by Judith Curry
Interpretation of statistical or dynamical predictions of future climate change needs to appropriately interpret the modes of natural internal climate variability, such as the Atlantic Multidecadal Oscillation (AMO), the North Atlantic Oscillation (NAO), the Pacific Decadal Oscillation (PDO) and the North Pacific Gyre Oscillation (NPGO). This interpretation is needed in the context of forced climate change (e.g. solar, greenhouse gases).
We are currently in the warm phase of the AMO (since 1995) and the cool phase of the PDO (flickering since 1999; decisively cool since 2008). The previous similar regime was in the 1950’s, which was characterized by above average rainfall in the Sahel and south Asia, drought in the southwest U.S., and many intense hurricane landfalls in the U.S. Based upon previous regime shifts, it might be anticipated that this regime will continue for at least another decade. The challenge is to predict the change points for these regimes.
Interpreting past such variability and making informed projections about potential future variability requires (i) identifying the dynamical processes internal to the climate system that underlie such variability and (ii) recognizing the chain of events that mark the onset of large amplitude variability events, i.e., shifts in the climate state. Such shifts mark changes in the qualitative behavior of climate modes of variability, as well as breaks in trends of hemispheric and global mean temperature. The most celebrated of these shifts in the instrument record occurred in 1976/77. That particular winter ushered in an extended period in which the tropical Pacific Ocean was warmer than normal, with strong El Nino-Southern Oscillation (ENSO) events occurring after that time, contrasting with the weaker ENSO variability in the decades before. Global mean surface temperature also experienced a trend break, transitioning from cooling in the decades prior to 1976/77 to the strong warming that characterize the remainder of the century.
[In Tsonis et al. 2007] it was hypothesized that certain aspects of the climate system behave in a manner analogous to that of synchronized chaotic dynamical systems. Specifically, it was shown that when these modes of climate variability are synchronized, and the coupling between those modes simultaneously increases, the climate system becomes unstable and appears to be thrown into a new state. This chain of events is identical to that found in regime transitions in synchronized chaotic dynamical systems. This new state is marked by a break in the global mean temperature trend and in the character of ENSO variability. Synchronization followed by an increase in coupling coincided with all the major climate shifts of the 20th century, and was also shown to mark climate shifts in coupled ocean-atmosphere simulations.
Using a new measure of coupling strength, this update shows that these climate modes have recently synchronized, with synchronization peaking in the year 2001/02. This synchronization has been followed by an increase in coupling. This suggests that the climate system may well have shifted again, with a consequent break in the global mean temperature trend from the post 1976/77 warming to a new period (indeterminate length) of roughly constant global mean temperature.
Tsonis et al. 2007 explain the mechanism as follows:
First let’s consider the event in 1910s. The network synchronizes at about 1910. At that time the coupling strength begins to increase. Eventually the network comes out of the synchronous state sometime in late 1912 early 1913. The destruction of the synchronous state coincides with the beginning of a sharp global temperature increase and a tendency for more frequent and strong El Nino events. The network enters a new synchronization state in the early 1920s but this is not followed by an increase in coupling strength. In this case no major shifts are observed in the behavior of global temperature and ENSO. Then the system enters a new synchronization state in the early 1930. Initially this state was followed by a decrease in coupling strength and again no major shifts are observed. However, in the early 1940s the still present synchronous state is subjected to an increase in coupling strength, which soon destroys it. As the synchronous state is destroyed, a new shift in both temperature trend and ENSO variability is observed. The global temperature enters a cooling regime and El Ninos become much less frequent and weaker. The network synchronizes again in 1950. This state is followed by a decrease in coupling strength and, as was the case in 1920s no major shifts occur. Finally, the network synchronizes again in the mid 1970s. This state is followed by an increase in coupling strength and incredibly, as in the cases of 1910 and 1940, synchronization is destroyed and then climate shifts again. The global temperature enters a warming regime and El Ninos become frequent and strong. The fact that around 1910, 1940, and in the late 1970s climate shifted to a completely new state indicates that synchronization followed by an increase in coupling between the modes leads to the destruction of the synchronous state and the emergence of a new state.
Tsonis et al. (2007) speculate on climate shifts in the context of greenhouse warming in the 21st century:
The above observational and modeling results suggest the following intrinsic mechanism of the climate system leading to major climate shifts. First, the major climate modes tend to synchronize at some coupling strength. When this synchronous state is followed by an increase in the coupling strength, the network’s synchronous state is destroyed and after that climate emerges in a new state. The whole event marks a significant shift in climate. It is interesting to speculate on the climate shift after the 1970s event. The standard explanation for the post 1970s warming is that the radiative effect of greenhouse gases overcame shortwave reflection effects due to aerosols. However, comparison of the 2035 event in the 21st century simulation and the 1910s event in the observations with this event, suggests an alternative hypothesis, namely that the climate shifted after the 1970s event to a different state of a warmer climate, which may be superimposed on an anthropogenic warming trend.
Swanson and Tonis (2009) conclude:
If as suggested here, a dynamically driven climate shift has occurred, the duration of similar shifts during the 20th century suggests the new global mean temperature trend may persist for several decades. Of course, it is purely speculative to presume that the global mean temperature will remain near current levels for such an extended period of time. Moreover, we caution that the shifts described here are presumably superimposed upon a long term warming trend due to anthropogenic forcing. However, the nature of these past shifts in climate state suggests the possibility of near constant temperature lasting a decade or more into the future must at least be entertained. The apparent lack of a proximate cause behind the halt in warming post 2001/02 challenges our understanding of the climate system, specifically the physical reasoning and causal links between longer time-scale modes of internal climate variability and the impact of such modes upon global temperature.
JC’s comments: This is a post pulled together quickly, based papers that I am currently reading in an attempt to figure out how we can make some sort of sensible scenario based climate predictions on decadal time scales. My current interest in this is of an applied nature, particularly in the context of needs of military/security (more on this topic soon). I don’t have any particular insight in Tsonis’ work in terms of the chaos/nonlinear dynamics aspects (which I am not an expert on). But I find these ideas very intriguing and they make more sense to me than anything else I’ve read on trying to interpret the the climate record of the past decade and make projections a few decades hence. I would appreciate comments on this from the denizens that are knowledgeable on this topic.
In terms of any critique of this that I can provide, I am not exactly sure which of the regime indices are best to use in such an analysis. I don’t think that ENSO and PDO are independent in a multidecadal sense. On the other hand, the NPGO seems to be a mode independent to PDO. With regards to the AMO/NAO/AMOC, I wish somebody would sort these out; different communities use different indices (and on different timescales) and its not obvious which is preferred for what application. My own conceptual reasoning about this has used the AMO/PDO.
Moderation note: This is a technical thread, comments will be moderated for relevance.
Update: Tomas Milanovic provides this lucid summary and interpretation of Tsonis (2007):
As the referenced Tsonis papers are not easily readable, I will try to resume for you and the interested readers what it is actually about.
- First, Tsonis is NOT doing chaos theory, he is doing statistics.
- Second, the important paper is 2007. 2010 is a minor update with no interest in itself.
- Third, the Tsonis&al 2007 paper may be considered as minor in the field of synchronization of dynamical systems as opposed to major papers likehttp://amath.colorado.edu/faculty/juanga/Papers/PhysicaD.pdf
So now I’ll focus on the 2007 paper only. As I have written multiple times, the main reason why spatio temporal chaos is untractable is the fact that the phase space (the space of the system’s states) is uncountably infinite dimensional because of the adition of space variables to the usual time variable. That’s why all approaches of spatio temporal chaos begin with a discretization of space by taking a grid or a network which transforms the continuous spatial functions in a finite number of nodes so that the phase space becomes finite dimensional.
Tsonis acknowledges that the climate is a spatio temporal chaotic system so he looks for a spatial discretization too. Of course as the fact of being chaotic doesn’t imply that the GHG play no role (just that they play some role), he proceeds with the mandatory genuflexion to orthodox AGW by saying that “… the climate shifted after the 1970 event in another warmer state which may be superimposed on an anthropogenic warming trend.” This certainly allows him to avoid inflammatory articles by the usual suspects in the newspapers.
His discretization is to choose 4 indexes – PDO, ENSO, NAO, NPO. Why those 4?
Well as he is interested in decadal scales, those are the main ones. Shorter doesn’t exist and longer can’t be captured by the method. As a particular but important remark, one has to notice that the physical meaning of the indexes is irrelevant because what Tsonis is interesting in is their interaction. This is the first and last (weak) link to the chaos theory, after that it is just statistics.
Having a network with 4 nodes (the 4 indexes) and therefore a phase space with 4 dimensions (a huge progress to an uncountable infinity:)), he now needs a metrics. Equation (1) defines d(t), the metrics of what is called in the paper “synchronization”. It is actually just an average of the cross correlation coefficients between the 4 indexes for a gliding window 11 years wide with t in the middle of the window. If d(t)=0 then all indexes are completely correlated with each other and if d(t) = √2 then each index does what it wants. Figure 1a shows the d(t). As the values are around 1 , the indexes are rather uncorrelated (or non synchronous in Tsonis vocabulary). Nothing much interesting sofar.
Now comes the original contribution of the paper. As the purpose was not to compute correlations between time series what has been done a million of times but the coupling strengths between the indexes (and hopefully between the underlying physical processes), the paper defines a measure of “coupling strength” in Equation 2.
Also here again, like in Equation 1, the terminology is misleading because it is not really a coupling that is measured but a relevance of a predictor. Tsonis defines a “phase” for each index by considering 3 contiguous points. F.ex if the 3 points go up, the phase is 0 , if they go down, the phase is π etc. For every t there is then a 4 vector of phases Zn (n for the year) and Tsonis looks how well a least square predictor can predict Zn+1 from Zn. If the prediction is good, the “coupling “is said strong and if the prediction is bad, the “coupling” is said weak.
At this point I would criticize extremely strongly the term of “coupling”. The right use of the coupling constant and the right definition of coupling is given f.ex in the paper I linked above. Tsonis’ “coupling” is of course nothing such and yet implies that with a “good” predictor the underlying physical systems are strongly coupled (ie interacting) what is misleading. Here the strong “coupling” in Tsonis sense just means that the phases are identical, e.g if one index goes up, the otehr go up too and conversely. Anyway. The Figure 1b shows the phase predictor. The value is around 0.5 so the predictor is not specially good.
The last part of the paper is an eyeballing exercice. Tsonis added under the correlation and the predictor error figures the average temperature and the ENSO index. Now he observes that there were 4 (kind of) minima on the correlation curve. In 3 out of 4 cases the predictor error decreased (Tsonis vocabulary: “coupling” increased) and in those cases the average temperature trend as well as the ENSO variability changed significantly. In the 4th case the predictor stayed bad (weak “coupling”) and nothing special happened.
Tsonis conclusion: When the decadal oscillations synchronise and the coupling increases, then the system destroys the synchronization and jumps to a new very different (unknown) state.
My translation: When the 4 indexes are relatively strongly correlated and begin to tend to evolve all in the same direction, then they decorrelate fast .
In 3 out of 4 cases in the 20th century this decorrelation coincides with a change in the average temperature trend. The jump from this rather modest observation to a statement concerning the climate itself which can’t be resumed by an average temperature only, is daring to say the least. Of course the question whether the 4 indexes are a univoque proxy for something physical and relevant stays open.
And my conclusion. Despite the clear shortcomings of the paper (especially as far as the coupling is concerned) it suggests that the behaviour of the indexes follows correlation-decorrelation pseudo cycles. This observation has no predictive virtue so I don’t think that it could be used for your intent to elaborate a decadal scenario. All that Tsonis says, is that the behaviour (of the indexes, not of the system itself!) significantly changes when the correlation is strong and the predictor good. This situation happened in 2001 again. So according to Tsonis something will change/has changed significantly. As his paper is neither quatitative nor predictive, he cannot say WHAT will change and HOW.
However the general paradigm to consider the Earth system as a finite network of coupled (chaotic) oscillators is a good one and if one had the idea of the number of the oscillators, their average frequency and especially of the laws that govern them, it would certainly have some predictive capacity. The problem, that I have also already elaborated on, is that these oscillators are in reality not causally independent but they are ALL just emergent local manifestations of GLOBAL dynamics of the system. The coupled oscillator model is just an approximation which would be probably valid only for short term predictions (decades or so)