Main

Global temperatures are currently rising, and future scenarios suggest large changes in precipitation patterns and temperatures15. Reconstructing past climate is essential for enhanced understanding of climate variability, and provides necessary background knowledge for improving predictions of future changes. From multi-proxy combinations1,2,3,4,7 of climate proxy data (for example, from tree rings, corals and ice cores), or from reconstructions based solely on tree-ring data5,6,16, past surface temperatures have been inferred by calibration to instrumental temperature data using statistical relationships. Past surface temperature changes have also been inferred from temperature profiles along deep terrestrial boreholes12, where physical laws rather than statistical relations are used to estimate temperature trends. Borehole measurements12 and some reconstructions based on tree-ring data6,16 indicate a larger warming trend in the past 500 yr than do multi-proxy reconstructions1,2,3,4,7.

Although differences in the amplitude of centennial temperature variability have been discussed in the literature8,15, the picture with relatively small variability (shown by multi-proxy reconstructions1,2,3,4,7) is arguably best known by a wider audience. One reason for this is the prominent role that the multi-proxy reconstruction by Mann et al.1,2 had in the latest IPCC report15 and in public media. Recent findings14, however, suggest that considerable underestimation of centennial Northern Hemisphere temperature variability may result when regression-based methods, like those used by Mann et al.1,2, are applied to noisy proxy data with insufficient spatial representativity. It is thus important to explore other techniques and other data types, and also to use data from more regions than previously examined.

A view has been expressed that only tree-ring and other high-resolution data are useful for quantitative large-scale temperature reconstructions3,8. Tree-ring data, however, have a well-documented difficulty in reliably reproducing multicentennial temperature variability17. Special standardization techniques for extracting multicentennial information exist6,16, but they do not ensure an accurate reconstruction10. Natural archives with lower temporal resolution (often various sediments) have potential for providing climate information at multicentennial timescales that may not be captured by tree-ring data9. Low-resolution data, on the other hand, can sometimes have dating errors of up to more than 100 yr (ref. 9). Such errors are intolerable at interannual to multidecadal timescales8, but if these data are used only for longer timescales the errors become relatively small in relation to the timescales of interest.

Our aim is to combine low-frequency climate information (contained in low-resolution proxy data) with high-frequency information (from tree-ring data) in order to derive a 2,000-yr-long Northern Hemisphere temperature reconstruction in which we avoid using each proxy type at timescales where it is most unreliable, but instead use it only where it has its greatest advantages. To achieve this, we developed a method that allows a timescale-dependent data decomposition by application of a wavelet transform11 technique.

The number of available 2,000-yr-long local-to-regional scale temperature proxy series is very limited8. We found seven tree-ring series and eleven low-resolution proxy series. For the period before ad 1400, this number is similar to previous reconstructions1,2,3,4,5,6,7. Among the eleven low-resolution series were nine already calibrated to local/regional temperatures for different Northern Hemisphere regions, whereas two were only available in original proxy data units. The data set includes climatic information from the North American and Eurasian continents and from the Atlantic and Indian oceans (Fig. 1, Table 1; see Supplementary Information for further details and references).

Figure 1: Locations of proxy data sites.
figure 1

Shown are the locations of eleven low-resolution proxy records (blue circles, numerals 1–11, see Table 1 for site details) and seven tree-ring series (red triangles, letters A–G). Dashed latitude lines indicate the Equator, the Tropic of Cancer and the Arctic Circle. See Supplementary Information for further details and references.

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Table 1 Summary information for low-resolution proxy series
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Various averages (see Methods) of the nine already calibrated low-resolution series (Table 1, site numbers 2–10) depict, when low-pass filtered to highlight multicentennial variability (Fig. 2a), a temperature maximum in the ninth or tenth centuries and a minimum in the sixteenth century, with a total range of 0.6 to 0.9 K. This is a substantially larger multicentennial temperature range compared to previous multi-proxy reconstructions1,2,3,4,7, exemplified in Fig. 2a with the Northern Hemisphere reconstruction by Mann and Jones7. The conflicting views provided by the low-resolution series and this reconstruction illustrate a clear need for further research to determine the size of natural low-frequency climate variability.

Figure 2: Estimations of Northern Hemisphere mean temperature variations.
figure 2

a, Previous multi-proxy reconstruction (MJ: from Mann and Jones7, black line) with ± 2 s.d. uncertainty (grey shading), and various averages (blue, green, magenta; see Methods) of smoothed low-resolution temperature indicators (nos 2–10 in Table 1). b, Our multi-proxy reconstruction ad 1–1979 (red) with its >80-yr component ad 133–1925 (blue) and its jack-knifed estimates (light blue), and the instrumental record19 (green). c, Forced ECHO-G model13,14,26. d, Low-frequency component of multi-proxy reconstruction in b (blue curve) with confidence intervals for three separate uncertainties. The innermost medium-blue band shows the uncertainty due to variance among the low-resolution proxy series. The two outer bands show the uncertainty in the variance scaling factor (light blue) and the constant adjustment (outermost blue band) separately. Each uncertainty is illustrated with an approximate 95% confidence interval (see Supplementary Information). Also shown are ground surface temperatures estimated from boreholes12 with their uncertainty interval (brown; see Methods), and the >80-yr component of a previous multi-proxy reconstruction (MBH: from Mann et al.1,2, orange) with ± 2 s.d. uncertainty (yellow). e, f, Wavelet transform (see Methods) of the series in b and c where warm/cold anomalies are red/blue. Temperature anomalies in a, b and d are with respect to the 1961–90 average.

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Simple averages of temperature proxy series, such as those shown in Fig. 2a, can yield adequate estimates of Northern Hemisphere century-scale mean-temperature anomalies14. But to obtain a reconstruction covering a complete range of timescales we created a wavelet transform11, supposed to be approximately representative for the Northern Hemisphere (Fig. 2e), such that only information from the tree-ring records contributes to timescales less than 80 yr and all eleven low-resolution proxies contribute only to the longer timescales (see Methods for details). From the wavelet transform, which was calculated using standardized (that is, unitless) proxy series, a dimensionless reconstruction was obtained by calculating the inverse wavelet transform11. Given the small number of tree-ring series, their contribution is best thought of as an approximation of the statistical character of variability at <80-yr scales. A sample size of eleven low-resolution series is reasonable for reconstructing >80-yr variability, given that the number of spatial degrees of freedom on the entire globe is about five at centennial timescales18. The contribution from each low-resolution proxy series to the total variance at >80-yr scales in the Northern Hemisphere reconstruction is given in Table 1.

To calibrate the reconstruction, its mean value and variance were adjusted to agree with the instrumental record of Northern Hemisphere annual mean temperatures19 in the overlapping period ad 1856–1979 (Fig. 2b). This technique avoids the problem with underestimation of low-frequency variability associated with regression-based calibration methods14. Jack-knifed estimates (light-blue curves in Fig. 2b) of the low-frequency component (> 80-yr scales, dark blue), where each of the eleven low-resolution proxies are excluded one at a time, are all very similar, demonstrating that the reconstruction is robust to the omission of any single low-resolution proxy series.

The reconstruction depicts two warm peaks around ad 1000 and 1100 and pronounced coolness in the sixteenth and seventeenth centuries, with an overall temperature range for the low-frequency component (> 80-yr scales) of about 0.65 K. This amplitude can be compared with that in the smoothed and averaged low-resolution series in Fig. 2a, where the data used had been calibrated to temperatures by their original investigators. The size of the overall amplitudes of the series in Fig. 2a (0.6–0.9 K) and Fig. 2b (0.65 K, blue curve) indicates that the reconstructed multicentennial variability in Fig. 2b has not been inflated by the standardization, the wavelet processing and the subsequent calibration technique. The peaks in medieval times are at the same level as much of the twentieth century, although the post-1990 warmth seen in the instrumental data (green curve in Fig. 2b) appears to be unprecedented.

Changes in radiative forcing due to variability in solar irradiance, the amount of aerosols from volcanic eruptions and greenhouse gas concentrations have been important agents causing climatic variability in the past millennium1,8,20,21,22,23,24,25. Reconstructions of the temporal evolution of these variables have been used to drive climate models, ranging from simple energy balance models to fully coupled atmosphere–ocean general circulation models8,13,14,20,22,23,25. The Northern Hemisphere temperature series obtained from such an experiment with the coupled model ECHO-G13,14,25,26 for the ad 1000–1990 period (Fig. 2c) is qualitatively remarkably similar to our multi-proxy reconstruction, although the model shows a somewhat larger variability. Particularly strong qualitative similarity is seen at timescales longer than centennial (compare the two wavelet transform patterns, Fig. 2e, f), but some high-frequency details are also in good agreement (for example, the double peaks around ad 1000 and 1100, and two short cooling periods at ad 1460 and 1820). The model's variability before the twentieth century is largely determined by the combined effects of the reconstructed solar and volcanic forcing (that is, natural forcing) that was used in the integration13,25, whereas the notably strong warming in the model data after ad 1900 is largely due to rapidly increasing concentrations of anthropogenic greenhouse gases13,25,27. The similarity between our reconstruction and the ECHO-G model series supports the case of a rather pronounced hemispheric low-frequency temperature variability resulting from the climate system's response to natural changes in radiative forcing.

As in all palaeoclimate reconstructions, there are uncertainties in this one. Efforts to quantify uncertainties in the low-frequency component are illustrated with blue bands of different colours in Fig. 2d. Accounting for the total uncertainty, the cooling from the maxima around ad 1000 and 1100 to the minimum near ad 1600 is between 0.3 K and 1.1 K for the >80-yr component. Only the smallest value is similar to the corresponding temperature change in previous multi-proxy reconstructions1,2,3,4,7. (Compare with the reconstruction of Mann et al.1,2, which is also shown in Fig. 2d (orange curve, yellow uncertainty range) after smoothing to show >80-yr variability.) In contrast, the warming trend depicted by our reconstruction in the past 500 yr is entirely consistent with estimates of Northern Hemisphere ground surface temperature (GST) trends from temperature measurements in nearly 700 boreholes12. Although trends at individual borehole sites are very noisy, hemispheric mean GST trends are robust to different aggregation and weighting schemes12 (illustrated by the two brown curves in Fig. 2d), and show a warming of ∼1 K during the interval ad 1500–2000, of which about half fell in the twentieth century.

There are several reasons for the notable differences between our and previous multi-proxy reconstructions. The reconstruction of Mann and Jones7 has a large amount of data in common with ours, but these workers combined tree-ring data with decadally resolved proxies without any separate treatment at different timescales. Furthermore, our data set contains some centennially resolved data from the oceans, while Mann and Jones used only annually to decadally resolved data from continents or from locations very near the coast. Different calibration methods (regression in the work of Mann and Jones versus variance scaling in this study) are another reason. Possible explanations for the small low-frequency variability in the multi-proxy reconstruction of Mann et al.1,2 have recently been discussed in detail elsewhere14.

Our multi-proxy reconstruction achieves a relatively large multicentennial variability by separately considering the information in tree-ring data and low-resolution proxy records. Much more effort, however, is needed to develop new proxy data series and to determine how proxy data should best be chosen, combined and calibrated. The wavelet approach allows for separate weighting of proxies at different timescales. A goal for further research could be to determine how such weighting should be undertaken, while simultaneously taking spatial representativity into account. New experiments with distorted ‘pseudoproxy’ data14,28,29 from forced general circulation model runs, using various types of distortions, should be useful in this context.

We find no evidence for any earlier periods in the last two millennia with warmer conditions than the post-1990 period—in agreement with previous similar studies1,2,3,4,7. The main implication of our study, however, is that natural multicentennial climate variability may be larger than commonly thought, and that much of this variability could result from a response to natural changes in radiative forcings. This does not imply that the global warming in the last few decades15,19 has been caused by natural forcing factors alone, as model experiments that use natural-only forcings fail to reproduce this warming15,23,27,30. Nevertheless, our findings underscore a need to improve scenarios for future climate change by also including forced natural variability—which could either amplify or attenuate anthropogenic climate change significantly.

Methods

Wavelet transformation

The wavelet transform11 (WT) decomposes a time series into time–frequency space, enabling the identification of both the dominant modes of variability and how those modes vary with time. We used the Mexican hat11 wavelet, after linear interpolation to annual resolution, to decompose each proxy series into 22 wavelet ‘voices’. These are 22 separate time series, where each depict the variability in the original series at each of the timescales near the Fourier periods 4, 4√2, 8, 8√2, …, 4,096√2 yr. This ranges from the smallest possible scale for the Mexican hat wavelet up to a few times the length of the 2,000-yr-long time interval of interest. Before calculating the WT, padding with surrogate data to extend the proxy series from their last value to the year ad 2300 was applied to limit boundary effects at the longest timescales. As padding data we used the mean value for the last 50 yr with data in each series. For those records that do not have data back at least to 300 bc, similar padding was also made at the beginning of records.

Averaging of calibrated low-resolution temperature indicators

Nine low-resolution proxy series (Table 1) are available as calibrated local/regional temperature indicators (numbers 2–10). Five are annual mean (nos 2, 5, 6, 8, 10), one is a spring (no. 4) and three are summer (nos 3, 7, 9) temperature indicators. Multicentennial variability (highlighting >340-yr scales) in these series was extracted by first applying the WT to each series and then the inverse WT only for wavelet voices 14–22. Timescales of >340 yr are long enough to ensure that only information at frequencies lower than the Nyquist frequency for the most poorly resolved proxy series are used. Figure 2a shows arithmetic (green) and cos-latitude weighted (blue) averages of all nine indicators. Jack-knifed estimates of the cos-latitude weighted averages, where each of the nine indicators were removed one at a time, are also shown (magenta). These series are plotted in Fig. 2a for the period ad 133–1925 (when all have data) such that their mean values agree with the Mann and Jones reconstruction7 in the interval ad 200–1925. Minor differences between the arithmetic and cos-latitude weighted series indicate robustness to weighting choice. The similarity among the jack-knifed estimates indicates that the overall temperature range is relatively little affected by the removal of any individual indicator.

Timescale-dependent reconstruction

The multi-proxy reconstruction in Fig. 2b was constructed as follows. First, the data set of 19 proxy series in Fig. 1 was divided into two half-hemispheric subsets (western and eastern half). After wavelet transformation of each individual proxy series into 22 voices as described above (here using standardized series obtained by subtracting the mean and dividing by the standard deviation, after linear interpolation to annual resolution), a scale-by-scale averaging of wavelet voices was undertaken. For each wavelet scale from 1 to 9 (Fourier timescales <80 yr), the voices from the individual tree-ring series were averaged and, similarly, for each wavelet scale from 10 to 22 (Fourier timescales >80 yr) the corresponding voices from the individual low-resolution proxy series were averaged. Merging of the tree-ring-data average voices 1–9 with the low-resolution-data average voices 10–22 gave one complete WT with voices 1–22 for each half-hemispheric subset. The average of these two WTs then gave the whole-hemispheric WT shown in Fig. 2e. The rationale for dividing into half-hemispheric subsets is similar to that used in gridding; namely, to ensure that regions with many data series are weighted the same as regions (of the same size) with few data series. However, for our data set, little difference would be obtained if all data were placed in one whole-hemispheric set. A dimensionless Northern Hemisphere temperature reconstruction was obtained by calculating the inverse transform. Finally, this time series was calibrated by adjusting its variance and mean value to be the same as in the instrumental data19 in the overlapping period ad 1856–1979 (Fig. 2b). Separate estimates of uncertainties due to variance among individual low-resolution proxy data and in the determination of the variance scaling factor and constant adjustment term are explained in Supplementary Information.

Plotting GST trends

The two curves for GST trends12 shown in Fig. 2d correspond to the upper and lower bounds for different area- and occupancy-weighted GST reconstructions, as illustrated in figure 3 of ref. 12. To help visual comparison with our multi-proxy reconstruction, the GST trends are plotted with reference to the ad 1961–90 average in Fig. 2d. This was achieved by shifting the GST trend-curves such that they cross the zero level at 1958.5, which is the time when the twentieth century linear trend of the Northern Hemisphere instrumental surface air temperature19 (anomalies with respect to ad 1961–90) crosses the zero level. (The same technique was used in figure 5 of ref. 12.)