## Tuesday, August 21, 2007 ... /////

### Tipping points, sweet spots, and model ensembles

In his Musings about models, Gavin Schmidt discusses three topics:

1. Tipping points
2. Sweet spots
3. Model ensembles

Because there are both valid points as well as significant confusion in his short text, let's try to clarify the situation.

Tipping points

The term "tipping point" is often presented by global warming advocates as a well-established notion in natural sciences that is based on a solid theory and that should impress the audiences. In reality, the term is, at best, a vague talking point in the context of sciences. If you look what a "tipping point" means according to Wikipedia, you are being explained that it is a concept in sociology, not science, describing a point where some behavior suddenly becomes much more common. The name was chosen in analogy with "tipping points" in mechanics: sociologists were entertained when they saw that adding weight to a bananced object can eventually topple it and decided that they must use this fascinating phenomenon in their work, too. ;-)

The disambiguation page offers you several additional meanings of the term:

1. the term in sociology we mentioned
2. a book about sociology
3. a musical album
4. a band
5. a computer security provider
6. climate surprise.

You see that only the last meaning, the "climate surprise", is related to natural sciences. Why is it called "climate surprise"? Well, it is because these hypothetical effects have a very low probability, as the Wikipedia page explains. Although "tipping points in the climate" and "climate surprise" are the same thing, certain people prefer to talk about "tipping points" so that they hide that these effects have a very low probability.

A collapse of the thermohaline circulation or rapid deglaciation of both polar ice sheets are examples. There has been a lot of recent literature explaining why these events are very unlikely and commenters may mention some links to the papers in the comments. Don't worry: the Gulf Stream is certainly not stopping especially because it is driven by winds i.e. indirectly by the rotation of Earth and so far, not even James Hansen predicts that the Earth will stop spinning.

Schmidt refers to an article by Tim Lenton who talks about the tipping points and also writes the following:

The parameters controlling the system can be transparently combined into a single control, and there exists a critical value of this control from which a small perturbation leads to a qualitative change in a crucial feature of the system, after some observation time.
Well, if Tim Lenton knew concepts in thermodynamics, he wouldn't have to invent this new awkward terminology. A closely related concept in thermodynamics is called "phase transition" while the "single control" is called "order parameter". Clearly, we need to generalize the thermodynamical concept if we want to cover diverse speculative and complex scenarios about the climate but it's possible.

A more important question is whether such tipping points are around or whether it is at least somewhat likely that they are nearby.

This question should be answered individually for different kinds of tipping points but let me say a few general words instead. The tipping points could hypothetically appear in situations that may be roughly divided to two groups:
1. clean physical systems with a predictable behavior
2. chaotic physical systems with a largely unpredictable behavior and a lot of mutually interacting objects

Quite generally, the tipping points in the first group are easily accessible to physicists and they may resemble sharp phase transitions. On the other hand, the hypothetical tipping points in the second case are always fuzzy and they only influence a small part of the physical system because different components of the system respond differently.

Let me say a few examples. If you have a lot of uranium in one place, you may eventually reach a tipping point - the critical mass - that will lead to a nuclear explosion, a chain reaction in which the number of neutrons exponentially grows for a while. Such an exploding mass of uranium is a rather clean (conceptually) system that may be studied by physicists and the change of the behavior is fast, indeed.

If your temperature reaches the melting point or another temperature of a phase transition, ice can start to melt or water may start to evaporate. There is indeed a tipping point - a phase transition - waiting for us once the temperature of oceans reaches 100 Celsius degrees. Will it happen by Christmas 2014? I leave this question to Al Gore.

The Arctic regions don't have too much life in them and they are rather simple physical systems. We mostly know what can happen with these physical systems and there are no tipping points nearby because they would have to resemble conventional phase transitions that have been classified. On the other hand, dynamics of the atmosphere and biosphere in the moderate zones is so complex that no hypothetical tipping point is really sharp or qualitative and no hypothetical tipping point influences the whole biosphere coupled to the atmosphere at the same time.

Rationally speaking, we simply don't expect any discontinuous transitions of this kind. The higher number of components you have, the more continuous the behavior of any kind of physical average becomes. Of course that there can always exist some transitions that we haven't thought about and that will look like climate miracles or other miracles. But I, for one, prefer if scientists only believe miracles that are supported by some rational arguments. If Jesus Christ returns to the Earth this winter, then - well - let Him rule. It's not a business for science to analyze unlikely scenarios that can't be studied by doable experiments and robust mathematics.

We should end up with the conclusion that any conceivable, large enough, physically driven effect of the climate on life will proceed continuously and we will never be completely shocked. As far as science goes, tipping points don't exist. Let us look at the second topic.

Sweet spots

What does Gavin mean by the sweet spots? He means a vague idea that also occurs in sweet-spot supersymmetry. We have already discussed a recent article by Doug Smith et al. The term "sweet spot" refers to a balance between the natural effects and the industrial influence. The idea is that the natural effects are just a short-term noise while the industrial influence is the effect that survives in the long run. The sweet spot is what we see in the medium term (five years?). This assumption itself is a kind of bias: it would be more reasonable to link humans with the short-term changes of the Earth while the natural effects dominate in the long run. But let us assume that their identification is fine and proceed.

Smith et al. realize very clearly that regardless of their detailed calculation, it is rather likely that there will be no visible warming until 2009. And I think that they are driven by their belief in global warming and are afraid that others won't believe it if there are several additional years without warming. So they essentially say that until 2009, the natural forces may still be winning while after 2009, a warming may start again.

Is it possible? Of course that it is possible. But in science, we must go well beyond the labels possible/impossible because virtually everything that doesn't grossly violate the laws of physics is possible. We must care whether it is likely and whether we have evidence that it is likely. Imagine that there will be cooling from 2005 to 2009. People in 2009 may state the hypothesis of Doug Smith et al.:

• Natural forces were winning and cooling the Earth in 2005-2009 but a warming trend will start really soon.

Will this sentence be true? Well, we must realize that this is not one sentence but two sentences:

1. "Natural forces were winning in 2005-2009 and their net impact was cooling" will be a proven statement.
2. "A warming is gonna start in 2009" will be an unproven hypothesis.

It is a popular strategy of various demagogues to connect a true, proved assertion with a speculation (or even untrue statement) and sell them as one product. The proved part of the product gives it credibility while the other part gives the demagogue what he wants. The demagogues do their best to convince people not to distinguish the very different parts of the package. For example, a package says that "the globe has warmed by 0.6 Celsius degrees or so; our survival requires us to stop all CO2 emissions." The first part is likely to be true but the second part is complete nonsense. Demagogues will give you some evidence for the former statement and pretend that they have proved the latter statement.

Well, I would encourage every single person to be careful about these tricks. Every composite sentence must be separated into pieces that must be evaluated independently.

When you do so in the case of Doug Smith et al., you will see that their paper is really a union of two independent papers. One of them tries to analyze the climate in the short run and shows that there will be some particular fluctuations until 2009. And the other part of the paper tries to repeat clichés about anthropogenic global warming. These two parts are incoherently connected into a single paper.

That's not how a wise scientist should analyze complex problems. A wise scientist should follow Galileo's recipes and always try to separate a complex situation into pieces that can be studied in isolation because we can only reliably understand a complex system if we understand its components. If you do so, you will find out that it is the natural causes that are at least partially understood - and the weather can be predicted at least for a few days - while the industrial influence is not demonstrated or quantified. The research of the natural phenomena in the climate is a natural science where a large amount of data exists and many of them are processed in some kind of scientific way that makes some progress.

But the research of the industrial influence is something else: it is a doctrine about a single number - the overall temperature change caused by CO2 - that has never been measured or proven to be significantly nonzero and that has never been used in any kind of scientifically nontrivial calculation. But ths single number is claimed to be one of the key results of all of science. Once again, these two very different human activities are being sold as one package. One must be careful: climatology is not pure junk. Current climatology is a combination of science and junk science.

Finally, we approach the third topic:

Model ensembles

It is a great news to see that Gavin Schmidt realizes that averages and probabilities calculated from an ensemble of models are not the same thing as averages and probabilities in the real world.

If you work with one thousand climate models and run them on one million computers, it doesn't mean that the statistical characteristics of this ensemble will give you a more accurate representation of reality. Imagine that an ensemble of one million models predicts that the temperature will change by 2 degrees plus minus 1 degree by 2100. Does it mean that you should take this number very seriously because you used one million models?

Not at all. The actual temperature change can be very different. The accuracy indicated by the ensemble of the climate models can be both much larger as well as much smaller than the uncertainty in reality. Let me explain why.

If someone actually has a very accurate model, for example because he is a better physicist, he could predict the temperature change very accurately. And maybe, the temperature change could be pretty exactly calculable if one is smart enough. But if you add almost one million of other models that are not that good, their statistical distribution becomes fuzzy even though someone might be able to do a better prediction individually.

The opposite situation occurs more often. If you have one million models, it doesn't mean that they nicely cover the neighborhood of the right answer. Even one million models may share a systematic error, a neglected yet important physical effect, and other things. The authors of these models could have been copying from each other and perhaps, none of them understands the physics too well. As Richard Feynman emphasized in his cute story, you can't get a good idea about the length of the Chinese emperor's nose just by averaging a large number of answers by people who haven't seen the emperor. Try to find emperor's assistant and ask her.

And that's the memo.