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 CO
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 test its ability to predict the major temperature patterns observed in the record from 2014 to 2020. In the short, medium, and long time scales the semi-empirical models predict: (1) temperature maxima in 2015–2016 and 2020, which is confirmed by the 2014–2020 global temperature record; (2) a relatively steady global temperature from 2000 to 2030–2040; (3) a 2000–2100 mean projected global warming of about 1 °C. The semi-empirical model reconstructs accurately the historical surface temperature 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.
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