Seasonality of low-frequency variability in early-instrumental European temperatures

Marina V. Shabalova and Susanne L. Weber
Appeared in:
Geophysical Research Letters
Volume 25, Number 20, Pages 3859-3862,
October 15, 1998.


The seasonality of low-frequency temperature variability is studied by application of multichannel singular spectrum analysis to 7 long early-instrumental European temperature records. Focus is on timescales longer than 50 years. We find that the temporal pattern of low-frequency variability is clearly season-dependent. Opposing winter/summer tendencies result in a weak variability on timescales longer than 50 yr in the annual-mean data. Summer temperature variations seem to exhibit a preferential timescale in the range 60-80 years. An oscillation with this timescale is found to be significant against red noise surrogates when analysing 4 long European paleo proxy records for summer temperature. The present results stress the necessity of using seasonally homogeneous datasets of paleo proxies for reconstructing low-frequency variability patterns.


With concern over anthropogenic effects on the global climate, estimates of natural climate variability on timescales from decades to centuries are of increasing interest. Given the shortness of the global instrumental record, estimates based on instrumental data are still provisional or even controversial [e.g., Allen and Smith, 1996] and are subject to revision with longer paleo proxy records. As the sensitivity of different paleo indicators to temperature is season-specific, paleo datasets are seasonally inhomogeneous. Analyses of instrumental data [Briffa and Jones, 1993; Kushnir, 1994] showed the existence of season-specific features of variability on decadal timescales. It seems reasonable to assume that on longer timescales variability is independent of seasonality [Mann et al., 1995; Mahasenan et al., 1997]. However, Bradley and Jones [1993] point out that long paleo records of temperature variations may show clear seasonal differences. A striking example is the seasonal Antarctic ice-core data of Morgan and Ommen [1997].

In order to address the issue of seasonality, we analyse 7 of the longest early-instrumental European temperature records [Jones and Bradley, 1992] at the locations Trondheim, Stockholm, Leningrad, Berlin, De Bilt, Geneva and Central England. The Central England Temperature (CET) [Manley, 1974] is a composite record based on various sites. Four missing years in the Leningrad record (1801-1804) were filled in by the (seasonal) mean values over the whole period. All series are seasonal anomalies with respect to the 1901-1950 reference period; the common length of the data is 220 yr. We analyse the winter, summer and annual-mean temperatures separately, focusing on timescales $\tau$>50 yr. The analysis method is described in section 2 and the results are given in section 3. In section 4 the oscillation with a timescale of ~70 yr, which seems apparent in the early-instrumental summer temperatures, is evaluated using 4 longer European paleo records. Section 5 gives the conclusions.


Singular spectrum analysis is a technique which decomposes timeseries into several modes of variability (monotonic and oscillatory) and the remaining low-amplitude noise. A number L of timeseries can be analysed simultaneously by Multichannel Singular Spectrum Analysis (MSSA) [Broomhead and King, 1986; Plaut and Vautard, 1994; Unal and Ghil, 1995]. In the MSSA, the timeseries (input channels) are expanded in terms of the eigen vectors of the matrix of cross-covariance coefficients of the different channels at lags 0 to M. One or a few terms in the expansion describe a mode of variability (reconstructed component) in the original series. MSSA identifies an oscillation, with period smaller than M, by forming a pair of consecutive eigen vectors. Such a pair should satisfy three criteria: first, the corresponding eigen values must be nearly equal, second, the two timeseries of projections of the data onto the eigen vectors (the spatio-temporal principal components - ST-PCs) must share the same frequency, and third, the ST-PCs must be in quadrature [Vautard et al., 1992; Plaut and Vautard, 1994]. The significance of an oscillation has to be additionally checked, as pure red noise processes are also shown [Allen and Robertson, 1996] to generate pairs of eigen vectors satisfying the above criteria. Variability on timescales longer than M is described by the so-called trend component, which may represent an oscillation with a timescale beyond M or a combination of a monotonic trend with an oscillatory mode.

The significance of the identified MSSA modes is estimated against red noise surrogates (500 Monte Carlo simulations of L independent first-order autoregressive processes AR(1)) projected onto the eigen vectors of the data matrix, as proposed by Allen and Robertson [1996]. The relative number of surrogate eigen values exceeding the data eigen value is taken as a measure of statistical significance. This test is applicable to statistically independent channels. Therefore, the timeseries were first subjected to principal component analysis and the spatial principal components (PCs) were used as L input channels to the MSSA. The signals in the original timeseries are computed by convolving the reconstructed components in PCs with the corresponding spatial modes.

The consistency of the reconstructed trend component with the raw data is checked at each individual location with Kendall's Tau-test [Conover, 1971]. The quasi-periods (if any) are identified by the high resolution MultiTaper spectral Method (MTM) of Thomson [1982], which provides also a statistical significance test. All oscillations shown are significant at the 99% level in the Fisher-Snedecor test [Vautard et al., 1992].

Prior to the analysis, the long-term mean was subtracted from the timeseries after which the series were standardized with their respective standard deviations. We found that the first 4 spatial PCs account for not less than 85% of the squared variance in each of the analysed datasets. All results shown are for L=4. Results are essentially the same when the original timeseries are used directly as the input channels.

Seasonal variability, $\tau$> 50yr

First we analyse the summer, winter and annual-mean temperatures separately, with an analysis window M=50 yr which is about one fourth of the common length of the dataset. Variability on timescales outside the window width is found to be described by the very first (ordered) MSSA components. Higher order MSSA components were found not to contain a trend. The reconstructed trend components shown in Figure 1 are significant at the 95% confidence level in the Allen and Robertson [1996] test and in the Kendall test of randomness.

Figure 1: Low-frequency components $\tau$> 50yr) in 7 early-instrumental timeseries of summer (top) and winter (bottom) temperature, as obtained by MSSA with a
50-yr window. The long-term mean is removed.

In the summer dataset the trend $\tau$>50 yr) is described by the first two MSSA components. They account for 23% of the squared variance in the four leading spatial PCs. The corresponding reconstructions of low-frequency summer temperature variability (multiplied by their respective standard deviations) are shown in Fig. 1, top. The summer trends appear to exhibit a preferential timescale of variability in the range 60-80 years. Prior to 1900 the general tendency is a cooling.

Low-frequency variability in winter temperatures is described by the single first MSSA component, which accounts for 16% of the variance in the four leading PCs. The winter trends are monotonic (Fig. 1, bottom), without any characteristic timescale. Until the early 20th century there is a pronounced warming. The cooling evident in the last few decades may be partly an artefact of the method, as the MSSA-based reconstructions are less reliable near the series endpoints.

Clearly, the temporal behavior of the MSSA-based reconstructions is very different in the two seasons. This result is robust with respect to changes in parameters of the analysis (increasing the sampling rate from 1 yr to 5 yrs, varying M by ±20%, increasing the number L of retained PCs from 4 to 7). The seasonal difference persists, if the analysis is restricted to the data segment prior to 1900. To ensure that the seasonal trends are not affected by degeneracy between higher order MSSA components, we repeated the analysis using the pooled summer and winter dataset. In this case both seasonal datasets are expanded over the same basis. Reconstructed winter/summer trends are opposing at most locations (not shown). These opposing tendencies of winter/summer trends result in a weak variability on timescales $\tau$>50yr in annual-mean temperatures.

The above results imply that reliable low-frequency variability patterns may only be detected on the basis of seasonally homogeneous datasets. Averaging the data within the year leads to confusion of distinct season-specific features.

Multidecadal oscillation in summer temperatures, $\tau$ ~ 70yr

The multidecadal timescale, which seems to appear in the summer trends, cannot be detected with confidence in the short early-instrumental series. We evaluate this apparent oscillation by analysing four long European records of paleo proxies for summer temperature, which are annually resolved. Two tree-ring series Fennoscandia (65-70°N, 10-30°E) [Briffa et al., 1992] and N. Urals (65°N, 65°E) [Graybill and Shiyatov, 1992] were calibrated by their originators using temperature data from the instrumental record. Both reconstructions explain about 50% of the variance over the fitting period. The record for C.Europe (47°N, 8°E) [Pfister, 1985] is mainly based on early-instrumental data for the period 1750-1980 and on documentary data for the earlier period. The correlation of the Svalbard ice-melt record [Tarussov, 1992], located in the European Arctic (79°N, 15°E), with the instrumental data is 0.55 for the decadal anomalies [Barnett et al., 1996]. The common period of the 4 paleo records is 1550-1980.

Analysis of the pooled paleo/early-instrumental dataset, with the parameters as in section 3, shows first that the trend components in the paleo and early-instrumental data are consistent and second that they can now be more clearly associated with a timescale of 70-80 yr. Next MSSA is applied to the paleo dataset alone with M=120yr and L=3 (one spatial PC does not contain significant power on $\tau$> 50yr and therefore it was not included). The application of a longer window enables to resolve the multidecadal timescale. The second and third MSSA eigen vectors form the pair of interest which satisfies the pairing criteria outlined in Section 2. First, the eigen values are very close ($\lambda2 ~ $\lambda3 ~ 11.5); second, the principal components ST-PCs 2 and 3 share approximately the same frequency (f2 ~ 0.0156 c/yr; f3 ~ 0.0146 c/yr), so that 2M|f2-f3|<0.75, and third, the between-pair cross correlation CC is maximum (CC ~ 0.79) at a lag of about 17 yr. This implies that the pair-2,3 describes an oscillation with a quasi-period of approximately 70 yr; the corresponding reconstructions are shown in Figure 2. The eigen spectrum of the paleo data, shown in Figure 3 together with the surrogate error bars, indicates that the pair-2,3 contains more variance than would be expected from red noise surrogates at the 95% confidence level. Fig. 2 suggests a bi-polar pattern of the multidecadal oscillation in summer temperatures, with one centre in the Arctic and the other in central Europe.

Figure 2: The 70-80 yr oscillation in 4 paleo records, as obtained by MSSA with a 120-yr window. The series are scaled with their respective standard deviation $\sigma$, after removing the long-term mean.

Figure 3: Eigen values of the paleo data for the first 20 ordered eigen vectors as obtained by MSSA with M=120yr. The surrogate error bars span the 5th to 95th percentiles of the corresponding diagonal elements of the surrogate matrix projected onto data eigen vectors. The pair (2,3), which describes an oscillation with a timescale ~70yr, is marginally significant above the 95.0th percentiles.

As a further test for the presence of a ~70 yr timescale, univariate SSA is applied to a number of the stack paleo records, obtained as average of normalised original records, in different combinations. Such averaging enhances the coherent signal. As an example, Figure 4 shows the spectrum of the record of differences between the Svalbard and C.Europe, representing two opposite centers of multidecadal variability. For each stack record, its spectrum shows the presence of a multidecadal pair; the null hypothesis that corresponding oscillation is generated by a red noise process, can be rejected at the 90% confidence level at least.

Figure 4: Eigen values of the stack paleo series, representing the difference between the normalised series Svalbard and C.Europe for the period 1550-1980, as obtained by SSA with a 120 yr window. The 95.0th and 5.0th percentiles of the diagonal elements of the surrogate matrix were computed from 500 realisations of a red noise process, with the same variance and lag-1 autocorrelation as the stack series. The pair (4,5), describing the multidecadal oscillation, lies clearly above the 95.0th percentiles.


We examined early-instrumental temperature records at 7 European locations, applying MSSA to the summer, winter and annual-mean data. The analysis is restricted to the MSSA-based trend component, which describes variability on timescales $\tau$longer than the analysis window width ($\tau$>50yr). It is shown that, on these timescales, the temporal behavior of trend components is clearly season-dependent. Winter temperatures show a monotonic warming, while low-frequency variability in summer temperatures seems to be associated with a timescale in the range 60-80 yr. Variability in the annual-mean data is weak, as averaging the data within the year distorts the signals evident in the seasonal data.

The timescale of summer temperature variations is evaluated by application of MSSA with a longer window to 4 paleo series of summer temperature proxies, covering the period 1550-1980. We find that the ~70 yr oscillation can be distinguished from red noise surrogates at the 95% confidence level. While individual paleo series contain only a weak multidecadal signal [Mahasenan et al., 1997], the spatial coherence of this mode results in a significant signal in the present multivariate analysis. The spatial pattern of the multidecadal oscillation is a dipole, with one centre in the European Arctic and the other in central Europe.

A multidecadal cycle with $\tau$~ 84yr was earlier associated with Euroasian temperatures by Schlesinger and Ramankutty [1994] on the basis of regional-mean and annual-mean instrumental data. Schlesinger and Ramankutty stress that this timescale only appears after removing a linear trend assumed to be due to anthropogenic forcing. The present analysis of longer seasonal records indicates that, at least in Europe, this oscillation is masked in the annual-mean data by opposing temperature tendencies in the summer and winter series.

The present results stress the necessity of using seasonally homogeneous datasets of paleo proxies in analyses of low-frequency variability. The existence of natural multidecadal cycles may complicate the detection of an anthropogenic signal, to the extend that these cycles may not be adequately represented in the climate models used to provide estimates of internal variability for detection studies.


We thank Phil Jones for making the paleo data available to us. Aryan van Engelen (KNMI) kindly provided the De Bilt temperature series. The other early-instrumental temperature records were obtained from the World Data Centre A for Paleoclimatology (Boulder, USA). We benefitted from helpful suggestions of M.Allen. Constructive criticism by an anonymous referee is gratefully acknowledged. MS was supported by the Netherlands National Research Programme on Global Air Pollution and Climate Change, registered under nr. 951244.


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