The current hot phrase bandied about by talking heads and parotted by news pundits is “tipping point.” We are told that the climate may be near a tipping point, if it has not crossed one already, and that can't be good. But what is a tipping point, where did they come from and how can we identify one when we see it?

According to Malcom Gladwell, author of The Tipping Point, the phrase “tipping point” comes from the world of epidemiology. It's the name given to that moment in an epidemic when a virus reaches critical mass. “It's the boiling point,” says Gladwell, “it's the moment on the graph when the line starts to shoot straight upwards.” He goes on to explain that he started seeing this pattern everywhere. “One of the things I explore in the book is that ideas can be contagious in exactly the same way that a virus is,” he stated in an online interview.

It certainly seems that that the idea of a tipping point has spread like a virus, particularly among climate catastrophists who see tipping points everywhere. It is found in news headlines around the world, such as: “Energy review ignores climate change 'tipping point',” found in the UK's Guardian. Or how about this from Juliet Eilperin in the Washington Post: “Debate on Climate Shifts to Issue of Irreparable Change, Some Experts on Global Warming Foresee 'Tipping Point' When It Is Too Late to Act.” There was even an episode of the TV show CSI Miami titled “Tipping Point,” so you know the phrase has total market penetration. There are countless other examples.

All of this has led Gavin Schmidt, in the RealClimate.org blog article “Runaway tipping points of no return,” to opine:

I wonder if any [one] else has noticed that we appear to have crossed a threshold in the usage of the phrase 'tipping point' in discussions of climate? We went from a time when it was never used, to a point (of no return?) where it is used in almost 100% of articles on the subject. Someone should come up with a name for this phenomenon…

Two often cited examples of tipping points are the meridional overturning circulation in the North Atlantic (i.e. the ocean conveyer belt or MOC) and summer sea ice coverage in the Arctic. Both systems seem to exist in a state of equilibrium, showing some variation but within stable limits. In both of cases, these system can be radically disrupted by small changes in a contributing factor, freshwater and increasing polar amplification, respectively. Alter the system enough and it ceases to function, the MOC quits flowing or the Arctic icepack vanishes. Unfortunately, scientists are not very confident of exactly where these points are, or how much disturbance they can tolerate before a radical change takes place.

In mathematical terms a tipping point is a non-linear response, where a small change in a function's input value causes a huge change in its output value. In some cases it can be likened to falling off a cliff. There area several areas of mathematics involved with studying such phenomena. One such area is a special branch of dynamical systems theory called Catastrophe Theory. Catastrophe Theory originated by the French mathematician René Thom in the 1960s. It studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circumstances. Catastrophes are bifurcations between different equilibria, or fixed point attractors.

If a shift between equilibria occurs abruptly the event is called a discontinuity. If you bend a piece of wood it will bend and then suddenly break. The failure of the wood is a discontinuity in the distortion of the wood as it bends. The eruption of volcanoes and earthquakes are other examples of sudden discontinuous events.

There have been a number of rapid climate shifts in Earth's past that have led many scientists to speculate that climate change doesn't follow a smooth arc. Instead they theorize that there are a number of stable equilibrium points that climate prefers. When sufficient change in a driving force occurs (a forcing) climate shifts rapidly from one stable mode to another. This is an attractive concept when one looks at the transitions into and out of glacial conditions during an ice age. Chaos Theory, another mathematical field that studies systems that change their behavior disproportionately with respect to input changes or initial conditions, provides a mathematical model of systems that jump between two or more stable regions, called attractors.

An early pioneer of the theory was Edward Lorenz, whose interest in chaos came about accidentally through his work using computers to predict the weather. In 1961, Lorenz discovered that small changes in initial conditions produced large changes in the long-term results generated by his computer model. Lorenz's discovery, which gave its name to Lorenz Attractors, proved that meteorology could not reasonably predict weather beyond about a week. In 1978, Mitchel Feigenbaum published the article “Quantitative Universality for a Class of Nonlinear Transformations,” where he described the universality of chaos, permitting the application of Chaos Theory to many different phenomena.

The Lorenz Attractor for values r = 28, σ = 10, b = 8/3.
From Wikimedia.

For much of Earth's history, the climate has been considerably warmer than it is today. But around 34 million years ago, at the Eocene-Oligocene boundary, the world suddenly changed. Our planet rapidly transitioned to a much cooler glacial climate that continues to this day. Within just 200,000 years—a rapid change in geological terms—Antarctica went from being a rather temperate, hospitable place to a frozen continent buried under miles of ice. The transition was abrupt, initially overshooting the new equilibrium point with a temporary super-glaciation, dubbed the Oi-1 climate event, which lasted a few hundred thousand years. The current manifestation of this global cooling is known as the Pleistocene Ice Age and scientists are pretty sure we are still in the midst of it.

Since the change to a cooler Earth, glaciers have advanced and retreated many times. During the past million years the northern parts of North America, along with parts of Europe and Asia, have been covered in ice sheets more than a mile thick. The episodes of falling temperatures, when the glaciers advance, are called glacial periods and last on average about 100,000 years. In between the glacial periods are warm spells, called interglacials. They last on average 10,000-15,000 years, though some have lasted as long as 28,000 years. We are currently 12,000 years into an interglacial called the Holocene.

If climate change really does manifest as a multi-equilibrium system with sudden shifts, we must recognize that threshold behavior in one direction is often accompanied by threshold behavior in the reverse direction. The amount of coercion the system needs to jump from one stable state to another can differ in size (see the figure). For example, modern climate/ice-sheet models exhibit considerable hysteresis, requiring atmospheric carbon dioxide concentrations to rise well above the original initiation level to melt the Antarctic ice sheet. A future tipping point transition into a warm Eocene-like climate state may thus be delayed, but if and when it does occur, the transition could be abrupt.

Taken from “Tipping Pointedly Colder” by Lee R. Kump,
Credit P. Huey/Science Feb 2009.

Because Earth's climate is an enormously complicated system, and historical climate records are notoriously incomplete, it is difficult to point to an incedent in the climate record and conclusively demonstrate that it was the result of tipping point behavior. A team of scientists, led by Vasilis Dakos, recently published an article in PNAS, titled “Slowing down as an early warning signal for abrupt climate change,” where they analyzed tipping point events. The researchers chose to analyze a number of historical shifts in climate: the greenhouse-icehouse transition, termination of three glacial periods, the Younger Dryas period in Greenland, and the savannah-to-desert transition in North Africa.

These events were chosen because they are universally regarded as significant climate shifts, and positive feedback mechanisms have been widely suggested as their causes. The data were filtered to eliminate long trends; autocorrelation was determined using an ordinary least-squares fit to a first order autoregressive model. In statistics, an autoregressive model is a type of random process which is used to model and predict various types of natural phenomena. Autocorrelation is the similarity between observations as a function of the time separation between them—it is the cross-correlation of a signal with itself. In each of the cases investigated, autocorrelation was found to increase prior to the abrupt change in climate, and the effect was most pronounced for the sharpest and most dramatic transitions. Here is the abstract for the PNAS article:

In the Earth's history, periods of relatively stable climate have often been interrupted by sharp transitions to a contrasting state. One explanation for such events of abrupt change is that they happened when the earth system reached a critical tipping point. However, this remains hard to prove for events in the remote past, and it is even more difficult to predict if and when we might reach a tipping point for abrupt climate change in the future. Here, we analyze eight ancient abrupt climate shifts and show that they were all preceded by a characteristic slowing down of the fluctuations starting well before the actual shift. Such slowing down, measured as increased autocorrelation, can be mathematically shown to be a hallmark of tipping points. Therefore, our results imply independent empirical evidence for the idea that past abrupt shifts were associated with the passing of critical thresholds. Because the mechanism causing slowing down is fundamentally inherent to tipping points, it follows that our way to detect slowing down might be used as a universal early warning signal for upcoming catastrophic change. Because tipping points in ecosystems and other complex systems are notoriously hard to predict in other ways, this is a promising perspective.

So what are we to make of the claims that Earth's climate is at or near a tipping point, with irreversible change just ahead? Do the known physical tipping points behave like mathematical catastrophes, edging up to the precipice and suddenly falling off, or are they more like chaotic systems, hopping from one stable state to another? The tipping points described above all have natural timescales that determine when recovery is possible. Arctic sea ice, for instance, has timescales of around five years to a decade; a collapse of summer ice cover could conceivably be reversed after only a decade or so. Model simulations of the MOC indicate that for small perturbations, recovery can occur in a few decades.

Many scientists think that the Younger Dryas period, a sharp return to glacial conditions at the beginning of the Holocene warming that last 1,000 years, was caused by a sudden disturbance of the MOC. The disturbance of the system may have been caused by the sudden release of a large volume of fresh water from northern glacial lakes into the Arctic Ocean basin. If this is true then we have an example of a rapid shift from warm to cold, followed a millennium later by an equally rapid return to warm conditions. This seems to be an example of a bistable system that can quickly change state but just as quickly recover.

Scientists generally think that variations in Earth's attitude and orbit around the Sun are responsible for the cycling between glacial and interglacial periods (the Croll-Milankovitch Cycles, see chapter 9 of TRE). By many accounts, the shift from cold to warm occurs rapidly, as witnessed by the rapid onset of the Holocene, while the shift from warm to cold is a more leisurely affair. If this is true then this tipping point may behave more like a catastrophe than a strange attractor. Of course it is possible that if the MOC was disrupted during the onset of a glacial it might not have recovered so quickly, if at all. Science has much yet to learn about such things.

Jim Hansen, NASA's resident climate crank, has been widely quoted as stating that we have only 10 years left in which to take serious actions to prevent “dangerous anthropogenic interference” with Earth's future climate. He described this as a “tipping point,” but it should now be clear that he was not using the term correctly. Similarly, the new rash of tipping points come from people who really don't know what they are saying, but they know that it sounds scary and they have heard other “experts” use the term. So beware the next time you hear that we are approaching a “tipping point” that will do Earth “sudden” and “irreversible” harm—its really just a talking point by a climate change extremist.

Tipping points do occur in Earth's climate and other complex systems. Many such events can be identified in the paleo-record of our planet's climate history. However, predicting them remains a significant problem. Most of the claims about tipping points present and future remain just wild speculation. Of course Earth may get hit by another extinction causing asteroid (asteroids often have chaotic orbits). Now that would be a tipping point.

As always, enjoy the interglacial and stay skeptical.

An attractor by Alexis Rufatt that was just too pretty to leave out