Monday, January 30, 2006

Tipping points and climate change

A couple of years ago I read Malcolm Gladwell's The Tipping Point: How Little Things Can Make a Big Difference. For those who haven't read it, a "tipping point" is the point where a trend goes from rarity to ubiquity, where everything changes. Gladwell focused on sociology and marketing, and used murder and suicide rates and fashion trends as his examples. However, there's also a similar concept in chaos theory, of bifurcation, where an insignificant change in a value leads to phase or state change in a system (as illustrated in this diagram of the long-term behaviour of the logistic equation, or by the Lorenz attractor).

The relevance of this is that the global climate is a chaotic system - and scientists are becoming increasingly concerned about tipping points which could lead to irreversible climate change.

We've known that there are such tipping points for some time. A study of our planet's past climate shows that there have been sudden phase changes in the climate - and not just on a geological timescale, but a human one. According to The Weather Makers, ice cores from Greenland have shown that "spectacular shifts in the North Atlantic climate [have] occurred over just five annual ice-layers". They also show repeated shutdowns in the Gulf Stream (caused by large flows of fresh water into the North Atlantic due to melting ice) as the Earth came out of the last glacial period, leading to sudden coolings of up to 5 degrees for as little as two hundred years. In short, the changes can be sudden, jagged, and against the overall climate trend.

The Washington Post article linked above focuses on three possible tipping points:

widespread coral bleaching that could damage the world's fisheries within three decades; dramatic sea level rise by the end of the century that would take tens of thousands of years to reverse; and, within 200 years, a shutdown of the ocean current that moderates temperatures in northern Europe.

Flannery focuses on the Gulf Stream and two others: the desertification of the Amazon rainforest (due to higher CO2 reducing transpiration, and hence rainfall), and the release of methane from deep-sea clathrate beds (due to an increase in deep-sea temperatures). The latter two would produce massive positive feedback, accelerating existing warming trends and making them far, far worse. The former would paradoxically freeze Northern Europe and North America precisely at a time the world was warming overall. However, it would also lead to massive climate shifts in tropical regions due to heat being trapped at the equator.

The problem is that while we know of these tipping points and positive feedback loops in the global climate, we don't know exactly when they will occur - and therefore what level of CO2 emissions is safe (or at least manageable). Worse, we may already be past the tipping point, and not know it. The inertia in the global climate means that the full effects of today's emissions will not be felt until around 2050. We are already physically committed to at least a degree of climate change - and we have no idea yet whether that will be too much.

That alone should encourage us to adopt a precautionary approach, rather than simply leaving it for future generations to solve.


A key aspect of the the global climate is the remarkable stability of mean temperatures over periods of thousands of years. This stability is reflected in all the models by control loops. As an engineer who implements control loops on a daily basis, this aspect is especially compelling to me. The effect of a control loop, (or negative feedback) is to maintain a controlled variable (in this case temperature) stable against variations in a process (in this case external solar irradiation and internal changes such as the Great Ocean Conveyor current).

Most of the loops I deal with are very simple to analyse and predictable to work with. For example, opening a valve will increase the flow of steam into a heating vessel and will normally increase it's temperature in a predictable manner. In some cases however the material being heated exhibits an exothermic characteristic, and the temperature rise will be much harder to predict. The three big challenges to stable control are multiple variable interactions, non-linear responses, and time delays. In an industrial process we usually design the system to manage these three challenges. By contrast in the physical world, the nature of the processes that we are participating in are both complex and non-linear. And in many cases we are aware that our modelling is incomplete.

All attempts to analyse the global climate grapple with these challenges. One of the most alarming aspect is that mathematically we know that this class of process with these kinds of characteristics are prone to chaotic behaviour at the limits. The concept of "control limits" is crucial to this discussion. Going back to my simple steam heating loop. Normally if the temperature in the vessel is getting hotter than I want, all I have to do is close the steam valve somewhat and eventually the vessel will cool as desired. But if the process is behaving exothermically (ie it is generating it's own internal heat from a chemical reaction) then I will need to close the steam valve a lot more to stabilise the temperature. In fact it is quite possible that even fully closing the steam valve may not stabilise the temperature of the vessel. In other words I have reached the limit of my control action, and I have lost control of the process. (At the Motonui Methanol plant this point would be closely followed by a large explosion.)

Of course this is only an example. The key point to take away, is that control loops always have limits, and that when those limits are reached, the loop ceases to control. In terms of the global climate, it is entirely reasonable to assume that human greenhouse gas emissions are curently being "controlled" by a complex of feedback mechanisms. For this reason the observed temperature rise in the face of these emissions may well be small, UNTIL one or more of these loops reaches a limit.

Here is the problem though. In the case of my steam valve I can quite readily predict when the limits will occur, they will happen when it is fully closed or fully open, or I run out of steam. In the case of the global climate, we not only know far too little about the nature of the total system, but we know even less about it's control limits, and almost nothing about the likely behaviour at those limits. In fact the kind of linear loop analysis I am familiar with is totally inadequate to address this kind of is the specialty of mathematicians and numerical analysis experts who derive powerful and complex models using statistical methods to attempt these predictions. But however well evolved these models become, it is almost axiomatic however that chaotic and non-linear behaviour is an extremely likely consequence of unconstrained and rapid changes of the kind the human race has been indulging in over the last 50 short years.

Posted by Anonymous : 1/30/2006 02:19:00 PM

Observation of chaotic systems will always be hopelessly beyond us. We are limited by scale, by insufficient measurement of a system dependent on initial conditions, by the anthropic principle and its associated effect on outcomes. Quantum entanglement and probabilities complicate things further. Cause and effect become discrete things.

For good or ill, change is constant.
Every moment is a tipping point, a point of no return. While we can make some guesses as to causes of climate change, I think most of our energies would be better spent wargaming responses. How will we adapt if such a such?

Necessity is the mother of invention. It has got us this far. Unfortunately, I think it will take something suitably cataclysmic to focus our attention. As Alan Moore pointed out in Watchmen, give the world a big enough shock and the survival instinct supercedes everything, even fame, fortune and power.

Posted by Will de Cleene : 1/31/2006 01:46:00 AM

Icehawk, one can test aerodynamics in wind tunnels. You cannot testdrive earth's climate in one. A good example of this is the controversy over cloud seeding. In essence, one cannot replicate a cloud, so silver iodide may or may not help induce rain. We will never know.

I threw the anthropic principle and entanglement thing in a bit brutally. What I meant to convey was the limitation of human faculties on observing our surroundings. I'll happily withdraw the justifications, as they are best explained in a pub!

The New Orleans flood was nothing. You've got to get the scale right for a disaster to be an effective learning tool. Remember, an apocalypse is a revelation. Coal won't screw the Ozzies. Desertification and cane toad syndrome will do that.

M'lud, the scientist to first propose global cooling in the '70s (can't remember his name or where I read it) has since agreed that his theory was based on naive evidence. Climatology has come a long way since the 70s, but we are still like Newton on the shores of knowledge.

And as for weather, TV One predicted a little fog might hit Wellington South on Sunday morning. It shrouded the entire city all day and closed the airport.

Posted by Will de Cleene : 2/01/2006 09:33:00 PM