Timescales, Special Cases, Limitations, Etc.

Subtitle: Some Physical Thoughts on the notion of “Climate Sensitivity”.

It is generally agreed that the central issue in the climate debate is the magnitude of warming one would expect to occur as a result of a doubling of CO2, which results in a “forcing” of ~3.7 watts per meter squared. However, in a moment of sudden insight, I realized that, from a physics perspective, there are several problems with the way this is talked about. But let’s start with a definition. The “equilibrium climate sensitivity”-what most people in this debate think they want to know-is equal to the eventual change in temperature of the Earth that would occur per unit change in the radiative “forcing” of the system. Think about that for a few seconds.

If you have any knowledge of physics, you have probably already realized  how this notion can get you into serious trouble. Consider the following case: We shut off the sun. The Earth will begin to cool, and it will do so for a very long time, until it reaches ~0 degrees Kelvin, or a cooling  of ~288.15 K. Again, this is eventually, not on a timescale which is really relevant to policy, say. But never mind that. Incoming solar radiation in this circumstance has been reduced ~342 w/m^2. Thus the “equilibrium climate sensitivity” MUST be ~0.84 K/wm^-2, or a little over three degrees for a doubling of CO2. That is, of course, assuming that the figures I’m using for incoming solar radiation and mean surface temperature are correct. Of course, this does not correspond to the sensitivity to a doubling CO2 necessarily. For one thing, the physics governing the feedback mechanisms will be very different at temperatures that low, since the atmospheric gases would have long since ceased to be gases. However, I can only think of things which might plausibly mean that the sensitivity thus derived is too high, not too low. So one might say that very large negative forcing is a “special case” because the response is sure to be very different when the greenhouse effect can’t apply because water vapor will have frozen out, along with CO2 and everything else.

Timescale is also a serious issue. If it continues to warm indefinitely, never reaching “equilibrium” after doubling CO2, just very slowly, well, who cares if in a billion years the warming would reach 5 degrees if in the next thousand it was only 2? I know I wouldn’t. And yet it is technically the long, irrelevant period which is the “equilibrium” sensitivity. Indeed, it stands to reason that the Earth never gets to realize true equilibrium response to external perturbation, if it operates on timescales that long, the forcing is constantly changing on timescales far too short to fully realize the response.

Now I don’t mean to say that the whole concept is bunk, but there seem to be details which people overlook about this.

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3 Responses to “Timescales, Special Cases, Limitations, Etc.”

  1. Steve Fitzpatrick Says:

    Off topic:

    You commented over at Lucia’s that you have never voted for a president, but object to people calling George Bush stupid. Well, in defense of all the presidents, I do not believe that any truly stupid person could ever get elected president (which is why Palin has no chance of being president; she really is a borderline moron)

    However, unlike you, I am quite old enough to have have voted in a bunch of different elections, and have watched and listened to many presidents. I can assure you they really do vary in their ability to learn about and understand complex issues. Differences in intellect tend to inversely correlate with the frequency of counterproductive (“idiotic” may be better) decisions on important issues, although it must be said that none were immune form making poor decisions at least some of the time. So for what it is worth, here is my listing of presidents according to “apparent intellectual capacity”, in order of increasing capacity:

    1. GW Bush
    2. Carter
    3. Ford
    4. Eisenhower
    5. Nixon
    6. Obama
    7. Kennedy
    8. Reagan
    9. GHW Bush
    10. Clinton

    GW Bush really was the least intellectually capable president I saw in action since the 1950’s, and made unbelievably bad decisions… on a too frequent basis.

  2. timetochooseagain Says:

    It may well be that we would disagree about the relative intelligence of various politicians. I tend to believe that the views people have are more often than not shaped by the media’s portrayal of the person in question. Bush as an idiot is a meme like any other and one with a lot of popularity. There is a broad narrative to the media’s world view, and the narrative tends to be people more like Bush, stupid/evil, people like Obama, intelligent/divine. But it is my opinion that the media is more often than not totally wrong/misleading in this regard.

    That being said, I certainly don’t think Bush was the smartest of the presidents, or even close, and certainly not the best, not very close there either. But I find that a lot of people would sooner foam at the mouth than say he was better than any other President, much less outside their bottom ten. Which is crazy if you look back on some of them we’ve had.

    Incidentally, having attempted the exercise of ranking the Presidents, all of them, from historically greatest to worst, I tend to find that it is VERY difficult to do so. President’s reputations also change over time, even among historians. Truman was looked at as a terrible President by many contemporaries (at the DNC, the delegates had signs “We’re Mild About Harry!”) but now usually makes it into the list of better Presidents, rather than worse.

  3. Steve Fitzpatrick Says:

    Well, the press say what they say, and I don’t often give a hoot about it; they sure couldn’t change my mind about my list. I limited the list to presidents I have personal memory of, so I can’t comment on others. Could someone from the turn of the last century have been worse? Sure, but I either have to trust the evaluation of others or do a lot of independent research to draw my own conclusions… not gonna do that.

    But all that being said, George W really was (is) not very smart, and made many just awful decisions, which I think history will tread quite harshly. His only real rival for bad decisions in the ten I listed is Jimmy Carter… and historians are already sharpening their knives for Carter, just waiting for him to exit the scene. When Jimmy was voted out of office, I said “There is no way we will ever have such an incompetent president again, at least not in my lifetime.” George W proved me wrong.

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