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In this paper, the role of oceanic Rossby waves in climate variability is reviewed, as well as their dynamics in tropical oceans and at mid-latitudes. For tropical oceans, both the interactions between equatorial Rossby and Kelvin waves, and off-equatorial Rossby waves are privileged. The difference in the size of the basins induces disparities both in the forcing modes and in the dynamics of the tropical waves, which form a single quasi-stationary wave system. For Rossby waves at mid-latitudes, a wide range of periods is considered, varying from a few days to several million years when very-long-period Rossby waves winding around the subtropical gyres are hypothesized. This review focuses on the resonant forcing of Rossby waves that seems ubiquitous: the quasi-geostrophic adjustment of the oceans favors natural periods close to the forcing period, while those far from it are damped because of friction. Prospective work concentrates on the resonant forcing of dynamical systems in subharmonic modes. According to this new concept, the development of ENSO depends on its date of occurrence. Opportunities arise to shed new light on open issues such as the Middle Pleistocene transition. [ABSTRACT FROM AUTHOR]

In this paper, the role of oceanic Rossby waves in climate variability is reviewed, as well as their dynamics in tropical oceans and at mid-latitudes. For tropical oceans, both the interactions between equatorial Rossby and Kelvin waves, and off-equatorial Rossby waves are privileged. The difference in the size of the basins induces disparities both in the forcing modes and in the dynamics of the tropical waves, which form a single quasi-stationary wave system. For Rossby waves at mid-latitudes, a wide range of periods is considered, varying from a few days to several million years when very-long-period Rossby waves winding around the subtropical gyres are hypothesized. This review focuses on the resonant forcing of Rossby waves that seems ubiquitous: the quasi-geostrophic adjustment of the oceans favors natural periods close to the forcing period, while those far from it are damped because of friction. Prospective work concentrates on the resonant forcing of dynamical systems in subharmonic modes. According to this new concept, the development of ENSO depends on its date of occurrence. Opportunities arise to shed new light on open issues such as the Middle Pleistocene transition.

Two major climatic phenomena that occurred during the Holocene are interpreted from the resonance in subharmonic modes of long-period Rossby waves winding around the North Atlantic gyre, the so-called gyral Rossby waves (GRWs). These are, on the one hand, the change in atmospheric circulation that occurred in the North Atlantic in the middle Holocene, and, on the other hand, the occurrence of abrupt cooling events more frequently than what is generally accepted. The amplitude of GRWs is deduced by filtering, within bands characteristic of various subharmonic modes, climate records from the Greenland ice sheet, pollen, and tree rings in northern Fennoscandia, and from two Norwegian glaciers in northern Folgefonna and on the Lyngen peninsula. While the subharmonic modes reflect the acceleration/deceleration phases of the western boundary current, an anharmonic mode is evidenced in the 400–450 year band. Abrupt cooling events of the climate are paced by this anharmonic mode while the western boundary current is decelerating, and the northward heat advection of air favors the melting of the pack ice. Then, the current of the northernmost part of the North Atlantic gyre cools before branching off to the north, which alters its buoyancy. On the other hand, according to high subharmonic modes, high-pressure systems prevailed over the North Atlantic in the first half of the Holocene while low-pressure systems resulted from baroclinic instabilities of the atmosphere dominate during the second half, favoring the growth of glaciers in Scandinavia by a better snowfall in winter and cooler summers.

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. These changes in the forcing are too small to explain the observed climate variations as simple linear responses. Consequently, to strictly apply the Milankovitch’s theory, a mediator involving positive feedbacks must be found, endowing the climate response with a resonant feature. This mediation should help explain the Mid-Pleistocene Transition (MPT) by involving orbital variations as the only external forcing, contrary to the current theory that supposes the coevolution of climate, ice sheets, and carbon cycle over the past 3 million years. Supported by both observational and theoretical considerations, recent work shows that long-period Rossby waves winding around subtropical ocean gyres meet the requirements of the sought mediator. Propagating cyclonically around the subtropical gyres, the so-called Gyral Rossby waves (GRWs) owe their origin to the gradient β of the Coriolis parameter relative to the mean radius of the gyres. The resulting modulated western boundary current, whose velocity is added to that of the steady anticyclonic wind-driven current, accelerates/decelerates according to the phase of GRWs. This amplifies the oscillation of the thermocline because of a positive feedback loop ensuing from the temperature gradient between the high and low latitudes of the gyres. Multi-frequency GRWs overlap, behaving as coupled oscillators with inertia resonantly forced by solar and orbital cycles in subharmonic modes. So, the efficiency of forcing increases considerably as the forcing period approaches a natural period of the GRWs. Taking advantage of (1) the alkenone paleothermometer in sediment cores sampled in the Tasman Sea floor, we show that, in the same way as during the MPT, but with periods 10 times longer, a transition occurred at the hinge of Pliocene-Pleistocene. Both transitions as well as the observed adjustment of the South Pacific gyre to the resonance conditions during the MPT are explained from orbital forcing alone—(2) data set of individual Globigerinoides ruberδO 18 spanning the Holocene and the Last Glacial Maximum from sediment core in the eastern equatorial Pacific, we show how the El Niño–Southern Oscillation (ENSO) activity is modulated according to subharmonic modes. Periods of warming induce a decrease in ENSO activity while periods of cooling induce an increase.

During recent decades observation of climate archives has raised several questions. Concerning the mid-Pleistocene transition problem, conflicting sets of hypotheses highlight either the role of ice sheets or atmospheric carbon dioxide in causing the increase in duration and severity of ice age cycles. The role of the solar irradiance modulations in climate variability is frequently referenced but the underlying physical justifications remain most mysterious. Here, we extend the key mechanisms involving the oceanic Rossby waves in climate variability, to very long-period, multi-frequency Rossby waves winding around the subtropical gyres. Our study demonstrates that the climate system responds resonantly to solar and orbital forcing in eleven subharmonic modes. We advocate new hypotheses on the evolution of the past climate, implicating the deviation between forcing periods and natural periods according to the subharmonic modes, and the polar ice caps while challenging the role of the thermohaline circulation.

The study of resonantly forced baroclinic waves in the tropical oceans at mid-latitudes is of paramount importance to advancing our knowledge in fields that investigate the El Niño–Southern Oscillation (ENSO), the decadal climate variability, or the resonant feature of glacial-interglacial cycles that are a result of orbital forcing. Indeed, these baroclinic waves, the natural period of which coincides with the forcing period, have a considerable impact on ocean circulation and in climate variability. Resonantly Forced Waves (RFWs) are characterized by antinodes at sea surface height anomalies and nodes where modulated geostrophic currents ensure the transfer of warm water from an antinode to another, reflecting a quasi-geostrophic motion. Several RFWs of different periods are coupled when they share the same node, which involves the geostrophic forces at the basin scale. These RFWs are subject to a subharmonic mode locking, which means that their average periods are a multiple of the natural period of the fundamental wave, that is, one year. This property of coupled oscillator systems is deduced from the Hamiltonian (the energy) of the Caldirola–Kanai (CK) oscillator. In this article, it is shown how the CK oscillator, which is usually used to develop a phenomenological single-particle approach, is transposable to RFWs. Subharmonic modes ensure the durability of the resonant dissipative system, with each oscillator transferring as much interaction energy to all the others that it receives periodically.

Two major climatic phenomena that occurred during the Holocene are interpreted from the resonance in subharmonic modes of long-period Rossby waves winding around the North Atlantic gyre, the so-called gyral Rossby waves (GRWs). These are, on the one hand, the change in atmospheric circulation that occurred in the North Atlantic in the middle Holocene, and, on the other hand, the occurrence of abrupt cooling events more frequently than what is generally accepted. The amplitude of GRWs is deduced by filtering, within bands characteristic of various subharmonic modes, climate records from the Greenland ice sheet, pollen, and tree rings in northern Fennoscandia, and from two Norwegian glaciers in northern Folgefonna and on the Lyngen peninsula. While the subharmonic modes reflect the acceleration/deceleration phases of the western boundary current, an anharmonic mode is evidenced in the 400–450 year band. Abrupt cooling events of the climate are paced by this anharmonic mode while the western boundary current is decelerating, and the northward heat advection of air favors the melting of the pack ice. Then, the current of the northernmost part of the North Atlantic gyre cools before branching off to the north, which alters its buoyancy. On the other hand, according to high subharmonic modes, high-pressure systems prevailed over the North Atlantic in the first half of the Holocene while low-pressure systems resulted from baroclinic instabilities of the atmosphere dominate during the second half, favoring the growth of glaciers in Scandinavia by a better snowfall in winter and cooler summers. [ABSTRACT FROM AUTHOR]

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. These changes in the forcing are too small to explain the observed climate variations as simple linear responses. Consequently, to strictly apply the Milankovitch's theory, a mediator involving positive feedbacks must be found, endowing the climate response with a resonant feature. This mediation should help explain the Mid-Pleistocene Transition (MPT) by involving orbital variations as the only external forcing, contrary to the current theory that supposes the coevolution of climate, ice sheets, and carbon cycle over the past 3 million years. Supported by both observational and theoretical considerations, recent work shows that long-period Rossby waves winding around subtropical ocean gyres meet the requirements of the sought mediator. Propagating cyclonically around the subtropical gyres, the so-called Gyral Rossby waves (GRWs) owe their origin to the gradient β of the Coriolis parameter relative to the mean radius of the gyres. The resulting modulated western boundary current, whose velocity is added to that of the steady anticyclonic wind-driven current, accelerates/decelerates according to the phase of GRWs. This amplifies the oscillation of the thermocline because of a positive feedback loop ensuing from the temperature gradient between the high and low latitudes of the gyres. Multi-frequency GRWs overlap, behaving as coupled oscillators with inertia resonantly forced by solar and orbital cycles in subharmonic modes. So, the efficiency of forcing increases considerably as the forcing period approaches a natural period of the GRWs. Taking advantage of (1) the alkenone paleothermometer in sediment cores sampled in the Tasman Sea floor, we show that, in the same way as during the MPT, but with periods 10 times longer, a transition occurred at the hinge of Pliocene-Pleistocene. Both transitions as well as the observed adjustment of the South Pacific gyre to the resonance conditions during the MPT are explained from orbital forcing alone—(2) data set of individual Globigerinoides ruber δ O   18 spanning the Holocene and the Last Glacial Maximum from sediment core in the eastern equatorial Pacific, we show how the El Niño–Southern Oscillation (ENSO) activity is modulated according to subharmonic modes. Periods of warming induce a decrease in ENSO activity while periods of cooling induce an increase. [ABSTRACT FROM AUTHOR]

During recent decades observation of climate archives has raised several questions. Concerning the mid-Pleistocene transition problem, conflicting sets of hypotheses highlight either the role of ice sheets or atmospheric carbon dioxide in causing the increase in duration and severity of ice age cycles. The role of the solar irradiance modulations in climate variability is frequently referenced but the underlying physical justifications remain most mysterious. Here, we extend the key mechanisms involving the oceanic Rossby waves in climate variability, to very long-period, multi-frequency Rossby waves winding around the subtropical gyres. Our study demonstrates that the climate system responds resonantly to solar and orbital forcing in eleven subharmonic modes. We advocate new hypotheses on the evolution of the past climate, implicating the deviation between forcing periods and natural periods according to the subharmonic modes, and the polar ice caps while challenging the role of the thermohaline circulation. [ABSTRACT FROM AUTHOR]

The study of resonantly forced baroclinic waves in the tropical oceans at mid-latitudes is of paramount importance to advancing our knowledge in fields that investigate the El Niño–Southern Oscillation (ENSO), the decadal climate variability, or the resonant feature of glacial-interglacial cycles that are a result of orbital forcing. Indeed, these baroclinic waves, the natural period of which coincides with the forcing period, have a considerable impact on ocean circulation and in climate variability. Resonantly Forced Waves (RFWs) are characterized by antinodes at sea surface height anomalies and nodes where modulated geostrophic currents ensure the transfer of warm water from an antinode to another, reflecting a quasi-geostrophic motion. Several RFWs of different periods are coupled when they share the same node, which involves the geostrophic forces at the basin scale. These RFWs are subject to a subharmonic mode locking, which means that their average periods are a multiple of the natural period of the fundamental wave, that is, one year. This property of coupled oscillator systems is deduced from the Hamiltonian (the energy) of the Caldirola–Kanai (CK) oscillator. In this article, it is shown how the CK oscillator, which is usually used to develop a phenomenological single-particle approach, is transposable to RFWs. Subharmonic modes ensure the durability of the resonant dissipative system, with each oscillator transferring as much interaction energy to all the others that it receives periodically. [ABSTRACT FROM AUTHOR]