The climate during Holocene, which began with the interglacial period about 12500 years ago, can be studied from proxies of solar irradiance and Earth’s average temperature in both hemispheres. Superimposed on oscillations are several distinct climate steps which appear to be of widespread significance, the most prominent being observed 8.2 Kyr, 5.5-5.3 Kyr and 2.5 Kyr (Kyr=103 years) BP. These events, which are recognized as part of the millennial scale quasi-periodic climate changes, alongside the Dansgaard–Oeschger (D-O) cycles, and are characteristic of the Holocene [O’Brien et al, 1996; Bond et al, 1997; Bianchi and McCave, 1999; de Menocal et al, 2000; Giraudeau et al, 2000].
As observed during the glacial-interglacial era, the temperature of the earth’s surface is subject to the resonance of gyral Rossby waves that results from solar and orbital forcing. From this follows the resonant nature of the climate system. The forcing is all the more efficient as its period is closer to one of the resonance periods, the latter being locked in subharmonic mode (Pinault 2018d, 2020a).
During the Holocene that began 12,000 years ago with the end of the last glaciation, climatic variations, which can be observed from the analysis of ice cores, occur mainly in two frequency bands.
In the North Atlantic, there are similarities between the Total Solar Irradiance (TSI) multiplied by the forcing efficiency and the global temperature into the band 576-1152 years characteristic of the 64×12=64x3x22=768 year period whose subharmonic mode is 3×22 (number of turns made during half a period). The two curves show a similarity mainly over the interval covering 9000 to 6000 years BP, that is, when the forcing efficiency is maximum.
The forcing efficiency, that is, the sensitivity of the global temperature (°C) to the solar insolation (W/m2), varies over time: equal to 1.5 °C(W/m2)-1 between 9000 and 6500 years BP, it decreases to 0.5 °C(W/m2)-1 after 5000 years BP. This is because the response of the gyre to the variations in the TSI is all the more enhanced as the gradient of the sea water temperature between low and high latitudes of the gyre is steeper. At the beginning of the Holocene, the pack ice extended further south, which explains the high radiative forcing efficiency. Then, gradual withdrawal of the pack ice made the positive feedback of the polar current on the thermocline depth less efficient.
Between 5000 and 2500 years BP the amplitude of solar irradiance into the band 576-1152 years decreases, and the Gyral Rossby Wave (GRW) disassociates from the solar irradiance cycle, both the amplitude and period. During this period of decoupling the GRW does not weaken because of the remanence of geostrophic forces throughout the gyre and along the drift currents (collective effects of the gyres in the various frequency bands), but its period lengthens, which indicates that the centroid of the gyre drifts poleward. The GRW is coupled to the solar cycle again between 2500 years BP and present during the upsurge of the solar cycle. Therefore the resonance of the 3×22 subharmonic mode GRW appears to be the main driver of climate variability during the Holocene.
GRWs are resonantly forced within the 96-192 year band, which results from the Gleissberg cycle of the Sun. The forcing efficiency varies a lot during the Holocene, mainly during the periods of low solar activity during which it weakens drastically.
Positive feedback loops amplify changes in a dynamic system; this tends to move the system away from its equilibrium state and make it more unstable. Negative feedbacks tend to dampen changes; this tends to hold the system to some equilibrium state making it more stable.
Like any system of resonantly forced coupled oscillators, quasi-stationary baroclinic waves oscillate in subharmonic modes, whether tropical or at mid-latitude. Their coupling occurs when they share the same modulated current (the node) at the origin of the exchanges between the antinodes (where the thermocline oscillates) in opposite phase.
The average period τ0 of the fundamental wave being annual according to the declination of the sun, the average periods of the subharmonics are deduced by recurrence. The period τm + 1 is deduced from the period τm so that τm+1 = nm τm where nm is an integer. The average periods of the main modes observed are 1, 4 and 8 years in the tropics (the average period of 4 years paces the El Nino phenomenon in the tropical Pacific). At mid-latitudes these are (in years) 1, 4, 8 = 4 × 2, 64 = 8 × 8, 128 = 64 × 2, 256 = 128 × 2 (solar forcing, Gleissberg cycle), 768 = 256 × 3 (solar forcing), 24576 = 768 × 32 (orbital forcing, precession), 49152 = 24576 × 2 (orbital forcing, obliquity), 98304 = 49152 × 2 (orbital forcing, eccentricity). The forcing efficiency is all the stronger as its period is closer to one of the periods of resonance of the climatic system.
To the long periods corresponds an integer number of turns made by the gyral Rossby wave around the gyre (anticyclonically) during half a period. This number of turns is the subharmonic mode. For the 128 year period the gyral Rossby wave travels 2 turns except in the South Pacific where it is 1 and the south of the Indian Ocean where it is 3/2.