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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.

It is generally well-known that the mean surface temperature of the globe has been rising during more than last century [

Privalsky and Fortus [

where ε_{j} is a zero mean white noise and values of p = 4 and autoregressive coefficients

1) We used data on instrumental temperature anomaly ΔT^{i} over 1880-2015 (http://cdiac.ornl.gov/ftp/trends/temp/hansen/gl_land_ocean.txt,

2) We modeled the global temperature with the less intricate autoregressive process of the second order (AR(2)).

3) We adjusted our model so that the simulated signal reproduced the following statistical properties of the actual temperature record:

a) coefficient of linear dependence of DT^{i}(t − 1) on ΔT^{i}(t) (

b) coefficient of linear dependence of DT^{i}(t − 2) on ΔT^{i}(t) (

c) standard deviation of high-frequency temperature variability (^{i} and the ΔT^{i} value smoothed by 30 years. All these properties can be reliably estimated using 135 year time series (see

We performed statistical experiments with three different AR(2) processes of the 1000 years length. Their properties are detailed in

^{2} | N_{1} | N_{2} | N_{3} | ||||||
---|---|---|---|---|---|---|---|---|---|

Process 1 | 0.90 | 0.062 | 0.0052 | 0.943 | 0.905 | 0.106 | 351 | 33 | 2 |

Process 2 | 0.80 | 0.165 | 0.0059 | 0.944 | 0.909 | 0.106 | 556 | 72 | 4 |

Process 3 | 0.70 | 0.265 | 0.0067 | 0.936 | 0.908 | 0.106 | 617 | 80 | 5 |

2000 simulations for each kind of AR(2) process (

In ^{m}(t − 1) and ΔT^{m}(t − 2) on ΔT^{m}(t), averaged over all 2000 simulations. _{1} is the number of cases in which one NGW episode took place during 1000 years. N_{2} and N_{3} are numbers of cases with two and three such events. The case of the simulated temperature which has two NGW episodes during 1000 years is shown in

of the instrumental temperature, showed that the frequency of occasion of NGW episodes is 0.19 - 0.35 per 1000 years. Therefore their return period is 2849-5180 years (one event per 2849-5180 years).

Thus, in frame of the used AR(2) model of climatic process the global warming of the last 135 years can very unlikely be fully explained by natural fluctuations.

Then we estimated probability of the part of the GW that was induced by intrinsic climatic variability. We repeated the statistical experiment but with the amplitude of temperature rise of 0.5˚C during 135 years-the Half Global Warming (HGW) episode. We found that the frequency of HGW events is 2.13 - 2.34 per 1000 years and their return period is 426 - 469 years. As to events analyzed by Privalsky and Fortus [

Numerical experiments with artificial signals (second order random processes), which have important statistical properties similar to that of the observed time series of temperature (1850-2015), indicate that the return period of climatic events analogous to the current GW (linear increase of temperature for 0.95˚C during 135 years) is 2849-5180 years. Correspondingly, the probability that the current global terrestrial temperature is going through the NGW episode is 0.026 - 0.047. This shows that the GW unlikely could be fully explained by natural variability of temperature. Therefore it is reasonable to regard the GW as a phenomenon exceptional from the point of view of intrinsic climatic oscillations, which need an additional external forcing factor for explanation. On the other hand, the statistical experiments showed that an appreciable part of the GW might be a result of natural fluctuations of climatic system. It was found that that the return period of climatic events with 0.5˚C warming during 135 years is less than 500 years. Thus, the probability that the half of the contemporary GW is produced by natural random oscillations of temperature is more than 0.25. Emission of greenhouse gases (carbon dioxide, methane, nitrous oxide) most likely is another possible contributor to the GW of the last centuries [

The work of M. G. Ogurtsov was partly supported by the program of the Presidium of RAS No 7 and RFBR grant 16-02-00090.

Ogurtsov, M., Lindholm, M. and Jalkanen, R. (2017) On the Possible Contribution of Natural Climatic Fluctuations to the Global Warming of the Last 135 Years. Atmospheric and Climate Sciences, 7, 256-262. http://dx.doi.org/10.4236/acs.2017.73018