The interannual changes in the ice extent of the Eurasian Seas of the Arctic Ocean appear to have a polycyclic character. The frequency structure of these changes revealed by several investigators is characterized by significant peaks for periods of 2-3, 5-7, 8-12, about 20, and 50-60 years (i.e., Volkov and Sleptsov-Shevlevich, 1970, 1971; Gudkovich et al., 1972; Karklin, 1978; Karklin et al., 2001; Karklin and Teitelbaum, 1987).

Although there are a variety of causes for the temporal structure of multiyear variability of hydrometeorological characteristics (including ice), the cyclic properties can be studied using methods of latent periodicities, such as periodogram and spectral analyses. Both methods yield more accurate results when analyzing series that present a sum of harmonic variability. During analysis of cyclic variability characterized by changes in duration (within some limits) and amplitude, the dominating periods (on the periodogram) or frequencies (on the spectrogram) can be "fuzzy" within the cycle's variability.

Our analysis of the spectrograms of ice extent variability in each of the seas under consideration revealed significant differences among them: a typical characteristic of the three western seas is significant low-frequency variability, while the three eastern seas exhibit relatively high-frequency variability. Therefore, to illustrate the temporal (frequency) structure of the variability of ice extent, analogous to the analysis of the linear trends, the Eurasian Arctic Seas were combined into two groups: western, including the Greenland, Barents, and Kara Seas, and eastern, encompassing the Laptev, East Siberian, and Chukchi Seas. The total ice extent in each of the groups was calculated on the basis of data for the period 1933-2003. The beginning of this period coincides with the start of regular airborne ice reconnaissance in the Arctic Seas; therefore, calculations for the latter two-thirds of the century offer higher reliability than calculations for the first third. The two available data series were subjected to spectral analysis with self-correlation functions calculated after 50 years, which is sufficient for distinguishing the frequencies in the low-frequency spectrum

Figure 2.4. Functions of the spectral density of variability in total ice extent during August in the western (Greenland, Barents, and Kara) seas (a) and in the eastern (Laptev, East Siberian, and Chukchi) seas (b).

Figure 2.4. Functions of the spectral density of variability in total ice extent during August in the western (Greenland, Barents, and Kara) seas (a) and in the eastern (Laptev, East Siberian, and Chukchi) seas (b).

region. The spectra characterizing both groups are presented in Figure 2.4, where cycles lasting about 50-60 and 20 years play a significant role in forming the structure of multiyear variability of ice extent in the western seas. Their total contribution to the total variability exceeds 30% and is much greater than the contribution of the same cycles in the eastern seas (Table 2.4). At the same time, in the eastern seas, a more significant contribution to the total variability occurs in cycles of about 9-12 and 7-8 years; their contribution is twice as large as the contribution of the cycles of same duration in the western seas (Table 2.4).

Region |
Month |
Linear trend |
Frequency, ljyears (cycles, years) | ||||

(20) |
(2-5.5) | ||||||

Western |
IV |
43 |
5 |
4 |
4 |
- |
- |

Western |
VIII |
24 |
17.5 |
13 |
6.5 |
7 |
32 |

Eastern |
VIII |
3 |
7 |
5 |
12.5 |
13.5 |
59 |

Cycles lasting 2-5 years play the main role in ice extent variability in the eastern Arctic Seas, forming the interannual variability, whose contribution comprises almost 60% of the total variability. The role of these cycles in the western seas is less significant (Table 2.4).

Some components of long-period changes in ice extent appear to have a greater role in climatic changes than others (see Table 2.4). In determining the variance, if we exclude the high-frequency variability not related to climate changes, we obtain different estimates. Thus, five-year smoothing of the initial series of ice extent for the western region in August (periods with variability up to five years are excluded), the variability decreases by 62%. Hence, the total contribution of 50-60-year and 20- year cycles to the long-term variability of ice extent of the region increases to almost 50%. The total contribution of these cycles and the linear trend comprises more than 88%.

A wavelet-analysis method and software developed by Torrence and Compo (1998) was applied to estimate the temporal variability of the spectral structure of ice extent. Assuming that the period of wave fluctuation (forms given in Figure 2.5) is 15 years and using a sampling of ice extent values for the period 1950-1964, one can assess the correlation coefficient between this type of wave (and the period) and ice extent data. Moving the starting point forward yields consecutive estimates of the energy of the variability with a period of 15 years for the intervals 1951-1965, 19521966, etc.

Similarly, we can vary the elementary wave period and successively derive estimates of the energy of variability for scales of 2, 3, 4, 5 years, etc. Two types of elementary waves were used in the analysis: the "Morlet wave" (Figure 2.5a) to reveal typical spectral components of long-period variability and the Mexican hat (Figure 2.5ft) to reveal the temporal structures of spectrum variability.

An important component of the analysis is checking the significance of the derived amplitudes of variability. The following method of assessing the significance is also proposed in Torrence and Compo (1998). Using the Monte Carlo method, red noise is generated with amplitude equal to series variance. By criterion \2, the red noise amplitude of 5% significance is determined. Then, if the amplitude of variability has a significance level greater than 5%, it can be said that at the given significance level the fluctuation of this period is probable.

We use the same approach to interpret results of the wavelet analysis as Monin and Sonechkin (2005). Figure 2.6 (see color section) presents wavelet-spectrum calculations of ice extent in August for 1900-2003 for six Eurasian Arctic seas (Greenland to Chukchi). For convenience of interpretation, the left-hand column (Figure 2.6a) presents the initial ice extent time series. The center column (Figure 2.6b) contains the results of wavelet-transformation of ice extent series in the form of the amplitude of variability (in 1000 km2) with a sign, and as a basic component, a wave fluctuation of the "Mexican hat" type is used. The right-hand column (Figure 2.6c) contains the total spectrum of ice extent variability, which was also estimated by wavelet-transformation, where, as a basic component, a different wave fluctuation of the "Morlet wave" type is used.

An analysis of Figure 2.6b shows that the long-period spectrum structures of the seas of the western and eastern sectors of the Eurasian Arctic are different. For the Greenland, Barents, and Kara Seas, approximately synchronous 50-60-year variability is well distinguished with maxima near 1910 and 1970 and minima near 1940 and 2000. On the contrary, for the Laptev, East Siberian, and Chukchi Seas, shorter variability of 20-30 years and less is apparent. All the seas are also characterized by short-period variability of 8-10 years. The spectra of the western sector and the Eurasian Arctic seas are similar in general to the structure for the Greenland and Kara Seas while the spectrum of the eastern sector is similar to the structure for the Laptev and East Siberian Seas. Analysis of the total ice extent spectra (Figure 2.6c) yields similar results. It is interesting to note that ~ 100-year and ^60-year variability is statistically significant only for the Barents Sea and ^60-year variability for the Kara Sea. The latter are also statistically significant in the western sector and Eurasian Arctic spectra. According to Monin and Sonech-kin (2005), ^100-year variability ought to be assumed as artificial.

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