Sunny’s post at Lib Con, questioning whether us lefties are angry enough, has prompted some interesting and wide-ranging exchanges, not least on the subject of climate change, during which DK threw this retort into the pot:

You know that I write about this a lot and, probably unlike you, I have looked at the raw data sets. I also happen to understand science and statistical analysis.

Ordinarily, I’d have nothing to quibble about when DK throws in that kind of assertion, but when it comes to climate science, DK’s retort becomes a little more questionable not because of any great fault in his own understanding of the material he’s reading and basing his views upon but because of underlying problems with the science he’s dealing with on both sides of the argument surrounding anthropogenic climate change theory.

There’s a perfect illustration of the problem is this recent post of DK’s on the role of ‘positive feedback’ in climate science and it relationship to ‘tipping point’ theory, which suggests that there will come a point at which changes in climate caused by human activity give rise to sufficient new processes to make those changes irreversible and, at the most extreme end of predictions based on this theory this could result in a ‘climate surprise’, a sudden and potentially catastrophic event such as the rapid and irreversible melting of the polar ice caps or the thawing of the Arctic tundra, i.e. a ‘doomsday scenario’.

Doomsday scenarios loom large in the politics surrounding anthropogenic climate change theory on both side of the debate. For those who support AGW (anthropogenic global warming) theory, tipping point theory delivers a set of hypothetical worst case scenarios of significant political and cultural value. Nothing sells, in the popular conscience, quite so well as good old fashioned scare story and climatology has some of the best and most ‘biblical’ you’ll find anywhere; floods, famine, desertification of temperate areas, you name it and there’ll be a doomsday scenario somewhere in the AGW canon to suit.

And on the other side of argument, considerable amounts of time and effort are, of course, invested in seeking to ‘debunk’ not just AGW theory but, in particular, its ‘tipping point’ elements for a variety of reasons, many of which have much more to do with politics than they would or could ever have to do with science.

Now, I’m not going to question DK’s motives here because, frankly, they’re of no great relevance to the issue at hand, which is the science, but if he and others think that the two papers referenced in his article serve to disprove ‘tipping point’ theory then he, and the others he links to who seem to believe the same thing, are sadly mistaken, and not because they’ve misinterpreted the papers in question or failed to understand their contents in scientific terms but because their authors have failed to acknowledge a critical limitation in their science, a limitation that runs through the vast bulk of research in climatology.

Perhaps the best way to begin to explain the problem is by way of one of may favourite, if possibly apocryphal scientific anecdotes, one that relates to the great physicist Werner Heisenberg. Heisenberg was, so the story goes, once asked by a journalist what questions he would ask god – presumably after his death – to which Heisenberg reputedly replied, ‘Why quantum mechanics?’ and, ‘Why turbulence?’, before mischievously adding, ‘I really think he may have an answer to the first question.’ (Heisenberg’s PhD thesis was on turbulence, hence his interest).

Now that may seem something of an odd and counter-intuitive observation to make, after all quantum mechanics is very much the stuff of ‘big’ science, of nuclear physics and cosmology, while turbulence seems to be something that is very more mundane and down to earth, presenting problems that are dealt with as a matter of routine by engineers when designing and developing everything from hydraulic control systems to jet aircraft and Formula 1 racing cars. Even the humble family saloon car gets a look-in as one of the better known effects of turbulence is aerodynamic drag, the reduction of which in car body design can improve fuel efficiency.

However, if one looks at things mathematically, turbulence is much ‘bigger’ science than it might, at first sight, seem, because turbulence, like many other real world physical systems, is non-linear and non-linear problems are complex, difficult to solve and difficult to understand. Unlike linear equations, which even if not exactly solvable still tend to be reliably predictable, non-linear equations are inherently unpredictable.

Even a relatively small scale non-linear system, say the turbulence one sees in cigarette smoke, is difficult if not impossible to map accurately with a high degree of mathematical precision – to get even a very close approximation would require massive amounts of computation power – and so, to get around that problem what scientist do is make use of linear equations which provide a ‘good’ approximation but which allow either for predictions to be made or, at least, being the computational power required for modelling a non-linear system within reach of the computer systems they have available to them. In scientific terms, the use of such approximations is a perfect valid approach, for example astronomers and space scientist will almost always use Newtonian gravitational equations to solve problems, even if these provide only a very (very) good approximation, rather than resort to Einstein’s equations which give greater accuracy but at the cost of being much more difficult (and time consuming) to solve because, in most case, the Newtonian equations are good enough for the job at hand.

Looking through the two papers in question, those of Miskolczi and Schwartz (both pdf) this is precisely the approach both have taken, which is perfectly reasonable as this is also approach that underpins Milne’s equations, which they claimed to have proved to be wrong. In actual fact, proof is far to strong a term to be using at this stage, what Miskolczi has suggested is a variation on the original equations, which relies on the inclusion of a term to account for negative feedback that may or may not prove to be valid in the long run. It’s actually too early to say, definitively, whether his equations are an improvement on Milne’s or whether his negative feedback term is an unnecessary addition similar to Einstein’s cosmological constant, which was subsequently shown to be incorrect by Edwin Hubble. That’s not to dismiss Miskolczi out of hand, merely to point out that much more empirical work stills needs to be done with his equations in order to establish their validity or otherwise, so its rather overstating the case to suggest, right now, that one should dismiss large tracts of existing climate science on the strength of one or two research papers – slam dunks just don;t happen in science all that often.

However, even if Miskolczi’s equations do prove to be correct they do not, contrary to the manner in which they have been presented, fatally undermine tipping point theory, in fact they have little or no bearing on tipping point theory itself because the theory actually relies on a very different kind of mathematics than that used by Miskolczi, or that of Milne for that matter.

I’ve already pointed out, a little earlier, the problems and complexities that arise in science when dealing with non-linear system, and by far the largest scale non-linear system we have to deal with, outside the rarefied realms of cosmology, is the Earth’s climate. As a result it is nigh on impossible to make accurate predictions about the future of the Earth’s climate, its sheer scale and non-linearity means that the mathematical and computational demands of accurately modelling the global climate are beyond the capacity of current technology and will stay well beyond that capacity for the foreseeable future but for a spectacular break-though in the very new and speculative field of quantum computing. So even the very best and most rigorous science on either side of the climate change debate will consist of nothing more than generalisations and approximations in which there is considerable margin for error, in fact, when bring chaos theory to bear, even the most minute of approximation errors in setting the initial conditions of a climate model can rapidly render the output of the model, its predictions, almost entirely meaningless, a concept generally referred to as ‘the butterfly effect‘.

Nevertheless, if we assume for the moment – as we actually do – that the climate of the Earth is currently is state of relatively stable equilibrium and has been for the last 8,000 years or so years, since the end of the last ‘ice age’ (the Pleistocene glaciation) – in fact, we live in an interglacial period between ‘ice ages’, although the most up to date research suggests that the next glacial period is probably not due for another 18-20,000 years give or take any effects of human activity which may, or may not, be having an effect on the global climate – then although chaos theory does not allow us to make accurate predictions about precisely what may happen if we hit a ‘tipping point’, or under what conditions a tipping point will be reached, it does allow us to make a general prediction that should such a point be reached then one of three things will happen:

1) The Earth’s climate will fly completely out of control, although in which direction is uncertain – we could wind up with a Venus-style hothouse or it could go the other way and precipitate a shift back into another severe ‘ice age’. (And before any of the usual ‘b-b-but it’s global warming‘ comments come in, if you don’t understand how an overall warming of the Earth’s atmosphere could trigger off a shift into another phase of rapid cooling and a ice age then you don’t understand enough about the science of climatology to comment on the subject.)

2) The Earth’s climate could shift out of its current state of relative equilibrium only to find a new state of equilibrium, which sounds reasonably unthreatening until one realises that its impossible to predict quite how far such a shift might go and how quickly it might happen, and while we are pretty resilient species its far from clear in what kind of state we might emerge from such a shift. Ice Age theory is, for example, broadly a reflection of this idea of the Earth shifting periodically between two states of equilibrium, which, in chaos theory, is called ‘multistability’.

3) The Earth’s climate could enter a phase of aperiodic (or chaotic) oscillation or, in layman’s terms, end up all of the place with no mean of predicting reliably, where the climate will go next or how quickly the next phase of changes will occur.

Relative to where we are now, i.e. the relative climatic stability of the holocene interglacial period, none of these three possibilities look particularly enticing, in fact they all look to have the potential for generating doomsday scenarios if the changes happen rapidly over a short space of time, as would be the case were there to be a ‘climate surprise’.

And that, is the actual basis of tipping point theory and the concept of a ‘climate surprise’ and, crucially, its a premise that exists and operates entirely independently of any ongoing research into anthropogenic climate change theory for the simple reason that the purpose of this research is not to try and prove (or disprove) tipping point theory but to actually try to identify whether or not we’ve actually entered (or are close to entering) a tipping point phase – in that sense, what climate science is attempting to do is predict the unpredictable.

And if that were not enough to be going on with, chaos theory has a couple more tricks up its sleeve to confuse and confound matters even further. A few paragraphs ago a I mentioned that while chaos theory does not allow us to make detailed predictions about the future of the Earth’s climate, it does allow us to make predictions about what will happen should we actually hit a tipping point…

…Well that’s not quite true, because it doesn’t really tell us what will happen, only that what might happen if the tipping point actually triggers a major change event. You see the tipping point isn’t isn’t actually a hard and fast rule, its more of a matter of risk and probability – the closer you are to reaching a tipping point, and certainly once you exceed such a point, the more likely it is that there will be a ‘climate surprise’ and/or a major change event, although its not certain, by any means, that such an event will happen. And this is true regardless of whether climate change is happening naturally or being forced by anything from human activity, to changes in solar activity and solar radiation output to any one of a number of cataclysmic events, i.e. volcanic activity, an asteroid strike, etc.

The other little surprise that chaos theory has up its sleeve is that its not necessarily the case that any increased risk of a ‘climate surprise’ is contingent only on global changes in climate, in fact such an event could just as easily be triggered by a localised change in climate. Remember the butterfly effect? You know, very small changes in initial conditions can give rise to massive difference in outcomes hence the idea that a butterfly flapping its wings in the Amazon could give rise to tornadoes in Surrey?

The inability of many opponents of AGW theory to grasp the importance of this concept is what spawns many of the more risible pieces of bad science – or rather the more risible pieces of bad reporting of good science, of which one of the ‘better’ examples can be found in this recent article in the National Post:

Snow cover over North America and much of Siberia, Mongolia and China is greater than at any time since 1966.

The U.S. National Climatic Data Center (NCDC) reported that many American cities and towns suffered record cold temperatures in January and early February. According to the NCDC, the average temperature in January “was -0.3 F cooler than the 1901-2000 (20th century) average.”

China is surviving its most brutal winter in a century. Temperatures in the normally balmy south were so low for so long that some middle-sized cities went days and even weeks without electricity because once power lines had toppled it was too cold or too icy to repair them.

All of which leads the article’s author, Lorne Gunter, to the following unscientific musings:

OK, so one winter does not a climate make. It would be premature to claim an Ice Age is looming just because we have had one of our most brutal winters in decades.

But if environmentalists and environment reporters can run around shrieking about the manmade destruction of the natural order every time a robin shows up on Georgian Bay two weeks early, then it is at least fair game to use this winter’s weather stories to wonder whether the alarmist (sic) are being a tad premature.

It would help immeasurably if journalist covering stories like this possessed even a basic understanding of the nature of the hydrologic cycle as it would save the trouble of embarrassing themselves with such dumbass observations as the actual science is simple enough, in fact its basic GSCE level at best. Increasing the air temperature, particularly in tropical regions, increases both the amount of water vapour in the atmosphere and the capacity of the atmosphere to hold water vapour; air currents move this warm humid and water-laden air around the globe until its hits cold air currents coming down (or up) from the poles (or from high mountainous regions) and there you go, you get localised increases in precipitation in certain areas, whether in the form of rain or snow, all caused by warming elsewhere – the fact that they may be freezing their tits off under several inches of unseasonal snowfalls in Beijing doesn’t mean its not getting warmer over all, it just means that Beijing is where all the additional water vapour thrown up into the atmosphere by warming in the Pacific is getting dumped.

Britain has its own version of this particular fallacy because its been suggested, perfectly reasonably, that warming in the Caribbean could result in climatic changes which leave the UK facing a ‘mini Ice Age’, a theory that, when it periodically surfaces, tends to get some sort of idiot (usually in Daily Mail) all hot under the collar, prompting them to announce that its all a fraud and that global warming couldn’t possibly be true because if it was scientists would predicting that Britain’s climate would be getting warmer not that there’s a risk it could get much colder.

The fact is that Britain’s climate should, all other things being equal, be both much drier and colder than it actually is, and this would indeed be the case were it not for the North Atlantic current of the Gulf Stream, which acts to keep things relatively mild up here if, generally, a little on the wet side when compared to other areas at the same latitude, and the importance of the Gulf Stream is perhaps best illustrated by comparing the climate in London with that of another city at roughly the same latitude, and for illustrative purposes we’ll take Kiev, in the Ukraine, which at a latitude of 50.30N is actually a matter of 69 miles close to the Equator than London. Looking at average high and low temperatures for the two cities, London ranges from a bottom end average of around 2.2C° in February to a top end average of 22.6C° in July with average monthly precipitation, over the year, in a relatively narrow range from 34mm (February) to 61 mm (October). Kiev, on the other hand, manages a bottom end average of -8.4°C in January and a top end average of 25.3°C in July and has a higher average level of precipitation, ranging from 39mm in March to 88mm in July – unlike London, where the second driest month of the year (July) is also the hottest, Kiev’s hottest month (also July) is also its wettest, and it also manages to have snow cover on the ground pretty much constantly from mid-November to the end of March, despite being a little closer to the Equator than London.

The Gulf Stream is what gives the UK its distinctive and relatively warm, mild, climate – without it our winters would certainly be much more akin to those experienced as a matter of routine by the residents of Kiev, and the predictions that global warming, particularly warming in the Caribbean, could result in freezing conditions in the UK are based on a relatively straightforward premise, one that suggests that one of the consequence of warming could be a shift in the direction of North Atlantic current, one that, if it were to move to the South, would leave us with the vast bulk of out prevailing weather being drawn down from the Arctic, in which case, global warming would leave us freezing our tits off.

What these examples illustrates – and there are certainly more, I’ve just picked on a couple of the obvious ones – is the central problem you too often find when reading the views of opponents of anthropogenic climate change theory, this being that while there are certainly valid questions to be asked about some of the evidence being advanced in favour of the theory, particularly where that evidence is derived from linear climate modelling, the stuff that too often makes the headlines and gets put up as ‘proof’ that AGW theory is invalid tends to be a load of unscientific bollocks like the ‘how can there be global warming if scientists are predicting that Britain might freeze’ stuff I’ve noted above. The ‘why’ of such predictions is actually very simple once you understand the underlying science, in fact its embarrassingly simple.

Speaking personally, I try to make a point of maintaining a healthy scepticism about both sides of this particular debate, not because I’m particularly sceptical about AGW theory itself – if nothing else, the one thing that chaos theory does predict is that even very small changes in atmospheric composition arising out of human activity could trigger a ‘climate surprise’, but then so too could any number of other natural events – but simply because I do think that that, in long run, other issues will come to overtake climate change at the top of the global political agenda. In fact we’re beginning to see one such issue emerge. Over the last year there have been protests in Mexico over the rising cost of basic foodstuffs and, in the last week or so, food riots in Egypt, each of which are signs that we may be moving into a period in which some of the currently dominant ideological assumptions of global capitalism may come under serious challenge, not least of which being the belief, held by many on the right, that the ‘market will provide’ – or at least regulate demand and encourage supply side innovation sufficiently to keep things ticking over nicely.

If those assumptions turn out not to be true, and the emergence of food riots/protests are one clear sign that critical global markets may be beginning to approach the kind of boundary conditions at which markets will cease to function ‘as intended’, then those who right to cling such beliefs may have rather more to be worried about than the validity of AGW theory.