V. Perelygin b**
a Marine Hydrophysical Institute, Russian Academy of Sciences, Sevastopol, 299011 Russia
b Odessa State Environmental University, Odessa, 65016 Ukraine
E-mail: *firstname.lastname@example.org, **email@example.com
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The results of the investigations of a transformed series of reconstructed air temperature data for the central part of Greenland with an increment of 30 years have been presented. Stationarization of a ~ 50,000-years' series of the reconstructed air temperature in the central part of Greenland according to ice core data has been performed using mathematical expectation. To obtain mathematical expectation estimation, the smoothing procedure by the methods of moving average and wavelet analysis has been carried out. Fourier's transformation has been applied repeatedly to the stationarized series with changing the averaging time in the process of smoothing. Three averaging time values have been selected for the investigations: ~ 400–500 years, ~ 2,000 years, and ~ 4,000 years. Stationarization of the reconstructed temperature series with the help of wavelet transformation showed the best results when applying the averaging time of ~ 400 and ~ 2000 years, the trends well characterize the initial temperature series, thereby revealing the main patterns of its dynamics. Using the period with the averaging time of ~ 4,000 years showed the worst result: significant events of the main temperature series were lost in the process of averaging. The obtained results well correspond to cycling known to be inherent to the climatic system of the planet; the detected modes of 1,470 ? 500 years are comparable to the Dansgaard–Oeschger and Bond oscillations.
Keywords: ice cores, nonstationary series, trend, stationarization, harmonic analysis
Fig. 1. Transformed series of reconstructed air temperature data for the central part of Greenland with an increment of 30 years.
Fig. 2. Initial series of reconstructed temperatures (thin line) with the imposed trends (heavy line) obtained by the method of moving average (a) with the averaging time of 450 years, (c) 1950 years, (e) 3870 years, as well as by the method of wavelet transformation (b) with the averaging time of 480 years, (d) 1920 years, and (e) 3840 years.
Fig. 3. Stationarized initial series of reconstructed temperatures obtained by the method of moving average (a) with the averaging time of 450 years and its spectrum (b); the same series obtained by the method of wavelet transformation (c) with the averaging time of 480 years and its spectrum (d).
Fig. 4. Stationarized initial series of reconstructed temperatures obtained by the method of moving average (а) with the averaging time of 1950 years and its spectrum (b); the same series obtained by the method of wavelet transformation (c) with the averaging time of 1920 years and its spectrum (d).
Fig. 5. Stationarized initial series of reconstructed temperatures obtained by the method of moving average (а) with the averaging time of 3870 years and its spectrum (b); the same series obtained by the method of wavelet transformation (c) with the averaging time of 3840 years and its spectrum (d).
- Kazakevich D.I. Principles of the Theory of Random Functions and Its Application in Hydrometeorology. Leningrad, Gidrometeoizdat, 1977. 320 р. (In Russian)
- Zalmanzon L.A. Fourier, Walsh, and Haar Transforms and Their Applications in Control, Communication, and Other Fields. Moscow, Nauka, 1989. 496 р. (In Russian)
- Grootes P.M., Stuiver M., White J.W.C., Johnsen S.J., Jouzel J. Comparison of oxygen isotope records from the GISP2 and GRIP Greenland ice cores. Nature, 1993, vol. 366, pp. 552–554.
- Meese D.A., Alley R.B., Fiacco R.J., Germani M.S., Gow A.J., Grootes P.M., Illing M., Mayewski P.A., Morrison M.C., Ram M., Taylor K.C., Yang Q., Zielinski G.A. Preliminary Depth-Age Scale of the GISP2 Ice Core. Special CRREL Report 94-1. Hanover, NH, US Army Cold Regions Research and Engineering Laboratory, 1994. 66 p.
- Stuiver M., Braziunas T.F., Grootes P.M., Zielinski G.A. Is there evidence for solar forcing of climate in the GISP2 oxygen isotope record. Quat. Res., 1997, vol. 48, no. 3, pp. 259–266.
- Stuiver M., Grootes P.M., Braziunas T.F. The GISP2 18O climate record of the past 16,500 years and the role of the sun, ocean and volcanoes. Quat. Res., 1995, vol. 44, no. 3, pp. 341–354.
- Monin A.S. Introduction to the Climate Theory. Leningrad, Gidrometeoizdat, 1982. 246 р. (In Russian)
- Klyashtorin L.B., Lyubushin A.A. Cyclic Climate Changes and Fish Productivity. Moscow, VNIRO, 2005. 235 р. (In Russian)
- Danova T.E., Perelygin B.V. Results of the Fourier analysis of data of temperature paleoreconstruction of in the central part of Greenland. Uch. Zap. Ros. Gos. Gidrometeorol. Univ., 2013. no. 32, рр. 83–93. (In Russian)
- Loeva I.D., Evseeva L.P. Statistical analysis of time series. Tr. GGO, 1983, vol. 475, рр. 101–108. (In Russian)
- Gribanov Yu.I., Mal'kov V.L. Spectral Analysis of Random Processes. M.: Energiya, 1974. 240 р. (In Russian)
- Kotyuk A.F., Tsvetkov E.I. Spectral and Correlation Analysis of Nonstationary Random Processes. Moscow, Izd. Stand., 1970, 103 р. (In Russian)
- Humlum O., Solheim J.-E., Stordahl K. Identifying natural contributions to late Holocene climate change. Global Planet. Change, 2011, vol. 79, nos. 1–2, рр. 145–156. doi: 10.1016/j.gloplacha.2011.09.005.
- Bond G., Showers W., Cheseby M., Lotti R., Almasi P., deMenocal P., Priore P., Cullen H., Hajdas I., Bonani G. A pervasive millennial-scale cycle in North Atlantic Holocene and glacial climates, Science, 1997, vol. 278, pp. 1257–1266. doi: 10.1126/science.278.5341.1257.
- Bond G., Kromer B., Beer J., Muscheler R., Evans M.N., Showers W., Hoffmann S., Lotti-Bond R., Hajdas I., Bonani G. Persistent solar influence on North Atlantic climate during the Holocene, Science, 2001, vol. 294, pp. 2130–2136. doi: 10.1126/science.1065680.
- Dansgaard W., Johnsen S.J., Clausen H.B., Dahl-Jensen D., Gundestrup N., Hammer C.U., Oeschge H. North Atlantic climatic oscillations revealed by deep Greenland ice cores. Climatic Processes and Climate Sensitivity, Geophysical Monograph 29. Washington, DC, Am. Geophys. Union, 1984. pp. 288–298.
- Bond G.C., Rusty L. Iceberg discharges into the North Atlantic on millennial time scales during the last glaciation. Science, 1995, pp. 1005–1010. doi: 10.1126/science.267.5200.1005.
- Danova T.E. Perelygin B.V. Application of wavelet analysis for updating Heinrich events age. Geofiz. Zh., 2015. vol. 37, no. 1, рр. 165–175. (In Russian)
- Primeau F. Characterizing transport between the surface mixed layer and the ocean interior with a forward and adjoint global ocean transport model, J. Phys. Oceanogr., 2005, vol. 35, рр. 545–564.
- Rapp D. Ice Ages and Interglacials: Measurements, Interpretation and Models. Berlin, Heidelberg, Springer-Verlag, 2009. 285 p.
- Taylor K.C. The Holocene-Younger Dryas transition recorded at Summit, Greenland, Science, 1997, vol. 278, pp. 825–827. doi: 10.1126/science.278.5339.825.
- Hughen K.A. Synchronous radiocarbon and climate shifts during the last deglaciation, Science, 2000, vol. 290, pp. 1951–1954. doi: 10.1126/science.290.5498.1951.
- Spurk M. Revisions and extension of the Hohenheim oak and pine chronologies: new evidence about the timing of the Younger Dryas/Preboreal transition. Radiocarbon, 1998, vol. 40, no. 3, pp. 1107–1116.
For citation: Danova T.E., Perelygin B.V. Harmonic analysis of a nonstationary series of temperature paleoreconstruction for the central part of Greenland. Uchenye Zapiski Kazanskogo Universiteta. Seriya Estestvennye Nauki, 2016, vol. 158, no. 2, pp. 293–310. (In Russian)
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