Harmonic Analysis of a Nonstationary Series of Temperature Paleoreconstruction for the Central Part of Greenland

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: *danova8@mail.ru, **satel@ogmi.farlep.odessa.ua

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Abstract

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

Figure captions

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).

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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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