21st Century Science Initiative Grant: Studying Complex Systems
Chapel Hill, NC, USA
Researcher: José A. Rial, Ph.D.
Grant Title: Synchronization of polar climate variability over the last ice age: In search of simple rules at the heart of climate's complexity
Grant Type: Research Award
Program Area: Studying Complex Systems
Duration: 4 years
The term synchronization is used here to describe the nonlinear frequency and phase locking that occurs when two or more coupled oscillators adjust their (initially different) rhythms to a common frequency and constant relative phase. In complex biological and ecological systems synchronization is a widespread phenomena, and some of the most intriguing areas of research in neuroscience include the study of synchrony among far away regions of the brain, and its behavioral meaning. Available evidence suggests that synchronization is also a common process in the earth’s climate, but research on detecting its presence and documenting its consequences is still at a very early stage. Though synchronization has mainly been studied in relatively low-dimensional discrete systems or networks, the possibility of similar dynamics occurring in extended spatiotemporal systems such as the earth’s climate could open an important new interdisciplinary area of research. The climate system is complex, whatever our definition of complexity may be, but if that complexity can be reduced in some measure by detecting and recognizing long-range symmetries caused by synchronization, our understanding of climate dynamics would greatly benefit. If applied to the history of climate, as proposed here, detection of synchronization among paleoclimate time series can likewise benefit climate science by explaining hitherto poorly understood processes.
For instance, one challenging problem is to explain the cause(s) of the last ice age’s rapid temperature variations, and whether such abrupt changes in the climate are global, rather than confined to northern latitudes and especially to the Arctic. Examples of the abruptness of climate change are best recorded in Greenland’s stable isotope climate proxies obtained from ice cores. These records exhibit large, sudden warming events (up to 15oC warming in high latitudes, 4-5oC in mid-latitudes) that last from centuries to several millennia, and occurred at least 24 times during the last 100ky (1ky=1000 years). Generally known as the Dansgaard-Oeschger (DO) temperature fluctuations, the transition to the high temperature state in the DO occurs in a matter of years or decades, and hence the importance of understanding the mechanisms of these events. If the climate system is capable of sudden temperature jumps in timescales comparable to a human life, and without the intervention of humans, it is urgent that we understand why, especially since humans are irresponsibly disturbing the climate system in ways that, it has been suggested, could possibly trigger abrupt climate change.
During the last glaciation the climate of the Polar Regions evolved in complicated ways, and as the ice core data from both Greenland and Antarctica reveal, there is suggestive evidence that the climatic fluctuations of the two poles are not independent of each other. For instance, recent highresolution data show that there is a phase shift of one-quarter of a period (π/2) between the southern and northern records that results in that Antarctica warms while Greenland is cold and as Antarctica begins to cool Greenland rapidly warms. This phenomenon has been known among researchers as the bipolar seesaw, though neither its origin, nor that of the phase shift, is clear or understood. The bipolar seesaw hypothesis proposes that anti-phase temperature shifts between the two Polar Regions are likely to be influenced by the Atlantic thermohaline conveyor-like circulation, which massively distributes heat to the two hemispheres. But how the conveyor links the poles, what is the physical meaning of these phase shifts, or what mechanisms cause the seesaw is not known, nor is there a model with enough explanatory power to describe it from first principles.
I propose that the simplest explanation of the data is that the paleoclimate oscillations of the Polar Regions are synchronized. To represent polar climate variability I borrow from the work of climatologist Barry Saltzman, who three decades ago showed how climate oscillations of polar temperatures may be explained by the nonlinear interaction between just two variables: sea ice extent and mean ocean temperature. Saltzman’s model explains that mean ocean temperature begins to increase when sea ice reaches its maximum extent. This is because sea ice is a very effective heat insulator, while a large portion of the ocean is still receiving solar heat. Eventually, after several hundred years of diffusive warming, the ocean reaches a threshold temperature that forces sea ice to retreat. As sea ice rapidly retreats polar ward accelerated by the ice-albedo positive feedback the ocean releases its stored heat and slowly cools. When the ocean becomes cold enough, sea ice begins to grow back advancing rapidly equator ward, again accelerated by the ice-albedo positive feedback. This cyclic build up and release of stored thermal energy is best described physically as a relaxation oscillation, and mathematically as the solution to the well-known nonlinear van der Pol differential equation. Saltzman’s two variables play a similar role to that of displacement and velocity in a simple linear pendulum oscillation, only that here the oscillation is a self-sustained, nonlinear one.
With a simple synchronization model I can show that polar climates can behave like two nonidentical Saltzman’s oscillators, each subtly influencing and influenced by the other through the intervening ocean and atmosphere, such that eventually their components synchronize to form a global oscillation. The close analogy with Christiaan Huygens’ famous 1673 experiments describing the (nonlinear) synchronization of pendulum clocks is inevitable. As Huygens noted, the clocks, coupled by the weak elastic forces along the wall on which they hung, always became synchronized, no matter how different their starting conditions, and so long as their natural frequencies were not too different. Through the slight motions induced on the wall each clock gently forced the other, speeding it up or slowing it down until synchrony was attained. Even if their coupling was very weak (clocks several meters away from each other), the clocks eventually synchronized to a common frequency (entrainment) and constant phase lock, which could be either in-phase, anti-phase, or out-of phase.
The out-of-phase solution is very suggestive, for paleoclimate data does in fact show a π/2 phase lead of Antarctica’s climate oscillation over the Arctic (Figure 1). Moreover, the instantaneous frequencies of the two polar oscillations should be theoretically the same for most of the last ice age, as shown below (see page 4). This means 1:1 frequency entrainment, which along with the π/2 phase lock suggest out-of-phase or lag synchronization. Thus, the oscillations of the two Huygens’ clocks are instructive analogues of the interaction between the climate of the Polar Regions: the wall is the analogue of the intervening ocean and atmosphere, and the weak interaction between the two clocks along the wall is the analogue to meridional heat transfer (diffusion, advection) and mass transport. In the real climate however the ‘clocks’ are usually chaotic and many forms of synchrony may occur, irregular or weak coupling or large detuning (disparity in internal frequencies) may result in only partial, temporary or sporadic (though dynamically important) synchronization. Further, detecting synchrony in paleoclimate data is not simple, requiring special statistical analyses and modeling techniques, some of which will be developed for this project, and some adapted from other disciplines. However, if proven, detection of any such linkages would signify a great advance in the understanding of climate dynamics.
Besides the possibility of explaining polar interactions and phase shifts, a major potential benefit of investigating synchronization in the climate system is discovering unifying principles for processes thus far considered distinct and/or unrelated. As mentioned above, one particular process we aim at is the Dansgaard-Oeschger temperature fluctuations of the last ice age. Polar synchronization would imply that the DO are responsive to Antarctic temperature variations, and therefore are not a Northern Hemisphere phenomenon, as generally believed. If they are indeed lag synchronized, Antarctica and Greenland climate proxy records may represent the components of a single global oscillation such that the abruptness of the DO temperature change may ultimately be linked to Antarctica. Another possible example where synchronization is likely to be involved is in climate oscillations that can have enormous impacts (some negative) on the ecosystem and on human life: recent studies show an apparent causal relationship between El Niño/Southern Oscillation (ENSO) and the Indian monsoon that suggests some degree of synchronization. I submit that, dynamically, a key to their long-range interaction may be that ENSO and the Indian monsoon are antipodal to each other (just like the two poles). The earth’s spherical shape has interesting consequences when considering the propagation of climatic influence especially through the atmosphere, as it provides a way to communicate information to the longest distances. Every bit of information released at a source will eventually converge with all other bits (provided it survives dissipation) at their geographic antipode. If the signals are sufficiently strong this process may induce the development of normal modes of climate oscillation, which is a form of global synchronization for wavelengths that fit the earth’s circumference an integer number of times. Thus, it may not be inconsequential to climate dynamics that ENSO and the monsoon (as well as the two Polar Regions) are antipodal to each other.