New paleoclimatic evidence of an extraordinary rise in temperature in the Northern Hemisphere in the last 3–4 decades

ABSTRACT Prognosis of temperature changes in the Northern Hemisphere for the period 1980–2020 was made using seven temperature paleoreconstructions covering the last 1–2 millennia and ending 1979–2016. Forecasts were made using the analogue nonlinear prediction method. A part of paleodata before 1800 (prior to the beginning of anthropogenic impact) was used as an information bank. In all seven cases, the forecast gave either a decrease or a very slight increase in temperature during 1980–2020. Statistical experiments performed with using prediction errors based on a conservative estimation of reconstruction uncertainties showed that a temperature increase of 0.25°C in the specified epoch is not excluded, but its probability is low (P < 0.20). This means that if the climate in the 20th - early 21st century was controlled by the same dynamic system as before 1800, the noticeable warming of the Northern Hemisphere in 1980–2020 should not be observed. Thus, it was shown that the data of modern paleoclimatology confirm that the climate of the Northern Hemisphere in the last 40–50 years was significantly influensed by an additional factor that did not act in the previous 1–2 millennia. It was also shown that if the actual uncertainties are significantly higher than the conservative estimates used, a warming of 0.5 degrees between 1980 and 2020 due to internal climate variability becomes possible.


Introduction
Global warming (GW)rise of the global temperature during the last 150 yearshas become the most important problem of climatology since the end of the twentieth century. Since the 1970s, this growth has become the most dramatic. Recently, the Intergovernmental Panel on Climate Change (IPCC) issued its 6th Assessment Report (IPCC 2021) which stated 'The likely range of humaninduced warming in global-mean surface temperature (GSAT) in 2010-2019 relative to 1850-1900 is 0.8°C-1.3°C, encompassing the observed warming of 0.9°C-1.2°C, while the change attributable to natural forcings is only −0.1°C-0.1°C'. Therefore, according to IPCC (2021), almost all of the temperature rise observed over the past 150 years can be attributed to human activities while the contribution of natural factors is minimal. The conclusions drawn by the IPCC are largely based on the results of climate modeling. However, some other studies have come to different conclusions. For example, Connolly et al. (2021) showed that using some reconstructions of the total solar irradiance (TSI) it is possible explain at least half of global warming since the nineteenth century. Lüdecke et al. (2013) showed that variations of the temperature in Central Europe after 1756 AD may be the result of the intrinsic dynamics of climatic system. Problem of assessing the contribution of various processes to global climate change is that our information about these processes is often not enough accurate. Our knowledge of some potential climatic forcings has appreciable uncertaintiessee Figure SPM.2 of IPCC (2021). Temperature paleoreconstructions show larger amplitudes of multicentennial temperature changes than those in the model simulations that may be related to the underestimation of internal climatic variability and the lack of some feedback mechanisms in model simulations (Wang et al. 2020). Thus the parameters of many modern climate models have uncertainties. This makes it possible to fit the calculated temperature to the measured one in various ways (see Ogurtsov and Veretenenko 2017). Ogurtsov and Lindholm (2006) and Ogurtsov et al. (2013) suggested another way to estimate the possible contribution of natural climatic fluctuations to the GW. They used paleoclimatic information to solve this problem. In this paper, the approach developed by Ogurtsov et al. (2013) was applied to the most recent paleoclimatic and instrumental temperature data. I estimated the probability that the warming in the Northern Hemisphere over the past 40-50 years is a result of climatic changes caused by natural factors (intrinsic dynamics of the Earth's climate, changes in solar and volcanic activity, etc.) and is not associated with any anthropogenic impact using the following procedure: I assumed that if the anthropogenic impact is weak and the climate of the last 150 years has been controlled by the same dynamic system as during the last millennia, the current state of the climate is a natural result of its past. This, in turn, means that paleoclimatic data about the past climate can be used to predict its future. In this case, using the Northern Hemisphere temperature reconstructions covering the last 1-2 millennia up to 1970, it is possible to predict further temperature changes in 1980-2020. This forecast will obviously describe the most probable scenario of natural climate change in the specified period. By comparing the forecast results with real instrumental data, one can estimate the possible contribution of natural climatic variations to the warming of the last 40-50 years. The obvious advantage of this approach is that it does not require any theoretical assumptions about the forcings that affect the Earth's climate. Indeed, although our knowledge of the various factors affecting the climate is limited, temperature changes over the past 1-2 millennia should contain all the necessary information.

The data
In the present work paleoclimatic reconstructions of Moberg et al. (2005), Loehle (2007), Christiansen and Ljungqvist (2012), Schneider et al. (2015), Wilson et al. (2016), Guillet et al. (2017) and Büntgen et al. (2021) were used. For the N-TREND2015 reconstruction of Wilson et al. (2016) an average between the data for North America and Eurasia was used. In three reconstructionsproxy records of Wilson et al. (2016), Guillet et al. (2017), Büntgen et al. (2021) warming of the twentieth century is unprecedented in more than last millennium, and in other reconstructions it is as not so anomalous. All data sets are described in Table 1.
As can be seen from the table, both purely tree-ring series and multi-proxies were used in the work. One of the time seriesthe reconstruction of Loechlewas obtained without the use of any tree-rung data. All seven paleorecords, averaged by 13 years and interpolated by decades, are shown in Figure 1.

Results and discussion
The nonlinear predictions were made using the method of analogs, which is based on the reconstruction of the trajectory of the dynamic system of the predicted series in a pseudo-phase space (Sugihara and May 1990). The method of nonlinear forecasting, proposed by Sugihara and May (1990), is a nonparametric method, which does not use any a priori information about the model used to create the time series. It uses only the information in the output itself. This method has been tested on a range of signals, including chaotic series, correlated noises and signals from the natural word, and has been shown to be able to predict them satisfactory (Sugihara and May 1990;Ogurtsov 2009). A detailed description of the analogue method, its testing and error evaluation is given in the Appendix. Data covering time intervals up to 1800 (80-181 points prior to start of anthropogenic impact) were used to construct a 'library' of past patterns i.e. as a bank of  information.
Step of prediction was 10 years. All four paleoseries were considered equally reliable and accurate sources of information, no preliminary weighting was carried out. Uncertainties of the forecast were estimated by means of prediction of 12 points of each series during 1850-1960 (see Appendix). The forecast results are shown in Figure 2. Figure 2 shows that if the GW is the result of natural climatic variability, i.e. the climate of the past 150 years is governed by the same dynamic system as in the previous one to two millennia, the increase in the average temperature of the Northern Hemisphere during 1980-2020 appears unlikely even given the large forecast uncertainties. In all cases, the prognosis gave either a decrease or a very slight increase in temperature during 1980-2020. Forecasts made by means of the autoregressive model of the second order gave similar results. Predictions made by Ogurtsov and Lindholm (2006) and Ogurtsov et al. (2013) led to analogous conclusions. Lüdecke et al. (2013), who considered temperature changes in Central Europe since 1757 as a result of mainly internal oscillations of the climate system, concluded that temperatures should drop after 2000 (see their Figure 6). Scafetta (2012), who used an empirical climate model based on astronomical cycles, also predicted only very moderate temperature increases during 2010-2020. While the observed instrumental temperature increased sharply throughout the entire five decades: see Figure 3. Figure 3 shows that observed instrumental temperature of the Northern Hemisphere increases by 1.30°C during 1970-2020 AD with a slope of the linear trend α obs = 0.260°C/10 years (0.235°C/ 10 years in summer temperature). In the extratropical part of the Northern Hemisphere, the temperature of which was reconstructed by Christiansen and Ljungqvist (2012) and Schneider et al. (2015), the increase of temperature was larger. Increase in rural Northern Hemisphere temperature is also more than 1.0°C (see Figure 7h after Connolly et al. 2021). Scafetta (2021) arrived at conclusion that up to 25% of the observed temperature rise could be associated with non-climatic biases. In this case, the slope during 1970-2020 would be α obs = 0.196°C/10 years. Whereas the corresponding slopes of the predicted temperature for the same time interval lie in range from −0.088°C /10 years to 0.014°C/10 years (see Table 2). The probabilities that the slope of the predicted temperature actually reaches some values α i were evaluated by means of a statistical experiment. It performed a few thousands of simulations in each of which the surrogate series was constructed by adding a random sequence to the record of temperature predicted for 1980-2020. Each random  Table 2. The probability that the slope of the predicted temperature trend in the Northern Hemisphere during 1970-2020 will reach the slope of the real trend α obs or some other values.

Time span
Angle of the observed trend α obs (°С/10 years) Angle of the predicted trend (°С/10 years) The probability that the angle of inclination will reach the value:  Table 2. Probabilities obtained with values 2E are shown in italics in brackets.
The statistical experiments carried out indicate that from the point of view of modern paleoclimatology, a natural rise in temperature in the Northern Hemisphere during the last four-five decades by ca 0.25°C, caused by internal fluctuations of the climate system, is possible, although not very likely. Its probability is P < 0.20 for errors E and P < 0.33 for errors 2E. With 2E errors (large uncertainties of temperature reconstructions) a temperature increase of 0.5°C during 1970-2020 becomes not completely excluded (probability up to 0.15-0.26). While the actual warming observed over the last 4-5 decades is very unlikely: P < 0.02 for errors E and P < 0.12 for errors 2E.
However, in order to assess the reliability of the obtained results correctly, one should take into account the divergence problema well-known anomalous reduction in the sensitivity of tree growth to changing temperature (ARS). ARS has been detected in many dendrochronological records over the last decades of the twentieth century (Briffa et al. 1998A, 1998B;D'Arrigo et al. 2007;Wilson et al. 2007;Esper and Frank 2009;Scafetta 2021). Despite some possible explanations listed by D' Arrigo et al. (2007) and Loehle (2009), the divergence problem has not yet been resolved. Obviously, if modern temperature reconstructions poorly reflect the sharp rise in temperature in recent decades, it is possible that similar increases in previous epochs were not recorded by them either. Then the tree-ring reconstructions contain only limited and approximate information about the temperature changes in the past. In this case, the forecast results based on limited information should be regarded as rather qualitative.
On the other hand, the Loehle (2007) reconstruction was made without using any tree-ring data, so the results of the forecast made with it are still valid in any case. The N-TREND2015 reconstruction of Wilson et al. (2016) also shows almost no late twentieth century divergence. Thus, the uncertainty associated with the divergence problem may somewhat reduce the reliability of the forecasts obtained, but unlikely can reverse them.

Conclusion
The results of the present work showed, that the hypothesis about the predominantly natural character of the warming of the Northern Hemisphere in the past 40-50 years meets with serious difficulties. From the point of view of data accumulated by paleoclimatology, the observed sharp increase appears to be very unusual or even anomalous. The analysis performed has shown that natural drivers could warm the Northern Hemisphere by 0.25-0.50°C but this is unclear. Predictions of temperature change after 2000 AD by Scafetta (2012) and Lüdecke et al. (2013), using the assumption of a purely natural origin of Earth's climate variations in recent centuries, also did not give a noticeable increase in temperature. Given all this, it is reasonable to conclude that, at least for the last five decades, the climate system actually was perturbed by an additional factor that did not act in the past. However, we should not forget that we do not know how accurately the available paleorecords reconstruct the real past temperature of the Northern Hemisphere. For more reliable estimates of the contribution of natural fluctuations of the climate system to the warming of recent decades, it is desirable to further reduce the uncertainty of temperature paleoreconstructions.
Appendix: Testing the predictive ability of an analog nonlinear prediction method.
Valuation of the prognostic potential of the temperature reconstructions and predictive power of the used technique of nonlinear forecast, was performed by testing the ability of the prediction of 12 points of each series during 1850-1960 using data covering time intervals before 1800 AD (80-181 points) as a bank of information. In this way, I assessed the quality of forecasts of temperature variations during the period of noticeable anthropogenic influence  made using information about temperature changes before the onset of any anthropogenic impact (before 1800). The results of these predictions were compared with the results of forecasts made for Gaussian white noise and some known chaotic series: logistic map, Chua's circuit and attractor of Henon using the same forecasting technique.
In Figure A1 the dependence of the coefficient of correlation between the predicted and actual value on the time of a prediction T p (T p time steps into the future) is given for some temperature proxies ( Figure A1A) as well as for chaotic and random series ( Figure A1B). As follows from Figure A1, the forecasting ability of temperature reconstruction is comparable with those of chaotic series and exceeds substantially the corresponding ability of the unpredictable white noise. To estimate the actual forecast error, the uncertainties of temperature reconstructions should be taken into account. This problem was solved by means of statistical experiments. It were performed a number of simulations in each of which the surrogate series was constructed by adding a random value to each point in the temperature record before 1800 AD. Each random value was generated by Gaussian white noise with a standard deviation equal to the corresponding value of the reconstruction uncertainty. A forecast for AD 1850-1960 was made using this random series as a bank of information. An example of such forecast is shown in Figure A2.
Individual prediction error ε i was estimated for every simulation i and final prediction error E was determined as a mean of all the individual errors.
where nsim is a number of simulations. Uncertainty of reconstructions of Schneider et al. (2015) and Guillet et al. Figure A1. A -Coefficient of correlation between observed and predicted value for temperature reconstructions: Christiansen and Ljungqvist (2012)   (2017) was determined by the authors. The estimation of the uncertainties of the other temperature proxies was made using the data of Anchukaitis and Smerdon (2022). Thus I used the uncertainty value, which changed from 0.2°C in the 19th and 20th centuries to 0.5°C in the first century (see Figure 1 of Anchukaitis and Smerdon (2022)). Such an estimate can be considered quite conservative. Figure A3 shows than majority of forecast errors lay in range 0.1-0.3°C. Only uncertainty of prediction for proxy record of Christiansen and Ljungqvist (2012) gives large error. The big error is the result of the fact that the series of Christiansen and Ljungqvist (2012) in 1850-1960 has a very sharp rise (about 1.5°C), which is poorly predicted using the pre-anthropogenic part of the series. In order to evaluate the impact of uncertainty in estimates of reconstruction errors in the past on the forecast error, I considered an extreme case and estimated the prediction errors with twice the reconstruction errors. It turned out that with a twofold increase in the reconstruction uncertainty, the prediction errors E can increase by a factor of 1.35-2.0.
Thus, the performed testing showed that it is possible to more or less reliably predict the future of the studied temperature reconstructions several steps ahead, although sometimes with appreciable errors.