From chaos to pattern in ocean-driven climate

Part 1

The Atlantic Meridional Overturning Circulation (AMOC) owes its existence to an instability. Periodically, the Gulf Stream bringing warm water from the Caribbean to Europe combines in a positive feedback with the downwelling of cold water in the Northeast Atlantic Norwegian Sea. “Deep water formation” is what links the global surface and deep ocean floor circulations that otherwise flow almost independently of each other. Water always gets cold in the Arctic of course but in the Norwegian Sea what is different is the extra salinity of the water owing to its transport from warmer regions with the Gulf Stream. Thus you get very cold and very saline water which is exceptionally dense and downwells energetically to the ocean floor, acting as a propeller of the global ocean deep circulation.

Now this downwelling is self reinforcing because it draws up more water with the Gulf Stream which it mutually strengthens. Also the south flowing deep current driven by the downwelling also further impels the Gulf Stream. So what we have is a positive feedback.

What climate science fails to understand is that positive feedback does not cause a runaway process for all time, until it causes the end of the world. Instead, in the real world, positive feedback causes a temporary excursion of self reinforcement which is self-terminating because it sets in motion processes that will terminate it. In the case of the North Atlantic, this is Greenland ice melt caused by the warming influence of the strengthening Gulf Stream. This melt causes a raft of fresh water that interferes with the saline downwelling in the Norwegian Sea. So the positive feedback excursion is choked off.

But weakened Gulf Stream means cooling and eventually a resumption in the cold downwelling up North which strengthens the Gulf Stream, the the positive feedback switches back on. And so on…

What you have is an intermittent positive feedback resulting in alternate strengthening and weakening of the Gulf Stream. This gives rise to the oscillation called the AMO. (The AMO is an oceanic, not atmospheric or astrological phenomenon. It is driven like all climate processes by the ocean. The tail does not wag the dog and the sign of the zodiac plays no role.)

But this AMO oscillation is not regular or monotonic. It is not always 60 years in period. Palaeo data makes this clear, sometimes it is shorter and sometimes longer in period.

Ocean circulation like all liquid flow tends toward turbulence and looking at Nullschool animations of ocean currents nicely shows how turbulent it is. Turbulence represents high dimensional chaos. However internal positive feedbacks such as the AMOC involving Norwegian Sea downwelling as described above, have an important interaction with chaotic systems. Positive feedback, otherwise known as “excitability” of a system, reduces the dimensionality of chaotic systems, changing high dimensional turbulence to lower dimensional chaos. Lower dimensional chaos is much more interesting than high because it is near the border of chaos and linearity that emergent pattern formation arises – such as an intermittent AMO with the AMOC fluctuating in strength.

Climate science tries to write off chaos as being high dimensional turbulence only. They don’t realise that two things can lower the dimensionality of chaos to the region where climate patterns and oscillations can arise from the system. These are internal feedback as already described, but also external periodic forcing, from cycles such as the annual cycle, tides and solar oscillations. For instance solar oscillations by themselves don’t have enough energy to change climate very rapidly – the ocean has too much heat capacity for that. But if solar cycles periodically force the internal feedbacks of the ocean which possess much more energy, then they can entrain oceanic climate oscillations.

If external forcing is strong, then the system oscillation will mirror the forcing oscillation. However often periodic forcing of nonlinear oscillations is weak, and here things get more complicated. The emergent frequencies in a weakly periodically forced oscillator can be very complex and bear little resemblance to the forcing frequency. This makes it harder to analyse and identify what if anything a natural oscillation is being forced by. There probably are mathematical clues but you would have to do the maths to identify them.

Climate scientists such as Mann who deny natural oscillations are denying chaos. The ocean driven climate system has all the ingredients needed for complex chaotic dynamics:

– an open dissipative system transporting heat from equator to poles on a rotating planet covered with a liquid film

– turbulence inevitably develops in flowing liquid especially with complex coastlines and ocean topography

– both internal positive feedbacks – excitability – and external periodic forcing, such as solar or complex tidal, are available to lower the dimensionality of chaotic circulation to low dimensional regimes where spontaneous pattern formation and oscillations arise.

The AMO as an intermittent oscillation of the AMOC is a good example of pattern from reduced chaos dimensionality caused by internal feedback plus possibly external forcing.

There is no excuse to saying natural oscillations can’t exist because “we don’t know what causes them”.

https://www.nature.com/articles/s41612-020-00147-6

Another recent paper showing AMOC accelerations and decelerations corresponding to warmer and colder climatic periods respectively over the last 50,000 years:

https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2020PA004068


Part 2

My comment on Kip Hansen’s post “Chaos and Weather” at WattsUpWithThat, July 25, 2020:

https://wattsupwiththat.com/2020/07/25/chaos-and-weather/

Kip

8F97DF63-1A37-4EA5-8B79-8CCE27ED6217

Your last figure is a nice diagram of Hopf bifurcations leading up to the transition to chaos. Generally it is at the border of transition to chaos, where the system is still low-dimensional, where the interesting emergent pattern phenomena occur; rather than in high dimensional turbulent “full blown chaos”.

Reading some research in chemical engineering by Matthias Bertram and others, I came to realise that one scenario highly relevant to the climate system is the opposite of the Hopf diagram; that is, rather than the progress of an initially linear system over the threshold into chaos, the transition of an already chaotic turbulent system from high down to lower dimensionality, nearer to the Hopf boundary regime where pattern formation can occur. In other words, the reduction rather than the increase in chaotic behaviour and dimensionality.

How can this occur? Bertram and others give some interesting examples from chemical engineering model systems on thin films, including the platinum-catalysed oxidation of CO and the Belousov-Zhabotinsky reaction. Bertram’s goal as an engineer was to control chaotic processes, and he shows two ways to do this: adding feedback, and adding periodic external forcing. To quote:

Spontaneous pattern formation and spatiotemporal chaos (turbulence) are common features of spatially extended nonlinear systems maintained far from equilibrium. The aim of this work is to control and engineer such phenomena. As an example, the catalytic oxidation of carbon monoxide on a platinum (110) single crystal surface is considered. In order to control turbulence and to manipulate pattern formation in this reaction, two different control methods, global delayed feedback and periodic forcing, are employed.

https://pure.mpg.de/rest/items/item_740669/component/file_740668/content

Click to access Influence_of_time_delayed_global_feedbac20160726-18806-1lqlhg4.pdf

In a nutshell what they do is reduce the dimensionality of the chaotic system by either of these two factors, delayed feedback or periodic forcing. In this way they reduce the “chaoticness” of the system bringing it to the borderline chaos region where interesting and – for them – useful pattern and oscillation emerge.

This made me think of oceanic systems where feedbacks are linked to oscillation. For instance ENSO. You have the Bjerknes feedback whereby Peruvian oceanic upwelling (linked to the Humboldt current) interacts with the trade winds to create intermittent positive feedback which reinforces both the upwelling and the trade winds. (The cold upwelling sets up a sea surface temperature gradient which impels the trade winds).

Another longer term oscillation is the Atlantic Meridional Overturning Circulation (AMOC) which oscillates in strength, giving rise to the AMO – Atlantic Multidecadal Oscillation. Here again there is an intermittent positive feedback. The Gulf Stream increases the salinity of sea surface water in the far North Atlantic and the Norwegian Sea. As this water cools it becomes very dense, causing substantial downwelling all the way to the ocean floor resulting in the “deep water formation” that drives the ocean circulation system. This down welled water flows back south along the ocean floor, completing the 3D loop of the AMOC and reinforcing the Gulf Stream.

In both these cases, ENSO and AMOC, it’s fair to say that the ocean circulation system in 3D is chaotic and turbulent. A glance at the NullSchool ocean circulation animations will confirm this:

https://earth.nullschool.net/#current/wind/surface/level/orthographic=-40.76,39.11,587

Applying the paradigm of Matthias Bertram to this, we can suggest that the presence of feedback in these oceanic systems – the Bjerknes feedback with ENSO and the salinity feedback with AMOC – is “reducing the dimensionality” of the turbulent chaotic circulation systems and causing quasi-regular oscillations to arise.

And as Bertram also found with the BZ reaction, periodic forcing can also bring about emergent oscillation in a chaotic ocean system. ENSO is known to be phase-locked to the annual cycle such that El Niños typically happen at Christmas (this their name).

Tziperman, Cane and Zebiak have shown how ENSO can be modelled as a delayed oscillator periodically forced by the annual cycle:

https://dash.harvard.edu/bitstream/handle/1/3425922/Tziperman_ControllingSpatiotemporal.pdf?sequence=2

Climate scientists and modelers try to write off chaos as just noise in the evolving climate system. They may be right if they are talking about only high dimensional turbulence. However they miss the fact that both feedbacks and external periodic forcing (from annual, solar and other astrophysical sources) can reduce the dimensionally of climate subsystems with the result of emerging pattern and oscillation. This can be on many timescales up to century and millennial.

This process, the reduction of dimensionality of chaotic climate systems by feedback or periodic forcing, provides a paradigm to understand how observed fluctuations and oscillations occur in the climate where a direct proximal cause seems elusive. ENSO, AMO and PDO are some examples. Here a real case can be made for chaotic-nonlinear dynamics being the cause of much more substantive climate change than just short term noise. It makes such a model the null hypothesis for much natural ocean driven climate change that is observed over many time scales.

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