Sunday, September 11, 2005

Quantifying climate uncertainty

What is the probability that in 10 or 20 years, the climate will be cooler in average than it is today? If you read the newspapers and the texts of various "concerned" scientists - where the adjective "concerned" is probably meant to be inequivalent to "biased" although it is hard to see what's exactly the difference - you may believe that the probability is more or less zero. There is a "scientific consensus" - whatever exactly this oxymoron means - and a certainty that the Earth is warming up. Trillions of dollars (about one hundred of Katrinas) will probably be spent in the next 20 years for policies that are based on the assumption that the Earth is warming up on the timescale of several decades.

This certainty is often compared to the certainty with which we know some elementary laws of physics - and those who are not certain or even those who believe the warming but who don't believe that it will have catastrophic dimensions are often compared to physics crackpots (even if they are among the 25 of the world's most influential scientists of 2004 together with Edward Witten).

How certain are we if we are "really" certain as scientists? For example, try to make a bet that the Tevatron will observe a particle that moves by 1.1% of the speed of light. I will offer you odds 10,000:1 because my psychological certainty that "c" is the ultimate speed limit is at least 100,000,000:1 (this question is about the Lorentz symmetry being valid either in the deep UV or the deep IR, depending on your viewpoint) and the previous number is the geometric average of 10,000,000 and 1 which I believe is fair. The climate scientists seem pretty certain, so you could expect similar (although a bit more modest) odds to be offered by them. What are the actual odds they will offer you?

Concerning the "compromise", I believe that the fairest "intermediate" probability "p" to be used for a bet has the property that its function "ln(p/(1-p))" - something that nicely stretches the interval (0,1) to (-infty,infty) - is the arithmetic average of "ln(p/(1-p))" calculated from the probabilities believed by the two parties who want to agree about the odds. If one of these probabilities is very close to zero (or equivalently to one because my formula respects the symmetry between "p" and "1-p"), the fair intermediate probability is roughly the square root of the more extreme probability (taken to be close to zero). Quite exactly, my prescribed odds are the geometric average of the proposed odds treated as fractions.

William Connolley disagrees that my formula is fair but his counter-arguments seem confusing to me because he apparently assumes that the expected gain of both parties (calculated from their private estimates of the probability) should be the same even if the odds are very far from 1:1 - which seems unjustified to me. His algorithm does not explain why should one use the other party's estimated probability to calculate his expected gain (instead of my or the intermediate probability); different choices lead to different results and neither of them can be argued to be more fair than others because the actual probability is unknown. Correct formula needs some "moral input" and my logarithmic compromise simply "looks" fair.

In Russia, there is pretty much a "scientific consensus" that the global warming theory is rubbish. Actually, it seems that many Russian scientists must believe that cooling is more likely; it is hard to find a different explanation for the straight $10,000 bet (1:1) that two Russian solar physicists (Galina Mashnich and Vladimir Bashkirtsev) have negotiated against James Annan. What is the message of this bet? The message is that according to the gambling market thriving within the international scientific community, there is a 50% probability that the Earth will warm up and a 50% probability that the Earth will cool down in the next 10 years. Sounds fair. Another possible interpretation is that the scientists have a reason to believe that the Sun will be turning off in the next 10 years. ;-)

Actually, the previous sentence is not quite a joke. NASA announced that all the sunspots disappeared in October 2004 and very soon we may expect a solar minimum (of the 11-year sunspot cycle) - something that may show whether it is nuclear physics or atmospheric physics that is capable to generate bigger temperature differences. ;-) There have been no sunspots 50 years after 1650 (Maunder minimum), which is the beginning of the first major minimum (and the coldest period) of the Little Ice Age. Coincidence?

Of course no one knows the right answer. We have enough data to say that the simple reasoning that the Earth is guaranteed to warm up because of our industrial activity is definitely wrong. Such a conjecture has been demonstrably falsified by the period 1940-1970 which was a period of intensive human activity and a period of cooling (and 1944 or 1945 was the warmest year in a long period ended by 1982, despite the post-war industry), and the available data simply can't say whether it was just an irrelevant fluctuation. I am slightly biased towards warming as the more likely answer for 2020; it's been warming for 15 years and there is some chance - and very vague arguments - that it is a part of a cycle or a local trend that may continue for a few more decades. Let me guess that the probability that 2013 will be warmer than 2003 is something like 52%, and this probability may jump to something as high as 60% if you compare multi-year averages to reduce the interannual variability.

Surely, those global warming proponents would offer you much better odds than 3:2, you may think; something that is remotely comparable to the odds I offer for exceeding the speed of light. However, you will be disappointed. Brian Schmidt who is a climate scientist currently on vacation in northern Montana is used to 2:1 odds against temperatures getting colder in 10 years and 3:1 odds against temperatures getting colder in 20 years. They won't accept more attractive odds. Sorry.

It's unimpressive, is not it? What does it mean? It means that according to the money that the "mainstream" climate scientists are actually willing to invest, there is a 33%-50% probability that the Earth will cool down in 10 years and roughly a 25% probability that it will cool down in 20 years. Let me translate this sentence - a sentence whose numbers may actually be realistic in my opinion - in one more way. There is a 33%-50% probability that 1.5 trillion U.S. dollars that will be spent by 2015 for Kyoto-like policies will actually make a "global problem" (cooling of the average temperature) infinitesimally worse instead of making it better; and there is a 25% probability that 3 trillion U.S. dollars to be spent by 2025 will make the same "problem" worse on a longer timescale.

Don't you think that someone has lost his mind? Imagine that someone will tell you that a particular chemical compound added into drink water will globally reduce lung cancer in 20 years by 1% of patients with probability 70%, and it will make the problem worse by 1% with probability 30%. The number 70% has been measured from the scientific consensus of 1,000 papers in which all statements that could help the oil corporations, the Coca Cola company, and tobacco companies have been carefully filtered out; Russia obtained the opposite result (30%) but you are encouraged not to trust the Russian scientists - probably because they're not a part of the global scientific consensus. Only the people who agree with a certain opinion are allowed to participate in a "consensus".

Now imagine: the chemical costs 3 trillion dollars. No doubt, thousands of lives that you may save are even more important than a few squared kilometers that will be claimed by the ocean as the sea level rises by a few inches (as one of the consequences of the "catastrophic global warming"), for example. Will you pay 3 trillion dollars for the magical substance? I think it's completely crazy. There are hundreds of uncomparably more reasonable ("local") ways to reduce lung cancer. Note that the actual Kyoto policies are even crazier because of many reasons - especially the fact that unlike the case of cancer, no actual predicted problems are known; it is not known whether the cooling or the warming should actually be compared to cancer. There can exist no "global" climate problems. The problems with the weather and climate are always local. The average temperature or any other quantity moving in a certain direction "globally" always produces its winners as well as losers; and my guess is, of course, that rising temperatures and a rising concentration of CO2 creates more winners than losers because agriculture is easier, people don't spend so much for heating and they may swim in the ocean in September (unlike me today - despite the sunny skies, it was just too cold).

OK, at any rate, if you look what the global warming proponents actually believe, it is clear that most of them believe the same thing as everyone else who has at least some traces of common sense: the probability of the Earth getting warmer in any foreseeable future is pretty much close to 50% because the temperature graphs seem virtually indistinguishable from random walk and these graphs from the past still represent the most reliable "model" to make predictions about systems that are as complex as the climate.

And the probability that it will be warmer at even longer timescales is unpredictable; the latter quantity involves many well-known as well as unknown natural cycles and effects - and also potentially substantial changes in the technologies that our grand-grandsons will be using (and that may make our/their tools to mess up with the global climate cheaper by many orders of magnitude).

All claims that there is some certainty that the things must evolve in one particular direction are simply lies; I say lies because these gambling stories make it pretty clear that the proponents of the global warming hypothesis - and the "reliable" predictions of the future climate - actually don't believe their statements themselves.

(And it's no science if you predict that one number, namely the average temperature in 2015 - that will only be measured once - will be higher than the present value with probability 33% because this statement can't be falsified and 33% can't be approximated by 0%, unless QCD is exactly a large N limit of AdS/CFT. ;-) To make probabilistic predictions falsifiable, we require the measurements of the same number to be repeated many times. But the world will be a completely different place in 2100 and the present theories and models will definitely not apply to that world, and therefore it is impossible to make the experiments repeatable; as you can see, several defining features of science are violated.)

However, they must tell you that they do believe it because this is what they are paid for; and they need the money for their trips to glaciers in Montana and for their $10,000 bets against the Russians (where did the Russians get their money is open to discussion, too); so they should rather protect their role of modern messiahs (who are undoubtedly more fiscally moral than the large corporations, aren't they?) and defend their miniscule fraction of the resources being wasted for the Kyoto-like pseudoscience. Well, this is how the "postmodern" world works in some cases.


  1. We work like a horse.
    We eat like a pig.
    We like to play chicken.
    You can get someone's goat.
    We can be as slippery as a snake.
    We get dog tired.
    We can be as quiet as a mouse.
    We can be as quick as a cat.
    Some of us are as strong as an ox.
    People try to buffalo others.
    Some are as ugly as a toad.
    We can be as gentle as a lamb.
    Sometimes we are as happy as a lark.
    Some of us drink like a fish.
    We can be as proud as a peacock.
    A few of us are as hairy as a gorilla.
    You can get a frog in your throat.
    We can be a lone wolf.
    But I'm having a whale of a time!

    You have a riveting web log
    and undoubtedly must have
    atypical & quiescent potential
    for your intended readership.
    May I suggest that you do
    everything in your power to
    honor your encyclopedic/omniscient
    Designer/Architect as well
    as your revering audience.
    As soon as we acknowledge
    this Supreme Designer/Architect,
    Who has erected the beauteous
    fabric of the universe, our minds
    must necessarily be ravished with
    wonder at this infinate goodness,
    wisdom and power.

    Please remember to never
    restrict anyone's opportunities
    for ascertaining uninterrupted
    existence for their quintessence.

    There is a time for everything,
    a season for every activity
    under heaven. A time to be
    born and a time to die. A
    time to plant and a time to
    harvest. A time to kill and
    a time to heal. A time to
    tear down and a time to
    rebuild. A time to cry and
    a time to laugh. A time to
    grieve and a time to dance.
    A time to scatter stones
    and a time to gather stones.
    A time to embrace and a
    time to turn away. A time to
    search and a time to lose.
    A time to keep and a time to
    throw away. A time to tear
    and a time to mend. A time
    to be quiet and a time to
    speak up. A time to love
    and a time to hate. A time
    for war and a time for peace.

    Best wishes for continued ascendancy,
    Dr. Howdy

    'Thought & Humor'

    P.S. One thing of which I am sure is
    that the common culture of my youth
    is gone for good. It was hollowed out
    by the rise of ethnic "identity politics,"
    then splintered beyond hope of repair
    by the emergence of the web-based
    technologies that so maximized and
    facilitated cultural choice as to make
    the broad-based offerings of the old
    mass media look bland and unchallenging
    by comparison."

  2. IN blog entry below ths one, I gave perspective on the idea that investment in alternate energies should hae been done on the idea that methods would produce results in terms of returns on those same investments.

    I spoke of Germany for a reason.

    Total investment costs and returns had a secondary effect in terms of emissions. So while investment dollars are being accounted for, secondary effects are taking place as well.

    This should speak for itself and whether one would agree or diasagree, the nature of emissions are not some "elixir" that will fuel the climatologist that might support his statements about the interference processes.

    I see in the air around us. We know interactive processes can take place once Pierre Auger understood this, and so did the recognition of the Oh my God Particle:)

    Looking for this basis of time variable measure, the very water we see in this planet, would have been deterred by "other" influences? Non!

  3. It is important that we no longer hold onto the views of oil multinationals as the saviors for our immediate now.

    Moving toward the future and considering all probabiltic avenues, the outcome change in perception gaurantees, other pathways will be established.

    Such alteration in our views change the outcome of any society whether we like to think it does or doesn't.

    Sustainable Resources

  4. It's not surprise at all that global warmers have started to use Katrina as a strong evidence that global warming is causing more frequence and more severe hurricane. If they can figure out the global average atmospheric CO2 content a million years ago from a few air bubbles trapped in one piece of ice found in one location; Or they can figure out the global average temperature a thousand years ago from tree rings of one single tree; You bet that one single statistical sample of Katrina is all they need to do accurate statistical modeling and predict hurricanes of the next few hundred years.

    Such data is junk and such scientists are doing junk science. I see no reason to believe any of the data they measured or averaged one way or the other, due to credibility reflected on the more clearly ridiculous cases, like tree rings, and their own willingness to accept such ridiculous data without any questioning.

    There is very convincing reason, whether you believe in the global warming theory or not, that you have to admit that the amount of CO2 we human can possibly add to the atmosphere, is tightly capped below a certain MAXIMUM, far before it could cause any singificant impact.

    The reason is very simple: We release CO2 into atmosphere from fossil fuels. The fossile fuel is a limited resource, therefore there is only a limited amount of CO2 we can release. If you do a little bit calculation you find that the maximum amount of CO2 we can release is actually a very small percentage compared to the atmospheric CO2 concentration.

    There are one trillion barrels of petroleum reserve that could potentially be mined, according to official figures. But considering that there are plenty of political insentives to exagerate that figure by individual OPEC member states, 600 billion barrel is more realistic. One barrel is 32 gallon. One gallon is 3.785 litre. You can roughly say one litre of petroleum, when burned, produces one kilogram of CO2.

    The total figure is 7.3x10^13 kg, averaging 12000 kg per human being on the earth, rich or poor. But when averaged onver the surface of the earth, it's only 1.4x10^-5 kg per square centimeter surface of the earth.

    We know the surface atmospheric pressure is 1 kg per square centimeter, so 1.4x10^-5 kg/cm^2 divided by 1 kg/cm^2, that's just 14 ppm.

    The current atmospheric CO2 content is 377 pm. So at the maximum, we can add a little bit more, 14 ppm, so it could reach 391 ppm. And we can in no way increase it beyond that.

    The real crisis is not going to be caused by the 391 ppm CO2. The real crisis is the fact that we simply will NOT be able to add more CO2 even if we want to. The oil is running to and end rapidly. At current consuption rate, 30 billion barrel per year. The oil reserve can run at most 20 some more years.

    And the oil crisis does not need to wait until the last drop of oil is gone. It starts when the demand outpace the production. Actually it started already this year, as we see how oil price start to skyrocked. And the US government, like other industrialize and developing nations are all in a panic buy mode trying to increase their strategic petroleum reserve, although that has little invain significance when the world's oil wells inevitably run dry.

    Face it, the oil crisis is real and imminent, and it is an unprecedented crisis shaking the fundation of human civilization. It's a far worse than a few extra ppm of CO2 in the atmosphere.


  5. You say: "It means that according to the money that the "mainstream" climate scientists are actually willing to invest, there is a 33%-50% probability that the Earth will cool down in 10 year".

    No. You have misunderstood (which is odd, because I explained it pretty carefully, with a worked example, at my blog). My best estimate of the chances of 2013 being cooler than 2003 is 1/9. Not 1/3, not 1/2; but 1/9. You appear to have confused the odds I'd like to bet at, with the probability of the event. But obviously I'm not interested in a bet with (from my perspective) an expected gain of zero!

    The 1/9 chance is not the chance of a long-term cooling trend: the chances of that are much lower. The 1/9 takes into account natural variation, as explained... above.

    Now clearly, we disagree over the best method to average out our disparate odds. You appear to have plucked a function from thin air and declared it "fair". I have a definition - equality of expected gain - that is simple (you're a smart chap: I don't see how it has managed to confuse you) and at least appears fair with some theoretical basis.

    But the bottom line is: according to you, you believe that the chances of cooling are 1:1. So why aren't you prepared to take 7:3 odds, which gives you an expected gain of 2/3 your stake?

  6. I just want to correct one statement in Lubos' post, identifying me (Brian Schmidt) as a "climate scientist". I'm not a scientist, just a layman who is very interested and concerned over global warming, and am willing to be that it is happening.