atmosphere Article Reconstruction of the Interannual to Millennial Scale Patterns of the Global Surface Temperature Nicola Scafetta Department of Earth Sciences, Environment and Georesources, University of Naples Federico II, Complesso Universitario di Monte S. Angelo, Via Cinthia, 21, 80126 Naples, Italy; [email protected] Abstract: Climate changes are due to anthropogenic factors, volcano eruptions and the natural variability of the Earth’s system. Herein the natural variability of the global surface temperature is modeled using a set of harmonics spanning from the inter-annual to the millennial scales. The model is supported by the following considerations: (1) power spectrum evaluations show 11 spectral peaks (from the sub-decadal to the multi-decadal scales) above the 99% confidence level of the known temperature uncertainty; (2) spectral coherence analysis between the independent global surface temperature periods 1861–1937 and 1937–2013 highlights at least eight common frequencies between 2- and 20-year periods; (3) paleoclimatic temperature reconstructions during the Holocene present secular to millennial oscillations. The millennial oscillation was responsible for the cooling observed from the Medieval Warm Period (900–1400) to the Little Ice Age (1400–1800) and, on average, could have caused about 50% of the warming observed since 1850. The finding implies an equilibrium ◦ ◦ climate sensitivity of 1.0–2.3 C for CO2 doubling likely centered around 1.5 C. This low sensitivity to radiative forcing agrees with the conclusions of recent studies. Semi-empirical models since 1000 A.D. are developed using 13 identified harmonics (representing the natural variability of the climate system) and a climatic function derived from the Coupled Model Intercomparison Project 5 (CMIP5) model ensemble mean simulation (representing the mean greenhouse gas—GHG, aerosol, and volcano temperature contributions) scaled under the assumption of an equilibrium climate sensitivity of 1.5 ◦C. The harmonic model is evaluated using temperature data from 1850 to 2013 to Citation: Scafetta, N. Reconstruction test its ability to predict the major temperature patterns observed in the record from 2014 to 2020. In of the Interannual to Millennial Scale the short, medium, and long time scales the semi-empirical models predict: (1) temperature maxima Patterns of the Global Surface in 2015–2016 and 2020, which is confirmed by the 2014–2020 global temperature record; (2) a relatively Temperature. Atmosphere 2021, 12, 147. steady global temperature from 2000 to 2030–2040; (3) a 2000–2100 mean projected global warming https://doi.org/10.3390/ of about 1 ◦C. The semi-empirical model reconstructs accurately the historical surface temperature atmos12020147 record since 1850 and hindcasts mean surface temperature proxy reconstructions since the medieval period better than the model simulation that is unable to simulate the Medieval Warm Period. Received: 31 December 2020 Accepted: 19 January 2021 Keywords: global climate change; climate oscillations; harmonic models; climate change forecast Published: 24 January 2021 Publisher’s Note: MDPI stays neu- tral with regard to jurisdictional clai- ms in published maps and institutio- 1. Introduction nal affiliations. Numerous studies highlighted that the climate system is modulated by oscillations likely induced by a number of astronomical phenomena [1]. These oscillations nearly cover the entire spectrum: the daily (0–25 h), the monthly (25 h–0.5 year), the annual (0.5–2.5 year), the interannual, (2.5–10 year), the decadal/secular (10–400 year), the millen- Copyright: © 2021 by the authors. Li- nial (400–10,000 year) and Milankovitch (10,000–1,000,000 year) scales. Longer oscillations censee MDPI, Basel, Switzerland. are also observed at the tectonic (1–600 million year) scales. These spectral bands are char- This article is an open access article distributed under the terms and con- acterized by soli-lunar tidal oscillations, solar oscillations, terrestrial orbital oscillations, ditions of the Creative Commons At- and galactic oscillations linked to the journey of the solar system around the galaxy [2–10]. tribution (CC BY) license (https:// Multiple criteria suggest that solar and astronomical quasi-harmonic forcing modulate a 14 10 creativecommons.org/licenses/by/ number of terrestrial variables: C and Be production, Earth’s rotation, ocean circulation, 4.0/). paleoclimate, geomagnetism, etc. [11,12]. These results suggest that harmonic models could Atmosphere 2021, 12, 147. https://doi.org/10.3390/atmos12020147 https://www.mdpi.com/journal/atmosphere Atmosphere 2021, 12, 147 2 of 36 approximately capture part of the natural variability of the climate under the condition that the frequencies chosen to represent it have a physical origin. In this regards, it is worth noting that the most accurate and well known geophysical model is the tidal one, where up to 40 harmonics are used to forecast tidal levels at multiple time scales [13]. In contrast, it is observed an absence of internal multidecadal and interdecadal os- cillations in climate model simulations [5,14,15], which likely indicates that the physical origin of most of the observed climatic patterns is still unknown. Yet, if the claimed climatic oscillations are real [16], they cannot be ignored for correctly interpreting climate changes. For example, several studies showed that the Holocene has been characterized by a very large quasi-millennial oscillation [4,17–24]. This large oscillation was responsible for several warm periods such as those that occurred during the Roman and Medieval times [17,21,25]. The existence of such a millennial oscillation would have important implications for the correct interpretation of the observed post-industrial global warming [5]. The frequency range from the interannual to the millennial scales during the last century and millennia are particularly important to properly understanding and model- ing the natural climatic variability necessary for validating the climate models and for providing reliable climate projections and forecasts for the near future. In the scientific literature, many relevant climatic oscillations have been hypothesized such as the Atlantic Multidecadal Oscillation, the El Niño Southern Oscillation, the Pacific decadal oscillations, the Interdecadal Pacific Oscillation, the Arctic Oscillation, the North Atlantic Oscillation, the North Pacific Oscillation, and others [26]. The Intergovernmental Panel on Climate Change Fifth Assessment Report [27] ac- knowledges that the natural climatic variability of the climate system is still not understood well and that the Coupled Model Intercomparison Project 5 (CMIP5) global circulation models (GCMs) poorly simulate it. In fact, a mismatch has been observed between the model predictions and the data, such as the temperature standstill observed since 2000 that has been not reproduced by the models predicting warming of about 2 ◦C/century: see Figure1[5,28,29]. A significant mismatch between climate model predictions and data has also been observed throughout the Holocene (during the last 10,000 year) where climate models simulate continuous global warming, mainly in response to rising CO2 and the retreat of ice sheets, while marine and terrestrial proxy records suggest global cooling during the Late Holocene, following the peak warming of the Holocene Thermal Maximum (from about 10,000 to 6000 year ago) [30,31]. Indeed, according to Milankovi´ctheory, the Earth’s climate should be approaching the next ice age due to astronomical orbital oscillations [32] although the exact involved physical mechanisms are still unknown. Understanding the climatic changes of the past—e.g., why the last interglacial warm period (130,000–116,000 years before present) was warmer than the Holocene—is still challenging, but improvements are made [33]. Current climate models use radiative forcing (RF) functions as their external in- puts [27]. These functions include a total solar irradiance forcing, a volcano forcing, and several anthropogenic forcing functions deduced from atmospheric concentration vari- ations of greenhouse gases (GHG), aerosol, land-use change, and others ([27], Figure 8.18). The models process them to obtain climatic functions such as local and global surface temperatures. At equilibrium, the global mean surface temperature response DT to a = ∗ radiative forcing variation DF is determined by the equation DT l DF/F2×CO2 , where l is the equilibrium climate sensitivity (ECS) to radiative forcing. Doubling the CO2 atmo- = 2 spheric concentration results in an additional forcing of F2×CO2 3.7 W/m that should induce about 1 ◦C warming [34]. In fact, according to the Stefan–Boltzmann law (J = sT4), to increase by 1 ◦C the temperature of a black-body at a temperature T = 255 K (which would be the mean Earth’s temperature if our planet was a black-body without feedbacks) a radiation increase of ¶J/¶T = 4sT3 = 3.8 W/m2K would be needed. The value of l is very uncertain because the physics of the main climatic feedbacks (wa- ter vapor and cloud cover) is still poorly understood [35,36]. However, the IPCC AR5 [27] Atmosphere 2021, 12, 147 3 of 36 reports that the net feedback should be positive and that the climate sensitivity likely range ◦ should be between 1.5 and 4.5 C for CO2 doubling. In general, it is claimed to be unlikely that the ECS is less than 1 ◦C or larger than 6 ◦C[36]. The IPCC ([27], page 745) states the “very high confidence that the primary factor contributing