This article, which is aimed at anyone wishing to learn about the causes of climate change, attempts to realistically address the phenomena observed in a time scale ranging from several years to several hundred thousand years. In particular it focuses on the natural climate variability in order to give a plausible explanation for the warming observed over the second half of the 20th century and so offer an alternative to the theory of anthropogenic global warming (resulting from human activities) and catastrophist scenario claimed by the Intergovernmental Panel on Climate Change (IPCC). The theoretical expectation that the climate is sensitive to CO2 (e.g. Arhennius, 1896; Manabe & Wetherald, 1967) was strengthened in the 80s owing to a statistical correlation observed between the increase in carbon dioxide concentration in the atmosphere and the rise in average global temperature of our planet, has produced the economic and political media frenzy we know, unprecedented in the history of science. Yet the physical basis on which it is based show that anthropogenic warming contributes only about a third of the warming observed during the 20th century. Any amplifier effect is not based on proven physical basis. Worse, its foundations are now contradicted by observations.
Indeed, the greenhouse effect caused by atmospheric carbon dioxide alone does not help explain the warming in its interely, an amplifier effect was desperately sought by the proponents of anthropogenic warming. This implies a positive feedback between CO2 and atmospheric water vapor so that an increase in global temperature leads to increased water vapor, which itself induces a very effective greenhouse effect. This conjecture is now challenged by the observations.
Numerical models became more and more sophisticated to attempt to explain the inexplicable phenomena in an inappropriate physical context omitting the essential. It was to miss out our ignorance in the natural climate variability and its causes. Subsequently the anthropogenic warming became less and less credible in view of the stagnation of global temperature after 2004 despite the increase in carbon dioxide. Also, consider the causes of global warming realistically is an absolute necessity in a context where obscurantism has given way to pseudo-scientific arguments claimed by the IPCC.
Our ignorance of the mechanisms controlling climate variability results from the fact that research has mainly focused on atmospheric phenomena over the last few decades, whether they refer to human activities or solar cycles. But the driver of climate change is not the atmosphere but oceans, the atmosphere playing only the role of vector between oceans and continents. The oceans resonate with solar and orbital cycles, storing or on the contrary restoring heat: the resonance called « gyral » because occurring around the five subtropical gyres, closely affects the energy balance of our planet. The amplifying effect of solar and orbital forcing comes from the positive feedback exerted by the polar current of the gyral barocline wave: the oscillation of the thermocline is amplified by the polar current which warms or cools, as the western boundary current accelerates or slows down.
Thus, the gyral resonance helps explain, through observations and based on irrefutable physical basis, climate change at different time scales. Based on this new phenomenon, this article discusses climate variability with fresh eyes while solving some puzzles on ocean circulation.
The climate is little subject to human activities
Global warming in recent decades is not exceptional since, if we look at the past 11,000 years since the last ice age, at least three episodes were warmer than today. The current global warming follows the end of the Little Ice Age.
Over the past 600 million years, global temperature has not followed the CO2 concentration which was much higher than what it is today without runaway temperatures. The thesis that the increase in atmospheric CO2 is responsible for global warming by radiative forcing therefore is not based on any physical basis. One cannot infer any causal relationship given the correlation between global temperature and CO2 concentration observed between 1977 and 2004.
The Vostok core analysis shows that this is the rise in temperature which increases the CO2 in the atmosphere (mainly ocean degassing) and not the reverse. This process is still valid today but not noticeable yet because changing equilibriums of the mixed layer of the ocean requires several hundred years.
The Sun, a good candidate
This confrontation between the proponents of global warming due to human activity, supported by the IPCC, and skeptics reflects a misunderstanding of the mechanisms involved in climate variability. If carbon dioxide did not cause warming of the 20th century, what is the reason? A good candidate is the Sun.
Solar activity over the past 11,400 years has been reconstructed by analyzing jointly the concentration of radiocarbon in tree rings and isotopic abundance of beryllium-10 in ice cores. 14C and 10Be isotopes, which are produced by cosmic rays in the upper atmosphere, indeed reflect solar activity because in periods of high activity cosmic rays are deflected in the solar system and therefore produce less cosmogenic isotopes.
The reconstruction of solar activity shows that it varies continuously. During the last millennium, humanitarian disasters generated during periods of low activity suggests that the global temperature has dropped, as was the case during the last Little Ice Age: there is undoubtedly a causal relationship between solar activity and global temperature.
However the solar irradiance variability has low direct impact on climate
In 1995, Henik Svensmark discovered a strange correlation between the flux of cosmic rays from space and cloud cover. Thus was born a theory called cosmoclimatology according as some cosmic rays, that are deflected by the variable magnetic field of the sun and that ionize gases of air, create agglomerates of water and the formation of cloud droplets; thanks to their reflectance, they decrease the amount of solar radiation that reaches the surface, thereby causing a decrease in surface temperature, this with an impressive correlation between low altitude cloud cover measured by satellite (International Satellite Cloud Climatology Project), and the cosmic ray intensity measured at Climax, Colorado. Thus, the variation of the electromagnetic activity of the sun and changes in the intensity of cosmic radiation from space lead to a periodic warming or cooling of the earth’s surface.
In addition, by analyzing over longer periods proxies of low altitude cloud cover and cosmic rays Svensmark observed very similar trends during the Little Ice Age, when the sun was particularly inactive, successive polarity changes of the magnetic axis of the sun being able to cause these cooling periods such as that known at the end of the reign of Louis XIV. After 1750, the sun becoming more active again, the cosmic ray flux decreased, cloud cover too, and temperatures rose. A change in the cloud cover of 3 to 4% caused by variations of the cosmic ray flux would be sufficient to explain a change in temperature by several degrees due to the cloud reflectivity.
But, it is a fact, as interesting though it may be, this theory accounts for only a small part of the phenomenon of amplification of the effect of changes in solar activity on the Earth’s average temperature. In addition, based on the deflection of cosmic rays by the solar wind, it cannot account for the selective solar forcing on climate: how can the 11-year cycle, during which solar activity varies of a few tenths of a percent, be so quiet? Although low, this amplitude is of the same order as that of longer cycles. But this 11-year cycle has little influence on the climate compared to Milankovitch cycles, of very long-periods, which reflect the variations in the orbital parameters of the earth around the sun. Those have a significant impact, setting periods of glaciation, in particular. This selectivity and the variability in the efficiency of solar and orbital forcing during glacial-interglacial periods highlighted from the analysis of ice cores originating from Greenland and Antarctica suggest that resonance phenomena occur, filtering out some frequencies in favor of others while amplifying or mitigating according to the extension of the polar caps.
A novel concept: the resonance of baroclinic ocean waves
The direct impact of solar irradiance does not explain climate variability at different time scales. Such an assumption would come to imagine a submissive climatic system while it has its own frequencies, a considerable inertia, and manifests many whims, harbingers of resonant phenomena. The effects claimed by one and the other of these theories are marginal and does not permit to quantitatively explain the observed phenomena. The dynamics of climatic phenomena suggests a leading role of oceans whose influence, though long recognized, remains poorly understood. The oceans offer indeed a field of investigation whose scope is considerable, and that concerns the resonance of the oceanic planetary waves: it not only allows explaining and reproducing the warming of our planet, more precisely the middle and long-term climate variability, but also the El Niño phenomenon, the succession of wet or dry years observed in Western Europe since the 70’s…
Is that the tropical belt of the oceans produces long-waves, whose wavelength is several thousand kilometers. Trapped by the equator due to the Coriolis[i] force resulting from the earth’s rotation, they are deflected at the approach of the continents to form off-equatorial waves. These long tropical waves resonate with the forcing exerted by trade winds, whose period is annual, to produce sub-harmonic whose period is multi-annual. These long-waves that oceanographers appoint of the name of baroclinic[ii] result of the oscillation of the thermocline one hundred meters deep or more that separates the warm surface waters from deep cold waters, denser.
This tropical oceanic resonance is one of the drivers of ocean surface circulation, i.e. above the thermocline, and contributes to the formation of strong western boundary currents[i] such as the Gulf Stream in the North Atlantic and the Kuroshio in the northeast Pacific, by introducing a sequence of warm or cold waters according to the oscillation of the thermocline. Around latitude 40°N or S, those western boundary currents, which flow poleward in both hemispheres, leave the boundary of the continents to join each of the five oceanic subtropical gyres, giant vortexes at the north and south Atlantic and Pacific oceans and the southern Indian ocean. These resonantly forced baroclinic waves then become gyral, suiting their wavelength to the period inherited from the tropical oceans.
For periods between half a year and eight years, the forcing of these gyral waves is induced from the sequence of warm and cold waters conveyed by western boundary currents, and now cause the oscillation of the thermocline of the gyre. But these gigantic gyral waves also have the ability to tune with the long-period solar cycles of one to up to several centuries, as well as Milankovitch cycles that affect the occurrence of glacial and interglacial periods, which reflect the changes in terrestrial astronomical parameters throughout tens of thousands of years.
These resonant baroclinic waves have the ability to ‘hide’ the thermal energy that drives them by lowering the thermocline; due to a positive feedback those warm deep-waters favor the acceleration of the western boundary current and the development of sea surface temperature anomalies, supporting the heat exchanges between the ocean surface and the atmosphere: thermal surface anomalies induce atmospheric instabilities say again baroclinic, depressions or cyclones, which, carried by the jet-streams[ii] at high altitude, travel throughout the continents.
In this way, surface temperature of continents respond to thermal anomalies of subtropical gyres. Positive or negative according to the motion of the thermocline, these thermal anomalies of sea surface tend to produce the same anomalies at the surface of continents due to the large heat capacity of seawater on the one hand, and the cyclonic or anticyclonic activity of the atmosphere stimulated at mid-latitudes secondly. This thermal balancing internal to our planet, which occurs over the years, smooth the climate variations we observe daily at mid-latitudes. The imbalance between the energy received and re-emitted by the earth mainly depends on the depth of the thermocline of gyral waves.
This approach firstly allows to account for long-term climate variability, and secondly to reproduce with high accuracy global warming observed during the second half of the 20th century, then the stagnation of the average temperature of the planet, precursor of the beginning of a slow cooling that will continue for several centuries. This warming effect results in the accumulation of warm seawaters by coupling with solar activity which showed a burst in the 20th century, what climatologists call the modern maximum which indicates the end of the Little ice age that occurred between the 16th and 18th centuries and also that of the Ice Age that happened more than 10,000 years ago.
The resonance of tropical waves
To understand the oceanic gyral resonance, driver of mid- and long-term climate variability and its coupling with the solar and orbital cycles, first we have to focus on the resonance of oceanic tropical waves from which are inherited periods of resonance. The study of the quasi-stationary waves in the three tropical oceans consists in bringing out sea surface height anomalies and modulated currents in characteristic bands such as the 8-16 month band for annual waves. From measurements of sea surface height are deduced the amplitude and phase of sea surface height anomalies, but also the speed and phase of the modulated geostrophic currents from the slope of the sea surface[iii], thanks to the use of cross wavelets.
Quasi-Stationary-Waves are formed, representing a single dynamic phenomenon within a characteristic bandwidth. Geostrophic forces closely constrain the behavior of the baroclinic waves at the limits of the basin, forming antinodes at the place of Sea Surface Height anomalies and nodes where modulated geostrophic currents ensure the transfer of warm water from an antinode to another. Modulated geostrophic currents that change direction twice per cycle, are superimposed on the background current. The observed current is the resultant of the modulated geostrophic current and the background current. Although these terms node and antinode are abusive because the phase of Quasi-Stationary-Waves is not uniform, which may involve overlapping of nodes and antinodes, they explicitly reflect the evolution of the wave during a cycle.
The Atlantic Ocean
The dynamic representation of the nodes and antinodes of the tropical quasi-stationary wave allows distinguishing (Pinault, 2013):
- Three antinodes of very unequal amplitude, two antinodes on either side of the equator and one antinode along the equator. The northern antinode has the highest amplitude, around 10 cm in November. It extends from the Brazilian coast to the west coast of Africa that it follows northwards. The equatorial antinode, which extends from South America to the West African coast, forms a ridge in January. The antinode south of the equator, barely perceptible, is divided into two branches: extending from the coast of South America, it forms a ridge in April.
- Two main nodes, both coinciding with the western part of antinodes, to the north and along the equator. The modulated current located north of the equator flows mainly to the west, its velocity reaching 30 cm/s in October-November (in February in the northern portion). It straddles the North Equatorial Current and the North Equatorial Counter-Current. The maximum velocity of the modulated equatorial current is, on the other hand, reached in May.
Evolution of the quasi-stationary wave
Following the geostrophic forces acting in the tropical basin, which result from the conjugate effects of rotation and gravity, Rossby waves are formed both north and south of the equator. Under the effect of wind stress these waves partially reflect against the eastern coast of South America to join the equatorial wave. A part leaves the tropical basin to merge with the western boundary currents flowing north and south. The other part forms the Kelvin wave trapped by the equator which propagates eastward to the coast of Africa, producing a coastal Kelvin wave. It propagates mainly southward from the Gulf of Guinea. Under the effect of recession, some of these Kelvin waves are reflected against the African coast to form the equatorial Rossby wave which, trapped by the equator and stimulated by trade winds, propagates westward to the south American coast where it is diverted to the north along the North Equatorial Counter-Current. This is due to the Doppler Effect: Rossby waves propagate apparently eastward when the counter-current that drags them is faster than their phase velocity[i].
Thus, geostrophic forces resulting from antinodes control the motion of Rossby and Kelvin waves, allowing their reflection against the eastern and western limits of the basin, or otherwise promoting their leaving as this occurs when the northern Rossby wave flows westward. In order that the resonance occurs, the average period of the complete cycle must be confused with that of forcing, i.e. one year. The adjustment of the basin to forcing results from the northern wave which owes its existence to the North Atlantic Counter-Current. It actually plays the role of a « tuning slide » so that the sea surface height of the tropical basin adjusts to allow the forced wave to achieve its cycle in an average time of one year exactly.
The evolution of tropical waves is subject to resonant forcing due to trade winds. The entire tropical basin adjusts to resonate, allowing it to capture the maximum energy. This resonant basin mode outweighs the non-resonant modes that are not synchronized with forcing. In this case the waves are damped very quickly as inevitably opposed to forcing during their evolution. Under these conditions, for the Atlantic Ocean the Rossby wavelength obtained from the dispersion relation[i] is 24,700 km at the equator for the period of one year, which corresponds to the cycle of winds. It is 12,350 km for the Kelvin wave, faster, whose period is 2 months.
Resonant forcing, which involves the transfer of warm water between the two hemispheres, takes advantage of trade wind rocking from an hemisphere to another as does the inter-tropical convergence zone (ITCZ), what sailors call « doldrums ». The inter-tropical convergence zone is a belt of low pressure areas around the Earth, close to the equator. Its location oscillates on both sides of the equator from one hemisphere to the other according to an annual pace, following the declination of the Sun. During the austral winter the ITCZ migrates to the northern hemisphere while trade winds blow in the southern hemisphere, forcing the southern annual wave. During the boreal winter the ITCZ migrates to the southern hemisphere when trade winds blow in the northern hemisphere, forcing the northern wave.
Seasonal upwelling[i] in the Gulf of Guinea is impeded during the eastward phase propagation of the resonant equatorial wave whereas it is stimulated during the westward phase propagation, whence cold water replaces warm water in the mixed layer. In boreal winter, the ridge is formed along the equator while the northern anomaly deepens, cold water gradually replacing the warm water that has just left the tropical basin to supply the western boundary currents. At the end of the boreal winter the northern antinode forms a trough, which promotes migration to the northern hemisphere of warm water accumulated during the austral summer in the southern hemisphere. This is due to the sea surface height of the tropical ocean: geostrophic currents flow along the steepest lines (from positive to negative antinodes). Furthermore, the equatorial Rossby wave is deflected by the western boundary of the basin, merging with the North Atlantic counter-current. Six months later the northern antinode is reversed to form a ridge. This ridge, which is associated with the deepening of the thermocline, goes with the recession of the wave during which the western boundary currents are fed with warm water, and the cycle can start again…
During a cycle, the warm waters migrate from the southern antinode to the northern antinode via the equatorial antinode. At each step the volume of warm water increases by cumulating to that already in place, in formation, which is displayed by the amplitude of antinodes. These warm waters leave the northern antinode to join the two western boundary currents that are the Gulf Stream north and the North Brazil Current south, with an annual periodicity.
The Pacific Ocean
As the Atlantic Ocean, the Pacific is subject to the resonance of equatorial waves formed from the first baroclinic mode (vertical) Kelvin waves, and the first baroclinic mode, first meridional mode Rossby waves. However, while under the effect of forcing resulting from wind stress the resonance occurs at a frequency of one cycle per year in the Atlantic Ocean, due to the width of the basin, 17,760 km instead of 6,500 km, the period of tropical waves in the Pacific is necessarily multiyear. The resonant basin mode produces the El Niño phenomenon well known for its meteorological effects on a global scale (Pinault, 2015).
The annual wave
On the other hand, an annual quasi-stationary wave is observable north of the equator between latitudes 0°N and 12°N. The dynamic representation of the quasi-stationary wave shows two long-crested waves, almost in opposite phase, which extend from the eastern coasts of Southeast Asia to Central America, suggesting that they result from resonant forcing of the first baroclinic mode, fourth meridional mode Rossby wave. Meridional modes indeed show an increasing number of zonal energetic strips as the mode increases (one for the first mode, two strips for the second and so on).
The nodes are the two zonal surface currents flowing north and south of the equator, i.e. between 4.5°N and 7.5°N, forming the North Equatorial Counter-Current, and 0°N, 4.5°S, forming the South Equatorial Current. The period of the modulated currents is one year, too. The modulated South Equatorial Current feeds the western boundary currents, the outlet being located near the equator, i.e. off North Maluku and north Sulawesi islands in the Indonesian archipelago.
Evolution of the quasi-stationary wave
Only the stimulation of a high meridional mode can indeed explain the structure in strips of the wave and the two nodes whose analysis reveals that they are only one, being highly correlated. The antinodes are mainly visible in the northern hemisphere when they should appear antisymmetric in the southern hemisphere: only the southernmost antinode is visible west of 160°W, in phase with the southernmost antinode in the northern hemisphere, as the trade winds are weaker south of the equator.
The wavelength, which is 9400 km, is less than the width of the basin. The phase of the quasi-stationary wave thus reverse at both ends, which may explain the large variability from one cycle to the other of the observed waveform. In the illustrated realization, the speed of the modulated component of the Counter-Current peaks in September-October in the northern hemisphere, as it flows eastward, in phase with the South Equatorial Current in the southern hemisphere. This occurs while warm water has been transferred to the southernmost antinode in each hemisphere, then a few months later at the northernmost antinode.
The quadrennial wave
The pattern of antinodes and nodes of the quadrennial wave recalls what is observed in the tropical Atlantic (the frequency representation of the sea surface height and the speed of the geostrophic current near the equator west of the basin show that the period is about 4 years with a high variability). As in the Atlantic basin this mode shows a main node where the modulated equatorial current extends into the western half of the basin, two antinodes on both sides of the equator west of the basin and an equatorial antinode: the central-eastern antinode results from the superposition of the first baroclinic mode, first meridional mode Rossby wave and a Kelvin wave, both trapped by the equator, but propagating in opposite directions. Western antinodes on the one hand and the central-eastern antinode secondly separate the Pacific into two parts where the thermocline oscillates almost in phase opposition.
The north-western antinode forms a curl joining the eastern coast of central and southern Philippines, overlapping the North Equatorial Current in its northern part, and riding the North Equatorial Counter-Current and the South Equatorial Current in the Southern part. A Rossby wave, which is reflected against the eastern coast of the Indonesian archipelago, spreads along the curl, driven by the North Equatorial Counter-Current.
The south-western antinode forms a tongue extending to the coast of north-eastern New Guinea through the Solomon Islands. It also proceeds from a Rossby wave that is reflected against New Guinea, driven by the South Equatorial Current.
The main node is the modulated component of the South Equatorial Current flowing westward along the equator between latitudes 0°N and 8°S.
Evolution of the quasi-stationary wave
The evolution of quasi-stationary waves during a cycle can be expressed relative to the ENSO event that occurred during the cycle. The westward phase propagation of the quasi-stationary wave along the equator begins when the ridge is reflected against the South American coast, during the maturation stage of the ENSO event. It lasts almost two years during which the thermocline rises along the central-eastern antinode. At the end of the westward phase propagation, the main modulated current, which then flows to the west, reaches its maximum speed and partially leaves the equatorial belt to feed the western boundary currents. In the absence of a powerful counter-current south of the equator, which prevents any reflection of the equatorial ridge to the south-western antinode, the resonant wave is partly reflected to the curl forming the north-western antinode. The westward phase propagation of the resonant wave along the equator stimulates upwelling at the eastern limit of the basin, i.e. the South American coast, while the trough of the wave is formed along the central-eastern antinode. Thus, in the central and eastern part of the basin cold water gradually replaces the warm water leaving the equatorial belt.
When the phase is ± 2 years relative to the ENSO event, under the effect of winds western antinodes form a ridge with the deepening of the thermocline in the « warm water pool » down to 250 m. The ridge of the north-western antinode as well as the speed of the North Equatorial Counter-Current flowing eastward reach their maximum at the same time as the south-western antinode. Meanwhile, the trough deepens at the central-eastern antinode, stimulating the migration of warm water from the western antinodes, replacing cold water while upwelling weakens off the South American coast.
As in the Atlantic Ocean, the north-western antinode plays the role of « tuning slide », but the propagation time along the curl is short compared to the period of the quasi-stationary wave, so that only a fine tuning of the period occurs. Again, the south-western antinode acts as a heat sink.
Coupling of basin modes
The functioning of the quadrennial quasi-stationary wave cannot be dissociated from the ENSO. Indeed, El Niño events are triggered at a critical time in the cycle of the wave when, at the end of the eastward phase propagation, the ridge reaches the west coast of South America. These El Niño events stimulate evaporation from the surface of the central-eastern equatorial anomaly, which cools the mixed layer, and thus raises the thermocline. ENSO is also a way of forcing of the resonant wave because it stimulates the propagation of the ridge to the west. More La Niña, which announces the resumption of the Walker circulation[i] with increased surface stress from easterlies, is also a way of forcing because it becomes effective after El Niño, so during the westward phase propagation of the ridge.
However, the equations of motion show that forcing associated with ENSO is not sufficient to explain the amplitude of antinodes and speed of modulated currents. Thus, a coupling between annual and quadrennial basin modes has to be invoked. The modulated components of the North Equatorial Counter-Current and South Equatorial Current, which form an integral part of the annual quasi-stationary wave, indeed merge with the main node of the quadrennial quasi-stationary wave along a narrow equatorial strip west of 150°W. The special location of the island of Papua New Guinea, near the equator, modifies the current lines of zonal flows and instabilities are exacerbated along a narrow line between 136°E and 141°E longitude and between 0 N° and 2°N latitude.
These instabilities result from the North Equatorial Counter-Current that flows closer to the equator and in the amplification of the modulated current acceleration common to both basin modes. Off the Cape d’Urville 137.5°E 0.5°N the North Equatorial Counter-Current may accelerate from 0 to 1.5 m/s within one month, which is considerable. Some of these accelerations are harbingers of an ENSO event. In this case the current accelerates rapidly eastward and its speed decreases before increasing again, reaching a maximum two months later. The geostrophic current off the Cape d’Urville is perturbed at an early stage of the development of an ENSO event, and then returns to its original speed. This occurs 7 times late 1992 to mid-2015: the corresponding ENSO events occur in 08/1994, 11/1997, 12/2002, 12/2004, 12/2006, 11/2009 and 09/2012 (an event is maturing in June 2015).
On the other hand, these instabilities anticipate the maturation stage of ENSO events of 4 to 6 months, this time depending on how the surface temperature anomalies develop during the evolution of ENSO. The acceleration of the North Equatorial Counter-Current that flows closer to the equator at the western part of the basin stimulates a baroclinic Kelvin wave, crossing the basin from west to east in two months and causing a deepening of the thermocline in the central-eastern part of the basin. Geostrophic forces in the tropical basin make that two Kelvin waves cannot succeed in less than one year and a half. This is the minimum time required for a complete cycle of the quasi-stationary wave to occur, the tilt along the equator of the sea surface having to promote the propagation of Kelvin waves to the east. Therefore all the current accelerations, whose average period is one year, do not produce a Kelvin wave. This is why some accelerations, even of large amplitude as that of 2003, does not produce ENSO event. In this case geostrophic forces remain confined to the west of the basin.
The periods of coupled oscillators
Applied to the case of coupled ocean waves, the theory of Sub-harmonic mode locking in coupled oscillators with inertia indicates that the average periods of the coupled waves are multiples of the average period of the fundamental wave[i], i.e. one year here when we consider that the trade wind cycle is the temporal reference of the tropical basin. The quadrennial wave is indeed subject to a sub-harmonic mode locking of the annual mode. This holds true irrespective of the variability of the period from a cycle to another. As a result, the average periods of the two basin modes are precisely 1 and 4 years. This latter period is unambiguously determined from the distribution of ENSO events.
The 8-year period sub-harmonic
A sub-harmonic whose average period is 8 years exhibits three antinodes and a main node like the quadrennial quasi-stationary wave. The central-eastern antinode extends between 160°E and 130°W. The north-western antinode is located off the Philippines against which Rossby waves are reflected. The south-western antinode, parallel to the equator, stretches from the eastern Australian coast to 130°W between latitudes 25°S and 20°S. The functioning of this basin mode is reminiscent of the quadrennial mode. The central-eastern antinode is formed in the waveguide formed by the equator, the north-western antinode plays the role of « tuning slide » and the south-western antinode is a heat sink.
This basin mode involves Rossby and Kelvin waves whose phase velocities are necessarily lower than these of the quadrennial basin mode: the second baroclinic mode Rossby and Kelvin waves have to be invoked. The phase velocity is nearly 1 m/s, i.e. less than half that of the first baroclinic mode. This second baroclinic mode (or vertical) not correspond to the oscillation of the thermocline, more precisely the interface at the basis of the pycnocline, depth of 200 to 250 m, but the oscillation of the interface atop the pycnocline at the depth of 125 m.
The main node coincides with that of the quadrennial basin mode west of 170°E, so that this mode is coupled to the previous basin modes of 1 and 4-year period: the average period is 8 years since a sub-harmonic mode locking occurs. This basin mode contributes to the ENSO less than the quadrennial basin mode because the central-eastern antinode interferes little with the cold currents in the eastern basin.
In this way, the outlet of the tropical Pacific, where the modulated currents leave the basin to supply the western boundary currents, is common to the three basin modes. Thus the Pacific Ocean differs from the Atlantic Ocean, due to the superposition of strong modulated currents at the output of the tropical basin whose average periods are 1, 4 and 8 years.
The Indian Ocean
As well as the Atlantic and Pacific oceans, the functioning of the tropical Indian Ocean is subject to resonant forcing of long waves, leading to introduction in the only western boundary current, the Agulhas, of alternately warm and cold water at a characteristic frequency. The tropical Indian Ocean is involved in the same way as the other oceans in the resonance of long waves at mid-latitudes leading to subtropical oceanic gyre forcing. But it has two features, its closing north, which prevents any western boundary current from flowing northward, and its openness to the Pacific Ocean to the east, which produces the Throughflow, i.e. an Indonesian system of surface currents flowing from the Pacific to the Indian Ocean through the Indonesian seas. In this way, the Pacific Ocean influences the Indian Ocean, in the region extending from 17.5°S to 7.5°S in particular, due to the propagation of Rossby waves from the western Pacific to the Indian Ocean. The Throughflow plays an important role in the transport of heat in the climate system, linking the warm waters of the Western Pacific pool and the cold waters of the South Equatorial Current of the Indian Ocean.
Another feature of the tropical basin is that its width, which is 6,300 km from the east coast of Africa to the west coast of Sumatra, is close to half the wavelength of a Rossby wave of biannual frequency, i.e. 12,100 km. Considering the first baroclinic mode, the propagation time of a Rossby wave, then a Kelvin wave in return is nearly two thirds of the period to make a round trip along the equator, which enables the tuning of natural and forcing periods due to the delayed response of the Quasi-Stationary-Wave at the western antinode.
The Indian Ocean is subject to a phenomenon comparable to El Niño, which is an irregular oscillation of surface temperatures in which the western part of the ocean becomes alternately warmer and colder than the eastern part, forming the Indian Ocean Dipole (IOD). When the dipole is positive temperature anomalies are observed in the western part of the basin, which induces an increase in rainfall in East Africa and a higher than normal Indian monsoon. Cooling then occurs in the eastern part of the basin, which tends to cause drought in Indonesia and Australia. When the dipole is negative conditions are reversed, with warm water and an increase in precipitation in the eastern Indian Ocean, and cooler and drier conditions west.
However, again, the functioning of the tropical Indian Ocean cannot be understood adequately without involving the resonant forcing of long ocean waves. This concerns the IOD, of course, but also the Somali, a modulated current along the eastern coast of Africa in front of Somalia. Two quasi-stationary long-waves can be identified, a biannual equatorial wave which is the superimposition of a Kelvin and a Rossby wave, and an annual off-equatorial Rossby wave. It spreads across the Indian Ocean from the outlet of the Timor passage at 120°E along the South Equatorial Current. It is deflected northward approaching the western boundary of the Indian Ocean, then follows the Somali and the monsoon drift, avoids the Indian subcontinent south of Sri Lanka to go along the coast of the Bay of Bengal.
The biannual wave
The biannual quasi-stationary wave seesaws from the western part of the basin to its eastern part, the equator acting as a waveguide, as shown by the amplitude and phase of the cross-wavelet of sea surface height. The geostrophic component of the modulated zonal current, which is the Equatorial Counter-Current, preferably flows east between longitudes 50°E and 90°E, but may reverse. This inversion indicates that during a cycle exchanges occur between western and eastern antinodes.
The quasi-stationary wave is the superposition of a westward propagating Rossby wave and a Kelvin wave in the opposite direction, both reflecting on the limits of the basin that are the coast of Eastern Equatorial Africa on the one hand, Malacca and Sumatra secondly. The western antinode forms a ridge in March and September, and the Eastern antinode in May and November, whence a slight asymmetry in the duration of transfers between the eastern and western tropical basins due to the difference in phase velocity of the Rossby and Kelvin waves. The speed of the modulated current is maximal in May and November when directed eastward, i.e. it is in phase with the eastern antinode. The resulting basin mode is tuned to the monsoon winds.
Evolution of the quasi-stationary wave
Quasi-stationary equatorial waves are the superposition of the first baroclinic mode Kelvin wave and the first baroclinic mode, first meridional mode Rossby wave. During the eastward phase propagation, warm water is transferred from the western antinode to the eastern antinode where it partially leaves the tropical basin to join the eastern boundary current while cold water replaces warm water to the west of the basin by stimulating upwelling off the eastern coast of Africa, leading to the rise of the thermocline. This phase, during which upwelling off the coast of Sumatra is reduced, ends in spring or autumn.
The speed of the Equatorial Counter-Current, which flows preferentially to the east, increases in spring and autumn: the Kelvin wave is reflected against the west coast of the Indonesian archipelago, forming coastal waves that propagate poleward.
During the summer and winter, the modulated current vanishes or reverses. Warm water replaces cold water at the western antinode while upwelling is reinforced along the coast of Sumatra, causing the rise of the thermocline.
During a period the mixed layer, warm, is advected from the western antinode where it is formed to the eastern antinode. According to the geostrophy of the tropical ocean, advection may also be performed back, when the modulated current reverses. Thus, the biannual basin mode induces heat transfer between the western and eastern parts of the tropical Indian Ocean while stimulating or reducing upwelling at the boundaries of the basin.
Due to the seasonal reversal of monsoon winds, forcing mainly occurs at the eastern antinode and southern India. Northwest winds reach their maximum in April-May and October-November, and are reversed in March and September, in phase with the eastern antinode. Thus, the biannual basin mode turns out to be the response of the tropical ocean to resonant forcing induced by the seasonal reversal of the monsoon winds.
The annual wave
Unlike the biannual equatorial wave and its sub-harmonics the annual quasi-stationary wave has a leading role in the circulation of the western boundary current, which here is the Agulhas propagating southward. In this way it is involved in the long-term climate variability like the tropical quasi-stationary waves in the Atlantic and Pacific oceans.
Two main antinodes are visible in both hemispheres. The southernmost antinode extends westward from the Timor passage, longitude 80°E, following first the Indonesian Throughflow then the South Equatorial Current. The northernmost antinode follows the southwest monsoon drift off the east coast of Africa, south of the Arabian Sea, to the southern tip of the Indian subcontinent. Less extended, antinodes develop along the coast of the Bay of Bengal. To the east they are formed from the coastal Kelvin waves, as evidenced by the phase change north of the bay.
Three main nodes are recognizable. To the south is the South Equatorial Current between the Timor passage and longitude 60°E, to the west the Somali, a current that follows the eastern African coast, to the north the northeast monsoon drift that is mostly visible south of the Indian subcontinent. South of the coast of Java the South Equatorial Current flows mainly to the west, vanishing periodically, while the Somali and monsoon drift are reversing currents.
Evolution of the quasi-stationary wave
The annual Rossby wave is formed at the outlet of the Timor passage to cross the Indian Ocean; once deflected by the East African coast, the Rossby wave propagates eastward into the northern hemisphere to join the monsoon drift, the southern coasts of India and Sri Lanka acting as a waveguide. The wave propagation in the northern hemisphere results from the Doppler Effect when the speed of the current flowing eastward is higher than the phase velocity of the Rossby wave flowing westward. When the phase is reversed, the Rossby wave propagates westward, and the Somali along the coast of Somalia is reversed, too, a part of this current leaving the tropical ocean to feed the western boundary current along the eastern coast of Madagascar and the coast of southeast Africa to form the Mozambique current.
Antinodes show a north-south seesaw of warm waters of the tropical ocean. From the Pacific they accumulate during the boreal summer to form the southern antinode whereas, due to upwelling that is stimulated in the Bay of Bengal and the Arabian Sea, cold water overruns the northern part of the basin. In spring the phenomenon is reversed, warm water accumulating in the north of the basin. Upwelling weakens as well as the South Equatorial Current; reversing of monsoon drift promotes seesaw of warm waters.
Thus, the thermal energy is transferred from the western basin in the Pacific, which acts as a heat sink, to the Indian Ocean via the Timor passage. Then, heat exchange occurs between the two hemispheres via the Somali and the monsoon drift, each reversing periodically in phase. The annual wave feeds the western boundary current, i.e. the Agulhas, through a succession of warm and cold waters.
In contrast the Equatorial Counter-Current is not part of this system, being out of phase with the two nodes that are the Somali and the monsoon drift. The biannual equatorial wave and sub-harmonics thus behave independently of the annual wave, which itself propagates out of the equator. These two systems have no node in common, the first producing the Equatorial Counter-Current and the second the South Equatorial Current, then the monsoon drift. This situation, which is unprecedented in the functioning of tropical oceans, highlights two independent basin modes in the tropical Indian Ocean.
The gyral resonance
To the 5 subtropical gyres correspond 5 western boundary currents that are the Gulf Stream and the Brazil Current in the North and South Atlantic, the Kuroshio and the eastern Australian current in the North and South Pacific, the Agulhas in the South Indian Ocean. Under the influence of resonantly forced baroclinic waves, the three tropical oceans feed those western boundary currents through a sequence of warm and cold waters to one cycle every 1/2, 1, 4 and 8 years. Tropical oceans behave indeed as « resonators » under the effect of forcing due to surface stress and ENSO as regards the Pacific.
In fact, during these cycles the temperature of the water carried by the western boundary currents does not change, or very little. The wavelet analysis of the sea surface temperature does not show anomalies in the different characteristic frequency bands. It is the depth of the thermocline that varies, thus the warm water mass transported poleward, without generating the formation of baroclinic waves that, facing west, would inevitably be wiped out against the coasts.
This is no longer true when the western boundary current reaches a latitude nearby 35° to 40°N or S. At high latitudes, the velocity of the western boundary current increases as the phase velocity of the baroclinic waves decreases: baroclinic waves are formed when the velocity of the western boundary current becomes higher than their phase velocity.
More precisely, the western boundary current becomes unstable when its speed becomes twice the phase velocity of Rossby waves, this condition inducing a resonance. Any obstacle causing the current to move away from the coast leads to the formation of quasi-stationary Rossby waves, either because of the line of the coast or the collision with a current flowing in the opposite direction along the coast: the western boundary current orientates gradually eastwards while Rossby waves propagate in the opposite direction.
Rossby waves being non-dispersive, for a given latitude their phase velocity does not depend on frequency. In other words their wavelength is directly proportional to the period. Thus, for the period of 8 years, the wavelength is 2,780 km in latitude 40°, whereas it is only 174 km for the biannual wave.
Where the resonance occurs the cross-wavelet analysis of sea surface height reveals two antinodes in opposite phase (sometimes more), as occurs in the North Atlantic for the 8-year period Rossby wave. Off the Cape Hatteras, the Gulf Stream leaves the eastern North American coast around 35°N. The westernmost anomaly faces east, along the subtropical gyre, followed by the second anomaly headed north-east along the north Atlantic drift. The phase change occurs at the longitude 50°W. These antinodes are always associated with a modulated geostrophic current at the node of the quasi-stationary wave.
The most important consequence of the gyral resonance concerns the long-term variability of climate. The gyral resonance occurs indeed at very specific frequencies that are inherited either of tropical waves or of the oscillations of solar irradiance for longer periods. Direct observation of the gyral resonance can be done from sea surface height for short periods, as has been done for the North Atlantic gyre using the available data sets covering a period twenty years. For longer periods one is interested in sea surface temperature anomalies using data sets this time covering nearly a century and a half. In practice, using sea surface height series jointly with sea surface temperature series, quasi-stationary waves can be observed at frequencies ranging from 2 cycles per year to one cycle for 128 years.
The resonance occurs when the speed, facing east, of the ageostrophic current is higher than the phase velocity, facing west, of the Rossby wave. In this case, the length of the Rossby wave adapts so that its natural period coincides with the forcing period. The ridge of the western antinode is advected of a half-wavelength to the eastern antinode during a half-cycle, the troughs are then translated in the next half-cycle. This leads to eastward transfer of a sequence of warm and cold waters.
Since the phase velocity of the Rossby waves only depends on latitude, the resonance that supposes the adequacy of the frequency and the wavelength occurs at all frequencies. Otherwise, the lack of synchronization between the waves of different frequencies and forcing would inexorably lead to their destruction.
Evolution of short-period gyral waves
The observation of quasi-stationary waves for different periods teaches us how the sequence of warm and cold waters is transferred from the western boundary to the east. This is particularly clear for the wave of 8-year period of the North Atlantic. A ridge is formed at the western antinode and a trough at the eastern antinode. The speed of the western modulated zonal current is maximum, facing west. The resulting modulated current, sum of ageostrophic and geostrophic currents, vanishes or reverses. At this time the speed of the eastern modulated current, facing east, is maximum. Thus warm water flows from the western antinode to the eastern antinode while the transfer from the western antinode to the western boundary is low due to geostrophic forces that prevent it.
Half a cycle later, a trough is formed at the western antinode and a ridge at the eastern antinode. The velocity of the resulting current at the western boundary is maximum, being the superposition of two eastward propagating currents. Gradually the trough of the western antinode gives way to a ridge while the speed of the resulting modulated current vanishes or reverses in the east, being the superposition of two currents flowing in opposite directions: this locks out any transfer from the eastern antinode to the western antinode. The same mode of transfer occurs for different frequencies of gyral waves due to the proportionality between the wavelength and the period.
Growth of the western antinode induces a horizontal pumping effect, as evidenced by the modulated current when it is oriented to the east, west of the basin, being the superposition of the ageostrophic current and the modulated geostrophic current. This pumping effect drastically increases the flow of the western boundary current. Another consequence is the rapid change in potential vorticity of the western boundary current when it leaves the coast to flow eastward.
Another important aspect of the resonance relates to the simultaneity of the phases of western antinodes. Synchronism of resonances in the five subtropical gyres reflects a common mode of forcing. This is particularly evident for the resonance at the frequency of 2 cycles per year which occurs in April and October, an indicator in the three tropical oceans of forcing by trade wind stress, active during the boreal winter in the northern hemisphere and during the austral winter in the southern hemisphere. The transfer time of the mixed layer from the equator to mid-latitudes is short compared to the period of gyral waves. Thus, the synchronism persists at mid-latitudes regardless of the period. A final aspect of the resonance involves the coupling of gyral waves of different frequencies that share the same node at the western boundary of the basin, which again leads to a sub-harmonic mode locking in accordance with the periods 1/2, 1, 4 and 8 years.
How the gyral wave moves poleward after leaving the gyre reflects the thermohaline circulation which is generated by differences in temperature and salinity of water masses acting on their density. Thermohaline circulation occurs when the currents approaching the ice cap, water cooled and salted sinks to depths between 1 and 3 km to participate in the deep ocean circulation.
The long-period gyral resonance
For periods exceeding 8 years, the length of resonantly forced Rossby waves exceeds the width of the oceans at mid-latitudes, so that the long-period waves necessarily develop around the subtropical gyres. The gyre of the North Atlantic allows the estimation of anomalies for periods extending up to 128 years relatively accurately because sea surface temperature measurements were already performed in 1870 in a systematic way, which is not true for the other gyres (http://hadobs.metoffice.com/hadisst/data/ download.html).
Like for short periods the baroclinic Rossby wave follows the subtropical gyre from the western boundary of the basin while changing the potential vorticity of the western boundary current to allow it to enter the gyre. Again, the gyral resonance of Rossby waves requires the speed of the ageostrophic current of the gyre, which is anticyclonic, is higher than the phase velocity of the Rossby wave, which itself is cyclonic. The latter remains constant around the gyre as only depending on the mean latitude of the gyre.
In contrast to ageostrophic current that is divergent (or convergent), the geostrophic current is non-divergent. This can be ascertained by observing that the current lines remain substantially parallel around the gyre. Multiple turns may overlap, which implies that the Rossby wavelength has not upper limit. In other words, first baroclinic mode, first radial mode Rossby waves of long-period can resonate at mid-latitudes, tuning to long-period solar cycles.
Suppose that the number of coils corresponding to a half-wavelength is N. Within a period a warming phase occurs during which warm water is accumulated along the overlapping turns, followed by a cooling phase during which the warm water leaves the gyre. The gyral resonance can occur indeed only if an antinode develops outside the gyre, in phase opposition with the antinode around the gyre, as this happens for short periods. In the course of its evolution the gyre is subject to radial transformations. During the warming phase the two edges of the gyre converge towards the median current line, while the Rossby wave is retained around the gyre. In contrast, during the cooling phase the movement reverses when the wave leaves the gyre.
In this way the resonance of Rossby waves of long-period is similar to that of 4 or 8-year period for which antinodes are separated by a half-wavelength, because of the adequacy between the length of Rossby wave and the period. Gyral waves sharing the same node where the western boundary current leaves the coast to merge with the subtropical gyre, a sub-harmonic mode locking occurs, so that the average periods of the coupled waves are multiple of short periods.
Sea surface temperature anomalies during the warming and cooling phases
Referring to thermal anomalies of ocean surface, ocean-atmosphere exchanges mainly result from the latent heat flux. The impact on climate of these sea surface temperature anomalies, which either stimulate or, on the contrary, reduce evaporation, is substantial because they generate baroclinic instabilities that may lead to the formation of cyclonic or, on the contrary, anticyclonic systems of the atmosphere.
The direct impact of variations in solar irradiance on the sea surface temperature would be low if the gyral baroclinic waves did not come into resonance. In this case, the heat budget would be balanced, i.e. the input and output heat fluxes through the surface of the ocean would be equal (as a first approximation, if we ignore fluxes carried by ocean currents), and in the absence of sea surface temperature anomaly, the effectiveness of forcing would be of the order of 0.1 °C(W/m2)-1. But it is much higher, around 1.0 °C(W/m2)-1 in the conditions that have been prevailing for the last few thousand years.
As shown in the dynamic representation of the North Atlantic, surface temperature anomalies observed in the band 96-144 years are indicative of an imbalance between incoming and outgoing fluxes through the surface of the ocean. According to the equations of motion the oscillation of the thermocline of the baroclinic wave is in quadrature with respect to forcing. Lowering the thermocline accelerates the western boundary current which thereby reduces the temperature gradient between low and high latitudes. In turn, the increased heat flux from the equator to the poles tends to further lower the thermocline. This positive feedback induces a phenomenon of amplification of the oscillation of the thermocline. Acceleration of the polar current stimulates upwelling off the eastern boundary of the basin where the current lines tighten, i.e. the Canary Current in the North Atlantic, the Benguela Current in the South Atlantic, the West Australian Current in the South Indian Ocean, the California Current in the North Pacific, and the Peru (Humboldt) Current in the South Pacific, by vertical pumping effect without changing vorticity significantly. Cooling the polar current compensates warming the western boundary current due to acceleration, which prevents from runaway effect resulting from the positive feedback.
Due to these effects the observed thermal anomaly may be delayed relative to forcing, which occurs in the northern and southern part of the gyre. Besides, the surface temperature anomaly out the gyre, which reaches 0.10°C, is in phase opposition with respect to the anomaly around the gyre.
The functioning of long-period gyral waves is derived from the equations of motion.
How evolve the anomalies when the period increases?
Considering the gyral resonance for the 128-year period, a question arises: how evolve the anomalies when the period increases, knowing that both the wave damping due to friction and increase in the duration of exposition to solar irradiance of the mixed layer are proportional to the period but with antagonistic effects? The amplification factor, considering as constant the forcing terms, tends asymptotically to 1.7 regardless of the damping coefficient used to friction. Furthermore gyral resonance does not occur when the period of the oscillations of solar irradiance is less than 128 years. We can deduce that the bandwidth of subtropical gyres for radiative forcing is a low-pass band below one cycle per 128 years.
Where the earth is warming… or cooling
The earth does not warm evenly: these are the regions impacted by the resonant thermal anomalies of oceanic origin which warm or cool the first.
Baroclinic atmospheric instabilities
The gyral and tropical resonance producing positive or negative surface temperature anomalies these can induce high and low atmospheric pressure systems that affect the climate globally. To quantify the energy transfer from the thermal anomaly to the continents, the unperturbed state of the system in the absence of resonant thermal anomaly (produced by gyral waves) has to be considered at first, which implies that the average energy captured by the earth is completely re-emitted in space. This is only true if the energy transfers are averaged over one or even several years to remove fingerprints of non-resonant phenomena that cause an imbalance in energy budget during the annual cycle: this is the case, for example, of the formation of sea ice during the winter and its melting during the summer.
Then oceanic thermal anomaly is considered as a perturbation and the perturbed system tends to a new steady state. In the perturbed state the resonant thermal anomalies act either as a heat source, or on the contrary as a heat sink. The perturbation behaves as an isolated thermodynamic system because heat transfers between oceans and continents mainly involve latent heat with low shortwave radiative forcing. Minor effects are induced by a variation of humidity as a result of high or low pressure systems. A slight amplification effect may occur because energy gain resulting from downwelling longwave radiations outweighs the albedo effect due to low clouds when humidity increases.
In such a quasi-isolated thermodynamic system thermal transfers between oceans and impacted continental areas occur until a thermal equilibrium is established between the oceanic and continental anomalies. Processes that lead to this balance, i.e. how high and low pressure are formed from resonant thermal anomalies and move to the continents, result from baroclinic instabilities of the atmosphere. Due to the large heat capacity of seawater relative to the continents and to the feeding or to the draining of warm water at the antinode, resonant thermal anomalies warm or otherwise cool the impacted land areas without weakening significantly. Then, more global processes take over to warm or cool the continents globally as a result of long-period SST anomalies. Thus everything happens as if the perturbed state were deduced from the unperturbed by equalizing both the resonant ocean and land surface temperature anomalies, considered as perturbations.
Although the areas covered by oceanic thermal anomalies are small compared to the ocean surface, they generate atmospheric baroclinic instabilities that have a key role in the transfer of heat between the oceans and continents. However, the mechanisms involved differ depending on whether one considers the tropics or mid-latitudes. As we will see by referring to the rainfall oscillation in the band 5-10 years, thermal transfer, positive or negative, between the resonant oceanic anomalies and impacted continental regions is performed in two main ways. On the one hand the oceanic temperature anomalies at mid-latitudes deflect tropical cyclones to mid-latitudes or otherwise confine them within the tropical belt according to the sign of the anomalies. On the other hand they promote depressions, anticyclones and troughs at mid-latitudes, these atmospheric phenomena being aroused under the effect of the polar or sub-tropical jet-stream. In all cases, atmospheric baroclinic instabilities may generate heat transfers to the synoptic scale[i], mainly in the form of latent heat.
Rainfall in the band 5-10 years allows to highlight how certain land areas are affected by atmospheric baroclinic instabilities induced by resonant thermal anomalies of oceanic origin. Indeed, the transfer of heat from the oceans to the continents mainly resulting from evaporation and condensation processes according to what has been seen previously, how rainfall varies over time characterizes the impacted regions.
Resonant rainfall oscillation
To highlight how some land areas are affected by atmospheric baroclinic instabilities induced by resonant thermal anomalies of oceanic origin, it is convenient to use monthly rainfall height data which are known since 1901 on the terrestrial scale. Indeed, heat transfer from the oceans to the continents mainly resulting from processes of evaporation and condensation according to what has been seen previously, how rainfall varies over time characterizes the impacted areas.
The resonant oscillation of precipitation, i.e. linked to the resonant origin of oceanic thermal anomalies, is recognizable by its large amplitude in the characteristic bands of the periods 1/2, 4 and 8 years with a low amplitude of the annual oscillation. Resulting from depressions formed or guided by resonant thermal anomalies, rainfall in the impacted areas is distributed evenly between seasons due to the moderator effect of the oceans. Indeed, the thermal anomalies produced by annual waves reach their maximum during the boreal / austral winter.
In contrast, non-resonant precipitation exhibits strong seasonality, whether due to tropical cyclones, tropical and extra-tropical depressions or monsoon, i.e. seasonal changes in atmospheric circulation and precipitation associated with the asymmetric heating of land and sea.
The dynamic of sea surface temperature anomalies and the oscillation of rainfall in a characteristic frequency band reveals the mechanisms leading to atmospheric baroclinic instabilities and the formation of high and low pressure systems to cause oscillation of precipitation. In particular, the analysis of rainfall in the band 5-10 years allows to connect resonant oceanic and atmospheric phenomena unambiguously because sea surface temperature anomalies of 8-year period are well identified, resulting from the higher baroclinic mode in the three tropical oceans, while not being sensitive to ENSO. In addition, the 8-year period is close to the time required to balance the oceanic and terrestrial thermal anomalies of the perturbed state, which reduces their phase shift.
This analysis emphasizes the regions impacted rapidly by the resonant thermal anomalies of oceanic origin where baroclinic instability of the atmosphere originates preferentially. These baroclinic instabilities are most active when the resulting systems of high or low pressure are stimulated and guided by the jet-streams, these ribbons along a winding path through which flows from west to east a strong and rapid airflow at high altitude. The strongest are the polar jet-streams, around latitude 60°, while the subtropical jet-streams are located between 20° and 40° latitude, which explains the key role of subtropical gyres on climate variability.
To obliterate the changes in rainfall linked to the local context, particularly the relief, latitude and proximity to the ocean, rainfall is reduced, i.e. divided by its standard deviation. Being dimensionless, the temporal variations of reduced rainfall are homogenized this way on global scale and a causal relationship can be established between sea surface temperature and rainfall anomalies. The amplitude of reduced rainfall anomalies highlights areas primarily impacted by oceanic thermal anomalies. Phase allows to discern transfer mechanisms.
The main areas subjected to resonant rainfall oscillation, that is to say those that warm or cool at first, are a) The south-west of North America, b) Texas, c) The south-east of North America, d) The north-east of North America, e) The southern Greenland, f) Europe and Central and Western Asia, g) Region of the Río de la Plata, h) Southwestern and southeastern Australia, i) The Southeast Asia.
The climate at different time scales
State of the art
In many cases paleoclimatology is still at the stage of speculating what may have been the underlying causes of rapid climate transitions, cycles and forcing effects. This leads us to how the climate system responds to external stimuli with its own dynamics. When the internal dynamics of the climate system is consistent with an external stimulus, a resonance phenomenon occurs. The study of such resonances therefore tells us about the internal dynamics of the Earth system, spearheading our understanding of the mechanisms involved in vagaries of climate.
Understand the vagaries of climate becomes possible from the archives of past climate. We have, in fact, over the last decade data of exceptional quality for tracing the climate up to several million years before present (BP), with a resolution of a few years. This technological feat was made possible through the analysis of stable isotopes[ii] in ice cores from the Arctic and Antarctic ice caps and in sediment cores from the ocean trenches.
The analysis of ice cores plays a key role in understanding the different mechanisms involved in the natural evolution of climate over the last major cycles of glacial and interglacial periods. The oldest records obtained to date cover 800,000 years, the second half of the Quaternary. Deuterium data 2H obtained from Antarctica Dome C ice core (European Project for Ice Coring in Antarctica EPICA) are used for global mean temperature estimate in the southern hemisphere considering for calibration 5.53‰ 2H/°C [Jouzel et al, 2007]. 18O data obtained from Greenland Summit Ice Cores GISP2 (Greenland Ice Sheet Project 2 Ice Core), Grootes and Stuiver,  are used as proxies of global mean temperature in the northern Atlantic. 18O data are calibrated considering a variation of 0.67‰ 18O/°C [Jouzel and Merlivat, 1984].
Sediment cores allow the study of the composition of the different layers of sediment accumulated over time on the ocean floor. There are fossil microorganisms composed of calcium carbonate. By studying the « abundance ratio » of 18O and carbon isotope 13C, past climates can be reconstructed going back millions of years. They establish how the oceans have evolved in different climatic periods (temperature, salinity, nutrients, …).
Understanding the temporal variation of cosmic radiation and solar activity during the Holocene allows specifying the solar-terrestrial relationship. 10Be and 14C which are stored in polar ice cores and tree rings, offer the opportunity to reconstruct the history of cosmic radiation and solar activity. In series obtained by Steinhilber et al.,  different 10Be ice core records from Greenland and Antarctica are combined with the global 14C tree ring record to provide total solar irradiance variations (W/m2).
The last few million years have been punctuated by many abrupt climate transitions. Many of them occur on time-scales of centuries or even decades. The ability of climate to change abruptly has been one of the most surprising outcomes of the study of Earth history [e.g., Jouzel et al 1987, Taylor et al 1993; Petit et al 1999, Dansgaard et al 1993; Alley, 2000, Jouzel et al 2007].
Climate changes at the planetary scale are responses to external forcing mechanisms, that’s what we strive to show in this chapter. The role of the Sun in climate variability, and specifically solar irradiance fluctuations which reflect the internal dynamics of the Sun but also orbital forcing that alter the net radiation budget of the Earth are frequently referred [e.g. Magny, 1993, Karlén and Kuylenstierna, 1996, Chambers et al., 1999, Bond et al., 2001, Gavin et al., 2011]. Nevertheless, the internal mechanisms involved in long-term climate variability are poorly understood. The idea often mentioned that the deep ocean is the only candidate for driving and sustaining long-term climate change (of hundreds to thousands years) because of its volume, heat capacity, and inertia [e.g. Maslin et al, 2001], can easily be counteracted in the glow of the present results. Indeed, variations in the flow and temperature of deep water that is known to have a direct effect on global climate is a consequence of a mechanism of much greater scope involving the resonance of sub-tropical oceanic gyres.
The Holocene began with the interglacial period, about 12,500 years ago. During this period there has representative indicators of both solar irradiance and global mean temperature in both hemispheres. We can therefore deduce information about the internal dynamics of the climate system from the coupling between solar radiation and the global mean temperature.
The current climate
The 128-, 256- and 768-year period components are obtained by filtering the total solar irradiance in the bands 96-192, 192-576 and 576-1152 years, multiplied by the forcing effectiveness that is taken equal to 1.0 °C(W/m2)-1 for the band 96-192 years, and 1.2 °C(W/m2)-1 for the following bands so that the amplification factor increases with the period (to reach 1.7 asymptotically for long periods). The forcing effectiveness of the 768-year period component was observed from the ice core records during the Holocene. Furthermore each component is shifted by a quarter period in order to be in quadrature with respect to forcing.
The global mean temperature into the band 96-192 years increases by 0.27 °C from 1930 to 2000, which matches with the sea surface temperature anomaly of the gyre of the North Atlantic at mid-latitudes that ranges from ±0.14 °C. However, some biases are to be taken into account. Firstly the sea surface temperature anomaly must be multiplied by the factor 1.3 for homogenizing the bandwidths: this ratio is determined by comparing the amplitude of the sunspot number when it is filtered in both bands 96-144 and 96-192 years because, due to the limitation of the series, the amplitude of the sea surface temperature was performed in the band 96-144 years and not in the characteristic band 96-192 years.
On the other hand the sea surface temperature anomaly refers to the North Atlantic gyre whereas the global mean temperature involves the five sub-tropical gyres. As we see in the figure, the anomalies are weaker in the southern hemisphere than in the northern hemisphere so that the anomaly in the North Atlantic overestimates the variations in the Earth’s average temperature. Discrepancies between the two hemispheres is especially noticeable between 1950 and 1960 when the sea surface temperature increases significantly in the northern hemisphere.
Nevertheless, one can conclude that, for the band 96-192 years, the two estimations of the Earth’s average temperature, i.e. from the solar irradiance whose effectiveness is deduced from ice core records, and from the sea surface temperature anomaly, are of the same order of magnitude, what is however a significant result.
As regards the 12-96 year band to which the coupling does not occur by direct forcing between solar irradiance and the gyral wave the different components are harmonics of gyral waves of longer periods. The sea surface temperature anomaly observed at high latitudes of the subtropical gyres is therefore considered. The components of the average global temperature of 16-, 32- and 64-year periods are obtained by filtering within the bands 12-24, 24-48 and 48-96 year of sea surface temperature in regions considered as representative of exchanges between the oceans and the continents.
Let’s return to the observed and modeled temperatures. The warming observed over the second half of the 20th century is well reconstituted from the gyral resonance. The rise in temperature observed from 1940 to 1960 is due to harmonics, within the band 12-96 years, of long period gyral waves, in the northern hemisphere exclusively.
Gyral thermal anomalies of 128, 256 and 768-year period increased simultaneously during the 20th century, which is attributed to the oscillations of the solar irradiance. The first component rose by 0.27 °C from 1930 to 2000, the second by 0.30 °C from 1885 to 2007 and the third has increased regularly by 0.20 °C since 1850, without having reached its maximum yet. For the late century, the 64-year period component rose by 0.23 °C from 1975 to 2004, which is attributed to the main harmonic of the gyral resonance.
The glacial-interglacial period
Although the study of Holocene alone brings key elements necessary for understanding current climate variability, new properties of gyral resonance emerge when looking at the glacial-interglacial era, properties that will allow us to raise some mysteries surrounding the climate of the past few million years.
A very wide range of frequencies
To summarize what we have seen in the previous chapters, three systems of gyral waves coexist depending on whether they are forced by the warm and cold water sequence inherited from the tropical oceans, solar cycles or Milankovitch cycles. Periods vary between 1/2 and nearly 100,000 years. The frequency range covered by the gyral resonance is considerable, of the order of 19 octaves: just to be convinced, imagine a piano keyboard which is almost 3 times more extended than the standard keyboard of 7 octaves!
What is the future of our planet?
The Response of the ice cap to global warming
One of the most important consequences of global warming is melting the polar ice. This is followed with the greatest attention. In particular, the satellite measurement of the concentration of sea ice by microwaves provides relevant information on the temporal evolution of the polar ice: the amplitude of the variations in the percentage of ice highlights the most impacted areas.
The filamentary structure of the main anomalies observed in the Arctic is parallel to the southern limit of the ice, which shows unequivocally that the melting or the glaciation are tightly controlled by the ocean. In Antarctica, the structure of the anomalies is more diffuse and more evanescent. Currently the anomalies disclose a very active replenishment of the ice, the acceleration of the phenomenon being due to the change in the albedo. In all cases, melting occurs primarily where sea ice is in contact with the antinodes of baroclinic quasi-stationary waves after they have merged with the North Atlantic drift current in the northern hemisphere or with the Antarctic circumpolar current in the Southern Hemisphere.
How will the Earth’s temperature change over the next decades?
These observations leave no doubt about the resonant character of melting ice cap. At the end of the millennium, the amplitude of the sub-harmonics of 128, 256 and 768-year period is such that it gives rise to strong positive temperature anomalies that are almost in phase in the five subtropical gyres. Their fingerprints are recognizable where antinodes of gyral waves are in contact with sea ice.
As we have seen, the Earth’s average temperature is deduced from the gyral thermal anomalies mainly at high latitudes. These are the sum of components defined in the bands 12-96 years and 96-1152 years, the latter itself being the sum of three components in the band 96-192, 192-576, 576-1152 years.
If the long-period components of the band 96-1152 years can be extended until 2045, this is not true for the band 12-96 years. Long-periods are indeed obtained from proxies of solar irradiance, shifted by a quarter period. This shift is the delay with which the variations in solar irradiance impact the gyral thermal anomalies.
As against, the resonant thermal anomalies in the band 12-96 years being not produced directly from the oscillations of solar irradiance, they appear as harmonics of long-period oscillations around the subtropical gyres. Their behavior seems unpredictable. Only speculation on the amplitude of the forthcoming oscillations allows establishing different scenarios (as this occurred 64 and 128 years ago), both hypotheses allowing to frame prediction by a high and low estimate.
The sum of the components exhibits a plateau until 2015-2020 and then inexorably decreases. This cooling will continue for centuries to suit the component of the 96-192 and 192-576 year bands, but very gradually because it is partly offset by the rise of the component of the band 576-1152 years. This is only a long-term trend because, due to components of shorter periods, other maxima will probably occur, but lower than that observed between the late 20th century and early 21st that resulted from a combination of exceptional circumstances due to the simultaneous increase in all components of the 48-1152 year band.
Anthropogenic warming and greenhouse effect
The anthropogenic contribution, added to the natural variability, allows replicate quite accurately the global temperature Tmg until today. Note, however, discrepancies about warming that occurred during the 1940s and between 1970 and 2000. In both cases, gyral waves are involved. Regarding warming that occurred:
- during the 1940s, it was mainly due to the oscillation of 64-year average period, which is evidenced from sea surface temperature anomalies, mainly at mid-latitudes of the 5 subtropical gyres. The spatial variability of these anomalies is substantial, especially between the two hemispheres, making sampling of contributory areas difficult.
- between 1970 and 2000, the model anticipates the rise of observed temperature, which suggests that a few years elapse between the formation of sea surface temperature anomalies and their continental impact: the delay is of the order of 5 to 8 years.
Forecasts show that natural variability will be decisive in the next decades, both models indicating a decline in Tmg beyond 2020. The different assumptions about the increase of CO2 in the coming decades have little influence on results; this is why only the most pessimistic scenario corresponding to an increase of 2 ppmv/year is considered. Also, although very significant as it represents about a third of the warming observed over the second half of the 20th century, anthropogenic warming does not justify the catastrophist assumptions advocated by the IPCC because of its slow growth in the coming decades, regardless of future emissions.
The position of the IPCC
For now, the IPCC does not include, or misuse, natural climate variability in climate models. It will take time for the concepts presented in this article be accepted by the scientific community, climatologists and oceanographers. Not that they are refuted, but because they are outside the mainstream and require a soak period.
The argument about the reliability of current models, despite their recognized imperfections , is based on their multiplication (18 teams) and their convergence. In all cases the introduction of human influence is essential to account for the warming observed since the mid-20th century because these models do not incorporate the resonance of oceanic baroclinic waves. Based on opportunistic assumptions, these models inevitably give biased results when applied outside the narrow period from which they have been calibrated. Thus the global temperature forecasted from the 38 current models exceeds the observations, the bias being widening over the years, which brightly demonstrates that these models over-react to carbon dioxide.
The IPCC asserts further that two observations betray human influence. The first is greater warming over land than over oceans, and more warming to the ocean surface than at depth. The second observation is that while the troposphere (the lowest atmospheric layer) warms, the stratosphere, that is to say the layer located just above, cools.
The interpretation of these observations is erroneous, both confirming the resonance phenomenon of oceanic baroclinic waves. On the one hand the oceans warm or cool not uniformly but at the antinodes of quasi-stationary waves, the thermocline being a thermal barrier between the surface and deep waters. Compare the average global ocean temperature to that of the continents is meaningless. As against the temperature variation at the oceanic antinodes of quasi-stationary waves located at mid-latitudes is very faithfully reflected by the change in global surface temperature of continents, whatever the time scale. On the other hand the troposphere warming confirms that it comes from the Earth’s surface, i.e. the oceans, not from the direct impact of solar activity on the stratosphere.
Another concept carried by the catastrophist theory and maintained by the most prestigious journals is possible shutdown of the thermohaline circulation due to global warming, which could result in Europe and in regions of high latitudes in a significant drop in temperature which would follow global warming. Thermohaline circulation, which indicates deep circulation of cold and salty water that occurs at high latitudes, acquires its kinetic energy during the sinking of dense water in the depths of the ocean. However, under this scenario, the increase in temperature should increase evaporation in the tropics and precipitation in regions of high latitudes, leading to a massive influx of fresh water in the vicinity of the poles, so a decreased marine salinity and density of surface water, hampering their diving in the ocean depths. This ignores the functioning of major ocean currents, especially gyre currents and western boundary currents associated with them, which results from wind stress, westerly winds at mid-latitudes and trade winds in the tropics, Coriolis forces due to rotation of the earth, gravity forces, and solar activity causing the gyral resonance, the thermohaline circulation being only involved at the northern or southern limit of the oceans, hence its minor role. It is indeed like an overflow while the variability of gyre currents reflects that of the solar irradiance.
The IPCC practices ‘cherry picking’, i.e. a very selective information is disseminated. If we take the example of the announcement « 2014, the warmest year on the globe », temperature differences relative to the normal of the twentieth century simply show that the plateau observed since 1998 continues, except measurement errors. If Europe has had a particularly warm year that must not obscure the fact that North America has experienced exceptional cold spell. Furthermore the map of temperature anomalies accredits the observed warming since 1980, which should not be a source of anguish. By cons cooling or low ocean warming at Western antinodes of quasi-stationary waves announces next cooling of the surface of the continents because of the large heat capacity of sea water compared to that of the continents.
Inform, persuade, beyond the dogmas and myths
The hyper-simplification of the IPCC between temperature and CO2, avoids the question of whether there are other causes. The observation of facts is not the major concern of theorists and modelers, who do not seek to know the actual climate change or its mechanisms, which they do ignore in their forecasts, while the real evolution is not that they predict. This focus, by default, on the greenhouse effect, is indicative of the state of climate discipline. Despite considerable progress in observing (including satellite) and data processing, climatology has been in a conceptual impasse for fifty years.
In this context, the study of resonantly forced planetary waves of very long wavelength, which has been ignored so far, is promising in physical oceanography and climatology. This may be a step forward in the areas that are still poorly understood, such as the formation and stability of the subtropical gyres and long and very long-term climate variability, citadels that remained invincible for more than half a century and therefore, can be overcame only by using new concepts. This article provides a physical basis for a resonant phenomenon that many researchers have foreseen for a long time, allowing to explain how the effectiveness of solar and orbital forcing could vary by a factor of 5 during glacial-interglacial periods, as well as the causes of global warming that prevailed during the second half of the 20th century, the anthropogenic component contributing for about a third. Its growth in coming decades should slow down regardless of future emissions, which in fine reports a slow cooling.
Remains a heavy work ahead, which still requires a lot of patience and perseverance, to urge the community of oceanographers and climatologists to broaden the scope of the expression and exchange of ideas, which implies disinterestedness, pragmatism, and questioning of dogmas and policy based on catastrophism. The exaggeration of anthropogenic warming, of scientific origin, drifted towards politics, then ideology and religion to finally become a global financial scam. Making climatology a science, a fight of every moment…
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[i] Heinrich events, first described by marine geologist Hartmut Heinrich, occurred during the last glacial period. During such events, numerous icebergs broke off from glaciers and traversed the North Atlantic. The icebergs contained rock mass eroded by the glaciers, and as they melted, this matter was dropped onto the sea floor as « ice rafted debris ».
[i] Dansgaard–Oeschger events (often abbreviated D–O events) are rapid climate fluctuations that occurred during the last glacial period.
[i] The dew point or dew temperature is the lowest temperature at which an air mass may be subjected, with fixed pressure and moisture, without the occurrence of a water liquid formed by saturation.
[ii] The term stable isotopes usually refers to isotopes of the same element. The relative abundance of such stable isotopes can be measured experimentally (isotope analysis), yielding an isotope ratio: relative abundances are affected by isotope fractionation in nature, hence their interest in geochemistry.
[i] In meteorology, synoptic scale phenomena are characterized by a length of several hundred to several thousand kilometers and a period of several days.
[ii] The horse latitudes, between 30 and 35°N or S, define an area highs, the quiet zone created by the subtropical descending column of the Hadley cell. It is said that the term comes from the days when Spanish sailing vessels transported horses to the West Indies. In the absence of wind in these latitudes prolongation of trip resulted in shortages of food and water and the crews were sometimes forced to throw horses overboard or kill them to prevent starvation on board.
[i] A standing wave is the phenomenon resulting from the simultaneous propagation in different directions of several waves of the same frequency. In a standing wave nodes remain fixed, alternating with antinodes.
[i] The fundamental quasi-stationary wave is in phase with forcing. In sound pipes, strings and vibrating membranes form harmonics whose period is a divisor of that of the fundamental wave. As regards the long ocean waves, sub-harmonics are formed whose period is a multiple of that of the fundamental wave as occurs for high rank baroclinic modes.
[i] Upwelling. Here, this term indicates an upward flow of deep water, therefore cold. The upwelling is associated with the functioning of tropical resonant waves.
[i] Western boundary currents. Western boundary currents, warm, deep, narrow and fast are formed along the western boundary of the ocean. They carry warm water from the tropics to the poles, forming the western branch of the subtropical gyres. It is the Gulf Stream (North Atlantic), the Brazil Current (South Atlantic) the Agulhas (South Indian Ocean), the Kuroshio (North Pacific), and the western boundary currents of the subtropical gyre in the South Pacific.
[ii] Jet-streams are fast winds aloft blowing from west to east. Along a curved and sinuous path, they play a major role in atmospheric circulation as they participate in the formation of depressions and anticyclones at middle latitudes, which then move under these powerful atmospheric currents.
[iii] Geostrophic currents are derived from measurements of wind, temperature and satellite altimetry. The calculation uses a quasi-stationary geostrophic model while incorporating an ageostrophic component resulting from wind stress. Geostrophic current thus obtained is averaged over the first 30 meters of the ocean.
[i] The Coriolis parameter f is equal to twice the speed of rotation Ω of the earth multiplied by the sine of the latitude φ: f = 2Ωsin φ. The Coriolis force, on the other hand, is perpendicular to the direction of movement of the moving body. It is proportional to the velocity of the body and the speed of rotation of the medium.
[ii] Baroclinic wave. In contrast with barotropic waves that move parallel to isotherms, baroclinic Rossby or Kelvin waves cause a vertical displacement of the thermocline, often of the order of several tens of meters. The seconds are usually slower than the first.
[i] SOI (Southern Oscillation Index). The SOI is the amplitude of the Southern Oscillation; it is a measure of the monthly change in the normalized atmospheric pressure difference at sea level between Tahiti and Darwin (Australia).
[i] In a homogeneous medium, propagation in a given direction of a monochromatic wave (or sine) results in a simple translation of the sinusoid at a speed called phase velocity or celerity. In a non-dispersive medium, the speed does not depend on the frequency (or wavelength). In this case every complex wave is the sum of several monochromatic waves that also undergo an overall translation of its profile, this without deformation. In contrast, in a dispersive medium the phase velocity depends on the frequency and the energy transported by the wave moves at a speed lower than the phase velocity, said group velocity.
[i] The dispersion relation, connecting the pulsation (or frequency) of a free wave (unconstrained) ω = 2π/T to its wavelength, takes a very simple form when the waves are non-dispersive, as is the case of the Kelvin and Rossby waves of long wavelength. In the first case, ω/k = c where k is the wave number (reciprocal wavelength) and in the second case ω/k = –c/(n+1), the sign – indicating that the wave propagates westward. c is the phase velocity of the first baroclinic mode, n is the rank (order) of the meridional mode.
[i] The Walker Circulation, El Niño, La Niña. In the tropics, the direct airflow on the surface towards the equator (called Hadley cell) forms the inter-tropical convergence zone. The Coriolis force is small at these latitudes but enough to divert to the west the circulation, giving the trade winds (north-east in the northern hemisphere and south -east in the south). The Humboldt Current from Antarctica cools the coast of South America. So there is a large temperature difference between the western and eastern Pacific that leads to direct circulation similar to Hadley circulation (air masses rise close to Asia and Australia and down along the coast of South America). If convective activity decreases in the western Pacific, the eastward aloft flow decreases or stops, cutting cold air intake in the eastern Pacific and the return surface flow weakens. The opposite of El Niño is La Niña. Convection in the western Pacific increases in this case which amplifies cell Walker bringing colder air along the coast of America.