William M. Briggs

Statistician to the Stars!

Climate: Uncertainty Means That Things Can Be Worse Than Our Best Guess: Part I

Crops and climateThe title sentence was spoken by professor Stephan Lewandowsky from the School of Psychology, University of Western Australia. The psychologist Lewandowsky is concerned that many are not as concerned about climate change as he is.

Lewandowsky is not fretting about the psychological states of warmer citizens. No, sir. He is instead deeply interested in such things as climate feedback sensitivity, heat transfer equations, cloud opacity, and so forth; such states of nature we may describe, in deference to the good prof’s training, as schizophrenic greenhouse gases.

Given his passion, I am sure he knows of what he speaks on these matters, so let’s not question him about physics; rather let’s look at his probability statements and see what we can learn. This will be interesting, because Lewandowsky represents a common type of academic sensitivity.

He beings his analysis with this quotation:

The Chairman of the Future Fund, David Murray, recently suggested on national TV with respect to climate change that “if we’re not certain that the problem’s there, then we don’t – we shouldn’t take actions which have a high severity the other way.

From this, he reasons:

In a nutshell, the logic of this position can be condensed to “there is so much uncertainty that I am certain there isn’t a problem.” How logical is this position? Can we conclude from the existence of uncertainty that there certainly is no problem?

And this is false. That is, Lewandowsky has falsely derived B = “there is so much uncertainty that I am certain there isn’t a problem” from A = “if we’re not certain that the problem’s there we shouldn’t take actions which have a high severity.”

From his fallacious argument, Lewandowsky then says, C = “Uncertainty should make us worry more than certainty, because uncertainty means that things can be worse than our best guess.” And from this gross absurdity, the good prof derives yet another error, which is more complicated to explain and which we’ll come to next time.

Now, B is, as Lewandowsky intimates, false itself. If there is uncertainty in a proposition, such as D = “the climate will change”, then it is a fallacy to claim because we are uncertain of D, therefore D is false.

But Murray did not make any claim even close to this. Instead, Murray said A, which is that if the uncertainty in D is significant then acting on the possibility of D such that we incur high (i.e. severe) costs is unwarranted. And this is true. Of course, it could be that the penalty we pay if D obtains is so astronomical that no matter how unlikely D is it is well to pay costs of “high severity” now.

But this is not the case with D, because climate change itself is of little interest. What is of importance is how things which matter to people change when the climate does. Let’s call these things E. An example might be E = “worldwide crop yields” (if you don’t like that, pick a horror from this list). It is thus the case that our uncertainty in E is larger than our uncertainty in D, assuming D influences E (which everybody does assume).

For example—a fictional, but reasonably close example—assume Pr(E | D true) = 0.9. It would be wrong to say, “The probability of E is 90%”. It would be right to say, “Assuming the climate warms, the probability of D is 90%.” To find the true uncertainty of E, we must first compute Pr(E | D false). Suppose this is 0.1 (or any other number less than 0.9). Now we need the probability D is true (given our knowledge of physics, etc.; I have suppressed this notation, but it is there). Suppose this is, as Lewandowsky frets, high; say 0.9 too. Then

     Pr(E | physics) = Pr(E | D true, physics) x Pr(D true | physics) + Pr(E | D false, physics) x Pr(D false | physics)

     Pr(E | physics) = 0.9 x 0.9 + 0.1 x 0.1 = 0.82

where I have “un-suppressed” the notation, and where “physics” means all we know of the physics (and biology, etc.) of climate and crops. The result is a number less than 0.9; i.e. we are less certain of E than of E given D is true.

The answer to this equation will always be less than Pr(E | D true, physics) as long as Pr(E | D false, physics) is smaller than Pr(E | D true, physics), and in all horror scenarios it always is. That is, we will always be less certain of E, which is what we wanted to show. So far it is Murray 1, Lewandowsky 0.

Too much information? Well, I’m sorry about that, but without considering it at this level of detail we won’t be able to appreciate Lewandowsky’s final mistakes. And it is not just Lewandowsky who makes these errors: these fallacies are exceedingly common, so it is worth spending some time on them. We’ll do that in Part II.

I am somewhat nearer the computer, but will still be mostly away. It looks like it won’t be Sunday until I rturn fully.

8 Comments

  1. William Sears

    15 March 2012 at 8:32 am

    Or as the engineers say: if you do not know what you are doing; do nothing.

  2. Ah you missed the nightmare scenario of global warming. Assume the following:

    1) global warming is occurring
    2) the effects will be disastrous
    3) mankind does have to capacity to prevent this catastrophic warming
    4) plans to deal with it all focus on reducing CO2 emissions
    5) CO2 is not the cause of the actual warming
    6) after reducing CO2 emissions mankind no longer has the wherewithal to prevent the actual cause of the warming

  3. It is thus the case that our uncertainty in E is larger than our uncertainty in D, assuming D influences E… The result is a number less than 0.9; i.e. we are less certain of E than of E given D is true.

    Yes, the uncertainty in E might be larger than one in D, but I don’t think you have correctly shown it. Does a smaller probability of happening mean “less certain”? Hmmm… let’s consider the two probabilities (suppressing the premises): P(E ) = 0.01 and P(D) = 0.5. Which probability statement presents more uncertainty or gives you more worries?

  4. This sounds like an example of: “All hail the experts! Until they disagree with hysterical reactions.”

  5. Ah, the twisted logic of the Precautionary Principle. Some alleged future harm is suspected but with uncertainty. Decison-makers should therefore anticipate and prevent said alleged harm, even though the “control measures” are also uncertain and in many cases, harmful in and of themselves. So we have the following probabilities to consider:

    E – the alleged harm that might occur, conditioned on D (global warming in the future) as Dr. Briggs noted, and

    F – the harm that the control measures might inflict

    I contend that Pr(E) is essentially zero. Indeed, warmer is better. That is, there exists outcome G which would a Good Thing, conditioned on D, that warming actually occurs in the future. Furthermore, the Pr(F) is close to 1, given that the decision-makers almost always make bad decisons that harm the public, regardless of whether D occurs or not.

  6. William Sears said: “…if you do not know what you are doing; do nothing.”

    As an engineer, I agree. The reason is simple. There are far more ways to to act wrongly than correctly. Picking a way to act at random is very likely to pick a wrong way. Doing nothing is almost certainly to be wrong too but it is less wrong than almost all the other wrong ways to act. At least you do no harm.

    By doing nothing, you do not expend resources making things worse. You thereby have resources left to act when and if the correct way to act becomes clear. Also, it might be that doing nothing was the best possible way to act. That outcome would be a huge win! It might also turn out the presumed catastrophe was not as bad as though and the harm experienced was much less than any of the “do something” demands would have caused. In any event, the medical principle of “First, do no harm” is a good place to start.

  7. Things could also be better …

    Climatologists love to talk about energy being trapped by carbon dioxide and thus not exiting at the top of the atmosphere (TOA.)

    It is nowhere near as simple as that. All the radiation gets to space sooner or later. Carbon dioxide just scatters it on its way so you don’t see radiation in those bandwidths at TOA. The energy still gets out, and you have no proof that it doesn’t, because you don’t have the necessary simultaneous measurements made all over the world.

    In the hemisphere that is cooling at night there is far more getting out, whereas in the hemisphere in the sunlight there is far more coming in. This is obvious.

    When I placed a wide necked vacuum flask filled with water in the sun yesterday (with the lid off) the temperature of the water rose from 19.5 deg.C at 5:08am to 29.1 deg.C at 1:53pm while the air around it rose from 19.0 to 31.9 deg.C.

    What did the backradiation do at night? Well from 9:15pm till 12:05am the water cooled from 24.2 deg.C to 23.4 deg.C while the air cooled from 24.2 deg.C to 22.7 deg.C.

    According to those energy diagrams the backradiation, even at night, is about half the solar radiation during the day. Well, maybe it is, but it does not have anything like half the effect on the temperature as you can confirm in your own backyard.

    This is because, when radiation from a cooler atmosphere strikes a warmer surface it undergoes “resonant scattering” (sometimes called pseudo-scattering) and this means its energy is not converted to thermal energy. This is the reason that heat does not transfer from cold to hot. If it did the universe would go crazy.

    When opposing radiation is scattered, its own energy replaces energy which the warmer body would have radiated from its own thermal energy supply.

    You can imagine it as if you are just about to pay for fuel at a gas station when a friend travelling with you offers you cash for the right amount. It’s quicker and easier for you to just pay with the cash, rather than going through the longer process of using a credit card to pay from your own account. So it is with radiation. The warmer body cools more slowly as a result because a ready source of energy from incident radiation is quicker to just “reflect” back into the atmosphere, rather than have to convert its own thermal energy to radiated energy.

    The ramifications are this:

    Not all radiation from the atmosphere is the same. That from cooler regions has less effect. Also, that with fewer frequencies under its Planck curve has less effect again.

    Each carbon dioxide molecule thus has far less effect than each water vapour molecule because the latter can radiate with more frequencies which “oppose” the frequencies being emitted by the surface, especially the oceans.

    Furthermore, it is only the radiative cooling process of the surface which is slowed down. There are other processes like evaporative cooling and diffusion followed by convection which cannot be affected by backradiation, and which will tend to compensate for any slowing of the radiation.

    This is why, at night, the water in the flask cools nearly as fast as the air around it. The net effect on the rate of cooling is totally negligible.

    The backradiation does not affect temperatures anywhere near as much as solar radiation, even though its “W/m^2″ is probably about half as much.

    And there are other reasons also why it all balances out and climate follows natural cycles without any anthropogenic effect. This is explained in detail in my peer-reviewed publication now being further reviewed by dozens of scientists.

    http://principia-scientific.org/publications/psi_radiated_energy.pdf

  8. David Murray was a beacon of common sense in a sea of alarmist absurdity.

    A shame he has now retired and his place is being taken by a more conventionally “political ” animal.

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