## Cyclic Oscillations

The two kinds ofchanges discussed in the preceding sub-chapters (trends and fluctuations) are relatively easy to identify in the long-term course of T. Analysing in detail the year-to-year variability of T, one can also discern more or less clear cyclic oscillations. This has already been pointed out in sub-chapter 5.1.3. The review of literature concerning temporal changes in climatic and astronomical time series (e.g. Kozuchowski 1985; Schonwiese 1987; Brazdil 1988; Charvatova & StfeStik 1991, 1992, 1993, 1995; Eisner & Tsonis 1991; Burroughs 1992; Silverman 1992) showed that cyclic oscillations in the mathematical sense practically do not occur. These oscillations are, in fact, quasi-cyclic. This means that, with time, both the period and amplitude of oscillation can change. Moreover, cyclic changes occurring in a given period may eventually disappear altogether.

The simplest method of computing the average periods of oscillation of Tor some other climatic element is to calculate the mean time between consecu tive maximums or minimums in a long-term course. Various other mathematical and statistical methods enable one to obtain more precise data about the cyclicity of a given parameter. The most popular are the methods of spectrum analysis of power density. One such method commonly used in recent years for computing the periodicity in climatic time-series is maximum entropy spectrum analysis (cf., Folland et al. 1984; Brazdil 1986, 1988; Loutre et al. 1992; Currie 1993). Its numerous advantages aside, the method also has serious drawbacks. Its main weaknesses include the appearance of spurious peaks in the spectrum and the difficulty of evaluating the statistical significance of spectral components (Loutre et al. 1992). The above considerations led to abandoning this method in favour of Singular Spectrum Analysis (SSA). As has already been mentioned in Chapter 3, this method is currently one of the better methods enabling a reliable identification of periodic oscillations in climatic time series; it was first used for computing the periodicity in paleoclimatic series (Fraedrich 1986; Vautard & Ghil 1989) and later also for current climatic series (Ghil & Vautard 1991; Eisner & Tsonis 1991; Vautard & Pires 1993; Przybylak & Usowicz 1994; Schlesinger & Ramankutty 1994).

The SSA method was used for the winter, summer, and annual means of for all the Arctic stations analysed and some Subarctic stations, whose series length was 40 years. Calculations were also made for chosen series of annual extreme temperatures, which were taken from the stations representing particular climatic regions and sub-regions of the Arctic. The results of the computations showed - predictably - that the cyclic oscillations of T., on the one hand, and of and on the other, are in most cases analo-

gous (Figure 5.29). For this reason there is no need to discuss separately the results pertaining to extreme temperatures.

Oscillation periods of seasonal and annual T. in the Arctic change within a broad time span - from 2 to 64 years (Table 5.16, Figure 5.30A and B). The only exception is the station Godthab, for which this period amounted to 128.0 years. A definite spatial pattern can be discerned in the distribution of the lengths of periods. The longest cycles in the annual series (>18 years) occur predominantly in areas of intensive atmospheric circulation (most of the territory of ATLR and BAFR). They are exceptionally long, however, on the western and south-eastern shore of Greenland and adjacent seas (64-128 years). The largest area characterised by the shortest oscillation periods of (2-4 years) is located in CANR (except for its north-western part). Oscillations of this magnitude were also observed in the western part of PACR and in southernmost fragments of the western Russian Arctic (Figure 5.30B). The oscillation period of T. from 8.1 to 13.0 years in the Arctic was noted only in Alaska and on the Beaufort Sea. In the winter, in the greater part of the Arctic manifest longer cyclicity than in the summer (Figure 5.30A). As will be demonstrated below, this is probably caused by the influence of atmospheric circulation, which is particularly strong in the winter and is characterised by long-term cyclicity.

upper panels - normalised eigenvalues; middle panels- reconstructed course of 77], and T^ (thick line) in comparison to the detrended original data