## Friday, November 05, 2010

### Tamino and man-made Arctic odds

Grant Tamino Foster (no suit on the picture) tries to answer the question:
How likely?
More precisely, the question is:
Now, my question is, if you know the answer: How high is the probability that arctic change is caused by AGW versus that is just natural variation of some kind (confidence level)?
His "calculation" is completely meaningless. It's not a real calculation.

A genuine calculation should try to find an objective - or mostly objective - value of an unknown number. However, Tamino's "calculation" uses two completely subjective (and unreasonably high) parameters as the input. They're inserted into Bayes' theorem, to achieve a completely nonsensical answer - namely that the probability above is 99.7%.

Tamino's article is another flagrant example of the pseudoscientific nature of the climate disruption ideology.

The role of mathematics has been reduced to the job of a prostitute whose task is to make this nonsensical propaganda look more serious. However, the results that the mathematics is obliged to produce are determined a priori. The values of the input paramaters - and details of the calculations - are simply adjusted to produce the results - or at least qualitative results - that were decided to come out before any calculation.

I still prefer ordinary types of religion that at least don't try to pretend that their dogmas can be proved mathematically. It's because I simply hate maths - the Queen of Sciences - to be abused in these perverse ways.

A more sensible calculation

The first fact you have to notice is that the propositions in the sentence whose likelihood we should compute are ill-defined. Both of them are ill-defined, in fact. Recall that we are expected to
calculate the probability that the Arctic change ("X") is caused by anthropogenic global warming ("A").
Both "Arctic change" as well as "Anthropogenic global warming" are undefined concepts - even though Tamino tries to make them a bit more precise but he fails. (Which change? Everything is changing in some ways. Which role of the humans? Humans are surely here so they inevitably can be observed directly or indirectly in some way, too.)

Even more importantly, the character of the "causation" whose probability we should calculate is unspecified. As written above, the question is completely meaningless. There are two extreme interpretations of what the "causation" could mean. One of them is:
All of the changes in the Arctic are determined solely by anthropogenic global warming.
Clearly, this is a preposterous statement because there are many other local meteorological - and other - phenomena that drive the variability and trends (we understand some of them), at many time scales, in the Arctic. So the probability of the proposition above is obviously 0%.

On the other hand, the statement could also mean:
The Arctic changes are influenced by AGW and the influence is nonzero.
Whatever AGW is, as long as it is well-defined and it exists, the probability above is clearly 100%. Every phenomenon has a nonzero impact on every other phenomenon although the influence may often be extremely small.

Now, we can interpret the sentence as "something in between" the two extreme sentences. We may be interested in the extent. By doing so, the resulting probability may be any number between 0% and 100%. But every probability is between 0% and 100% so we can calculate exactly nothing unless we define the things damn accurately.

But even if you clarified all these things, and talked e.g. about "at least 1/2 of the change of the Arctic sea ice in the last 50 years" and if you defined "anthropogenic global warming" or anything like that, the question about the probability is completely irrational for one more reason that completely eludes Tamino.

Tamino's question is equivalent to:
If we know that the Arctic was changing (in some way, to be specified in detail), what is the probability that AGW is real and it caused it?
In the real world, the condition in this conditional probability is redundant - simply because we know that the Arctic has experienced some changes. So in the real world - if you're allowed to use any known data about the world - the question is equivalent to the question
What is the probability that AGW exists?
It doesn't matter that the formulation of the question wants to focus our attention on the changes in the Arctic. If we're supposed to make the most accurate calculation of the odds in the real world, we must clearly use all the known data, not just those from the Arctic.

If looked at rationally, the Arctic plays absolutely no privileged role in the question. All places are equally relevant; for example, the Antarctica is relevant for Tamino the Penguin. ;-) This is another aspect of the irrationality of environmentalism: effects and places are taken out of the context and the readers are being brainwashed and led to think that nothing except for the out-of-context observations and places exists. When they repeat a statement about a polar bear, the goal is to make the listeners forget that there exists anything else than the polar bear.

But places and phenomena and data outside the Arctic exist, too. They surely do influence the probability of any proposition concerned with the human influence on the climate. And the non-Arctic considerations can't be sharply separated from the Arctic ones because most of them are correlated with the Arctic data to one extent or another.

On the other, the question could also mean that you are not supposed to use any other data except for those in the Arctic. Try to imagine that you're strict about it and you ask:
What is the probability that the observed Arctic change of something was caused by AGW? You're not allowed to use any other data than the fact that the Arctic has changed in the way one can describe.
Isn't not hard to see that one can't calculate the answer to this question at all. If we're not allowed to use the knowledge of physics about the actual climate, there's no conceivable way how we could calculate the probabilities that "A" causes "X". No scientific link between "A" and "X" can be uncovered without looking at some other facts about the global climate and its connections with the Arctic weather. Depending on additional choices, priors, and assumptions, the likelihood of the uncalculable proposition above may be anything in between 0% and 100%, too.

So there is a trade-off: the question above is completely uncalculable because you're actually not allowed to look at the global climate; or it has nothing to do with the Arctic; or something in between. This is another, independent reason why the answer to Tamino's question can be any number between 0% and 100%. The question makes no sense.

We can refine the question in somewhat more sensible ways. First, let us ask:
If we assume that AGW exists and its magnitude is equal to what we have actually observed in the global temperature graphs, what is the probability that it causes a positive warming of a random polar region in 50 years?
I have assumed that we're not allowed to use any "very specific" features of the Arctic that are not shared e.g. by the Antarctica. The question above is closer to the reverted conditional probability, an issue to be discussed later.

However, it's clear that the question above has another completely general and persistent bug: it has nothing to do with the adjective "man-made". The calculation cannot take the "man-made" property into account at all whether this property is real or not. If non-man-made effects are responsible for the very same changes of the global mean temperature, the probability above will be completely unchanged.

For rational people, it's not hard to see why but the AGW crusaders have a breathtaking difficulty to understand the following proposition: the temperature graphs themselves can't imply any attribution to humans.

Fine. So let us admit that no conceivable simple enough clarification of Tamino's question can be linked to the climate change's being "man-made" in any way. Let's continue to ask the same question, without the focus on the "man-made" adjective. First, let's ask:
If you assume the observed changes of the global mean temperature in the last 50 years, what is the probability that a polar region will get warmer in 50 years as well?
This is, of course, a much more well-defined question. The two parts of the sentence are not independent which is why the probability will be higher than 50%. After all, the polar regions contribute to the global mean temperature, so it's not unreasonable to expect that there is a positive correlation between the changes of the temperature of the polar regions (or other regions!) and the global mean temperature.

But how much higher the probability is compared to 50%? Can we calculate it?

Well, we may choose the maximum number of polar regions and estimate the probability directly from the observed statistics. The Arctic got warmer, the Antarctic got a bit cooler, so the probability that a polar region gets warmer - given the assumptions that were realized so we can forget them - is estimated to be 50%. It will get either warmer or cooler and the odds are equal.

This is a stretched calculation that only used two bits of information. You may correctly guess that we can use "more information" about the changes of the temperatures of the polar regions to get a result that could be expected to be more accurate. After all, the Antarctica's change was close to zero, so because the Arctic got warmer, it should make the warming of a polar region more likely than the cooling, right? Can we calculate how much more likely?

Yes, all such things may be calculated but none of the results will be terribly canonical and none of the calculated numbers will be robust. In the last 50 years, we may assume that the Arctic got warmer by "delta T" while the Antarctica didn't change. In the simplest "normal" model, the polar regions are changing by some number (signal) that may be correlated with the global mean temperature's change. But there's also some noise.

In this case, we may use the two pieces of data to quantify it. The average temperature of a polar region increased by "delta T / 2" (the signal). However, the standard deviation is "delta T / 2" as well because both "delta T" and "0" have this distance (the noise) from the average, i.e. from "delta T / 2".

So we know that the warming of a polar region in 50 years is statistically given by "delta T / 2" plus minus "delta T / 2". ;-) What is the probability that such a warming ends up being positive?

Well, that's a simple question about the normal distribution. It gets positive if we're on the right side from "-1 sigma" in the graph above. So the probability is 34.1+34.1+13.6+2.1+0.1 percent which is 84 percent. As far as the changes of the Arctic and Antarctic temperatures can say, the probability that a polar region gets warmer is 84%. Note that the odds are about 5-to-1 that it gets warmer.

While it is significantly more likely that a polar region will see the 50-year temperature change whose sign is aligned with the change of the global mean temperature, the opposite possibility has a probability that is certainly not negligible.

Even if you believe that the globe will "certainly" get warmer in the next 50 years - which is far from guaranteed - and even if you believe that this warming is linked to the human activity - which is unlikely and has no impact on the calculation, anyway - then there is still a 1-in-6 chance that your polar region will get cooler.

You throw dice and you get six. If that occurs, then the trillions of dollars that you will have spent to cool the globe (by a tiny bit) will have actually made the "climate change" (a tiny bit) worse for you because your favorite polar region (or another region) will have actually evolved in the opposite way than you assumed. Note that there will only be one 21st century so if the mankind loses the bet, there won't be any chance to get the money back (as statistics would allow for many repetitions of the 21st century).

If you include some realistic uncertainties about the question whether the globe will get warmer at all, and whether the human contribution is measurable or not, you will see that the probability that your trillions of dollars have "slowed down" or "sped up" the climate change on the place you care about are pretty much balanced.

You will have paid trillions of dollars for a lottery ticket that is almost equally likely to make your life better or worse. Moreover, if you realize that the carbon reductions will contribute negatively to the global mean temperature and a cooler globe is almost certainly worse for you, you can be pretty sure that by having paid trillions of dollars, you will have made the things worse much more likely than better. You will have paid twice.

And I even graciously overlook those trillions of wasted dollars (and their consequences) because you (who is an environmentalist in this thought experiment) will have stolen the money from others, anyway, so you clearly don't care. Environmentalists never care about the money because they steal them and they think that they can steal as much as they want by spreading a sufficient number of lies.

So far, I have asked what is the probability that the observed global change "helps to produce" a local change of the same sign. But Tamino's original conditional probability was ordered in the opposite way:
What is the probability that the globe gets warmer if a polar region gets warmer?
Again, these naive statistical calculations - that don't analyze the detailed physics and flows of energy - have absolutely no chance to say anything about the changes' being man-made, or about the proportion of the man-made contribution - simply because it makes no impact on any of the global/local considerations we are looking at.

However, the question above makes some sense. We have determined the opposite probability - that a polar region warms if the globe does - and a good enough number we ended up was 84%. Note that the detailed value of this number makes no sense in the real world; however, we may still say that it would be approaching 100% for a smaller globe with a small number of "independent meteorological regions" (where the concept of a global temperature would be more useful for everyone). If we knew "everything" about the real world, all probabilities of similar propositions would be either 0% or 100%. The numbers in between always require some ignorance and ignorance is always subjective as well as hopefully temporary, so there is no objective eternal meaning in any of these probabilities if they're between 0% and 100%.

However, they still have some subjective sense. The ordering of the conditional probability may be reverted by Bayes' theorem.
P(A|X) = P(X|A) P(A) / P(X)
We have calculated that "P(X|A)" - the probability of a warmer Arctic given a warmer globe - was 84%. But what are the other factors? "P(A)" in the numerator is the prior probability of global warming. It's important that for the Arctic to be a special condition that changes the game, we haven't used it yet. So we're not allowed to use other data from the real world, either because we couldn't isolate the knowledge about the Arctic from them.

It means that the prior probability of global warming, "P(A)", is 50%. Warming and cooling are equally likely. On the other hand, the "P(X)" in the denominator is the marginal probability of the Arctic warming. It's a normalization constant that is inserted to guarantee that the conditional probabilities "P(A_i|X)" add to one.

If we don't use any other information, the warming and cooling are equally likely both for the polar region as well as the globe so all these probabilities, including "P(X)", are equal to 50%. So the 50% factors cancel and the probability we wanted to calculate is 84% once again.

As I have mentioned, 84% is a very shaky probability to be certain about anything. It's less than two units of evidence supporting the aligned sign of the changes of the two temperatures. One can say that it's no scientific evidence at all. It's pure noise. Betting on the 84% being certainty - in an event that only occurs once - is a pure speculation because the figure depended on the details how it was calculated.

Also, there are several fundamentally inequivalent big uncertainties of this type in the climate disruption debate.

To "save the Arctic" by regulating the carbon dioxide according to the IPCC prescription, you need several - at least four - independent conditions to hold simultaneously. If at least one of them fails, you are going to waste your money. You need the expensive and annoying regulation to impact the CO2 emissions; you need the CO2 emissions to influence temperature more than the other, mostly natural factors; you need the Arctic's temperature to evolve in the same direction as the global one; you need to assume that a cooler Arctic is better for the world (and the locals) than a warmer Arctic.

Several extra conditions should be added in a more refined debate. But let's just work with these four.

Imagine that you're an AGW believer and in your opinion, it's similarly "more likely than not" for each condition to be satisfied - which is extremely improbably by itself - and the probabilities are 84% for each of them. What is the probability that all of them are satisfied? Well, it's
0.84 x 0.84 x 0.84 x 0.84 = 0.498.
The probability that you make things better because of the exact reasons you believed is actually lower than 50%. In the remaining 50% of cases, you either make things worse, or you can make them (slightly) better but for reasons that fundamentally disagree with your original orthodoxy.

I think this is an extremely bad justification to spend any money, especially if you will have paid several percent of your GDP and you will have made the people in 2100 n-times poorer than they would be otherwise because of the reduced growth. And it was really the most optimistic scenario for the AGW hypotheses.

Note that the longer chain of assumptions you need to assume, the less likely they are satisfied simultaneously. Tamino implicitly wants to deny this simple mathematical fact because he pretends that if you insert a new player to the story - the Arctic - the odds for AGW get closer to 100% by Bayesian inference.

However, the "whole real AGW" including the new links, projections, and superstitions obviously gets less likely if you add new links. The AGW demagogy builds on the method that they only offer evidence for an extremely weak, often tautological statement, e.g. "climate is changing", and they pretend that they have proved a sensational statement such as that the climate will be spectacularly "disrupted" by CO2 from fossil fuels. Vagueness about all the assertions and concepts is their main ally.

But the main problem of using AGW as science is that there's really no convincing - e.g. five-sigma - evidence supporting the key propositions which is likely to be because they are not "universally" right. There's so much data in the world that one could construct 5-sigma "proofs" of the key statements if this were possible. While 5-sigma proofs lead to a "substantially higher certainty", they're not much harder to be found. You need just 5 times more data to find a 5-sigma proof than a 2-sigma proof - assuming that your conjecture is right. If you can't get to 5-sigma proofs for a long time, it's probably because all the 2-sigma signals are noise.

So no such 5-sigma "proof" exists in the literature. If there existed a paper that actually contained solid evidence for the key theses of the AGW orthodoxy, the proponents of the carbon regulation wouldn't hesitate before they would show us such a paper. Clearly, the paper that would be analogous to "Zur Elektrodynamik bewegter Körper" which showed that special relativity was true simply doesn't exist.

So it's preposterous to claim that "climate disruption" is analogous to a scientific breakthrough. There's actually no scientific research of the climate that shows that things have to work in the new way and not in the old way. There is no counterpart of Einstein's paper. There are just out-of-context prayers worshiping the AGW arguments spread in various papers and just a foggy widespread "feeling" of some people who cherry-pick their 1-sigma "evidence" - to argue that it's always "more likely than not" that the AGW orthodoxy is true - and every sensible person knows why they're doing it. The money flowing to the climate science because of this lie has been multiplied by a factor of more than ten in less than two decades.

But one can't show - at any confidence level that would be OK from a scientific viewpoint - that there is an actual "climate disruption" going on. The climate is doing its business-as-usual, and so should the industrial societies. Meanwhile, the AGW crooks are likely to continue with their business-as-usual, too. For Tamino, it means to keep on writing demagogic articles about ill-defined concepts, using cherry-picked facts about the observed climate and employing all logical fallacies that can be useful to achieve an outcome with a particular sign.

1. Dear Lubos,
Excellent article. I read your blog regularly with delight. Thank you for that.
Tamino writes:
“How unlikely? With no AGW, a change such as hasn’t been seen for thousands of years, for which there’s no known cause, in fact the known sources of natural variation can be ruled out so there must be some entirely natural but unknown cause, is pretty damn unlikely. I don’t believe it’s sane to maintain that there’s more than 5% chance of the recent Arctic changes naturally. In fact I think that’s an overly generous estimate, but let’s say the probability of seeing “X” if “B” is true, is 5%”
I think also with this assumption he commits a fallacy that is widespread. It is about forgetting the basic population, in German “Grundgesamtheit”. Let’s assume that the observed arctic warming in the last 30 years has a chance of being caused by natural factors with a probability of 1%. Let’s further assume Taminos several thousand years means 3000 years. In this case we have 100 periods of 30years. The probability to observe one such event or more within this period of 3000 years would still be about 37% according to the binomial distribution. The probability to observe no such event within this period of 3000 years would also be about 37% according to the binomial distribution.Using Taminos 5%, we would observe one or more such events with a probability higher than 50% within the 3000 years.In other words, if “climate science” cannot rule out natural factors with a probability much lower than 5%, which is their usual 2-sigma level, they cannot rule out natural factors for the cause of the current observation with 2-sigma confidence. The attributed confidence level needs at least to be much lower. This is my perspective being an experimentalist.
Best regards Günter

2. Dear Günter,

thanks a lot! Your calculation may actually be much more coherent, insightful, and logical than mine. Some sources of uncertainty can be quantified pretty nicely and they can't go away too easily.

Best regards
Luboš

3. Hang on Gunter, on your 1% based calculation you say the probability to observe one or more such events in the last 3000 years would be about 37% and the probability to observe no such event would be about the same? That leaves a 26% probability of not seeing either zero, one or more events!