## Regime Shift?

There’s no reason that the climate needs to change gradually. Recently scientists have become interested in regime shifts, which are abrupt, substantial and lasting changes in the state of a complex system.

Rasha Kamel of the Azimuth Project pointed us to a report in Science Daily which says:

Planet Earth experienced a global climate shift in the late 1980s on an unprecedented scale, fueled by anthropogenic warming and a volcanic eruption, according to new research. Scientists say that a major step change, or ‘regime shift,’ in Earth’s biophysical systems, from the upper atmosphere to the depths of the ocean and from the Arctic to Antarctica, was centered around 1987, and was sparked by the El Chichón volcanic eruption in Mexico five years earlier.

As always, it’s good to drill down through the science reporters’ summaries to the actual papers.  So I read this one:

• Philip C. Reid et al, Global impacts of the 1980s regime shift on the Earth’s climate and systems, Global Change Biology, 2015.

The authors of this paper analyzed 72 time series of climate and ecological data to search for such a regime shift, and found one around 1987. If such a thing really happened, this could be very important.

Here are some of the data they looked at:

Click to enlarge them—they’re pretty interesting! Vertical lines denote regime shift years, colored in different ways: 1984 blue, 1985 green, 1986 orange, 1987 red, 1988 brown, 1989 purple and so on. You can see that lots are red.

The paper has a lot of interesting and informed speculations about the cause of this shift—so give it a look.  For now I just want to tackle an important question of a more technical nature: how did they search for regime shifts?

They used the ‘STARS’ method, which stands for Sequential t-Test Analysis of Regime Shifts. They explain:

The STARS method (Rodionov, 2004; Rodionov & Overland, 2005) tests whether the end of one period (regime) of a certain length is different from a subsequent period (new regime). The cumulative sum of normalized deviations from the hypothetical mean level of the new regime is calculated, and then compared with the mean level of the preceding regime. A shift year is detected if the difference in the mean levels is statistically significant according to a Student’s t-test.

In his third paper, Rodionov (2006) shows how autocorrelation can be accounted for. From each year of the time series (except edge years), the rules are applied backwards and forwards to test that year as a potential shift year. The method is, therefore, a running procedure applied on sequences of years within the time series. The multiple STARS method used here repeats the procedure for 20 test-period lengths ranging from 6 to 25 years that are, for simplicity (after testing many variations), of the same length on either side of the regime shift.

Elsewhere I read that the STARS method is ‘too sensitive’. Could it be due to limitations of the ‘statistical significance’ idea involved in Student’s t-test?

You can download software that implements the STARS method here. The method is explained in the papers by Rodionov.

### 29 Responses to Regime Shift?

1. John Baez says:

In email, Jan Galkiowski wrote:

Hi John!

I just downloaded the same paper this morning, but have not read it. I was drawn to its methods and mentions of STARS. I had heard of the cumsum technique, and have tried it, but not STARS. I did not dive into it because I tend to want to see a (posterior) probability of regime change assigned to each time tick, and because I could not tell from the short time I had to look if they were correcting for False Discovery Rate. As you may know, that’s a big deal in microarray analysis and Professor Brad Efron has advanced an “empirical Bayes” approach to handling these (to which I’m somewhat sympathetic) which resulted in a textbook (Large Scale Inference) and several papers:

Gelman argues that from a Bayesian perspective multiple testing is not (well, less) of an issue: http://www.stat.columbia.edu/~gelman/research/published/multiple2f.pdf

Regime change is reviewed as a problem by Rodionov, at

I prefer state-space methods for the reasons I cited. One is described in an attached paper, but, basically, when the Highest Probability Density Interval (HPDI) changes in high abruptly, I read a candidate for a regime change. See below for an annotated illustration which wasn’t made for the purpose, but I grabbed from a pile of things I have. I read two likely changes and noted them. The salmon-colored area to the right is a series of prediction intervals by the smoother for which the shown data have been held out.

The Ives and Dakos techniques are available in the R package earlywarnings and they have a Web site: http://www.early-warning-signals.org/

I will go back to the paper eventually.

Hope this helps.

2. Qiaochu Yuan says:

Why coin a new word when we already have the perfectly serviceable “phase transition”?

• John Baez says:

At least to me, ‘phase transition’ means something pretty specific: you have system whose thermal equilibrium state depends on a some parameters, and as you adjust the parameters, observable quantities vary smoothly except at certain points in the parameter space, which usually lying on hypersurfaces called ‘phase transitions’. The complement of these surfaces has connected components called ‘phases’. There are also more specific concepts like ‘first-order phase transition’ and ‘second-order phase transition’.

A ‘regime’ of a complex system like an ecosystem or the entire Earth is something much more elusive; such systems aren’t in thermal equilibrium, they’re always changing, but sometimes they change more dramatically than others. A ‘regime shift’ is a period of time when they’re changing in a significant, rapid and persistent way.

People are busy arguing about what a ‘regime’ is—but whatever it is, it’s not a thermodynamic phase. Similarly, what counts as a ‘regime shift’ is much contested.

Of course this vagueness may be inevitable. And of course you could use the precise term ‘phase transition’ in a metaphorical way to mean the more vague concept of ‘regime shift’. But there’s enough overlap between thermodynamics and the theory of complex systems that it seems good to have both.

In any event, ecologists talk about regime shifts. Here’s what the almighty Wikipedia has to say:

In ecology, regime shifts are large, abrupt, persistent changes in the structure and function of a system. A regime is a characteristic behaviour of a system which is maintained by mutually reinforced processes or feedbacks. Regimes are considered persistent relative to the time period over which the shift occurs. The change of regimes, or the shift, usually occurs when a smooth change in an internal process (feedback) or a single disturbance (external shocks) triggers a completely different system behavior.

The concept of ‘feedback’ is largely absent from the concept of thermodynamic phase, because feedback typically involves flow around loops, while in thermal equilibrium the principle of detailed balance prohibits flow around loops.

• I just now (May 2019) came across this blog entry, and wanted to chime in here.

I am an ecologist. ‘Regime shifts’ are still elusive, and multiply defined.

:|

• John Baez says:

I would still like to think more about these!

3. Nick Stokes says:

Looks to me from his datasets as if there may be some evidence of something happening in Switzerland in 1987. But I’m dubious about climate shift talk. When I do hear it, it is usually about a shift in 1976, as here. Or around 1950, as here. It seems like a moveable feast.

• John Baez says:

Of course we expect a number of different regime shifts, not just one.

• Nick, Since most of the climate shift is occurring in the equatorial Pacific, isn’t it possible that when the standing wave system transitions from a forcing above to below (or vice versa) the natural frequency that it will undergo a 180 degree phase reversal. This is known to occur and for example explains why equatorial tides are inverted [1].
[1] “Fee-Surface Hydraulics”, J M Townson, CRC Press, 1990

So its possible/plausible that something happened circa late 1970’s that shifted the forcing enough to transiently place it into an inversion.

To anyone with an engineering background this is college knowledge. e.g. you can show this by taking the Fourier transform of a standing wave 2nd-order DiffEq.

4. I have a derivation for a simplified case which shows using multiple series does not always help. In general, however, it should be a win.

• Don’t know how long it’ll take to get this reviewed and in the cycle here, or in what format, but the short notes are to examine the dependency of the Mahalanobis distance in multivariate statistics upon dimension, treating the $t$-th time point for each of $M$ series as each being a multivariate observation with $M$ rows.

5. Regime shifts in secondary phenomena? How many degrees of freedom are involved in the analysis is the question I would raise.

• John Baez says:

In systems where there’s a huge number $N$ of degrees of freedom but the dynamics couples these degrees of freedom, one can plot a time series of points in $\mathbb{R}^N$ and estimate its dimension—which may be fractional—to get an ‘effective’ number of degrees of freedom. This is the fractal dimension of an attractor. The best studies of this have been done for turbulence in fluid flow.

One can imagine doing this for the whole coupled atmosphere-ocean-biosphere system, but there won’t be enough data available to actually do it unless one restricts the problem in some way, e.g. by limiting the temporal or spatial scale. For some limited subsystem like the ENSO it should be doable.

• That’s exactly what I mean — they need to do it on ENSO instead. This team [1] made an attempt to do that and they saw the shift at 1980

[1]H. Astudillo, R. Abarca-del-Rio, and F. Borotto, “Long-term non-linear predictability of ENSO events over the 20th century,” arXiv preprint arXiv:1506.04066, 2015.

Another truly global phenomenon is the quasi-biennial oscillation (QBO) of strat winds, as that envelopes the entire equator. I have essentially zero degrees of freedom in the QBO analysis. And I find no evidence for fractal dimensionality or chaotic attractor.

http://contextearth.com/2015/11/21/qbo-model-sensitivity/

Something has to give with this kind of analysis, especially when it turns out that the result is dependent on elementary forcings, and is potentially much simpler than previously believed.

Google is planning on launching scores of transceiver-equipped balloons into the stratosphere in the coming years, with the intended result of improving global internet connectivity — Google “Project Loon”. Unless they have predictions of the wind direction and strength, they have no idea of where the balloons will drift to.

• John Baez says:

One reason for not looking only at ENSO when searching for a ‘regime shift’ is that one might want to understand the whole biosphere. It may well be true that changing ENSO behavior is a key driver of widespread changes in the whole biosphere. That would be an important thing to know. But we’ll only see if this true if we compare the behavior of ENSO to other things. So, studies like this one, that look at a huge range of different phenomena, can be useful.

Maybe ENSO changed in 1980 and other things followed along around 1987. The study here blames the eruption of El Chichón in 1982. I’m less intereted in that—since I don’t know enough to judge—than the general idea of the STARS method and other statistical tests for regime shifts.

• ENSO is likely the controlling factor for the short-term variability in climate (like we are seeing right now) therefore it should be center stage. At its root, ENSO is predominately a standing wave pattern in the Pacific ocean thermoclime and so doesn’t automatically require a huge amount of complexity. That’s based on experience with other standing wave patterns observed in nature.

A climate shift caused by ENSO could be something as simple as a phase reversal in the standing wave, which could easily happen — as there is little difference between the energy levels of one standing wave and another that is 180 degrees out-of-phase, and in the forcing required to flip it at a zero crossing.

As a related phenomena, consider that equatorial ocean tides are 180 degrees out of phase with tides outside of the equator. There is no overwhelming evidence for why that happens. That’s what I am trying to track down now.

Based my own results, I agree with Astudillo that a shift happened in 1980, but that assuming it was a phase reversal in the ENSO standing wave, this flipped back around 1995.

On the other hand, the QBO shows no evidence for any kind of shift over the 60+ years of measurement. There is some sort of physical relationship between QBO and ENSO so this is an important point to consider. IOW, why would ENSO change while QBO kept going?

6. Graham says:

This paper is key to the Bayesian approach, and it uses time-series as an example. It’s called ‘change-point analysis’ here.
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination.
PETER J. GREEN, 1995

7. This is a cool paper. the statistic that Rodionov devised is very interesting. We are always trying to answer this question in the factory: did something change for the worse, or have things always been this messed up?

A minor thing worth noting, this question seems to be so universal that it appears right away in “Statistics for Experimenters” (Box/Hunter/Hunter). I love the discussion there (chapter 2, an industrial example), such a beautiful explanation of basic statistics.

We are currently working on a sort of related problem here, trying to quantify for a particular sensor, what the optimum time to use it is before a regime change.

The statistic we use is “Allan Variance”. Curious to know if any of your readers every encountered it. It was invented to study very precise atomic clocks, and it is now part of the nomenclature of the inertial navigation community.

More importantly though, the readers of this blog will greatly enjoy Allan’s own blog. Evidently he has figured out how to debunk general relativity with chicken eggs.

http://www.allanstime.com/UnifiedFieldTheory/egg/index.html

• John Baez says:

So someone can invent a widely used statistic and still think that balancing eggs on end says something deep about gravity. Yes, I guess I knew it works like that.

8. […] John Baez at The Azimuth Project opened a discussion on the recent paper by Reid, et al […]

9. If a 180 degree phase reversal is applied to ENSO from the interval between 1981 to 1996 the time series is extremely stationary — and follows the forced response to the wave equation.

What happened between 1981 and 1996? There is no energy difference between two standing waves that are 180 degrees out-of-phase. Likely that interval was a metastable state that tipped back into the slightly more stable state. Same thing happens with equatorial tides, as they are 180 degrees reversed.

• The known time series of ENSO looks remarkably stationary apart from the one interval from 1981 to 1996.
The entire interval can be reconstructed from a multiple linear regression fit of 5 Fourier series factors trained on a single 18 year interval.

This is the wave equation transformed ENSO (average of SOI and NINO3)

What that indicates is that the information content in this one short interval is of enough resolution to reproduce the quasi-periodic cycle everywhere else.

And remarkably those 5 forcing factors are derived from lunar tidal periods.

Yet this analysis is all dependent on accepting that the phase reversal occurs — which is why this pattern is hard to discern. Methods that find the phase reversal are a little bit more complex, a wavelet scalogram is useful of course. Here is a scalogram created by Roundy showing a clear transition after 1980 that pops back after 1990.

• As everyone should know by now, given the huge impact that the current ElNino is having on local climate, ENSO is the biggest factor in overall climate variability. But ENSO itself is very curious in that many scientists believe it is nearly chaotic and therefore unpredictable. Yet, it has an internal timing which matches the QBO 28-month cycle, and one can easily extrapolate from short training intervals to regions that match rather precisely:
https://imageshack.com/i/p7jQxAcep

Another paper describes how Takens embedding theorem is used to support the idea that a stationary attractor exists in the ENSO time series.
Astudillo, H. F., R. Abarca-del-Rio, and F. A. Borotto. “Long-term non-linear predictability of ENSO events over the 20th century.” arXiv preprint arXiv:1506.04066 (2015).

The only region where Astudillo et al find something is amiss starts around 1981 — which is the region that I am suggesting is the start of a transient standing wave inversion.

• Eugene says:

The following paper may be relevant:
Mixed mode oscillations of the El Niño-Southern Oscillation ,
arXiv:1511.07472 [math.DS]

• WebHubTelescope says:

That paper describes a wave equation that has significant non-linear terms. Kind of like a predator-prey or Lotka-Volterra model. Notice that their Eq.(1) has no concept of forcing and so they are relying on the natural response to generate the complex dynamics of ENSO.

One thing I have learned in studying physics is that very few systems oscillate without a consistent forcing applied. Why does no one talk about that? It seems as if it shouldn’t be a taboo subject — after all, the same scientists would not hesitate to suggest that the AGW signal is caused by a forcing applied to the system.

• Eugene says:

One thing I have learned in studying physics is that very few systems oscillate without a consistent forcing applied.

I think you mean that if your systems has dissipation, it’s not going to oscillate without some forcing. Is this right?

• “I think you mean that if your systems has dissipation, it’s not going to oscillate without some forcing. Is this right?”

Certainly the dissipation is a contributing factor for the requirement of a significant forcing.

But what I actually mean is that I don’t see any indication of any kind of forcing in that paper. This situation really drives me nuts — if you consider the oscillations of ocean tides, that is a phenomenon that is entirely caused by periodic luni-solar forcing. Nobody is going to work out a tidal analysis without consideration of the periodic orbits of the moon and the earth around the sun and how the gravitational forces impact tides.

So where is the forcing for ENSO described? They have a left-hand side (LHS) in their differential equations but no right-hand side (RHS).

If you can see where I am coming from, now you can understand why I think I am making lots of progress on ENSO and QBO analysis. It took me a while to notice the missing forcing because it had always been implicit in the systems that I had been taught — i.e. electrical circuits, mechanical responses, etc. Then it slowly dawned on me that this periodic forcing piece was totally missing in the papers that I have surveyed. Yet, the forcing is described in the research on engineering hydrology, such as sloshing on tanker vessels. This is a hole in climate science research IMO.

But someone may have a different impression. Perhaps it is worthy of a deeper discussion, and someone could try to dissuade me of this notion that I have :)

Paul wrote:

So where is the forcing for ENSO described?

What I understood by briefly glancing at the paper is that the forcing is so to say “hidden” in the initial conditions. That is you start out with an initiial configuration of thermocline depth and temperatures (which is most probably influenced by all sorts of “forcings”, including lunar tides) and then you look what happens just by the fact that thermocline depth and temperatures are coupled in this way given by that sytem of differential equations. I think the reason why you don’t see a damping seems to be due to their weird construction of a periodic orbit which is composed of segments of solutions to 2 “limit” differential equation systems. I have no idea how close these “idealized” segmented solutions are to solutions of the orginal system, in particular I don’t know wether there are theorems about that in this what they call: “Geometric Singular Perturbation Theory”. Next to the ENSO data comparision it would have been interesting to see how good e.g. the solution of the z-component of that idealized assumption matches real thermocline data.

10. WebHubTelescope says:

“I think the reason why you don’t see a damping seems to be due to their weird construction of a periodic orbit which is composed of segments of solutions to 2 “limit” differential equation systems. “

There is nothing fundamentally “weird” about their formulation. Two coupled differential equations are the basic building blocks to the second-order differential equation used to derive a wave equation. That approach is well known. What they have added though are some non-linear terms, which serve to add some potentially chaotic elements to the mix.

I understand completely why they want to do this, because I was suckered into this trap as well. The trap goes like this: They essentially observe that the ENSO behavior looks chaotic, so immediately assume that some sort of non-linear effect is behind it. So they derive a non-linear perturbation to the wave equation that increases the complexity of the periodic solution. In sloshing hydrodynamics, the first order perturbation is called the Mathieu equation, and it does work well for known liquid volume configuations (see research by Frandsen and by Faltinsen).

Yet the jury is still out as to how significant this perturbation is to a system such as the equatorial Pacific ocean. It may be that the wave equation is modified only slightly, which is essentially describing a slight variation of the characteristic frequency over time.

If that is the case, what is causing all the complexity in ENSO? The possible solution lies in the complicated forcing applied to the wave equation, which is caused by angular momentum shifts in the earth’s rotation. That’s kind of the obvious place to look. I have been searching for research results that follow this line of path and usually end up at NASA JPL. But recently I discovered scientists in China that are looking at this as well:

Wang, W-J., W-B. Shen, and H-W. Zhang. “Verifications for multiple solutions of Earth rotation.” Journées Systèmes de Référence Spatio-temporels 2007. Vol. 1. 2008.

Wang, Wenjun. “Free acceleration of Earth rotation and energy source of ENSO.” 37th COSPAR Scientific Assembly. Vol. 37. 2008.

From the latter cite:
“Earth is a triaxial body. Triaxial body rotation has Euler dynamic model of nonlinearity with A¡B¡C. We develop a decomposition theorem for obtaining three true solutions for the rotation with two stable wobbles of Chandler and another decadal of period 14.6 a. The other may be an unstable inverted pendulum of one way sway. The nonlinear coupling of the two free wobbles provide free accelerations for the rotation or LOD with a period of 7 month and another 14.6 a. The fluctuation of period 14.6 a may cause bifurcation cascade in nonlinear coupling and a series of periods 7.3, 3.65 and 1.825 a may be observed with free accelerations and decelerations so that cause ocean water near the equator flow eastward and westward. This makes the energy source of ENSO in eigen periods of 7, 4, 2 a. Therefore in this study we verify that the energy source of ENSO is the free acceleration of Earth rotation. “

The bottom-line is that I have been looking for numbers that match the forcing I have been using to model ENSO. As it turns out, the numbers that Wang proposes for 3-axis Euler rotation wobble match well with what I have been using.

http://contextearth.com/2015/12/12/biennial-connection-from-qbo-to-enso/

Yesterday, I modeled a 7 month periodic forcing as Wang suggested, and sure enough, it showed up as a sharp factor centered at 0.5791 years = 6.95 months (albeit within the noise of ENSO). I am confident that Wang, Shen, Chen,et al are on to something, or that at least this effort is worth pursuing. The JPL scientists cite this research group, which indicates to me that they are not off the deep-end in their analysis.

The point is that there are alternate views to explain the behavior of ENSO. There are the geophysicists views as well as the climatologists views. I am leaning towards the former.

11. WebHubTelescope says:

G. Meehl on Tropospheric Biennial Oscillation (TBO):

“Of course, the TBO cycle depicted in Fig. 11 is not
perfectly biennial, as noted in other studies, and only
appears to operate intermittently or in a subset of years
(Meehl 1987; Barnett 1991; Terray 1995). However, recent
studies have shown that these associations involving
midlatitude circulation patterns and monsoon
strength are strong enough to be evident in composites
of a number of observed strong and weak monsoon
years (e.g., Yang et al. 1996).”

It looks as if other groups think this is white noise:

GEOPHYSICAL RESEARCH LETTERS, DOI:10.1002/August 2015,Tropospheric “Biennial Oscillation (TBO) indistinguishable from white noise”. Malte F. Stuecker,Axel Timmermann, Jinhee Yoon, and Fei-Fei Jin

https://www.researchgate.net/publication/281899198_Tropospheric_Biennial_Oscillation_TBO_indistinguishable_from_white_noise

White noise would not have stationary elements in the time series.

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