Milankovitch's theory

In accordance with Milankovitch cycles, most climate transitions that have occurred over the past millions of years have been recognized as resulting from variations in orbital parameters of the Earth, namely eccentricity, axial tilt, and precession, due to their synchronism. However, understanding the underlying physical mechanisms is encountering considerable problems so that how variations in Earth's orbit pace the glacial-interglacial cycles of the Quaternary are probably one of the greatest mysteries of modern climate science.

Problems raised by Milankovitch theory

Changes in orbital forcing are too small to explain the observed climate variations as simple linear responses. Difficulties reach their culmination when the Mid-Pleistocene Transition (MPT) is considered, that is a fundamental change in the behavior of glacial cycles during the Quaternary glaciations . The transition happened approximately 1.2 million years ago, in the Pleistocene epoch. Before the MPT, the glacial cycles were dominated by a 41-year periodicity coherent with the orbital forcing from axial tilt. After the MPT the cycle durations have increased, with an average length of approximately 100 years coherent with the orbital forcing from eccentricity. However, as shown in the figure, the intensity of the forcing resulting from the eccentricity is much lower than that induced by the axial tilt.

Amplitude of orbital forcing versus the period – a) Spectra of eccentricity, obliquity and precession are normalized (their area is unity) – b) real spectrum.

As suggested by some authors, non-linear interactions occur between small changes in the Earth's orbit and internal oscillations of the climate system. Consequently, to strictly apply the Milankovitch theory, a mediator involving positive feedbacks must be found, endowing the climate response with a resonant feature. Supported by both observational and theoretical considerations, a recent work approaches the Milankovitch theory in a new way in which the solar and orbital forcing of the climate system occurs under the mediation of very long-period Rossby waves winding around the subtropical gyres. Due to their specific properties, the so-called Gyral Rossby Waves (GRWs) are resonantly forced in subharmonic modes. This means that the forcing efficiency strongly depends on the deviation between the forcing period and the closest natural period of GRWs among the different subharmonic modes.

As we will see, the mediation of orbital and solar forcing by GRWs allows explaining most of the observed climatic phenomena that have occurred over the last millions of years. In particular, this mediation solves the enigma of climatic impact as a response to orbital forcing because GRWs very tightly control the western boundary currents, which regulate the amount of heat transported from the tropics to mid-latitudes. Involving only the intrinsic properties of GRWs, this new concept complements the Milankovitch approach. It even reinforces it since the mediation of orbital forcing by GRWs results in a coherent theory providing simple explanations for the many problems relating to the vagaries of the climate system, and which have remained pending issues.

Variations in the period of eccentricity versus time in the vicinity of 100 Ka in a) and 1200 Ka in b).  The red lines correspond to the resonance periods related to the subharmonic mode n₁₁ in a) and n₁₃ in b).

Mid-Pleistocene transition (MPT)

Using the calculated variations of the orbital parameters, the first figure a) shows that the forcing periods associated with the three Milankovitch parameters are nearly 26 Ka for the precession, 41 Ka for the obliquity, 100 Ka and 390 Ka for the eccentricity. However, the amplitude of the resulting radiative forcing is very unequal according to the forcing mode. The orbital forcing for which the amplitude is the highest is linked to the obliquity, then to the eccentricity at 390 Ka, then at 100 Ka, finally to the precession. The eccentricity also produces a peak around 1200 Ka, not visible in the figure b).

Resonance of GRWs

The main difficulty of Milankovitch theory is to explain the climatic variations from the orbital parameters knowing that the effects are not proportional to the amplitude of the forcing. But these apparent difficulties disappear when one brings in the mediation of the GRWs. In particular, the MPT finds a straightforward explanation. Furthermore, the relevance of this approach is confirmed by the observation of the transformation of subtropical gyres during MPT.

The amplitude of orbital forcing related to the obliquity being much higher than that related to the eccentricity or to the precession, the dominant ice age-interglacial period was 41 Ka before the MPT. This happened although the forcing period was far from the closest resonance period, namely 49.2 Ka corresponding to the subharmonic mode n₁₀, which required an adjustment of the subtropical gyres to resonate. Since then, the dominant period has been coherent with that of eccentricity while it was approaching to the resonance period related to the subharmonic mode n₁₁, namely 98.3 Ka (Figure a). The forcing period becoming remarkably close to one of the natural periods of GRWs, the orbital forcing efficiency, i.e. the forcing effect on the climate system, has increased drastically, so that the subharmonic mode n₁₁ prevailed over the mode n₁₀. The orbital forcing efficiency has continued to increase since 1.4 Ma BP, which suggests that the tuning is still improving.

Adjustment of the radius of subtropical gyres during the MPT

Before the MPT, the closest natural period was related to the subharmonic mode n₁₀, namely 49.2 Ka. The transition of the period from 41 Ka, when the subharmonic mode n₁₀ was tuned to the forcing period before the MPT, to the natural period of 49.2 Ka at present required an adjustment of the gyres. Indeed, the resonance which was exerted at 41 Ka is now done at 98.3 Ka, remarkably close to the forcing period, therefore no longer requiring a particular adjustment of the perimeter of the gyres.

By considering together paleothermometers at two sites in the Tasman Sea, it has been shown that during late Pliocene, a poleward displacement of the subtropical front compared to modern occurred between 40 and 44° S. A 4° drift of the subtropical front towards the south has increased the perimeter by almost 20%, which reflects the adjustment of the gyre to increase the natural period of the subharmonic mode n₁₀ from 41 to 49.2 Ka during the MPT.

This adjustment of the gyre radius required that, for the n₁ sub-harmonic mode, the propagation of the GRW around the North Atlantic gyre took 48 (=2⁴×3) years instead of the 64 (=2⁶) years as it currently occurs. More precisely, all the gyres underwent an increase in their perimeter in the ratio 64/48.

Before the MPT the subharmonic mode n₁₀=3$\times$2⁸ resonated at n₁₀×48=36,864 years instead of 49,152 years nowadays. Then, according to the dispersion relation of GRWs the fine tuning of the gyres to resonate at 41 Ka required a 1.3 ° poleward drift of their centroids to increase the resonance period from 36.9 to 41 Ka.

Pliocene-Pleistocene Transition

The MPT sparked a sustained creativity on the part of climatologists to find a plausible explanation. However, a resonance phenomenon comparable to what occurred in Mid-Pleistocene is highlighted at the hinge of the Pliocene and the Pleistocene, the periods being 10 times higher than during the MPT. This transition is more difficult to highlight than the previous one because of the periods mentioned, but the observed phenomena are similar. In both cases, the variation of the forcing period causes the GRWs to resonate, which has the effect of suddenly increasing the forcing efficiency (Figure b).

Whether it is Mid-Pleistocene or Pliocene-Pleistocene transition, two subharmonic modes compete with respect to orbital forcing. They are n₁₀ and n₁₁ whose natural periods are 49.2 and 98.3 Ka during the first transition, and n₁₃ and n₁₄ whose natural periods are 0.39 and 1.18 Ma during the second. In both cases, the natural period of the highest mode tunes transiently, but optimally, to the forcing period when both become remarkably close. Then, the two subharmonic modes swap the dominant mode, as attested by the nearly symmetrical opposite variation in the forcing efficiencies. The change in the dominant period occurred approximately 2.2 Ma ago when the amplitude of the 0.39 Ma period oscillation collapsed in favor of the 1.18 Ma period oscillation. Nowadays the transition is occurring in the other direction since the amplitude of the 1.18 Ma period oscillation is collapsing in favor of the 0.39 Ma period oscillation, both forcing having approximately the same amplitude. This transition involves a weak adjustment in the perimeter of the gyre because the deviation between the forcing and natural periods of the lower subharmonic mode is small, 0.41 and 0.39 Ma, respectively.

The Atlantic Multidecadal Oscillation (AMO)

The Atlantic Multidecadal Oscillation (AMO) signal is usually defined from the patterns of Sea Surface Temperature (SST) variability in the North Atlantic once any linear trend has been removed. AMO-like variability is associated with small changes in the North Atlantic branch of the Thermohaline Circulation. More precisely, the AMO is related to the resonance of 64-years average period GRWs at mid-latitudes of the North Atlantic gyre, being almost in phase with the Sunspot Number (SSN).

How some mysteries find an answer

Here are some explanations to the puzzles raised by the observation of climate records over the past decades (see Milankovitch cycles).

• Interpretation of unsplit peak variances follows from the property 3 of GRWs.
• Unsynchronized stage 5 observation follows from the property 6 of GRWs: there is no direct causal relationship between orbital variations and the climate response since orbital forcing is exerted through the mediation of GRWs.
• The asymmetry of the warming and cooling periods observed during the glacial-interglacial cycles is because the modulated current of the gyre produced by GRWs flows in the same direction as the wind-driven current, when anticyclonic. In contrast, it flows in the opposite direction when cyclonic, opposing to geostrophic forces that result from the combined effect of gravity and the rotation of the Earth. Therefore, slowing down the western boundary current, or even reversing it, takes much longer time than accelerating it.