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# Left panel: DFT of M6 (average from six central European instrumental time series). Right panel: same for SPA, interpolated time series of a stalagmite from the Austrian Alps for the period 500-1935 AD. In both DFT analyses the records were padded with zeros. The upper confidence curve (brown) is for 95 %, the lower (cyan) for 90 % against background noise, each of those established by 10 000 Monte Carlo runs. The most relevant peaks are indicated by their period length.

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The longest six instrumental temperature records of monthly means reach back maximally to 1757 AD and were recorded in Europe. All six show a V-shape, with temperature drop in the 19th and rise in the 20th century. Proxy temperature time series of Antarctic ice cores show this same characteristic shape, indicating this pattern as a global phenomeno...

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Context 1
... results of the DFT are shown in Fig. 3. The left panel of Fig. 3 depicts the power densities of the DFT for M6 with padded zeros together with the 90 % and 95 % curves of con- fidence yielded by the Monte Carlo simulations. The right panel shows the same for SPA. Figure 5 ...
Context 2
... results of the DFT are shown in Fig. 3. The left panel of Fig. 3 depicts the power densities of the DFT for M6 with padded zeros together with the 90 % and 95 % curves of con- fidence yielded by the Monte Carlo simulations. The right panel shows the same for SPA. Figure 5 ...
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... note that the ∼ 250-yr peak in Fig. 3 left results from only about one 250-yr period, which covers the entire record length. This is clearly insufficient to detect real oscillatory dynamics. The question thus, if there is in fact a 250-yr pe- riodicity, can only be decided by longer records. Fortunately the SPA record covers about 2000 yr. Its spectrum shows a strong peak ...
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... left results from only about one 250-yr period, which covers the entire record length. This is clearly insufficient to detect real oscillatory dynamics. The question thus, if there is in fact a 250-yr pe- riodicity, can only be decided by longer records. Fortunately the SPA record covers about 2000 yr. Its spectrum shows a strong peak at ∼ 235 yr (Fig. 3 right). Additionally, Fig. 4 shows that the 235-yr component of SPA follows roughly the overall shape of SM6. We have also ascertained that the appearance of the ∼ 250-yr period is not an artifact of the 254-yr record length of M6 by extending M6 by 100 yr with white noise random numbers. Also this 354-yr-long extended record yields the ...
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... follows roughly the overall shape of SM6. We have also ascertained that the appearance of the ∼ 250-yr period is not an artifact of the 254-yr record length of M6 by extending M6 by 100 yr with white noise random numbers. Also this 354-yr-long extended record yields the prominent ∼ 250-yr period. This and Fig. 4 suggest that the ∼ 250-yr peak in Fig. 3 left is not an artifact and corresponds to a real oscillation. The wavelet diagram shows that this cycle has been the dominant one since about 1100 AD (see Fig. 5) corresponding to the dominant strength of this cycle in ...
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... wavelet analysis (Fig. 5) shows that historically a ∼ 125-yr cycle was dominating the Earth temperature. Dur- ing the many decades this cycle has weakened and the strength shifted to the subharmonic (see Sect. 7) of ∼ 250 yr, which is now the dominant periodicity. In addition, the four lowest frequencies in Fig. 3 (right) show rather precisely the spectral pattern of the generation of the subharmonics (1, 0.5, 0.75, 1.25, which correspond to the evaluated periods 234, 512, 341, 182 yr of Fig. 3 right). Such subharmonic genera- tion is characteristic of the transition from periodic to chaotic oscillations of dynamic systems (Feigenbaum, 1978(Feigenbaum, ...
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... weakened and the strength shifted to the subharmonic (see Sect. 7) of ∼ 250 yr, which is now the dominant periodicity. In addition, the four lowest frequencies in Fig. 3 (right) show rather precisely the spectral pattern of the generation of the subharmonics (1, 0.5, 0.75, 1.25, which correspond to the evaluated periods 234, 512, 341, 182 yr of Fig. 3 right). Such subharmonic genera- tion is characteristic of the transition from periodic to chaotic oscillations of dynamic systems (Feigenbaum, 1978(Feigenbaum, , ...
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... all terrestrial weather dynam- ics (e.g., trade winds or El Niño). This interpretation as in- trinsic system dynamics is supported by the wavelet analysis of the stalagmite data. The latter shows a drift over 1600 yr of peak intensity from the 128-yr period to the 256-yr period. A further doubling to ∼ 500 yr (peak visible in the spectrum, right Fig. 3) causes the recent weakening of the 250-yr pe- riod, visible in the wavelet diagram. Such a shifting of en- ergy from a fundamental to a subharmonic frequency com- ponent is characteristic of the Feigenbaum universal scenario of transition to chaos by a cascade of subharmonics, for non- linear, dissipative systems with energy input ...
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... , 1983. Whereas harmonic generation is just an expres- sion of nonlinearity, subharmonic generation is peculiar to the Feigenbaum scenario, since it requires, different from harmonic generation, a particular phase-matching mecha- nism for sum-and difference-frequencies generated by the system non-linearities. The four lowest frequency lines of Fig. 3 (right) give additionally evidence of the climate os- cillations as intrinsic dynamics. They show the pattern char- acteristic of generation of two subharmonics, which corre- sponds rather convincingly to the Feigenbaum transition to ...

## Citations

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... Tularam and Ilahee (2010) studied by means of FFT (Fast Fourier Transform) the interaction between precipitation and temperature in Queensland (Australia) working on very short time-scales (from hours to 10 days). Lüdecke et al. (2013) compared the spectral features (maxima above the 95% confidence level) of an average series, derived from 6 temperature series from 1757 CE with that of the speleothems of the Spannagel Cave (Austrian Alps). Moreover Olafsdottir (2010) in a thesis for the MS degree at the University of Iceland showed the significant correlation, based on spectral analysis, between varve thickness of 2-lakes sediments and NAO-AMO summer indexes while Thiéblemont et al. (2015) proposed a 1-2 years lagged solar/AMO relationship, highly misrepresented in climate model simulations and Zanzi et al. (2007) suggested that Pinus montana growth in the Central Italian Alps, if not disturbed by external geomorphological factors, is controlled by environmental and/or climatic conditions that in the last~150 years oscillated on scales ranging from interdecadal (~20 years) to decadal. ...
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This work proposes a daily high-resolution probabilistic reconstruction of precipitation and temperature fields in France over the 1871–2012 period built on the NOAA Twentieth Century global extended atmospheric reanalysis (20CR). The objective is to fill in the spatial and temporal data gaps in surface observations in order to improve our knowledge on the local-scale climate variability from the late nineteenth century onwards. The SANDHY (Stepwise ANalogue Downscaling method for HYdrology) statistical downscaling method, initially developed for quantitative precipitation forecast, is used here to bridge the scale gap between large-scale 20CR predictors and local-scale predictands from the Safran high-resolution near-surface reanalysis, available from 1958 onwards only. SANDHY provides a daily ensemble of 125 analogue dates over the 1871–2012 period for 608 climatically homogeneous zones paving France. Large precipitation biases in intermediary seasons are shown to occur in regions with high seasonal asymmetry like the Mediterranean. Moreover, winter and summer temperatures are respectively over- and under-estimated over the whole of France. Two analogue subselection methods are therefore developed with the aim of keeping the structure of the SANDHY method unchanged while reducing those seasonal biases. The calendar selection keeps the analogues closest to the target calendar day. The stepwise selection applies two new analogy steps based on similarity of the sea surface temperature (SST) and the large-scale 2 m temperature (T). Comparisons to the Safran reanalysis over 1959–2007 and to homogenized series over the whole twentieth century show that biases in the interannual cycle of precipitation and temperature are reduced with both methods. The stepwise subselection moreover leads to a large improvement of interannual correlation and reduction of errors in seasonal temperature time series. When the calendar subselection is an easily applicable method suitable in a quantitative precipitation forecast context, the stepwise subselection method allows for potential season shifts and SST trends and is therefore better suited for climate reconstructions and climate change studies. The probabilistic downscaling of 20CR over the period 1871–2012 with the SANDHY probabilistic downscaling method combined with the stepwise subselection thus constitutes a perfect framework for assessing the recent observed meteorological events but also future events projected by climate change impact studies and putting them in a historical perspective.