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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.

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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... 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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... 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

... The calculated temperature values in the IPCC model (1-1) after the feedback are far too high and do not match the measured values on Earth (Weiss, 2015). The IPCC also did not incorporate the sun, T e , or natural cycles (such as the 65-year AMO/PDO cycle, the 200-year de Vries/Suess cycle or the 1000-year cycle (Lüdecke et al., 2013c;Weiss, 2015), or urban heat islands in their dataset (TranslatorsCafe.com, 1976). ...
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Economic- and ecological plan in (/outside) European countries: Income=Spending+Annuity[interest and redemption national debt]*. Solution for the financial-, energy-, climate-, trade- and food crisis.
... This indicated that temperatures in the southern hemisphere seemed to have an opposite trend in contrast with the northern hemisphere's temperatures on the millennial scale. This was consistent with previous studies on seesaw [42,45]. For example, the modeling work demonstrated that responses of regional temperatures to the solar forcing were not uniform [42]; although the millennial variations of the northern temperature kept the positive-phase consistency with the global change, a small part of the very southern regions presented a converse trend with the global variation [45]. ...
... This was consistent with previous studies on seesaw [42,45]. For example, the modeling work demonstrated that responses of regional temperatures to the solar forcing were not uniform [42]; although the millennial variations of the northern temperature kept the positive-phase consistency with the global change, a small part of the very southern regions presented a converse trend with the global variation [45]. ...
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The solar impact on Earth’s climate is both a rich and open-ended topic with intense debates. In this study, we use the reconstructed data available to investigate periodicities of solar variability (i.e., variations of sunspot numbers) and temperature changes (10 sites spread all over the Earth) as well as the statistical inter-relations between them on the millennial scale during the past 8640 years (BC 6755–AD 1885) before the modern industrial era.. We find that the variations of the Earth’s temperatures show evidence for the Eddy cycle component, i.e., the 1000-year cyclicity, which was discovered in variations of sunspot numbers and believed to be an intrinsic periodicity of solar variability. Further wavelet time-frequency analysis demonstrates that the co-variation between the millennium cycle components of solar variability and the temperature change held stable and statistically strong for five out of these 10 sites during our study interval. In addition, the Earth’s climatic response to solar forcing could be different region-by-region, and the temperatures in the southern hemisphere seemed to have an opposite changing trend compared to those in the northern hemisphere on this millennial scale. These findings reveal not only a pronounced but also a complex relationship between solar variability and climatic change on Earth on the millennial timescale. More data are needed to further verify these preliminary results in the future.
... If this relationship proves to be a real feature of planetary atmospheric physics, it will have far-reaching effects for how albedo and 'greenhouse' gas content are treated when calculating atmospheric temperatures in the future. The relationship tends to add to previous work that indicates the likelihood of a very low or a zero, climate sensitivity for CO2 [2][3][4]14,17,18,[24][25][26][27][28][29]. ...
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It has been discovered that there appears to exist a close relationship between relative differences in total solar irradiance and the atmospheric temperature, at a pressure of 1 bar, on all three terrestrial-type bodies which possess thick atmospheres. The apparent relationship is through the quaternary root of total solar irradiance at 1 bar, and applies to the planetary bodies Venus, Earth and Titan. The relationship is so close that the average surface atmospheric temperature of Earth can be easily calculated to within 1 Kelvin (0.5%) of the correct figure by the knowledge of only two numbers, neither of which are related to the Earth's atmosphere. These are; the atmospheric temperature in the Venusian atmosphere at 1 bar, and the top-of-atmosphere solar insolation of the two planets. A similar relationship in atmospheric temperatures is found to exist, through insolation differences alone, between the atmospheric temperatures at 1 bar of the planetary bodies Titan and Earth, and Venus and Titan. This relationship exists despite the widely varying atmospheric greenhouse gas content, and the widely varying albedos of the three planetary bodies. This result is consistent with previous research with regards to atmospheric temperatures and their relationship to the molar mass version of the ideal gas law, in that this work also points to a climate sensitivity to CO2-or to any other 'greenhouse' gas-which is close to or at zero. It is more confirmation that the main determinants of atmospheric temperatures in the regions of terrestrial planetary atmospheres which are >0.1 bar, is overwhelmingly the result of two factors; solar insolation and atmospheric pressure. There appears to be no measurable, or what may be better termed 'anomalous' warming input from a class of gases which have up until the present, been incorrectly labelled as 'greenhouse' gases.
... 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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The spectral periods in North Atlantic Oscillation (NAO), Atlantic Multidecadal Oscillation (AMO) and El Nino Southern Oscillation (ENSO) were analyzed and has been verified how they imprint a time series of European temperature anomalies (ETA), two European temperature time series and some phenological series (dates of cherry flowering and grapevine harvest). Such work had as reference scenario the linear causal chain MCTP (Macroscale Circulation ? Temperature ? Phenology of crops) that links oceanic and atmospheric circulation to surface air temperature which in its turn determines the earliness of appearance of phenological phases of plants.
... According to Harde [5] the Sun is the main contributor to global warming of the last century. Lüdeсke et al. [6] showed that variations of Central European temperature after 1757 were likely governed by periodic oscillations resulted from intrinsic climatic dynamics. Scafetta [7] [8] claimed that the global climate oscillations from 1950 to 2011 were appreciably influenced by astronomic planetary cycles, particularly by motion of Jupiter and Saturn. ...
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A number of numerical experiments with artificial random signals (the second order autoregressive processes), which have important statistical properties similar to that of the observed instrumental temperature (1850-2015), were carried out. The results show that in frame of the selected mathematical model the return period of climatic events, analogous to the current global warming (linear increase of temperature for 0.95˚C during the last 135 years) is 2849-5180 years (one event per 2849-5180 years). This means that global warming (GW) of the last 135 years can unlikely be fully explained by inherent oscillations of the climatic system. It was found however, that natural fluctuations of climate may appreciably contribute to the GW. The return period of climatic episodes with 0.5˚C warming during the 135 years (half of the observed GW) was less than 500 years. The result testifies that the role of external factors (emission of greenhouse gases, solar activity etc.) in the GW could be less than often presumed.
... Babich et al. [15] have found periods of ~1000, ~500 to ~350, and ~200 years in paleoreconstruction of the last 2000 years, predicting a strongly pronounced cooling until AD 2500. In this context, we need to mention Schlesinger and Ramankutty [16], Gervais [17], De Vries [18], Suess [19], Steinhilber et al. [20,21], Breitenmoser et al. [22], Cliver et al. [23], Raspopov et al. [24], Novello et al. [25], Wagner et al. [26], Lüdecke et al. [27,28], Friis-Christensen and Lassen [29], Van Geel et al. [30], Braun et al. [31], Lohmann and Schöne [32], Czymzik et al. [33], Adolphi et al. [34], Wirth et al. [35], Lockwood [36], Fleitmann et al. [37], Svensmark [38], Svensmark et al. [6], Marsh and Svensmark [39], Enghoff [40], Gray et al. [41], Haigh [42,43], Ineson et al. [44], Seidenglanz et al. [45], Kodera [46], Meehl et al. [47], and Leal-Silva and Herrera [48]. Lüning [49] provides an extensive compilation of pertinent references. ...
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The Sun as climate driver is repeatedly discussed in the literature but proofs are often weak. In order to elucidate the solar influence, we have used a large number of temperature proxies worldwide to construct a global temperature mean G7 over the last 2000 years. The Fourier spectrum of G7 shows the strongest components as ~1000-, ~460-, and ~190 - year periods whereas other cycles of the individual proxies are considerably weaker. The G7 temperature extrema coincide with the Roman, medieval, and present optima as well as the well-known minimum of AD 1450 during the Little Ice Age. We have constructed by reverse Fourier transform a representation of G7 using only these three sine functions, which shows a remarkable Pearson correlation of 0.84 with the 31-year running average of G7. The three cycles are also found dominant in the production rates of the solar-induced cosmogenic nuclides ¹⁴ C and ¹⁰ Be, most strongly in the ~190 - year period being known as the De Vries/Suess cycle. By wavelet analysis, a new proof has been provided that at least the ~190-year climate cycle has a solar origin.
... It is known that not all natural phenomena behave in this way because some natural processes, for example in hydrology (Hurst, 1951) (Koutsoyiannis, 2003) (Pelletier, 1997) and also in surface temperature (Lüdecke, 2013) (Alvarez-Ramirez, 2008 (Mali, 2015) (Munshi-Edwards, 2016) , are known to contain dependence in the time series mostly in the form of persistence. Persistence implies that the probability distributions of successive events in the time series are not independent but rather that they depend on what was drawn in the previous trials by forming a bias in the same direction as the deviations in previous events in the time series (Malamud, 1999) (Hosking, 1984). ...
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Zonal monthly means of UAH satellite based measurements of lower troposphere temperature anomalies 12/1978 to 4/2017 are examined for violations of the independence assumption of OLS linear regression. The Hurst Exponent (H), computed at a monthly time scale, is used as the measure of dependence. It is found that the independence assumption of OLS linear regression is violated in the UAH temperature anomaly time series. The apparent multi-decadal non-linearity found in a prior work may be related to non-linear dynamics implied by the Hurst phenomenon. The interpretation of OLS linear regression trend lines for these time series in terms of anthropogenic global warming should be made with caution, particularly so in view of the short time span of the data, because the data do not comply with OLS assumptions.
... Indeed, these observations are more frequent when the weather conditions are more favorable, when dust particles increase or the cloud cover decreases, etc. Therefore, the periods T 1 = 61.80 years for aurora sightings and T 2 = 62.00 years for sunspots are comparable to the 60-year climate cycles identified in some internally driven mechanisms such as the Atlantic Multidecadal Oscillation (AMO) (Delworth and Mann, 2000), the Pacific Decadal Oscillation (PDO) (d' Orgeville and Peltier, 2007;Minobe, 1997), as well as in the changes in levels of the Nile (Kondrashov, Feliks, and Ghil, 2005;Ruzmaikin, Feynman, and Yung, 2006), fluctuation in precipitation intensity of the Indian monsoon (Agnihotri et al., 2002;Yadava and Ramesh, 2007), correlation between the solar activity and the movement of atmospheric air masses (Veretenenko and Ogurtsov, 2012a,b), northern atmospheric pressure and air temperature (Mazzarella, 2007), global and some regional surface temperature (Lüdecke, Hempelmann, and Weiss, 2013;Scafetta, 2012), and other climate records. Chambers, Merrifield, and Nerem (2012) have demonstrated the existence of a quasi-60-year oscillation in the majority of the tide gauges examined during the twentieth century in every ocean basin. ...
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... Driven by multi-level natural cycles (Mokhov et al., 2012;Lüdecke et al., 2013) and reinforced by anthropogenic influences (Karl, 1988;Myhre et al., 2013), climate is the result of interaction of dynamic physical processes of atmosphere with the land and ocean surfaces (Solomon et al., 2011;Terray, 2012). The studies of centennial dynamics within the warm and dry 200-year period and the change points of the climate cycles contribute to the understanding of the paleoclimatic regularities and peculiarities from the older ages. ...
Article
The research deals with the analysis of centennial climate dynamics in Western Ukraine based on instrumental observations. The climate of the region is one of the least researched. Its local peculiarities require a deeper study. In the last 130 years, the temperature and precipitation characteristics in the region are observed to have undergone changes. Low mountainous regions and similar adjoining territories of canyon river valleys with complex topography are noted for differences in the character of the long and short-term dynamics. The temporal distribution of temperature manifests itself in two major periods of gradual decrease and rapid increase of annual temperature means. Within the first one, some shorter phases are identified, especially for the Precarpathian region. The precipitation distribution in the centennial scale shows no clear-cut trends. Still, some decadal periods or maybe cycles are distinguished. They are supposed to be related to the intensity and transformation of regional synoptic patterns.
... This station has for example been used by Slonosky (2002) to reconstruct 3 centuries of precipitation data in Paris blended from different sources. Homogenized temperature and precipitation data from this station have also been used to perform climate variability assessments (Dieppois et al., 2013;Lüdecke et al., 2013). It is included in the list of homogenized stations described in Sect. ...
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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.