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  1. It’s also worth noting that even if we couldn’t calculate a global mean temperature, we’d still know that climate is changing because we have multiple independent lines of evidence. These include (among many others) the changes we’re seeing in ice covered areas of the world, ocean heat content, species ranges, and the timing of key life events such as migration, bud burst, and flowering for a wide range of species.

    Comment by Paul Higgins — 25 Mar 2007 @ 10:41 AM

  2. Ultimately, it is energy that counts. Any global measure that is consistent with the tends in either atmospheric, ocean or atmosphere-ocean energy is potentially useful in describing what is happening to these parts of the Earth system. Thermodynamic temperature determined as simple weighted averages dealing with heat capacities and masses works as well as anything else for this. It seems that the authors of the indicated paper are trying to obscure something that is relatively simply and useful.

    To carry their argument further, in any macroscopic ensemble of atoms or molecules for which a good thermomenter will give a definite temperature throughout, there will be microscopic parts of the ensemble with translational kinetic energies per particle (temperture) which do not closely match what the thermometer indicates. No one with an understanding of basic theromodynamics would argue from this that the number given by the thermometer is not meaningful.

    Astronomers routinely determine temperatures of stars and planets from their spectra. Such temperature determinations result in a single number for something usually much larger than the Earth. For example, we know that the temeprature of the sun is not the same everywhere on its photosphere, but that doesn’t mean that a temperature can not be given for the sun’s surface as a whole. Such temperatures are important in astronomy for the classification of stars, and such classifications are used to determine stellar sizes and masses among many other objective quantities.

    This paper addresses a non issue.

    Comment by Bob Reiland — 25 Mar 2007 @ 10:44 AM

  3. It is also worth noting, that the activity of the sun is higher then ever in 8000 years:

    Maybe nobody here has noticed it?


    [Response:I’m not all that old… :-). Joke aside, there are some proxy-data, I seem to remember, suggesting that the solar activity in the last 50 years is the highest for a very long time. At least, that’s one interpretation. I have never been absolutely convinced that other factors may not play a role (i.e. local climatic effects of biology/chemistry/physics-related preferances?),although I see that the interpretation indeed is plausible. -rasmus]

    Comment by Hedwig Braun — 25 Mar 2007 @ 10:58 AM

  4. Reminds me of the futile arguments late into the night we used to have in our student days- “does what we sense observe really exist? or is this world/universe an illusion?”.

    As comment 1 by Paul Higgins clearly implies there are many ways/criteria to demonstrate that the average global temperature is changing. Asking the right questions and finding converging cross correlation of independent sources of observationn is the art of scientific investigation.

    Of course people have a choice – they can ignore all the lines of evidence that do not fit their world view- or they can try and discredit lines of evidence- but that’s not science.

    Also science is meaningless unless we derive wisdom from it.

    And was there ever a more pertinant time in human history for the latter to be realised?.

    Comment by Nick Riley — 25 Mar 2007 @ 11:10 AM

  5. In my limited understanding and in my layman’s terms, Rasmus is saying that the idea of “Global Mean Temperature” …

    (1) Is an term/idea of method, not a term/idea that refers directly to a physical phenomenon.

    (2) Is justified because it does logically, though indirectly, relate to a physical phenomenon.


    [Response:It does respond to the energy balance between the light from the sun and the heat loss to space. Or you may relate the saturated water pressure to the temperature. It’s really a bulk measure of the macroscopic behavious of a lot of molecules/atoms. So, it’s both a physical as well as a statistical concept. -rasmus]

    Comment by Burgess Laughlin — 25 Mar 2007 @ 11:23 AM

  6. Re: #3,

    Lawrence Solomon is put in his place by DeSmogBlog:

    Comment by Stephen Berg — 25 Mar 2007 @ 11:24 AM

  7. Waitaminute. Do Essex et al. propose a more meaningful measure? If so, what’s the trend? If not, what’s the point?

    Comment by Pat Cassen — 25 Mar 2007 @ 11:25 AM

  8. Paperclip pops up and asks:

    “Hi! You seem to be typing a {stock denial] phrase about {the sun} referring to {a paper} by {Solanki} that you read {a story about about} in {a newspaper article} and {assert incorrectly} your {belief} that {nobody here noticed}.

    “Would you like help typing {Solanki} into the Search Box (White Rectangle, Top Right of Main Page) so you can see the {about 48} previous responses and {about 2} main topics discussing {what you think nobody here knows}? or would you like to save time by confirming that {you didn’t look} because {you’re not real/you don’t care/you don’t read}?

    — I never thought I’d miss Clippy. But automated topic-bombing merits an automated response.

    Comment by Hank Roberts — 25 Mar 2007 @ 11:32 AM

  9. Anyone suitably motivated can read the preprint here:

    Does this mean when I heat my potatoes in a pot on the stove, adding a lid will actually result in a lower ‘average temperature’ for the water? That seems a bit physically counter-intuitive to me…

    Comment by SomeBeans — 25 Mar 2007 @ 11:36 AM

  10. In reality, since climate is chaotic, the relevant quantities that define the climate are its conserved quantities–energy, momentum, angular momentum and so on. These are the only variables that restrict what state the climate can assume. Now, in general temperature is the derivative of energy with respect to entropy. So, in the strictest sense, given that the matter is passing from the oceans to the atmosphere, that content of CO2 and other greenhouse gases is increasing, etc., it would be difficult to define any sort of equilibrated system we could take the temperature of. On the other hand, since we are not interested in any instantaneous value, and since a trend in temperature does indeed provide useful information, we can certainly define some procedure that allows us to see if climate is changing. So, while a layman might find it a trifle confusing and a thermodynamical purist might cringe, we certainly define temperatures for other systems where the definition must be stretched a bit. And it is a bit of a semantic point, since regardless of whether one speaks in terms of energy or temperature, climate is changing.

    Comment by Ray Ladbury — 25 Mar 2007 @ 11:59 AM

  11. If we are going to talk about average global temperature and then chart it, we must be sure it is an accurate measurement.

    To date, the global average temperature statistics have been adjusted so much and so many times that we do not know if it is truly warmer today than 1940 or warmer than the MWP.

    I think we should start over with a better measurement technique.

    [Response:One thing is the global mean estimated by instrumental data. Another issue is the proxy-based reconstruction of the global mean temperature. The paper addresses the former and questions whether an arthimetric mean of temperature measured around the globe is useful. The latter depends much on the quality of the proxy data as well as the link to the climatic parameters. -rasmus]

    Comment by George K — 25 Mar 2007 @ 12:17 PM

  12. Surely temperature is a product of the average energy levels of all of the molecules that make up the atmosphere. Surely any temperature is measured that way. When my thermometer is placed in a place away from direct sunlught in order to read the average energy of some of the molecules in its vicinity what am I measuring, an average surely and hence the amalgamation of large of thermometers world wide gives me an average global temperature?

    Comment by pete best — 25 Mar 2007 @ 12:36 PM

  13. In response to #3’s concerns regarding solar forcing.

    The folks running site don’t tend to miss much. This issue has been covered here several times:

    And a few other posts you will find in the index of the site.

    Bottom line is no correlation between recent rise in global temperature and solar activity.

    Comment by Peter Houlihan — 25 Mar 2007 @ 12:36 PM

  14. As an astronomer, my view is that we can measure the global mean temperature of the Earth (essentially the blackbody temperature) from its spectrum, just as we measure the temperature of the Sun (and Venus, Mars . . . ) spectroscopically.

    Comment by John Gribbin — 25 Mar 2007 @ 12:42 PM

  15. One can debate the meaning of temperature as a physical entity, yet biologists and chemists know from countless experiments in the laboratory that changing the temperature of a reaction (be it in a test tube or in a living a organism) by 10 degrees C will cause most reactions to vary in rate by a factor of 2-3, as predicted by the Arrhenius equation. So, temperature is a useful concept in biology and chemistry, and really, that is what will be most affected by global warming.

    As with global temperature, the concept of body temperature is also difficult to pin down, as there is considerable variation in the temperature of different regions of the body, and marked differences between skin temperature and core temperature. Yet, the notion that humans have a normal core temperature of around 37 degrees C, and an increase in core temperature above approximately 38 degrees C is a sign of something wrong, is quite useful in medicine.
    Of course, body core temperature is less variable than skin surface temperature, so medical doctors have it easy compared to climatologists concerned with atmospheric temperature at the earth’s surface. On the other hand, biophysical ecologists who model the heat balance of animals in the wild do pretty well at predicting body core temperature for, say, a lizard in the desert, or a mussel in the intertidal zone, by making some simplifying assumptions about body surface temperature and heat fluxes due to the emission and absorption of short wave and long wave radiation, evaporation, conduction, and convection. And while there may be significant variations in temperature from moment to moment, and from one square centimeter of surface to another, living organisms that don’t move around and that grow slowly, such as trees and corals, provide a useful long-term averaging of the temperatures of their particular micro-habitat – this is why they are used by climatologists, oceanographers, and others as temperature proxies for their particular environment.

    Comment by Chuck Booth — 25 Mar 2007 @ 12:44 PM

  16. Eli has five entertaining entries on this very subject on : starting back on March 15th.


    Comment by Fergus Brown — 25 Mar 2007 @ 12:44 PM

  17. Each scientific paper should bring something new or at least summarize the knowledge in the particular field (review). But if the article is neither of this, why was it accepted in impacted journal? Is the main reason, that it is not a climatologic journal?
    hmm… it’s like saying: “don’t supress the fire, we don’t know the exact temperature at every place!” :-)

    Comment by Alexander Ac — 25 Mar 2007 @ 12:51 PM

  18. You dont need a phd to relalise that the global mean temperature is spiralling out of control because of our love of fossil fuels. I could see daffodils in my garden today many weeks too early in southern england. We have hardly had any winter and yet the contrarians hog the media trying to convince us that all is OK. For the sake of our children when is this madness going to stop. When will the earth have had enough of our squandering our beautiful blue planet turning it into a Venusian hell. Thanks Real Climate for keeping us informed on our planet wide slow incineration

    Comment by FatBoy — 25 Mar 2007 @ 12:56 PM

  19. Seeing the question “Does a global mean temperature exist?” and the (to my mind) frivolous nature of the paper, I can’t resist sharing with you the “Meteorologist’s theorem”, which is: At any given moment, there are two antipodal (diametrically opposite) points on the Earth’s surface where the temperatures are equal and the barometric pressures are equal.

    There is a beautiful proof, which is not hard. If you can’t find the solution you might check with Dr Math (now at ).

    Comment by Dick Veldkamp — 25 Mar 2007 @ 1:37 PM

  20. Gavin, why do you prefer Kelvin to Celsius? Surely ONLY Celsius is practical to use and is easily and meaningfully divisible into tenths of a degree, and that degree of exactitude must surely be sufficient to be interpreted accurately if enough measurements are standardized as to time and location over a sufficiently long period of time? Please do not needlessly complicate the subject of regional and/or global mean temp trends and, by doing so, support the obfuscators which are still legion and able to distort the results of your recent debate when you repeated this persistent tendency you have to quote arcane numbers and statistics which leave your audience cold.

    Comment by Vern Johnson — 25 Mar 2007 @ 1:42 PM

  21. Is this a scientific weblog or a cyber-prayer meeting? The comments indicate it is the latter.

    Comment by W F Lenihan — 25 Mar 2007 @ 1:44 PM

  22. A useful question might be whether the global mean temperature serves as a useful index or proxy for anything more than publicizing global warming?

    For example, can we predict sea level or hurricane intensity or African drought conditions based on it?

    Comment by Jim Cross — 25 Mar 2007 @ 2:17 PM

  23. Re #2 (BR): “It seems that the authors of the indicated paper are trying to obscure something that is relatively simply and useful.” Thanks for the perfect one-line review!.

    Re #5 (BL): I think the key point is that even though a single thermometer located in, e.g., an area 100 kilometers to a side, will (in the short term, anyway) represent changes in heat content in that area very poorly, a mean of many widely distributed such surface temperature data points tracked over the long term is a reasonable way to approximate the change in global heat content. Of course the adjustments are tricky and of course there are error bars.

    Re #7 (PC): See my comment on #2.

    Re #8 (HR): May I steal that for future use?

    Re #9 (SB): No, it just means that the time needed for cooking cannot be predicted. That should have been intuitive!

    Re #10 (AA): Andresen is on the editorial board and the journal is very low impact. I suspect the paper got a pass on peer review (or perhaps there was none).

    Re #11 (VJ): You need to look up the definitions of Kelvin and Celsius. Note in particular the similarity of the gradations. Also, Gavin didn’t write the post.

    Re #12 (WF): Why spend time here when you could be re-reading your favorite Ayn Rand novel? It’s all you need to know, after all.

    Comment by Steve Bloom — 25 Mar 2007 @ 2:40 PM

  24. Re:#11

    Mr. Johnson, I suppose you are unaware that the only difference between the Kelvin and Celsius scales is the placement of where zero is. Zero Kelvin is absolute zero while zero Celsius is the freezing point of water. The temperature change for one degree on both scales is identical. There are reasons in the mathematics of thermodynamics to have a temperature scale where zero corresponds to the lowest possible temperature, hence the use of the Kelvin scale instead of the more familiar Celsius scale in such instances.

    By the way, it was Rasmus Benestad that posted this article, not Gavin.

    Comment by Jason DeRoche — 25 Mar 2007 @ 2:40 PM

  25. I found the comments in this post on Rabett Run (and links therein) rather illuminating:

    #14 SB: Thanks for the clarification, spuds now cooked and eaten ;-)

    Comment by SomeBeans — 25 Mar 2007 @ 3:01 PM

  26. re 11 by Vern: I admit I didn’t get the significance of using geometric mean, but anyhoo geometric mean is different for Kelvin and Celsius.

    Comment by Rod B. — 25 Mar 2007 @ 3:55 PM

  27. Re #14 Not the John Gribbin of popular novel writing in the subjects of quantum physics, relativity and cosmology is it per chance ?

    Comment by pete best — 25 Mar 2007 @ 4:04 PM

  28. #18 FB wrote: [[I could see daffodils in my garden today many weeks too early in southern england]]

    Please be careful with this statement. If I lived in certain exact places around the world, I would correctly be able to say that it is now COOLER outside than it was decades ago…changing ocean and pressure systems (NAO) (north atlantic oscilation), increases in light-reflecting industrial haze, changes in ozone concentrations (possibly) and such can cause cooling for local areas…but not currently for the global average.

    We need to look at the global average temperature changes as well as correlating data such as animal, plant and tree range changes animal, etc, timing changes, glaciers, sea levels, past climate changes, and changes in carbon-dioxide among others to help identify AGW (human warming).

    But yes, perhaps to you and the Inuit for example, the current changes are locally life-changing…and for the Inuit at this rate of warming in their local areas, this warming will almost certainly end their way of life…as it is currently doing right now.

    Comment by Richard Ordway — 25 Mar 2007 @ 4:20 PM

  29. To Jim Cross #22

    You could try Six Degrees of Warming by Mark Lynas.

    Comment by Ed Sears — 25 Mar 2007 @ 4:52 PM

  30. Re: #20

    Celsius is what is known in measurement theory as an interval scale, while Kelvin is a ratio scale. The difference is that 200 degrees Kelvin is twice a hot as 100 degrees. The same is not true of Celsius; 100 degrees C is not infinitely hotter than 0 C.

    It doesn’t really matter for an arithmetic average, but C is just an offset of K, so it is better form to use K. There are some operations that are not meaningful on interval scales that are fine on ratio scales. Using the correct scale avoids sloppy (and embarassing) mistakes.

    Comment by Tim McDermott — 25 Mar 2007 @ 4:54 PM

  31. #3, The easiest way to see if a solar forcing theory is correct as opposed to CO2, is by studying the impacts of a solar minima (now) as opposed to a maxima 2001-02, and compare the temperatures world wide, obviously the sun has a little trouble cooling down an evident upward spiraling temperature.

    Global Temperatures are simply essential and a remarkable figure, but not unique. I like the idea
    of pressure height temperatures (not often publicized), never hear enough about spectroscopy of our planet (taken from far away). Neither do we engage in MSU problems debate as opposed to Radiosonde
    data, contrarians really love MSU data. There is also other fascinating potential of Density Weighted Temperatures, almost ignored, yet compelling at times. Finally it is a tragic mistake not to use refraction of astronomical or terrestrial objects as a means of capturing the equivalent Optical temperature more precise and readily available by inexpensive means.

    Comment by wayne davidson — 25 Mar 2007 @ 4:54 PM

  32. I have looked at the Essex et al. paper quite carefully and for those who read the paper itself, a word of caution: Don’t be misled by their Figures 2 and 3. If you look at them incautiously, you might be tempted to conclude that they have shown that the average decadal temperature trend from a set of stations can indeed dramatically depend on the way one averages. And in a sense they have, but only by going to utterly ridiculous ways of averaging.

    In particular, note their x-axis in Figure 2: They take r-values from -125 to 125, where the r-value is essentially a moment of the distribution. So, r=1 corresponds to the standard arithmetic mean, r=2 corresponds to what is called the “root mean squared”, and even r=4 could conceivably be justified if, e.g., you wanted to average the amount of radiative energy emitted by that region of the atmosphere (which depends on the 4th power of the temperature). However, I don’t see how they can justify the much larger positive and negative powers of r as being at all reasonable. In fact, the reason that their graphs in Figures 2 and 3 seem to asymptotically approach certain values for the decadal trend is that these values are in fact the trend values you get if you look only at the lowest-temperature data point for each month over that period (which is picked out for large negative values of r) or if you look only at the highest-temperature data point for each month over that period (which is picked out for large positive values of r). [A similar story holds for their s-means of Fig. 3 except that now their range of s is even more extreme than their range for the r-means so you see an even broader range over which the decadal trend has essentially hit these asymptotic values!) This is clearly a very stupid way to perform an average!

    Using their own example (since they were kind enough to post the data they used on the web), I have reproduced their graph and find that even for r=4, the decadal trend in temperature for their 12 stations (0.056 C per decade) is only a little reduced from the r=1 values (0.060 C per decade)…And, my guess is that, if anything, the change would be less dramatic if the average were performed over many stations!

    Overall, their basic argument seems to hinge on the proposition that if one cannot rigorously (e.g., thermodynamically) justify one particular average as being correct, then any way of doing it is as good as any other. I can only imagine how much of modern science would be thrown out the window if we applied this logic across all of science…We’d be back in the Dark Ages!

    Comment by Joel Shore — 25 Mar 2007 @ 5:13 PM

  33. Well, at least I pretend that a global temperature exists! :-)

    I wrote a small program which models, sort of, the earlier ice age periods which came and went at 41 ky periods. The forcing F(t) is a sum of sine waves with periods and amplitudes for precession, 20 ky band, and obliquity, 41 ky band, but also a little for eccentricity, 95–400 ky band. So far we have to change the global temperature T,
    measured as the offset from the mean over time,

    dT(t) = r*F(t) – damping*T

    where the damping tern crudely represents radiative transfer effects (and stabilizes the equations to come). The damping represents a time constant of 4 ky, chosen for convience, not for the physics.

    Now we add W for greenhouse gases. Again W is to measure the offset from the mean of 230 ppm atmospheric CO2 in units of 100 ppm. I am assuming that the ocean provides an infinite source and sink for CO2, with only the temperature effect of

    dW(t) = T(t) – W(t) + Eff(t)

    changing W. The Eff(t) is added, non-linearly, to represent more efficient removal of CO2 from the air during cold periods. The term has small effect.

    Now the temperature change equation becomes

    dT(t) = r*(k*ln((2.3+W(t))/(2.3+W(t-1)) + F(t)) – damping*T

    where k = 2 seems to model well. Such interesting results! First, as expected, the amplification due to W enhances the power in the 41 ky band by about 50% and decreases the power in the 20 ky band by the same amount. The amplification provided by W enhances to swings by 150%. All seems to match expectations.

    However, increasing k beyond 2 just puts some power in the 372–585 ky band, but only 0.2%. But even with k = 2.3, already there is about 1% of the power at infinity. That is, the system is drifting a little, not just oscillating. Furthermore, the amplification drops slightly to 149%, and at k = 3, just 148%, the remainder going into drift.

    Comments and sugggestions are most welcome!

    Comment by David B. Benson — 25 Mar 2007 @ 5:24 PM

  34. It’s worth remembering that sampling is a big issue, though. There was a paper looking at heat content variability in HadCM3 and they found that they could “observe” spurious decadal variability if they calculated the heat content from a sub-sample of points (simulating real world observations of the ocean).

    I’m not sure if anyone has done the same thing for 1.5m temperature. I did get a bit worried about mean temperature being calculated simply from Mean=(Min+Max)/2, but I checked it (with model data) and, globally anyway, it came to the same thing as means constructed from timestep data. Locally there were large discrepancies, though. Possible that the sub-sampling could interact with this in a bad way.

    However, even then, it wouldn’t matter particularly if the bias it introduced was constant. Observational biases are most important when they are non-constant with time, which mostly happens when you switch from one observational device to another (as appears to be happening with the increase in ARGO data).

    Comment by Timothy — 25 Mar 2007 @ 5:37 PM

  35. >8 and >28 ‘may I steal that’
    Ill-advised, I’d say; it could’ve been marginally clever, maybe, but I feel bad having channeled Clippy in reply to a first-time poster, I shouldn’t’ve been hasty. Ill-tempered of me.
    Using that more than once? Nuh-uh, Clippy was an annoying troll in its first incarnation. If moderation fails to where trolls start replying to trolls, threads get impossible.

    Comment by Hank Roberts — 25 Mar 2007 @ 6:18 PM

  36. > spectroscopically.
    > Comment by John Gribbin


    Comment by Hank Roberts — 25 Mar 2007 @ 6:19 PM

  37. I suppose that one option, if these guys don’t like energy is to look at energy density at the surface–that way, we have to account not just for thermal energy, but also for the latent heat of all that ice that has melted.
    I think the objection to spectroscopic determination is that Earth is not a black body (despite what Monckton would have us believe).
    Re 32. Did you ever see the Spoof of the Microsoft Office assistant clippy who responds to an outpouring of despair by saying “You appear to be writing a suicide note. Microsoft Word can…”

    Comment by Ray Ladbury — 25 Mar 2007 @ 7:05 PM

  38. “The whole paper is irrelevant in the context of a climate change because it missed a very central point. CO2 affects all surface temperatures on Earth, and in order to improve the signal-to-noise ratio, an ordinary arthimetric mean will enhance the common signal in all the measurements and suppress the internal variations which are spatially incoherent (e.g. not caused by CO2 or other external forcings).”

    Is it possible to explain this a little better because to me it reads ‘the arthimetric mean enhances the readings for a CO2 cause and suppresses those that are not caused by CO2.
    Thank you.

    Comment by Ellis — 25 Mar 2007 @ 7:49 PM

  39. Ross McKitrick is the guy who doesn’t know the difference between degrees and radians. Figures.

    Comment by Dave Rado — 25 Mar 2007 @ 7:59 PM

  40. Re 35: Ellis, don’t get too freaked out by the terminology. Basically, you have a system with a lot of variability, but where there are interesting trends that emerge when it is examined over extended periods of time. Problem: How do you ignore the random fluctuations in order to spot the trends.
    Say you are tracking a stock. The closing price on any particular day is probably not of interest unless you are a daytrader or similarly impaired. So you look at the moving average. Clearer?

    Comment by Ray Ladbury — 25 Mar 2007 @ 8:17 PM

  41. About warm weather ending the lifestyle of the Inuit.

    Don’t forget that warming destroyed the culture of the Dorsett people, who preceded the Inuit and the Norewgians, about 500 A.D.

    I won’t jerk any tears from you by describing how the Interstate Highway system killed off all the poultry farmers in NY State, effectively ending my culture. But, hey, life goes on. I’d rather be blogging than raising chickens.

    Comment by joel — 25 Mar 2007 @ 8:18 PM

  42. Re #20, etc.

    Surely, the reason for Rasmus mentioning kelvin usage rather than celsius is even more elementary than hitherto explained.

    You just have to look at the respective formulae for arithmetic and geometric means to understand that if you have any zero value when calculating a geometric mean that the answer will always be zero (strictly speaking, undefined) since the geometric mean is the nth root of the product of your n temperature values.

    Of course, since all measurement has an associated error, I suppose you could reasonably choose any positive value other than zero within the error band of your measurement to obviate getting a zero geometric mean (but even then there are connotations). Then, how best to handle negative numbers …?

    It’s not got hot enough everywhere yet that zero and negative (celsius) temperatures are ancient history.

    Solution, use the kelvin scale.

    Comment by P. Lewis — 25 Mar 2007 @ 8:18 PM

  43. You say celsius or kelvin to the majority of American politicians/voters and their brains take a pass.

    Comment by J.C.H — 25 Mar 2007 @ 8:30 PM


    Joel Shore said…

    Actually, I have reproduced their calculation and, in fairness, they did use Kelvin.

    However, the problem is, of course, taking these large positive or negative moments (as denoted by r) is silly. In the limit that r is large and positive, you just get the trend in the maximum (of the twelve station values) for each month. In the limit that r is large and negative, you just get the trend in the minimum for each month. [I have verified this is indeed true….although the convergence for large positive r is slow. The s-values show the asymptotic trend values more clearly.]]

    It is worth noting that if you use any reasonable value of r, even r=4 that some claim might be justified if you want to average the radiative energy associated with that temp., you don’t get something very different from r=1. In fact, r=4 reduces the trend from 0.060 C per decade to 0.056 C per decade.

    Comment by Ken Williams — 25 Mar 2007 @ 8:58 PM

  45. If you mentioned kelvin to most of the UK population I dare say you’d get a broadly similar response.

    And the older generation in the UK still want their temperatures explained in “old money” as well as celsius when they get their weather forecasts.

    And I should have said, “Solution, use the kelvin scale if you intend to use the geometric mean.” (Why would you bother, I think, has been covered elsewhere here.)

    Comment by P. Lewis — 25 Mar 2007 @ 9:07 PM

  46. The repeated misspelling of “arithmetic” is a bit tedious, but to be honest the content of your post is rather more embarrassing. The reason for using an arithmetic mean is not that it enhances the signal-to-noise ratio! You could do worse than read Eli Rabett’s ponderings on the subject (several postings on ).

    It is interesting to note that this meme (which was previously published in McKitrick+Essex’s stupid book) subsequently gained an author from the editorial board of the journal in which it appears.

    [Response:Indeed, misspelling of “arithmetic” is embarrasing… That’s fixed now. -rasmus]

    Comment by James Annan — 25 Mar 2007 @ 9:31 PM

  47. To put the whole issue in perspective, Andy Rooney just ended his latest piece on 60 Minutes with, “Does anyone want to buy a barely used snowthrower?” Where I come from in Maine we called them snowblowers. Their need has diminished of late with the exception of the local anomalie of Oswego.

    Comment by Mark A. York — 25 Mar 2007 @ 10:01 PM

  48. Move over , Inhofe, Jerry Falwell is now ( 10.17 pm Sunday EST) on the air denouncing GW as a myth on his well watched weekly sermon.

    Comment by Russell Seitz — 25 Mar 2007 @ 10:19 PM

  49. I doubt there is any easy answer or methodology to answering “Does a global temperature exist?”

    Climate change uncertainty for daily minimum and maximum temperatures: A model inter-comparison
    Geophysical Research Letters 34 (5), 05715 (2007)
    “Several impacts of climate change may depend more on changes in mean daily minimum (Tmin) or maximum (Tmax) temperatures than daily averages.”…”Model differences in cloud changes, which exert relatively greater influence on Tmax during summer and Tmin during winter, were identified as the main source of uncertainty disparities. These results highlight the importance of considering separately projections for Tmax and Tmin when assessing climate change impacts, even in cases where average projected changes are similar. In addition, impacts that are most sensitive to summertime Tmin or wintertime Tmax may be more predictable than suggested by analyses using only projections of daily average temperatures. ”

    Implications of temporal change in urban heat island intensity observed at Beijing and Wuhan stations
    Geophysical Research Letters 34 (5), 05711 (2007)
    …”This result along with the previous researches indicates a need to pay more attention to the urbanization-induced bias probably existing in the current surface air temperature records of the national basic stations. ”

    Contribution of land-atmosphere coupling to recent European summer heat waves
    Geophysical Research Letters 34 (6), 06707 (24 Mar 2007)
    …”The experiments reveal that land-atmosphere coupling plays an important role for the evolution of the investigated heat waves both through local and remote effects. During all simulated events soil moisture-temperature interactions increase the heat wave duration and account for typically 50â??80% of the number of hot summer days. The largest impact is found for daily maximum temperatures during heat wave episodes. ”

    Irrigation cooling effect: Regional climate forcing by land-use change
    Geophysical Research Letters 34 (3), 03703 (2007)
    …”Given our results for California and the global importance of irrigated agriculture, past expansion of irrigated land has likely affected observations of surface temperature, potentially masking the full warming signal caused by greenhouse gas increases. ”

    Influence of Air-Conditioning Waste Heat on Air Temperature in Tokyo during Summer: Numerical Experiments Using an Urban Canopy Model Coupled with a Building Energy Model
    Journal of Applied Meteorology and Climatology 46 (1), 66 (2007)
    …”The waste heat from the air conditioners has caused a temperature rise of 1°â??2°C or more on weekdays in the Tokyo office areas. This heating promotes the heat-island phenomenon in Tokyo on weekdays. Thus, it is shown that the energy consumption process (mainly with air conditioning) in buildings should be included in the modeling of summertime air temperature on weekdays in urban areas.”

    Land use/land cover change effects on temperature trends at U.S. Climate Normals stations
    Geophysical Research Letters 33 (11), 11703 (2006)
    “Alterations in land use/land cover (LULC) in areas near meteorological observation stations can influence the measurement of climatological variables such as temperature. Urbanization near climate stations has been the focus of considerable research attention, however conversions between non-urban LULC classes may also have an impact.”…” In contrast, after the period of greatest LULC change was observed, 95% of the stations that exhibited significant trends (minimum, maximum, or mean temperature) displayed warming trends.”

    Incorporating model uncertainty into attribution of observed temperature change
    C Huntingford et al.
    Geophysics Research Letters 33, 5710 (Mar 2006)
    …”We find that greenhouse gas forcing would very likely have resulted in greater warming than observed during the past half century if there had not been an offsetting cooling from aerosols and other forcings. ”

    Global observed changes in daily climate extremes of temperature and precipitation
    Journal of Geophysical Research 111 (d5), D05109 (2006)

    Comment by BarbieDoll Moment — 25 Mar 2007 @ 10:45 PM

  50. Re Falwell’s GW Myth broadcast- Fallwell is the Liberty University guy,

    He cites Ball as his secular authority, but insists Satan is out to divert the church from its primary mission by stirring dissenters to talk of climate change. The exegetic details are available on DVD for $14.95.

    Comment by Russell Seitz — 25 Mar 2007 @ 10:49 PM

  51. According to an old chemistry textbook by Linus and Peter Pauling, Lord Kelvin devised his temperature scale so that the laws of thermodynamics could be expressed in simple form. As an example, the emission of longwave infrared radiation for a terrestrial object is proportional to its kelvin temperature raised to the 4th power. Thus, for an object at 250 K (assume it is a blackbody emitter, so emissivity, epsilon, = 1.0), IR radiant heat emission is 3.906 x 10^9 x Stefan-Boltzmann constant. As with the geometric mean, if the original equation for IR emission had been developed for use with the Celsius temperature, it would have had to accommodate multiplication by zero or negative numbers.

    Comment by Chuck Booth — 25 Mar 2007 @ 10:54 PM

  52. After thinking about this paper more than a bit, I think there are two principal strawmen on offer

    First what climatologists want to compare is the variation of temperature over time at all locations, not the temperature itself, either of a particular location or of the globe or some regional area. Essex, et al. don’t want you to recognize that.

    The global temperature anomaly series are optimized for such comparison. Indeed it is about impossible to use them to recover temperatures at any specific location. Once you use anomalies (see the GISS site for details), you are looking at something with positive and negative values and pretty much only the linear average makes sense.

    Second, Essex, et al. never come to grips with the nature of the data. For example, if you don’t get rid of seasonal variations you are in very deep trouble if you want to compare temperature changes in Norway and Argentina. The major thing you will find is they anticorrelate. It would be very tricky to balance the sample.

    There are lots of small things to pick on but they are somewhat subtle. For example they claim that the Earth’s emission is not black body, true enough within limits, but the same thing is true of the Sun’s radiation and they swallow that one whole. You get moaning about the pressure variation at the surface on land invalidating a simple scaling of energy with temperature, but they kinda din say much about what happens over the more 2/3 of the earth’s surface that is at sea level

    Comment by Eli Rabett — 25 Mar 2007 @ 11:53 PM

  53. Then say degrees above absolute zero, for the politically impaired.
    And for the UK, surely the Scots will know him:

    Comment by Hank Roberts — 25 Mar 2007 @ 11:54 PM

  54. For the first month of senior thermodynamics class, we weren’t allowed to use the word “temperature”. I think Christopher Essex, Ross McKitrick, and Bjarne Andresen have themselves wrapped around some similar axle.
    Dr. Solanki’s “The sun did it” is irrelevant. All deniers of the fact that WE did it are irrelevant because the fact is that we must be the thermostat for our planet now that we can be. We successfully prevented the ice age that would be starting now if we hadn’t burned fossil fuels. The problem is that the “we” thermostat is stuck in the “On” position. Changing from “accepting “god’s” will” [whatever that means] to controlling the climate is too big of a jolt for most people.

    Comment by Edward Greisch — 26 Mar 2007 @ 12:26 AM

  55. I’ve always thought that the emphasis in the media and IPCC on Global Mean Temperature is terribly misleading. Does it really just mean global air temperatures averaged across season, day, night, elevation and location? I’m sure that its a pretty good proxy for global heat content – but I don’t think it has sufficient explanatory power. How much lag does the hydrosphere have against air temp? As I understand things, a LOT and since we currently are in the heat acquisition phase of the curve before we reach equilibrium (whatever that means in a long term planetary heat bduget) – that lag would be important in making policy decisions. How soon does the air temp reflect greater ocean heat content? In warmer areas, the air temp remains close to the same despite extra heat as long as there is moisture to evaporate.

    So what do the individual components show us? Are all components rising equally across the globe? Obviously not. So, is the extra heat showing up as higher temps primarily at higher latitudes and elevations? I think so. Are the day time or night time temps showing the most change? Isn’t it the night time temps that have shown the most rise and at the highest latitude? Isn’t that a key finding indicating that GHG are to blame rather than higher solar input or fewer clouds?

    Global averages can be misleading.

    Man: “My average speed while driving 10 miles to the store increased from 35 mph to 35.7 mph.”
    Man’s friend: “Why the hell are you keeping track of such things?”
    Man: “For fun, but for the record, it went up 0.7 mph because instead of driving 25 mph for the 0.2 miles through your neighborhood – I drove 75 mph instead.”
    Man’s friend: “Are you insane? I’m calling the cops.”

    A 6C increase over Greeland balanced against a 0.3C increase over the Sahara (averaging to 1.5C accounting for land area) likely has a different outcome for the planet than simply a 1.5C increase over both.

    Comment by Robin Johnson — 26 Mar 2007 @ 1:34 AM

  56. Re #39 (Dave Rado)

    While you’re at the site provided by Dave ( ), check out some other posts by Tim Lambert on how McKittrick handles temperatures (about one page down from the top), for example:

    Comment by Dick Veldkamp — 26 Mar 2007 @ 2:19 AM

  57. [[Gavin, why do you prefer Kelvin to Celsius? Surely ONLY Celsius is practical to use and is easily and meaningfully divisible into tenths of a degree, and that degree of exactitude must surely be sufficient to be interpreted accurately if enough measurements are standardized as to time and location over a sufficiently long period of time?]]

    The gas laws, and indeed any physical laws which involve temperature, always refer to absolute temperature, never to human-reference temperature. PV/T = P’V’/T’ only if temperature is measured in either Kelvin degrees or Rankine degrees. Measuring it in Celsius or Fahrenheit would produce erroneous results. This is an elementary point of physical science.

    Comment by Barton Paul Levenson — 26 Mar 2007 @ 7:17 AM

  58. How the hell did the paper in question get into Non-Equilibrium Thermodynamics? Isn’t that a peer-reviewed journal? How did something as asinine as this get past peer review? When I think of the papers I’ve submitted that haven’t made the grade, I’m awfully inclined to start sending them to this journal now.

    [Response: See comment above. – gavin]

    Comment by Barton Paul Levenson — 26 Mar 2007 @ 7:18 AM

  59. [[A useful question might be whether the global mean temperature serves as a useful index or proxy for anything more than publicizing global warming?

    For example, can we predict sea level or hurricane intensity or African drought conditions based on it? ]]

    How about the habitability of the planet? Or the amount of energy tied up in the climate system? Both relate to the mean global annual surface temperature. A planet with mean Ts less than 273 K or greater than 303 K isn’t considered habitable by humans (Dole 1964). The more energy in the climate system, the more violent the weather, on average, and the greater the variation. Yes, it’s a useful measure, and it existed long, long before climate change became a political issue.

    Comment by Barton Paul Levenson — 26 Mar 2007 @ 7:21 AM

  60. [[I doubt there is any easy answer or methodology to answering “Does a global temperature exist?” ]]

    Well, you’re wrong. The average global temperature on any given day is the average of the temperature readings all over the globe, weighted for relative area coverage. The mean global annual surface temperature is the daily figures averaged over a year. Simple.

    Comment by Barton Paul Levenson — 26 Mar 2007 @ 7:28 AM

  61. “One could choose to look at the global mean sea level instead, which does have a physical meaning…”

    Correct me if I’m wrong, but isn’t the height of a gas molecule directly proportional to the heat (kinetic energy) of the air column its in.
    Therefore, the “height” of the atmosphere is proportional to the atmosphere’s heat content.
    Therefore, there’s also a “global mean atmospheric level”.
    Therefore, Global mean temperature is a physically meaningful concept.

    Somehow, I think it’s easier to just use mean temperatures.

    Comment by Alex Nichols — 26 Mar 2007 @ 7:33 AM

  62. [[Re Falwell’s GW Myth broadcast- Fallwell is the Liberty University guy,

    He cites Ball as his secular authority, but insists Satan is out to divert the church from its primary mission by stirring dissenters to talk of climate change. The exegetic details are available on DVD for $14.95. ]]

    I have some residual respect left for Falwell because he’s not personally corrupt in the way Bakker or Swaggert were, but oh, man, a lot of his political opinions are lunacy. I pray people don’t assume all or most Christians are like Jerry Falwell.

    Comment by Barton Paul Levenson — 26 Mar 2007 @ 7:51 AM

  63. Not sure if anyone has pointed this out but temprature is proportional to the average velocity of the molecules/atoms in a substance, velocity in turn is time over distance, try nailing down “time”, nope just an “illusion”, what about distance or is it spacetime?

    Turns out that “reality” is on very shakey ground. If you dig deep enough it’s apparently all just a mass of subatomic particles randomly popping in and out of existance. A kind of quantum “white noise” from which you and I “emerge”, (or are “created”, “recycled”, ect, depending on your spiritual outlook).

    My point being: Perhaps this paper belongs in a philosophical journal rather than a scientific one, although I’m sure the philosphers will also take exception to being told how to suck eggs.

    Comment by Alan — 26 Mar 2007 @ 8:22 AM

  64. This paper is the thought of things that Pauli called not even wrong. It is based on a misconception (although a common one) of what the global temperature anomaly records are constructed for and the information that they carry. It treats data as numbers without connection to the underlying physical reality, ignores, indeed belittles without reason, the myriad studies that support climate science and is the sort of trash that gets published if a member of the editorial board is one of the co-authors.

    Comment by Eli Rabett — 26 Mar 2007 @ 10:56 AM

  65. As ths thread winds down.
    One of the most interesting aspects of human nature is the influence of self-interest on perceptions of reality. Scientists with PHDs are not immune.

    Comment by Webster — 26 Mar 2007 @ 11:15 AM

  66. Q for scientists.
    Is the average temperature the same as the temperature that would be achieved if the atmosphere were to come to an at-rest thermal equilibrium?

    Why are the oceans so cold, trapped between a hot core and a warm atmosphere?

    Comment by kroganchor — 26 Mar 2007 @ 11:35 AM

  67. #52, Pressure is key in many ways, for instance if surface temperature is 20 C at 990 mb it is not exactly the same as 20 C at 1000 mb, refractive temperature (using an astronomical object as a fixed sphere of reference) makes the true temperatue warmer when the pressure is higher. Therefore a weighted temperature (with respect to pressure) has a more comprehensive meaning. The point is well taken though, some global mean temperatures are measured at various altitudes, which in its purest sense is a mistake. But it isn’t if the altitudes never change.

    Comment by wayne davidson — 26 Mar 2007 @ 11:37 AM

  68. As several responses have noted, any thermometer is subject to the same putative lack of physicality objected to by Essex et al: averaging out the various molecular temperatures it encounters. The Essex paper is so remarkably absurd, in this regard (what should we do, throw away our thermometers?) that intelligent people should long distrust this Journal of Non-Equilibrium Thermodynamics in which the Essex paper appeared. How does something this useless wind up getting published?

    Comment by Daniel C. Goodwin — 26 Mar 2007 @ 11:47 AM

  69. Ola, good text, I am new in the space. automatiamente I automatiamente translated of the Portuguese English.

    Comment by Iara Nunes — 26 Mar 2007 @ 11:48 AM

  70. I have only skimmed over the paper, but what I see is sort of a distinction without a difference. What it appears the authors are doing is to point out the existence of the other averages:

    M_r = (sum(v_i^r)/N)^(1/r)

    (Here _ is a subscript, and ^ is an exponent. N is the number of points, and i is the index that runs from 1 to N, and the values are v_i. You may want to stick an absolute value in there if the v values can be negative, depending on what you’re doing.)

    The normal average is with r=1. It is possible to change the sum into an integral if you want to extend to a continuous system (such as the surface of the earth).

    First of all, the other averages *do* exist and are sometimes meaningful. For example, it’s quite common to discuss the root-mean-square (RMS) value of an electrical signal. This corresponds to the choice of r=2. This is physically meaningful because the energy in the system goes like the square of the value being averaged, and often the energy is what is interesting. It’s also common for signals to use the r=1 choice, which computes the center point of the wave

    One other point is that as r goes to infinity this picks out the highest value in the data set. (Think about the case where the biggest point is 1 and all the others are between 0 and 1.)

    This all is well known in the mathematical study called “real analysis”. For a series functions to converge pointwise to a well-defined limit, the difference between them has to average to 0 in the r->infinity norm. In fourier analysis two wavefunctions are the same if they are the same in the r=2 sense. (And in physics, two wavefunctions are the same if they are the same in the r=2 sense.)

    What’s odd about this discussion is that aside from being obvious, it has nothing to do with any of the cases discussed in the introduction. For example, the claim that the viral infections in frogs are caused by “global warming” is actually a claim that the temperatures increased at the one point where the frogs are, and that the increase in temperatures caused the viral infections. The global average and whether it exists has nothing to do with it. The same is true for hurricane formation, etc.

    Furthermore, it has very little effect on the evaluation of climate models. If you make a prediction, then the correct thing to do is to compare the prediction with the real-world data. That is, you could either compute (a) the difference of the predicted and observed values at all the measuring stations on the earth and then average the absolute values, or (b) you could compute the two averages see if they’re different.

    What you’ll find of course is that your prediction won’t match the reality of course. If you do (a), it’s sort of up to you what value of r you pick. If you pick r=2, you are saying you get the RMS temperature right. It’s perfectly plausible that r=2 is an interesting thing to do. It gives greater weight to points that are “off more”, and is, for example, the standard procedure for evaluating the fit of a straight line to data. Likewise, it would even be possible to use the r->infinity norm – if what you want to do is evaluate the goodness of the prediction by the single biggest error anywhere on the earth that it made. (I think that would be pretty invalid, given the usual uses to which climate models are put.)

    If you use procedure (b), that’s a bit more problematic. You’d have to justify why you think a particular r is a reasonable measure to be comparing – presumably because there’s an underlying physical value that justifies it. For the case of temperature, the reason for r=1 could be (a) the average temperature of a gas is the proportional to energy contained in it and (b) the overall thing that is being tracked is energy because it’s conserved.

    One last point about all of this. Except for r=1, these averages don’t have the property that if you add a fixed quantity to the values (for example, by using Celsius rather than Kelvin temperatures) you get the same value for the average. The fact that we do use a temperature scale which shifted from the real zero by a fixed quantity indicates that for most physical processes, using r=1 is quite often a reasonable thing to do.

    Comment by Mitch Golden — 26 Mar 2007 @ 12:24 PM

  71. [[Why are the oceans so cold, trapped between a hot core and a warm atmosphere?]]

    Good question. I honestly don’t know. If I had to speculate, I’d say something like — the surface waters absorb sunlight and infrared well, so there’s little heating of lower levels, convection takes heat from the lower levels to the higher levels, and the surface radiates away enough heat to keep the lower levels as cold as they are. But maybe that’s wrong somewhere. Gavin, Mike, Ray?

    Comment by Barton Paul Levenson — 26 Mar 2007 @ 12:29 PM

  72. I am not an expert – but surely McKitrick is asking and answering the wrong question? He asks “what is the mean global temperature?” and because he can’t find a physical meaning for it dismisses it as an arbitrary mathematical construct. But a better question is “what use is the mean global temperature?”. And it is useful for telling us if temperatures are on the whole changing. There are loads of other ways of doing that: median, root mean square, geometric mean, ratio of increases to decreases, whatever, But the arithmetic mean has one rather nice property. A one degree change in any component has the same effect on the mean, whatever the component. i.e. it treats all degrees equally.

    Well I think this makes sense…

    Comment by Mark Frank — 26 Mar 2007 @ 12:49 PM

  73. Re 71. Deep water formation occurs in high latitude oceans where the surface waters are cold and dense, hence they sink and flow towards lower latitudes in the deeps. This is also how deep waters are ventilated. So deep seas are cold as is oceanic crust. Both oceanic crust and continental crust are pretty cold compared to the core and deeper mantle.

    Comment by Figen Mekik — 26 Mar 2007 @ 12:59 PM

  74. I think everyone should first look at the end of the paper’s section 2.1 where it makes the point that the equilibrium physical temperature that a system could reach depends on the thermodynamic process by which it gets there. e.g. if “they equilibrate reversibly, i.e. while producing work, their common final temperature will be (TaTb)”. Ta and Tb, of course, have to be given in absolute temperature, not, for example, Celsius, to give the right answer. This is a pretty weird choice for physical average temperature (rather than the usual isenthalpic equilibrium) but, hey, if that’s what turns Essex et al on, why not? Using this physical definition, I wouldn’t expect the global average warming to be much different from using the normal definition because that would require a substantial increase in temperature variation between different places to make a significant difference. If anything, I’d expect the isentropic definition to give a higher rate of global warming because temperature variation from equator to pole is expected to decrease with global warming.

    Anyway, Essex et al play fast and loose with the difference between Celsius and Kelvin in section 3.1.2 where they say AR4=(T1^4 + T2^4)^(1/4) and

    “R4 would appear in connection with black body radiation.”

    in which case T1 and T2 must be in absolute temperature to get any sort of physical meaning. Essex et al forget this pretty quickly however, when they put up an averaging example using this formula and for reasons best known to them decide to put Celsius values into their formulas rather than absolute. I wonder if this would have anything to do with them wanting to blatantly exaggerate their case?

    For someone who complains about normal calculations of average temperature having no physical meaning, Essex et al don’t seem to have the slightest difficulty ignoring physical meaning themselves.

    Comment by Chris O'Neill — 26 Mar 2007 @ 1:25 PM

  75. Regardless of what you believe, one side or the other, perhaps these folks may have an answer or two that may bring some important, middle-ground thoughts to the process.

    Comment by John D. — 26 Mar 2007 @ 1:32 PM

  76. Oh, right, check them out, if anyone doesn’t already know about them:

    Comment by Hank Roberts — 26 Mar 2007 @ 1:40 PM

  77. Sometimes you have to wonder if addressing every skeptic argument, doesn’t give them some unfortunate validity. But it’s nice to see Real Climate knock them apart.

    Comment by Benny — 26 Mar 2007 @ 1:41 PM

  78. Re #74 (John D) Middle ground

    Are you kidding?

    “This is the website that completely knocks the wind out of the enviro’s sails. See over 17,000 scientists declare that global warming is a lie with no scientific basis whatsoever.” And so on. And so forth.

    There is no middle ground half way between evidence based science and nonsense.

    Comment by Dick Veldkamp — 26 Mar 2007 @ 1:41 PM

  79. I have one further note on what I said in #70 – and it clarifies what some others have been saying.

    One reason it’s reasonable to use the r=1 case is that a lot of what happens in the earth is the mixing of the air, in a region in which its specific heat is more or less constant. If I have one body of air at 20 degrees C and another of about the same size at 30 degrees C and I mix them the resulting body of air is more or less at 25 degrees C.

    There are other physical systems where that need not be true. For example, if most of the effects of energy transfer were radiative, the relevant average would be r=4.

    That is, suppose we want to compute the amount of energy radiated by the earth into space. We would *not* want to average the temperature of the top of the atmosphere and plug that into the radiation formula. That’s because the amount of black-body radiation at a given temperature goes like T^4. The right thing to do is to compute the r=4 mean, and plug *that* into the formula.

    As I said, there’s nothing interesting about all of this, it’s mostly a question using the right measure to talk about the right things. The frogs die anyway.

    Comment by Mitch Golden — 26 Mar 2007 @ 1:44 PM

  80. It occurs to me that perhaps I need to remove my thermostat because there is no real mean temperature in my household.

    Either that, or perhaps I need to install several thousand thermostats to measure every cubic foot of air and every surface I can monitor, and only then will I know what to do with the air conditioning.

    Comment by El Cid — 26 Mar 2007 @ 2:24 PM

  81. #75
    If that side spouts obvious nonsense, then why would it be taking the wind out of the sails of such a solid IPCC report and the enviro movement?
    There never is middle ground if both sides are entrenched in the belief that the other side is spouting nonsense. I guess some folks just hear one side, take it at face value and run with it. Sounds like Bush and Iran right now. Total skepticism from both sides is really counter-productive to any scientific issue.

    For some reason, these people, educated in the same schools as the rest of you, have looked at the IPCC data and the politics and decided that some of it may be flawed. I’m sure out of 17,000 scientists, there must be at least a couple of hundred that may actually know what they are talking about, but if it falls on deaf ears, then none of it really matters. For instance, this entire web blog has really, only had a small fraction of scientists repeatedly participating and to a degree, reinforcing their collective opinions on subjects of the IPCC report, and that’s a good thing.

    Perhaps you should pressure the other side for an actual, full-blown, scientifically supported report. It could be an eye opener, or may cause a total surge to the IPCC camp.

    Comment by John D. — 26 Mar 2007 @ 3:11 PM

  82. Re 78:
    “There is no middle ground half way between evidence based science and nonsense.”

    I must beg to differ- it has been around since the end of the Hadean:

    Comment by Russell Seitz — 26 Mar 2007 @ 3:16 PM

  83. Certainly the average temperature (arithmetic average) has usefulness. All averages of temperature share the property that if *all* temperatures increase (decrease), then the average (arithmetic, geometric, root-mean-square, whatever) will increase (decrease). The essential property which defines the arithmetic mean (area-weighted) of temperature is that if one area increases by a single degree, and another area of equal size decreases by a single degree, then the arithmetic mean remains unchanged. The root-mean-square, geometric, whatever other averages will not.

    So if one wishes to address the question of the usefulness of the arithmetic mean in determining a physically meaningful measure of climate, one should ask whether an increase of a given temperature in one region, accompanied by a decrease of the same amount in an equal-size region, actually represents no change in the meaningful quantity.

    My examination of historical temperature records indicates that for the most part, during times when climate forcings were reasonably stable (so we expect that the “meaningful” measure should not change), global average temperature is also reasonably stable. This means that we should be able to connect the two phenomena, changes in forcings and changes in global average T, as physically related. The fact that global average T does not correspond precisely to a conserved quantity (like energy or momentum), does not invalidate its usefulness or meaninfulness.

    The relationship is meaningful in that a statistically significant change in global average T heralds some change in climate forcings. And that is exactly what we want from our single measure of global warming.

    One could study the behavior of other averages (geometric, rms, etc.) to see how stable they are during times of stability for climate forcings. This might identify a measure which is even more “meaningful” than global average T (but would in no way invalidate the usefulness of global average T). It appears that McKitrick and colleagues have not attempted this.

    Comment by tamino — 26 Mar 2007 @ 3:26 PM

  84. An over simplification?
    An average temperature? I really don’t need an average temperature to tell me there’s somthing wrong with the temperature. It’d be nice to be able to look at the dash and see the temperature warning light and then do somthing to halt the problem, pull over, add more water etc. Albedo, greenhouse gases and freak winds aside, the two or three main indicators are similar to a car’s radiator, we have where the air generally rises under the direct focus of the sun and where it generally falls at the poles. The poles are the easiest to measure temperature at, indicating how well the upper atmosphere reduced the heat content. Seems like the warning lights on, let’s pull over :?
    Another arguement along the same vein is boiling water, what is the temperature of boiling water? On average it’s 100C? If you said that you’d be right because you just look at it and see it boiling. Now prove that the water is boiling by taking temperature readings, let’s say it’s a small pot of water, you’d get many different readings, some above some below 100C, if you averaged them all together you might get close to 100C as long as the sample was high enough. Now we change the scenario, we boil the water from the top down, what’s the average temperature? The system is then changed to a circulating cooling system, the answer is there would be a large difference between upper and lower temperatures as heat rises but average heat would still rise. What if we heated the top edges of the pot of water? The surface water would tend to move from the edges to the surface center, plunge down to the bottom of the pot, get cooled down there, get pulled to the bottom’s edge and up again to get reheated. What if we had the heat source running along the top edge of the water in a circular motion… that sounds familiar. How about two pots of water rotating CCW and CW next to each other using the the same heat source where the two pots almost touch, what’s the average temperature of those two pots. Now place tropical fish in these pots and cold water fish in these pots and see where they migrate. The point seems to be that getting an average temperature seems to put us through a lot of trouble to get the same point we have now. However it does waste time so that people who don’t “believe” in global warming can make a few more million or billion and use that money to convince other’s their cause is correct and there is no reason to pull over and check under the hood. :? :?

    Comment by Harold Ford — 26 Mar 2007 @ 3:29 PM

  85. Re #81 (John D)

    John, sorry if was a little blunt in my response to you. However I’m afraid I have to stick with my point: there’s lots of evidence that GW is not a “a great lie” but actually happening (no need to list it all again, RC is your friend). If some of these 17,000 scientists have a problem with IPCC, there’s nothing to stop them to do their own research and publish in a reputable, peer reviewed journal. That would seem a more convincing strategy than signing a petition.

    Comment by Dick Veldkamp — 26 Mar 2007 @ 3:40 PM

  86. Re 74.:

    if “they equilibrate reversibly, i.e. while producing work, their common final temperature will be (TaTb)”

    should be

    if “they equilibrate reversibly, i.e. while producing work, their common final temperature will be square root(TaTb)”

    The square root symbol didn’t come through, sorry.

    Comment by Chris O'Neill — 26 Mar 2007 @ 3:54 PM

  87. The planetary energy imbalance does have a concrete meaning and could be measured. Let’s assume that in the pre-industrial era the planetary energy imbalance was zero. However, a planetary energy imbalance of zero can correspond to a number of different global average temperatures depending on the configuration of the climate system (land mass location, etc.). The calculation of an equilibrium climate response to external forcing means that the planetary energy imbalance is zero when equilibrium is reached, but is at a higher temperature. The rate of climate change is dependent on the size of the planetary energy imbalance; so measuring the planetary energy imbalance directly might be a useful thing to do. The Deep Space Climate Observatory was designed to measure this quantity, but has been mothballed:

    Comment by Ike Solem — 26 Mar 2007 @ 4:10 PM

  88. Just to get it right…

    They are scientist who publish a peer reviewed paper. But their paper, contra other peer revied papers expressing other opinions, are … crap? And who’s to tell me which is which, you? And I should listen to you because…you are scientist with peer reviewed papers?

    /Br. Rob

    [Response: yep that’s right. Peer review can be a bit of a crap shoot and is only the first line of defense against nonsense. So don’t listen to any one paper or person (including us), but put much more confidence in assessments like the IPCC or the National Academies reports. – gavin]

    Comment by Rob — 26 Mar 2007 @ 4:13 PM

  89. #75 Red Herring, John D.


    Your link is to a well-known fossil-fuel funded website: The Oregon Institute of Science and Medicine

    They have a link to to a well-known fraud: The Petition project.

    Comment by Richard Ordway — 26 Mar 2007 @ 4:51 PM

  90. RE: #73 Thanks for the lesson. If the poles are heating faster than the equator, is GW causing this engine to slow down, and could this be a stabilizing effect, or is it insignificant?

    Comment by kroganchor — 26 Mar 2007 @ 4:52 PM

  91. It occurs to me to wonder if this “no average” nonsense is a preemptive strike against pulling Triana /DSCOVR out of the warehouse and getting it launched.

    Ike’s link is useful as a reminder, it’s one missing piece of the instrumentation we know would help understand what’s up on Earth.

    It would give us the same view of Earth we have of other planets for which temperatures are reported — by viewing the whole visible surface of the planet, instead of by looking at lots of local thermometers, over time.

    It, from everything we know, would also be immensely popular as a video feed source. People _like_ watching Earth, a _lot_. Ask any astronaut.

    Comment by Hank Roberts — 26 Mar 2007 @ 5:03 PM

  92. Re #70, Mitch Golden wrote:

    “This all is well known in the mathematical study called “real analysis”. For a series functions to converge pointwise to a well-defined limit, the difference between them has to average to 0 in the r->infinity norm.”

    Mitch is correct about the well-knowing, but his example is wrong. A sequence of functions can converge pointwise to some function without converging in the C-infinity norm, which generates the distance function corresponding to the limit of the EMcA smokescreen averages as n goes to zero. A counterexample demonstrating this is a sequence where the n-th function in the sequence has a “tee-pee” from a zero value at x = 0 to a value of 1 at x = 1/n and back down to zero at x = 2/n. The value of the nth function is zero everywhere else (i.e., for x less than zero and x greater than x = 2/n). The C-infinity norm of each of the f_sub_n is 1 (because of the peak of the tee-pee) but the sequence converges pointwise to the function f = 0 for all values of x, which has a C-infinity norm of 0.

    Best regards.

    Jim Dukelow

    Comment by Jim Dukelow — 26 Mar 2007 @ 5:28 PM

  93. Re:90 kroganchor

    That’s one theory. This sinking and advection of deep water masses to lower latitudes in the Atlantic Ocean is called Atlantic meridional overturning circulation (AMOC) and there are theories that it will weaken with continuing global warming. But as Carl Wunsch says in his letter posted on this page, he considers this a less serious/likely outcome when compared to sea level rise as a consequence of global warming which is not only happening right now but is also projected to accelerate in the future. My $0.02

    Comment by Figen Mekik — 26 Mar 2007 @ 6:03 PM

  94. re #59

    [How about the habitability of the planet? Or the amount of energy tied up in the climate system? Both relate to the mean global annual surface temperature. A planet with mean Ts less than 273 K or greater than 303 K isn’t considered habitable by humans.]

    Nice to know, Barton, that a global mean temperature can predict that the Earth is habitable. Any more insights?

    We can quibble about thermodynamics, Celsius and Kelvin, and other such things in this article but the key point I pick up from this is that a global mean temperature, although we can define a way to calculate it, does not really provide anything useful. This may not be the only thing the authors intended and they may have had other agendas, but on the surface of it, I don’t see the arguments as particularly pro or anti GW.

    Comment by Jim Cross — 26 Mar 2007 @ 6:51 PM

  95. Jim, read the BBC article linked above. That explains exactly why this would be useful information to have about Earth, using the same methods we have it about other objects.

    Comment by Hank Roberts — 26 Mar 2007 @ 7:54 PM

  96. Looking at Ross McKitrick’s web site where he posts his math, I find myself a bit confused about what he has done.

    It appears to be true that temperatures in Kelvin were used as there is a conversion from C to K shown for the input to the calculations. Some stations have missing data and there is a flag set in the last column of the input file “giss12.txt” to indicate that the row has missing data. I don’t know how to program in the language used, but it appears that missing data for one site results in the loss of a month’s data for the all 12 sites, not just the missing data. I didn’t see a discussion in the paper of the impact of missing months on the calculated results.

    Furthermore, the value of “r” used in the “trender” program for calculating the values for figure 2 is incremented in the program in a way which does not regularly produce integer values of “r”. The loop for “r” begins with r = -120, then incrementing r by 1.2 at each step. On the 100th step, that would give r = -120 + 120 = 0. (It’s noted that r = 0 does not work and is computed separately.) The next step would give r = 1.2. The section in question is the loop after the comment “Trend through r-mean function”. Perhaps someone else might like to look at the program and give their evaluation.

    Comment by Eric Swanson — 26 Mar 2007 @ 7:56 PM

  97. #85
    My thoughts exactly, that they should publish their own study to see what they have to present, formally.

    Thanks for the heads up. I will look into that.

    Comment by John D. — 26 Mar 2007 @ 7:57 PM

  98. I agree with J.C.H (#43), “You say celsius or kelvin to the majority of American politicians/voters and their brains take a pass.”

    For me I simply rely on the scientists (like the RC scientists) and their talk about increases or decreases in global average temp — so the scale doesn’t matter much. I guess a 3 degree warming in celsius would be a 3 degree warming in kelvin (or at least a warming & not a cooling).

    It might even be good for those communicating with the public to put it also in Fahrenheit, since that’s what we’re used to in the U.S. Of course, not for using in a formula requiring multipication or division on the values (or doing the geometric mean) – since, like celsius, fahrenheit’s zero is not a true zero (in this case, total lack of heat) — I think it was the coldest day Mr. Fahrenheit happened to measure the temp.

    But I do think skeptics or contrarians throwing a lot of fancy stats and formulas at people, sort of awes them. They think, “Okay, that’s quite impressive. I believe you. Please don’t make me have to understand or memorize it.”

    So they hear “scientists” arguing about celsius and kelvin, arithmetic and geometric mean, in regard to GW being in doubt, and they think, “Whew, that was a close one. I almost starting believing GW was real, but now there’s lots of doubt. So on with my cross-country vacation in my Hummer.”

    Comment by Lynn Vincentnathan — 26 Mar 2007 @ 8:10 PM

  99. Re. 88, the journal it was published in is not a climate science journal and the article was not peer reviewed by any climate scientists. A scientist who is not a cvlimate scientist is no more an expert on climate than a well-informed layman is. So the “peer review” was meaningless.

    McKitrick, in particular, has never published anything in a climate science journal and is well known for his extraordinary disingenuousness and/or incompetence – e.g. see see here and here.

    Comment by Dave Rado — 26 Mar 2007 @ 8:32 PM

  100. re “Move over , Inhofe, Jerry Falwell is now ( 10.17 pm Sunday EST) on the air denouncing GW as a myth…”

    Geezz! Us serious skeptics are getting about all the help we can stand…..

    Comment by Rod B. — 26 Mar 2007 @ 8:59 PM

  101. Re 66: Krog, I’m not sure about the at-rest definition. As to the cold ocean question, the amount of thermal energy absorbed from the mantle (the ocean is thousands of miles way from the the core) is small compared to the mass of water. The vents, volcanoes, etc. only affect things locally. The upper ocean absorbs solar radiation, and so is warmer, while the lower ocean never sees the light of day, and so is cold. Since cold water is denser than warm water (unless the warm water is much saltier), the stratified situation is stable.

    Comment by Ray Ladbury — 26 Mar 2007 @ 9:25 PM

  102. RE #91, & “It occurs to me to wonder if this “no average” nonsense is a preemptive strike against pulling Triana /DSCOVR out of the warehouse and getting it launched.”

    You’d think if the denialists were so certain they’re right, they’d be pushing for its launch….so as to definitively prove that the sun is emitting more radiation, or whatever.

    Ergo, the denialists are NOT at all certain they’re right. In fact, methinks, they realize they’re wrong. They sort of remind me of lawyers who staunchly argue a person is innocent when they know he’s guilty as sin.– which is the beauty of our justice system, but is totally inappropriate for science. In my eigth grade science class we learned: “A scientist is honest.”

    I say, gather the evidence, and let the chips fall where they may. I’d be quite delighted if GW were proven false.

    One point: the celsius/geometric-average team is not presenting any new evidence or theory of some bizarre forcing, but, it seems, simply investigating how they can manipulate the existing data to get the results they want. I wonder how many different avenues and techniques they followed until they came up with the one they used in their report. And then how long it took to come up with a justification for using it.

    Comment by Lynn Vincentnathan — 26 Mar 2007 @ 10:13 PM

  103. [[I doubt there is any easy answer or methodology to answering “Does a global temperature exist?” ]]

    “Well, you’re wrong.”

    No its your opinion that I am wrong and its your opinion that the methodology you stated is the right one, only one, and the correct.

    I failed to see a scientific or mathematical citation stating your invoked methodology, as it relates to a global temperature and or global warming as the paper being discussed here indicates, was somehow the right one.

    There is no such thing as right or wrong. Who are you, or anyone else to judge what is right or wrong?

    Right or wrong is human created concept.

    Computations are just methodologies, often different, employed and invoked by a person.

    Not right or wrong.

    And thank you for your rudeness, lack of citations of your rightness and or my wrongness, that was offered with your god like assurances of what you hold in esteem to be right.

    Along with your intrusion to impinge upon my personal right to think and express what I choose.

    It was well received, not unsurprising, as the behavior seems
    to be rather common, as of late, upon realclimate by posters.

    Good day.

    Enjoy being right.

    Comment by BarbieDoll Moment — 26 Mar 2007 @ 11:13 PM

  104. #89

    Richard, I looked into it. Very educational. I learn something new from all sides every day. Thanks.

    By the way, there is a little known, yet huge side to the warming equations scientific studies: What the military knows of climate change that they are not divulging, and they know plenty.

    They have been studying atmosphere, oceans and icepacks globally, minute by minute with unlimited resources, since the 50’s for strategic reasons. They only let out normal information that never raises red flags or interests anyone. Be interesting to get into the real classified info that their scientists can’t talk about.

    Comment by John D. — 27 Mar 2007 @ 12:30 AM

  105. This is only vaguely related to the current topic, but I have a question. The temperature decrease from the 40s to the 70s I have heard is explained by the use of certain aerosols (don’t know details).
    If this is the case, then clearly aerosols can mitigate global warming since it already has. Couldn’t we, then, just take up aerosols like we did in that period to stabilize temperatures? We’d create our own pseudo-“temperature sink” through anthropogenic global cooling. :)
    I’m sure I’m not the first to have this idea by a long shot, so someone please explain to me why I’m wrong or this is a bad idea. Thanks.

    [Response:They are sulphate aerosols, mostly from coal burning. They are also acid rain, so aren’t a great idea. They also don’t stay up for long, so (unlike CO2) would need to be constantly replenished -William]

    Comment by David — 27 Mar 2007 @ 3:09 AM

  106. Rasmus points out:

    “The funny thing then is that the concept of regional mean temperature would also not be meaningful according to Essex et al.”

    Exactly the same applies to macroscopic temperature of any piece of material. e.g. any volume of gas contains a set of molecules each of which has its own independent translational kinetic energy and hence molecular temperature. Hence the “temperature” of a volume of gas is an “average” of the temperatures of all its molecules. Essex et al tell us that we could arbitrarily choose an “average” that would give us the temperature of the hottest or coldest molecule in the volume of gas and because of this inconsistency there is no such thing as “temperature” of a multi-molecule volume of gas.

    So folks, throw away all your thermometers, meaningless devices that they are. They are all just meaningless arbitrary averaging devices.

    Comment by Chris O'Neill — 27 Mar 2007 @ 4:54 AM

  107. In section 4.1 “Contradictory Trends in Global Temperature Averages”, the authors demonstrate with a particular set of data, you can get either a warming or cooling trend depending on what value of “r” or “s” you use for your r-means or s-means averaging.

    While that’s somewhat curious mathematically, the fact that they’re using data from just twelve (yes 12!) locations makes the whole example rather suspect.

    The authors in fact essentially acknowledge that: “Stations were selected to give reasonable geographic variation, but whether it is a ‘global’ sample or not is secondary for the purpose of the example.”

    That’s a bit disingenuous. Seems to me that if they really want to convince anyone that the global average temperature is meaningless, the authors should at least use a reasonably large number of points. I don’t know offhand what a reasonable number of points is, but offhand, 12 sample points to cover 500 million sq km of surface area seems a tad on the low side :-)

    If you use temperature data from a much larger set of locations, and then used different methods to compute the mean (r-means and s-means, with different values for “r” and “s”), would you still get such a large variation in the size (and even the sign) of the global warming trend? I rather doubt it.

    Comment by Gerry Beauregard — 27 Mar 2007 @ 5:39 AM

  108. Does a global Ocean PH exist? I am pretty sure that nobody is getting spot measurements and averaging them, or similar analogy to what we are measuring with global temperature. How can we be sure that PH has decreased (by 0.1 or whatever since industrialisation) and is this averaged out over the whole ocean? Just the measurable bits?

    Comment by Marco Parigi — 27 Mar 2007 @ 7:20 AM

  109. Hi, first time I’ve commented here, although I’ve been reading with
    interest for some time. I’m a (pure) mathematician.

    As well as the question of the small number of locations they used, they
    would only get results of the sort they did if (roughly speaking) their
    hottest and coldest sites both had a trend of cooling over the period
    they looked at. I looked at the data on the GISS website, and yes: they
    included two very hot sites (Cartagena, Colombia and Chiang Mai, Thailand)
    of which one had been cooling and one staying roughly the same over the
    period — this is just from looking at the graphs, I haven’t done any
    rigorous analysis — and one very cold site (Halley, Antarctica), that
    had been cooling, as well as nine intermediate sites that had mostly
    been warming or staying roughly the same.

    Is there a general trend of the very hottest and coldest places on Earth
    cooling rather than warming since 1980? Otherwise, it looks as though
    they’ve been very selective with their choice of locations.

    Comment by Jeremy — 27 Mar 2007 @ 7:26 AM

  110. #107 Gerry Beauregard
    If I understand the discussion above correctly then the very high values of r which they use mean that at the limits of the graph in r you select increasingly strongly the trend in the maximum and minimum temperature series.

    This would seem to imply that of the twelve stations they selected the hottest and the coldest stations both exhibited cooling.

    Comment by SomeBeans — 27 Mar 2007 @ 7:27 AM

  111. [[ I’m sure out of 17,000 scientists, there must be at least a couple of hundred that may actually know what they are talking about, but if it falls on deaf ears, then none of it really matters. ]]

    Why don’t you do a google search on “Oregon Petition.” This thing has been completely discredited. Of the alleged “scientists” signing it, the vast majority are engineers, doctors, or people with science degrees in fields other than climatology. The fact that you don’t realize this thing was discredited a long time ago indicates that you’re only reading information from your own side.

    Comment by Barton Paul Levenson — 27 Mar 2007 @ 7:35 AM

  112. [[the key point I pick up from this is that a global mean temperature, although we can define a way to calculate it, does not really provide anything useful. ]]

    Well the key point you pick up from this is wrong. Mean global annual surface temperature is used all the time in climatology and planetary astronomy. Essex and McKitrick, as usual, don’t know what they’re talking about. They won’t convince any scientists, but they’ll convince enough of the public to slow down efforts to mitigate the problem.

    Comment by Barton Paul Levenson — 27 Mar 2007 @ 7:40 AM

  113. [[There is no such thing as right or wrong. Who are you, or anyone else to judge what is right or wrong?
    Right or wrong is human created concept. ]]

    Then why are you arguing with me? If there’s no right or wrong, why are you saying I’m wrong to judge? You have to think these things through.

    Comment by Barton Paul Levenson — 27 Mar 2007 @ 7:43 AM

  114. Aside — John D. commented on not knowing “what the military knows” — and isn’t the first.
    Example from almost a decade ago —- opening up military archives of climate change info:

    ScienceDaily: Newly Declassified Submarine Data Will Help Study Of …
    The area is known as the “Gore Box” for Vice President Al Gore’s initiative to declassify Arctic …
    Arctic Sea Ice Shows “Striking” Decline Since 1960s …

    Comment by Hank Roberts — 27 Mar 2007 @ 8:08 AM

  115. re: 104 – John D.

    Regarding what the military “knows”…

    You might want to read “An Abrupt Climate Change Scenario and Its Implications for United States National Security”. Fortune ran a piece on it, as I recall, as did other sources.

    The site where it was located has gone dead, apparently:

    But Grist archived it:

    Seems the Pentagon was pretty clear about what it knew.

    [Response:Fair enough, as long as you read the caveats, which basically say its not going to happen. Still I guess the military got a fair few nice lunches out of it -William]

    Comment by J.S. McIntyre — 27 Mar 2007 @ 9:59 AM

  116. Apologies in advance for a not completely on-topic post, but in this morning’s LA Times, there’s an interesting column entitled, “Why the right goes nuclear over global warming”. It’s available at (free registration may be required).

    Here are some excerpts:

    So, the magazine asked the question again last month. The results? Only 13% of Republicans agreed that global warming has been proved. As the evidence for global warming gets stronger, Republicans are actually getting more skeptical.


    But the financial relationship doesn’t quite explain the entirety of GOP skepticism on global warming. For one thing, the energy industry has dramatically softened its opposition to global warming over the last year, even as Republicans have stiffened theirs…


    A small number of hard-core ideologues (some, but not all, industry shills) have led the thinking for the whole conservative movement.


    Meanwhile, Republicans who do believe in global warming get shunted aside. Nicole Gaudiano of Gannett News Service recently reported that Rep. Wayne Gilchrest asked to be on the Select Committee on Energy Independence and Global Warming. House Republican leader John Boehner of Ohio refused to allow it unless Gilchrest would say that humans have not contributed to global warming. The Maryland Republican refused and was denied a seat.

    Reps. Roscoe Bartlett (R-Md.) and Vernon Ehlers (R-Mich.), both research scientists, also were denied seats on the committee. Normally, relevant expertise would be considered an advantage. In this case, it was a disqualification….

    Comment by caerbannog — 27 Mar 2007 @ 10:18 AM

  117. re 102: Yes, Lynn, but 8th grade science teachers are not immune from little white lies. And to say scientists are ignores history and reality.

    Comment by Rod B. — 27 Mar 2007 @ 10:23 AM

  118. #109 Jeremy wrote: [[Otherwise, it looks as though they’ve been very selective with their choice of locations.]]

    This is one thing that the juried peer-review process is pretty good at: Weeding out problems such as selective cherry picking….purposeful or otherwise.

    It is one problem that gets the climate-change deniers in a lot of trouble. An example is many of their claims that the Earth is cooling because a few places on Earth have been cooling while tbe global average has been rising…”A few trees do not make the forest”…and to claim so is slimply deceitful.

    This is a real quote currently from one of their largely fossil-fuel funded websites…and I kid you not:

    [[Pensacola’s mean annual temperature has cooled by 0.06 degrees Fahrenheit. Not much global warming here!]]

    Comment by Richard Ordway — 27 Mar 2007 @ 11:30 AM

  119. Seeing what difficulty even solid state physicists have in agreeing beyond the first two decimal places on the characteristic temperatures of real crystals of real solids involving the lattice dynamics of more than one isotope , all I can say after viewing this dialog is that I feel your interdisciplinary pain – defining room temperature is no cakewalk either,because rooms don’t have temperatures.

    Things in rooms have temperatures. Unfortunately, those things tend to be made of stuff , and even specimens of the same stuff vary in their thermal characterization , because perfect solids don’t exist unless you build them one atom at a time.

    Forgive the reductionism, but that’s the way things are at 4 Kelvins , and while taking them up one crise de regime at a time to beyond the boiling point to mix into an atmosphere may provide gainful employment for practitioners of statistical thermo , it does not make matters easier for anybody else. Some problems are too large to frame perfectly in finite time.

    Comment by Russell Seitz — 27 Mar 2007 @ 11:31 AM

  120. Re #103: [There is no such thing as right or wrong. Who are you, or anyone else to judge what is right or wrong? Right or wrong is human created concept.]

    (Sigh) Semantic quibbling. You’re confusing the moral/ethical meaning of the words with the technical. Replace them with correct and incorrect, if you like.

    [Computations are just methodologies, often different, employed and invoked by a person. Not right or wrong.]

    OK, how about letting me take over your bookkeeping? I assure you I can come up with some really creative computational methodologies to conceal the amount of money I’ll be embezzling :-) There’s no such thing as an average account balance, is there? And as you say, who are you to judge what’s right or wrong, in either sense of the words?

    Comment by James — 27 Mar 2007 @ 11:54 AM

  121. re 115 – William’s comment

    As a follow-up to my previous post, I should likely add that I do not necessarily subscribe one way or the other to the analysis linked, and I apologize if I was taken to say the Pentagon is somehow transparent in the manner in which it plans, or that the report I provided represents a revelation of what the Pentagon “knows”. I am not a scientist nor a Pentagon analyst, just an everyday citizen. My only intent in providing the link was to answer in somewhat tongue-in-cheek fashion a remark that I found rather interesting as it was a bit of a non-sequitur. How does one claim of knowledge of unrevealed knowledge when one freely acknowledges he or she has no knowledge to support the claim? Curious.

    Regardless, the Pentagon has these assessments, and we can only guess at how seriously they might take them, particularly when we reflect on the relationship of the current Administration and climate science. Beyond that, what I do think is that the extreme climate change cited in the “analysis” is not needed for many of the scenarios discussed – and likely many yet to be imagined – to occur. The combination of even mild climate change with swelling populations, dwindling resources, political and religious differences and the ongoing use of our planet as humanity’s personal toilet bowl will likely have the potential of triggering a variety of incidents and blow-ups akin to the scenarios discussed in the report. The part of the report that discusses carrying capacity is rather illuminating in this regard.

    This is all my opinion, of course, somewhat informed in the layman’s sense, but an opinion nonetheless:

    It strikes me how the issue of global warming invariably parallel issues such as pollution, habitat loss, resource depletion and overpopulation. Even more interesting is how addressing the likely causes, such as carbon emissions, would likely have long-term positive effects economically and in terms of quality of life for people in general. We see the trends. We see the solutions. The question seems to be what we will do about them. Make plans for war we may fight over a problem we seem incapable of agreeing upon? That seems rather self-defeating, and I’m not even touching on the rather insane reasoning this kind of planning infers. Similarly, optimistic predictions of what will occur fifty years down the line rarely see fruition. If you doubt that, review the predictions made during the 1938 World’s Fair. (Or, even better, check out David Brin’s 1989 novel “Earth” and see how his predictions of the next fifty years are turning out.)

    The problem isn’t global warming, not really. In the sense it’s a done deal. We know it is happening; even the majority of denialists probably agree. The problem is taking the bull by the horns, if you’ll excuse the metaphor, and grappling with it in earnest. Yet here we are, better than a quarter-century into understanding we have a problem, with the reports we’re seeing becoming steadily more compelling regarding the need to act, and we’re caught up in arguments with people who do all they can to muddy the waters in an effort to delay addressing the problem. What has been done to address global warming is so miniscule in comparison with what needs to be done it is as if we have done nothing at all. The progress in addressing the problem can be measured in inches when it needs to be measured in miles. If this were a race, we wouldn’t even be in it.

    This is the real problem, the insurmountable problem: Invariably, as a species, as a civilization, our practice is to react to problems, whether man-made or those posed by nature. We wait for disaster before we move. The kicker here is the time-debt associated with global warming, something that natural tendency to delay doesn’t account for. Effects we experience today were caused 20-30 years ago, if I read the science correctly. When we finally reach a point where the effect is undeniable to the masses and decide to move, we’ll be much like the famous little Dutch Boy with his finger in the dike – only there will be millions of holes and he’s only got ten fingers.

    So given the nature of the real problem, the likelihood of how we’ll respond, you’ll excuse me if I remain a bit pessimistic about civilization’s chances. I hope, and try to do what I can – I have to, as I have a child and this future we’re shaping is going to belong to her and her generation, and to their children. But it is a sad hope, filled with necessary dread. I think they will learn to hate us.

    *sigh* Sorry. Didn’t mean to run on like that, but there it is.

    That said, have a bright day.


    Comment by J.S. McIntyre — 27 Mar 2007 @ 12:46 PM

  122. re 116, “…Only 13% of Republicans agreed that global warming has been proved….”

    I read and have to believe the stats. But as I’ve stated before, I’m at odds to figure out why AGW pro and con would naturally split between Rep/Dem or conservative and liberal. Can anyone explain it?

    Comment by Rod B. — 27 Mar 2007 @ 12:49 PM

  123. Some banks base fees on the average account balance.

    Comment by J.C.H — 27 Mar 2007 @ 1:26 PM

    Temperature on the Surface of Mars

    (A collection of different estimates, each interesting as an example of how such numbers are arrived at.)

    Comment by Hank Roberts — 27 Mar 2007 @ 1:49 PM

  125. Re #96 (Eric): I have reproduced the results of the Figure 2 of the Essex paper using their data but writing a program to do it in MATLAB (see my comments about the results in comment #32 above).

    You are right that they eliminate all months where any station has missing data and that they calculate the r at those values spaced by 1.2. However, neither of these are fundamental problems: The first may change somewhat exactly what the results are for this particular example but don’t fundamentally alter their basic point. The second is of no consequence. (For example, I computed for r spaced by 0.1.)

    I don’t think the problem with their paper is little choices they made like this. The issue is that there is no justification for going to such large positive and negative r’s that your averaging method basically becomes a method for picking either the lowest or highest temperature reading for each of the months.

    Yes, if I define my average in a completely silly way, I will get completely silly results. The solution is to not define my average in a completely silly way and not to be so rigid as to believe that if I can’t justify thermodynamically an absolutely best choice for an average, then any one is as good as any other. That’s just absurd logic…although the kind of logic that I think might be appealing to those non-scientists who think that science is always based on absolute rigor and certainty.

    Comment by Joel Shore — 27 Mar 2007 @ 2:48 PM

  126. Re #107, 109, 110: I tend to agree with you that they have likely cherry-picked their stations to give a particularly dramatic result. I.e., with a different choice of stations they would not have necessarily had the r-means and s-means converging to a significantly negative trend for large positive and negative values. However, for most sets of data of this size, they still probably would have tended to see a strong dependence of the trend on the r-means and s-means on the values for r and s if one allows r and s to range over ridiculously large domains as they do.

    [By the way, a very technical point: The large positive and negative values of r and s don’t exactly pick out the trend for the one station that is hottest and coldest on average. Rather, it picks out the trend you get if you use either the hottest or coldest station data point for each and every month over that period. So, for example, while the Antarctic station may tend to have the lowest temperature for some months of the year, it doesn’t for all months of the year. So, the trend you get as r or s become large and negative is not simply the trend for that one station.]

    I tend to think there is some truth to the statement that a data set with a much larger number of stations would tend to be better behaved. I haven’t tried to check this and my guess is that there could still be some significant variation with r if you look over a broad enough range but there may also tend to be a larger plateau region.

    However, it is important to recognize that even in their 12-station example, the temperature trend is pretty well-behaved as long as you choose a “reasonable” value for r or s. E.g., as I noted in comment #32, even changing r from 1 to 4 (which is about the largest change I can see coming up with any physical justification for) results in only a small change in the computed temperature trend.

    The “evil brilliance” of Essex et al. was in making a plot where r goes from -125 to +125 so that the region over which the temperature trend computed from the r-means is well-behaved gets very compressed on the plot!

    Comment by Joel Shore — 27 Mar 2007 @ 3:01 PM

  127. After reading the comments here I am now certain that I must convince Bill Gates to move to Elk River. That simple act on his part will make my humble town of Elk River among the more wealthy communities in the USA.

    The proposition might be true, but it has no context. Our leftist state legislature would likely “fix” our excessive Elk River wealth “problem” by raising my taxes.

    So I ask the global warming groupies here, are all averages indeed roughly “equal” in context? When someone says the Earth’s “average” temperature rises (or declines) by 0.0x degress, shouldn’t we really ask what they mean by that? Remember here in Minnesota we’re all above average as Garrison Keilor would put it.

    And for our erudite climate experts, just what type of averaging DO you use, (Arithmetic mean, modal average, median, RMS etc. etc. etc….ad infinitum) and more importantly why do you chose one method over another when calculating the current Earth “fever”, to recall how your most well known spokesman puts it.

    Is it possible that one method might produce an opposite trend to another? If so the issue is not quite so readily dismissed as your fans suggest it should be.

    Comment by Bruce G Frykman — 27 Mar 2007 @ 3:45 PM

  128. Re #70 and other comments. What counts is the ratio of the trend in the average to the year-to-year variability. The larger that ratio, the more significant the trend. The statistical theory for arithmetic averges (r = 1) is long-established, making such calculations easy to make and interpret. Using larger and larger values of r puts increasing emphasis on “outliers”, i.e., “oddballs”, making it increasingly difficult to detect the trend. An analogy: Suppose a drug company was testing a new blood-pressure drug and found that the AVERAGE blood-pressure reduction was 30% greater than that in a group using a placebo. They reject the drug, however, because in ONE case the reduction was only 1%. Thus, a potentially valuable drug is kept off the market because it didn’t work on one person. In the same way, using averages with high values of r would delay action to reduce greenhouse-gas emissions. (One would would have to wait longer before significance could be established.) But, perhaps that’s the point?

    Comment by Jerry Steffens — 27 Mar 2007 @ 3:51 PM

  129. It the verdict then that 20% of the earth gets 5-7 degrees hotter,the average goes up, and somehow this represents a real picture of earths temperature?

    Comment by Peter Brunson — 27 Mar 2007 @ 5:23 PM

  130. Re. 122, it’s all about policy, not science. Those with a very strong vested interested (whether emotional, political or financial) in there being no government action to reduce greenhouse gas emissions will try their hardest to convince themselves that the science is flawed. Hance the reason that anti-regulation lobby groups run almost all of the disinformation sites on the web.

    Comment by Dave Rado — 27 Mar 2007 @ 7:07 PM

  131. RE: 120 Re #103:

    I would suggest reading my original posting #49 “I doubt there is any easy answer or methodology to answering “Does a global temperature exist?” along with the citations.

    A comment was posted in relation to my #49 that was of a personal nature rather than a comment that discussed my provided citations as it related to the topic contained therewithin Essex et al, along with the topic/commentary provided and being discussed here at RC.

    The comment posted did not correspond or make sense in relation to what I originally posted, along with my citations, as an easy answer to a posited question.

    Especially as I posted it in relation to the theme being discussed, the original paper (Christopher Essex, Ross McKitrick, and Bjarne Andresen) which put forward the dimensions of global temperature as it related to the topic global warming.

    Does a Global Temperature Exist?
    “Physical, mathematical and observational grounds are employed to show that there is no physically meaningful global temperature for the Earth in the context of the issue of global warming. ”

    All that said, you are welcome to your thoughts and opinion as they related to my original posting and citations as they applied to the topic at hand; however, these comments, like the other, escape me as to how either would have been applicable to what I originally posted.

    And it’s certainly been noted about addressing the need for climate
    science metrics, hence my use of the word methodologies.

    Reconciling Observations of Global Temperature Change

    Review of the U.S. Climate Change Science Programâ??s Synthesis and Assessment Product on Temperature Trends in the Lower Atmosphere (2005)

    Thinking Strategically: The Appropriate Use of Metrics for the Climate Change Science Program (2005)

    Thank you for your comments.

    Comment by BarbieDoll Moment — 27 Mar 2007 @ 10:30 PM

  132. ,” an infinite range of such statistics is mathematically permissible
    if physical principles provide no explicit basis for choosing among them.”
    That argument my be true. One can drive meny nambers from the met data.
    But for global warming the only important questions are is “global temperature” defined and is it useful concept.

    1st. I understand that we mean “global surface temperature” surface mean the temp at standart met box
    and global mean (â�«Tds)/(surface fo earth) dim=[T] and “global teemperature” is well defined.
    2nd. Is “global temperature” is useful? In Venus global temperature is higher then in Earth I gess it is useful exemple.

    Comment by Eyal Morag — 28 Mar 2007 @ 7:11 AM

  133. [[I read and have to believe the stats. But as I’ve stated before, I’m at odds to figure out why AGW pro and con would naturally split between Rep/Dem or conservative and liberal. Can anyone explain it? ]]

    Because commentators like Rush Limbaugh who have huge audiences, and scientists funded by the big oil companies, who desperately want to be able to go on selling people fossil fuels, have turned it into yet another endless shouting match between conservatives and liberals. In a rational world this wouldn’t have happened, but we live in a US with a strong anti-intellectual current and a number of people ready to jump on any bandwagon that supports their party.

    Comment by Barton Paul Levenson — 28 Mar 2007 @ 7:15 AM

  134. [[
    Temperature on the Surface of Mars
    (A collection of different estimates, each interesting as an example of how such numbers are arrived at.) ]]

    Collections and reviews will list anything, even if it comes from some 50-year-old textbook. The American Heritage Dictionary still lists the mass of Mars as 0.15 that of Earth, which is actually the volume of Mars — the mass has been known to be about 0.11 that of Earth for more than a century.

    There haven’t really been any good studies of the thermal balance of Mars. A radio emission study from 1962 came up with the 218 K figure. Barth et al.’s 1985 standard atmosphere for Mars lists surface temperature as 214 K, which is what I usually use. But we really need a Mars climate orbiter…

    Comment by Barton Paul Levenson — 28 Mar 2007 @ 7:19 AM

  135. Simply picking the complete set of stations would not help. First of all, they are not uniformly distributed in area or time. Read the description of how the station data is put onto a grid at the GISS site for example. Second, changes will be dominated by changes in the annual cycle. You need a procedure to “deseasonalize” (help! I don’t remember the right word)which turns out to be taking the monthly averages at each data point for thirty years and subtracting that from each monthly average at that point. It is only after that step that you can sensibly compare the trend in Patagonia with that in New York (or at least the trends at the location of the nearest grid points to be more exact). Because only anolmalies make sense for looking at global trends, you get into the problem of finding averages with zero and negative and positive values, which quickly drivew you to linear averages. See the GISS web site.

    Our analysis concerns only temperature anomalies, not absolute temperatures. The temperature anomaly tells us how much warmer or colder than normal it is at a particular place and point in time, the ‘normal temperature’ being the mean over many (30) years (same place, same time of year). It seems obvious that to find the anomaly, you first have to know the current and normal absolute temperatures. This is correct for the temperature at one fixed spot (the location of one thermometer), but not true at all for regional mean temperatures.

    Whereas the individual reading represents just this spot but can be very different from nearby readings, the anomaly computed from those readings is much less dependent on location, elevation, wind patterns etc; it turns out to be representative for a region that covers several square miles. Hence we can combine anomalies from various stations to find regional mean anomalies. Regional absolute temperatures however cannot be obtained from observations alone. For a more detailed discussion, see The Elusive Absolute Surface Air Temperature.

    Comment by Eli Rabett — 28 Mar 2007 @ 8:44 AM

  136. Do Sato and Hansen plan to send a reply?

    Comment by Eli Rabett — 28 Mar 2007 @ 8:47 AM

  137. Re: #125 Joel Shore

    Thanks. It’s obvious that their technique can’t handle missing data. They exclude 33 of 264 months. I’ve looked at the data a bit and what they actually did is even more interesting.

    The Halley station is the source of most of the missing months in their data file with 20 missing. But, the NASA GISS data does not show any missing months “after homoteneity adjustment”. Are these guys using the raw data? They don’t actually say so.

    It gets better. The Chiang Mai station had 15 months missing in the GISS data set, but they only show 6 missing. And the Cartagena data is missing 9 months in GISS, but they show only 4 missing months. Why is this? They used interpolation to fill in where single months are missing. What’s this again? Is it that they don’t like the corrected GISS data, but they do think it’s OK to use THEIR corrections? They offered numerous objections to simple averaging and grid box binning, yet they apply a simple average to fill in the missing data? They don’t like the use of anomalies, where the long term average seasonal cycle could be used to fill in missing months, which is likely to be more accurate than interpolation.

    Just one more nail in the coffin. I think that the paper should be withdrawn.

    Comment by Eric Swanson — 28 Mar 2007 @ 10:02 AM

  138. What I find odd in all this, is that it is undeniable that we are seeing profound changes in climate–especially in polar latitudes. If anything, “global temperature” understates the magnitude of these changes–as indicated by all the nonscientists that claim to be unimpressed by a <1 degree change in global temperature. To my knowledge, not even Essex et al. would deny that climate is changing. If global mean is a useful metric for reflecting these changes, and if it can be calculated in a self-consistent manner, then it has validity. There may be other metrics that are better, but global mean temperature has the virtue of familiarity and history. It seems to me that the denialists are re-arranging the deck chairs on their sinking ship. I’d be happy to throw them a line if they’d just start swimming.

    Comment by Ray Ladbury — 28 Mar 2007 @ 1:02 PM

  139. Re #137 Eric Swanson

    Frankly, I don’t much care what they do with missing data. I doubt it
    makes much difference.

    But in another part of the article they state (correctly) that the limit
    as r goes to infinity of the “r-mean” is the maximum. So they clearly
    know that if they are looking at large values of r then the r-mean is
    going to be roughly the highest temperature. So their statement that
    “Stations were selected to give a reasonable geographic variation, but
    whether it is a ‘global’ sample or not is secondary for the purpose of
    this example” is frankly dishonest. They know perfectly well that it’s
    irrelevant whether it’s a ‘global’ sample, and all that matters for them
    to get the results they want is that they pick “hot” sites (for large r)
    and “cold” sites (for large negative r) that have a cooling trend. And of
    course, that’s what they’ve done.

    They may well be right that there is no particular reason to choose the
    arithmetic mean rather than other reasonable “averages”, but their
    assertion that taking an arithmetic mean of temperatures is no more
    sensible than taking arithmetic means of telephone numbers is frankly

    Comment by Jeremy — 28 Mar 2007 @ 6:06 PM

  140. RE#118, Richard noticed that CO2science is running a weekly ‘temperature record’ that shows cooling. What those people must do is sift through records looking for cooling trends, and then they claim that their selective reporting of data means that no global trend exists! This is just scientific fraud, and it’s the same behavior that Richard Lindzen railed against some years when he complained that record temperatures can’t be used as evidence of global warming. (Though I don’t hear Lindzen or Pielke condemning CO2science for using that approach!) However, I wouldn’t link directly to – that only encourages them. They’re run by Sherwood Idso, the same one who was attacking radiative calculations and modelling efforts back in 1980:

    “In 1980 a scientist at the U.S. Water Conservation Laboratory in Arizona, Sherwood Idso, joined the attack on the models. In articles and letters to several journals, he asserted that he could determine how sensitive the climate was to additional gases by applying elementary radiation equations to some basic natural “experiments.” One could look at the difference in temperature between an airless Earth and a planet with an atmosphere, or the difference between Arctic and tropical regions. Since these differences were only a few tens of degrees, he computed that the smaller perturbation that came from doubling CO2 must cause only a negligible change, a tenth of a degree or so.

    Stephen Schneider and other modelers counterattacked. They showed that Idso, Newell, and Dopplick were misusing the equations â�� indeed their conclusions were “simply based upon various violations of the first law of thermodynamics.” Refusing to admit error, Idso got into a long technical controversy with modelers, which on occasion descended into personal attacks..”

    If anything, this does show that efforts to discredit global climate science do indeed reach back almost 30 years. CO2science is the best example of how this process works (they also offer to help companies with ‘greenhouse gas reporting requirements’, which makes one highly skeptical about any the effectiveness of any ‘carbon trading’ schemes).

    Comment by Ike Solem — 29 Mar 2007 @ 12:06 PM

  141. As stated by several others here different values of ‘r’ yield averages with different physical meanings. I worked for many years in the field of particle sizing in that case there are many different ‘mean diameters’ resulting from different values of ‘r’ and the choice for a paticular application depended of the phenomenon being studied, for example r=2 gives a mean with the same surface area (useful in absorption), r=3 gives the same mass etc.. In the case of the earth it seems to me that r=4 has some merit as it’s significant with regard to radiation exchange and is presumably what one would determine at a distance from space?

    Comment by Phil. Felton — 29 Mar 2007 @ 1:01 PM

  142. Re #133 and upthread to #116: without going into the politics as such, but just to offer a clarification from the standpoint of survey research — the “13% of Republicans” figure refers to members of Congress. There is considerable, but less, partisan polarization among ordinary citizens. See, for instance, the Pew Center report here.)

    Attentive partisans tend to follow their political leaders. It’s striking, in the Pew report, that the gap between college-educated Republicans and Democrats is wider than the gap between their non-college-educated counterparts. (Of course education doesn’t equal attentiveness — it is only a crude proxy.)

    Comment by Mark Lindeman — 29 Mar 2007 @ 2:02 PM

  143. Re #122:

    Actually it stands to reason that there would be a split in tendency to believe the science based on political persuasion; those more inclined to favor collective action will be more willing to take seriously a phenomenon which seems to indicate a need for collective action than those who are disinclined.

    The huge opinion spread on climate change is disconcerting though, and the trend toward increasing disbelief among the right while the substantive evidence against them becomes ever more compelling is downright alarming.

    To some extent even this is actually not hard to understand. The commercial interests that are threatened by the actual facts of the matter have an enormous motivation to confuse the public discourse, and they play on natural inclinations. What is hard to understand is how spectacularly successful they have become in moving their audience ever further away from the center of gravity that the facts portend.

    I do note an increasing testiness and terseness from the leading posters on this site, and even occasionally from the editors in response to such provocations. I would like to caution that this behavior plays very much into the hands of the malefactors and their innocent sympathizers. They are trying, all too successfully, to convince their audience of several things including

    It all ties together into a pretty clever strategy:

    1. say things that are exasperatingly ignorant
    2. get real experts with little understanding of polemics to express their exasperation
    3. cast that exasperation as arrogance and bullying

    That’s not the whole strategy (for instance there’s the “house of cards” strategy that tries to make out that the whole “global warming theory” is abstruse and delicate, and that any single error is enough to “disprove” the “theory”) but it’s emerging as a central feature.

    The best counter is to avoid the appearance of arrogance in public forums. Accordingly, if I could venture my advice to serious informed posters:

    The fact that regular posters and even occasionally editors here are being baited into intemperate statements plays into the hands of the malefactors. Justifiable anger and frustration plays out as arrogance.

    Preaching to the choir is beside the point. That there is an influential segment of the society which is becoming more rather than less skeptical is a hugely serious problem. It would be best if realclimate were part of the solution, but we are up against very clever opponents who don’t want it to turn out that way.

    Please remember (though they may, by personalizing matters, try to make you forget) that your effect on the third party reader is vastly more important than your effect on the person who is writing. Your correspondent may well be deliberately trying to make you look nasty or arrogant under the pretense of some weakly substantive argument. Nothing you can say will cause that person to change their opinion, because what they are voicing is not actually an opinion about a matter of fact but rather a tactic in a battle for influence over the casually interested.

    If you find yourself angry the best way to fight back is to say nothing and let someone else do the talking. If you win the game of substance and your opponent wins the game of polemics, in the end your purpose in participating in the discussion is not achieved.

    Comment by Michael Tobis — 29 Mar 2007 @ 7:14 PM

  144. This helps with the Monckton part of the below:

    I think the objection to spectroscopic determination is that Earth is not a black body (despite what Monckton would have us believe).

    However, I’m surprised the real problem isn’t imprecision.

    Comment by Marion Delgado — 31 Mar 2007 @ 6:56 AM

  145. OIM is not, I thought, proven to be a fossil fuel funded enterprise. It did do the petition in conjunction with one. Let’s be precise.

    Robinson is a good example of a fringe scientist, not meaning an idiot or lunatic, but someone who simply is likelier than not to not be in the mainstream (because he’s long past his prime, because his increasingly ideological concerns make it hard for him to embrace anything he sees as anti-Jesus or anti-business, because he honestly believes some studies and some formulations trump all the others, because he’s been mostly stumping for contrarianism vs. boning up on the latest consensus). In any population you have honest people who disagree as well as paid hacks (albeit, I suspect what Robinson REALLY thinks he’s disagreeing with is not a scientific consensus but those damned lying atheist socialists).

    It cuts both ways: If a preponderance of climate scientists went the other way, you could easily, quickly come up with reasons to believe the minority who accepted anthropogenic GGs increasing warming. Indeed, I’d lean that way myself since I believe there literally are NO forces pushing a socialist or anti-business bias on scientific research. All the noise, in fact, comes from either generally right-wing or specific nest-feathering business spending.

    That the climate scientists are standing firm in an era where businesses will spend a fortune for defense but not one cent for tribute to reality, where the sole superpower FIRES PEOPLE for accurately reporting CARIBOU HERD OBSERVATIONS and CLIMATE DATA, indeed, puts young interns in charge of determining science policy on explicitly ideological grounds, should be all the human evidence we need. There’s always way more money on the business-flattering, elite-flattering, industry-appeasing side of the street.

    Indeed, most of the richest nations have comparatively conservative governments completely beholden to rich special interests, so why they’d insist on funding science in an anti-business direction is left as an exercise for recreation hour at the Rand asylum.

    Comment by Marion Delgado — 31 Mar 2007 @ 7:31 AM

  146. Could someone please explain how measurements of the earths temperature which depend on the method used or the programs used or the technology used could ever come up with the same temperatures for a particular year, day, hour, or century. Considering the inconsistent methods of temperature evaluation being used today, how is it possible for everyone to be coming up with anything that is even close to each other never mind to an accuracy of tenths of a degree f. The results of these studies need to be extremly accurate for them to have any value. Inconsistencies and inacuracies do not cancel each other out, instead they tend to contribute to cumulative error. The only way we can have an agreement on the temperatures of the earth today or yesterday or tomorrow would be to design a program that will give you the results you want. If anyone believes that this is not what is being done they are not living in the real world.

    I am particularly interested if anyone has an idea of what effects on the surface temperature does the core of the earth contribute to the earths overall temperature. It would seem to me that the core is what is actually keeping the earth warm, not the sun. I would like to know what temperature the earth would be without the heat being generated at the core. Considering that the core is not symetrical and not absolutly consistent, i imagine this would need to be a large part of any program that establishes the temerature of the earth in an accurate way. When we can all agree on the method and the result of todays temperature of the earth we can then go on to find a way to agree on yesterdays temperature and tomorrows temperature. I doubt that we agree on the method or the results for many years to come unfortunatly. My real problem is with those that say outside my window it was colder or hotter last year, I think.

    I am truly concerned for the planet but if global warming is occuring due to some other reason or if warming is not even really occuring we are only chasing our tails and the money and energy being spent to prove man generated co2 is causing the warming of the planet is being ill spent and could be used for projects that would actually help mankind.

    I ask these questions because i believe there are people who read this that will actually think carefully about these issues.

    If you think I am all wet please say so.

    Comment by papos frassica — 2 Apr 2007 @ 12:00 AM

  147. By mistake, I had posted this message to the wrong thread, here it goes again.

    Is there anybody out there that could provide an approximation to the following quantity? (back of the envelope calculation)

    Assuming a very simple system, where everything stays the same, except for the increased CO2, what is the extra amount of heat introduced into the climate system by the current CO2 level, relative to the total amount of heat that the Earth received from the Sun before the CO2 increase?

    This number should be relatively easy to estimate from basic physical considerations.

    It seems to me that this number is a crucial first step in demonstrating to doubters that the CO2 increase is indeed a potentially very serious problem, instead of getting tangled in knots talking about temperatures. After that comes the hard work of checking exactly how the climate system reacts to the increased heat input, and explaining to non-scientists all sorts of complicated things about feedbacks and such.

    Going straight into discussions about exact temperatures, climate sensitivities, feedbacks, aerosols, etc. just muddies the argument and obscures the main point: We are introducing a significant perturbation into the climate system. In general, if the inputs of a dynamical system are perturbed in a significant way, there is a non-negligible probablity that the behavior of the system will change in a significant way. And, change will most likely be for the “worse” because of the basic fact that there are many more “undesirable” (“disordered”) than “desirable” (“ordered”) states in any system (basic entropy considerations).

    Comment by Rafael Gomez-Sjoberg — 2 Apr 2007 @ 2:07 AM

  148. Papos, OK, you asked for it: You’re all wet. ;-) Here’s why. Earth gets about 4×10^13 watts from its interior–due to both radioactive decays and latent heat of condensation of liquid outer core onto solid inner core. Average insolation is about 10x that amount. What is more, heat from the interior can only decrease as its sources are depleted. If for some unknown reason we were seeing a blip in energy from the interior, it would lead to increased volcanism–which we aren’t seeing.

    Comment by Ray Ladbury — 2 Apr 2007 @ 7:59 AM

  149. [[ am particularly interested if anyone has an idea of what effects on the surface temperature does the core of the earth contribute to the earths overall temperature. It would seem to me that the core is what is actually keeping the earth warm, not the sun. I would like to know what temperature the earth would be without the heat being generated at the core.]]

    The net average contribution of sunlight to the climate system is about 240 watts per square meter; the geothermal flux is about 0.090 watts per square meter. Thus the geothermal flux is usually ignored.

    To convert a flux to a temperature we invert the Stefan-Boltzmann law (leaving out emissivity, which I’m not sure how to apply here):

    T = (F / σ)0.25

    where σ is the Stefan-Boltzmann constant (about 5.6704 x 10-8 in the S.I.). Thus if Earth depended on geothermal heating alone, its average surface temperature would be about 36 degrees K. For contrast, water freezes at 273 K and the Earth’s mean global annual surface temperature is about 288 K.

    Comment by Barton Paul Levenson — 2 Apr 2007 @ 8:17 AM

  150. Ray Ladbury (#148): Earth gets about 4×10^13 watts from its interior–due to both radioactive decays and latent heat of condensation of liquid outer core onto solid inner core. Average insolation is about 10x that amount.

    Barton Paul Levenson (# 149): The net average contribution of sunlight to the climate system is about 240 watts per square meter; the geothermal flux is about 0.090 watts per square meter. [240 / 0.090 = 2,667X]

    Whoa! Someone’s calculations appear to be way off!

    Comment by Chuck Booth — 2 Apr 2007 @ 3:04 PM

  151. #150 Heat from the interior (Chuck)

    Back of the envelope calculation: some googling gives me heat conductivity figures for rock Labda = 1-50 W/m/K. Going down, temperature rises by about 0.01 K/m, hence heat flow from the interior is p = 0.01-0.5 W/m^2. Your p = 0.09 W/m2 fits nicely in between and gives (ca): P = 4 Pi R^2 * p = 4.6e13 W as you say (R=6.4e6 m).

    Insolation is 1400 W/m^2 at the top of the atmosphere, or 350 W/m^2 if we average over the entire Earth surface area (including night side). Of course not all this reaches the surface, but in all cases heat from the interior does not seem to make much difference for the climate.

    Comment by Dick Veldkamp — 2 Apr 2007 @ 4:19 PM

  152. RE #116, “As the evidence for global warming gets stronger, Republicans are actually getting more skeptical.”

    I’m wondering if perhaps the number of Republicans is decreasing, esp those who believe AGW is real leaving the GOP — perhaps in addition those remaining falling more into party line.

    This is bizzare. A whole party becoming increasingly anti-science, anti-reality, and anti-common sense. (BTW, I used to be a Republican, but guess I got out in plenty of time to avoid the “great brain wash.”)

    This to me might indicate we are going through a period of cultural distortion (when the culture gets really out of whack with reality & real problems, and the strategies become more and more counterproductive, if not downright harmful). If so, we might be on the brink of a revitalization movement, a rather sudden change to a more satisfying culture more in line with reality & solutions that work.

    In that case we might soon be seeing a lot of Republicans leaving their sinking ship — if the sensible ones remaining can’t take charge and restructure the GOP, pushing the fanatics to the fringe.

    But another thought is that the big fissure is not between right and left, but between those adament about staying plugged into the matrix (the elusion of an endless consumer utopia), and those who have freed themselves and know we must take responsibility and work to solve this problem of AGW. Both the right and the left want endless prosperity without price (externalities), and perhaps the poor nations want their chance to live like the rich nations before the party of proligate extravagance is finally over.

    So that leaves a small number of people to start this revitalization movement — but that’s all it really takes. Since the effects of AGW are not going away soon, eventually other may follow & the movement gain momentum. I hope in time to avert the worst.

    Comment by Lynn Vincentnathan — 2 Apr 2007 @ 5:03 PM

  153. RE #151
    Those are not my calculations – that was Barton Paul Levenson. My problem with his calculation is that it is based on the Stefan-Boltzmann equation. I’m no physicist, but I’m pretty sure that equation deals with the emission of electromagnetic radiation, and has nothing to do with nuclear radiation which is the source of heat in the earth’s core. I’m sure one of the physical scientists will clarify this point.

    Comment by Chuck Booth — 2 Apr 2007 @ 6:12 PM

  154. Geothermal heat flux is on the order of 0.01 W/m^2 according to Barry Saltzman, Dynamical Paleoclimatology, page 12.

    Comment by David B. Benson — 2 Apr 2007 @ 7:47 PM

  155. Rafael (147), try here for what you asked for, the magical “double CO2 without changing anything else” — perhaps only possible for a string theorist, even in theory.

    Look here for the real world:

    Comment by Hank Roberts — 2 Apr 2007 @ 8:50 PM

  156. Re 153. Chuck, the Stefan-Boltzmann equation has to do with the electromagnetic radiation emitted by a black body at temperature T. Barton is just saying that if you took all the energy from the interior and that were the only energy, Earth would look like a black body at 32 K. That’s probably valid to first order.

    My reference for the heat coming from the core is's%20Thermal%20Regimes.htm

    About half the energy from the interior is still thought to be due to radioactivity–the rest due to cooling of the interior.
    and I meant to say it’s about 1/10%, not 10%.

    Comment by Ray Ladbury — 2 Apr 2007 @ 8:57 PM

  157. How appropriate. Interesting article in Science

    Seismostratigraphy and Thermal Structure of Earth’s Core-Mantle Boundary Region
    R. D. van der Hilst,1* M. V. de Hoop,2 P. Wang,1 S.-H. Shim,1 P. Ma,3 L. Tenorio4
    We used three-dimensional inverse scattering of core-reflected shear waves for large-scale, high-resolution exploration of Earth’s deep interior (D”) and detected multiple, piecewise continuous interfaces in the lowermost layer (D”) beneath Central and North America. With thermodynamic properties of phase transitions in mantle silicates, we interpret the images and estimate in situ temperatures. A widespread wave-speed increase at 150 to 300 kilometers above the coremantle boundary is consistent with a transition from perovskite to postperovskite. Internal D” stratification may be due to multiple phase-boundary crossings, and a deep wave-speed reduction may mark the base of a postperovskite lens about 2300 kilometers wide and 250 kilometers thick. The core-mantle boundary temperature is estimated at 3950 ± 200 kelvin. Beneath Central America, a site of deep subduction, the D” is relatively cold (T = 700 ± 100 kelvin). Accounting for a factor-of-two uncertainty in thermal conductivity, core heat flux is 80 to 160 milliwatts per square meter (mW mâ��2) into the coldest D” region and 35 to 70 mW mâ��2 away from it. Combined with estimates from the central Pacific, this suggests a global average of 50 to 100 mW mâ��2 and a total heat loss of 7.5 to 15 terawatts.

    Even so, this amount of heat can only decrease with time, and so cannot be responsible for warming.

    Comment by Ray Ladbury — 3 Apr 2007 @ 7:19 AM

  158. Re #157 Heat flux (ray)

    The Science data seem to be inconsistent. 50 mW/m2 gives 25 TW (2.5e13 W), and 100 mW/m2 gives 51 TW (5.1e13 W).

    Am I misunderstanidng something here?

    Comment by Dick Veldkamp — 3 Apr 2007 @ 8:44 AM

  159. Possibly they’re talking about the heat flux between core and mantle rather than from surface to space?

    Comment by Hank Roberts — 3 Apr 2007 @ 9:50 AM

  160. [[The Science data seem to be inconsistent. 50 mW/m2 gives 25 TW (2.5e13 W), and 100 mW/m2 gives 51 TW (5.1e13 W).
    Am I misunderstanidng something here? ]]

    No, you’ve bracketed the data for the geothermal flux neatly. Recent estimates all fall in the range 41-46 TW, the upper end yielding the 0.090 W/m2 figure I used earlier. Just divide the total power by the Earth’s surface area (about 5.1007 x 1014 m2). Solar influx is many times that level, both total and per square meter.

    Comment by Barton Paul Levenson — 3 Apr 2007 @ 10:43 AM

  161. [None of this article supports the McKitrick article, it is just a note on Geometric Means and the lognormal distribution.]

    One can get really hung up on choice of means – in computer performance analysis we’ve fought about the right choice for decades.

    For many data sets, a Mean alone is fairly meaningless, if unaccompanied (at least) by measures of dispersion and skewness, because otherwise one doesn’t have much feel for the shape of the underlying *distribution*. It’s always nice to see entire distributions, but summarization is needed for sanity.

    So, if one is using the usual Arithmetic Mean, one wants:
    – Standard Deviation (or variance, i.e., 2nd moment) as measure of dispersion.
    Smaller is better.
    – Skewness (3rd moment)
    And you want this to be not too far from zero (~symmetric distribution), because if you have a seriously-skewed distribution, the Mean gets further and further from the Median, and is more influenced by outliers on one side or the other.

    Then, given skew ~0, one might hope that the data is approximated by a normal (Gaussian) distribution (given all the wonderful properties, including being able to use Mean & Std deviation as a really good summary): one would use a normality test to check, and probably compute the Kurtosis and confidence intervals. Normal distributions arise as sums of random collections of small additive factors.

    Suppose one finds that the distribution x is far from normal. A common method is to transform the data onto a different scale, say y=1/x, y =x^2, y = ln(x), and analyze the distribution y to see if it is Gaussian normal, compute the various metrics, and then back-transform them onto the original x scale. Often, the transformation may give insight into underlying processes.

    The transform ln(x) is sometimes useful, and it turns out that the Geometric Mean is just an equivalent way of computing the correct mean:

    Geometric Mean (GM) = Product(x) ^ (1/n) = exp((1/n) Sum(ln(x)))

    Geometric (multiplicative) Std Dev (Sigma) = exp(stddev(ln(x)))

    If the logarithms ln(x) are normally distributed, the original x is called *lognormal* or log-normal, and this is a well-known distribution of use in many areas of science. It happens when the original distribution is created by combinations of small multiplicative effects (which are of course, additive on a log scale). Just as 66% of normal data is in range [mean-stddev, mean+stddev], 66% of lognormal data is in range [GM/sigma, GM*sigma]. Lognormals are right-skewed, so when one sees right-skewed data, it’s at least worth trying, and it copes better with larger standard deviations. On the other hand, normal and lognormal distributions with small dispersions look pretty similar, so one might as well use normal. Given this math, one of course cannot have negative data for lognormals, so that for instance, one needs ratios, rather than differences (which is where Kelvin might come in, and where we’ve used the Geometric Mean for years in the SPEC Benchmarking effort). talks about this general topic in climatology.

    Sometimes one runs into datasets that have several modes, and turn out to be aggregations of two normal distributions, and good insight can be gained if there is a simple rule to tell the two apart.

    Anyway, it is wise to be careful with *any* Mean unsupported by characterization of the underlying distribution. If one can say: “The Mean is X, the std-deviation is Y, and the data is normal”, one need say no more.

    Comment by John Mashey — 3 Apr 2007 @ 8:18 PM

  162. Re 161: John, I agree that the distribution of the data determines the appropriate statistics. The mean is just a measure of the central tendency of the distribution and is eqivalent to the first moment of the distribution. Standard deviation or variance look at distribution width (variance is a centralized 2nd moment). Skew, looks at asymmetry and is related to the 3rd moment. Kurtosis looks at how peaked the distribution is and is related to the 4th moment. And so on.
    I wonder if anyone has looked at the standard deviation of global temperatures. Wouldn’t a greenhouse mechanism be expected on average to narrow the standard deviation? Or does the added variability in a more energetic climate overwhelm this tendency? Has anybody looked at higher moments?

    Comment by Ray Ladbury — 4 Apr 2007 @ 7:42 AM

  163. Re: 161, 162

    It’s well to remember that temperature has physical significance in terms of a conserved quantity: energy. Therefore if one mass of air increases temperature by 1 deg.C, while another equal-size mass of air decreases temperature by the same 1 deg.C, we can say that the net change in total thermal energy of the combined system is zero (at least as a first approximation).

    I’m not claiming that global average temperature is a measure of atmospheric thermal energy; there are too many other variables at work, and too many unmeasured quantities, to make that statement. But can one not claim that it is a lowest-order approximation to the thermal energy content of the troposphere? As such, the only average which is appropriate is the arithmetic average, regardless of the distribution of temperatures.

    Comment by tamino — 4 Apr 2007 @ 9:50 AM

  164. RE #162, I’ve thrown it out here before that perhaps the standard deviation might be greater in a warming world, but didn’t get any response. I’m sort of imagining weather around the world thrashing around kicking & screaming as it gets dragged into a hotter scenario from the GHGs; I’m sort of imagining a natural rubber-band type pull away from the heating that we are forcing on the earth, since we are already at a natural thermal maximum (but that might be anthropomorphizing too much). Then if that rubberband breaks (bec nature also starts pulling in our direction of heating the world, by releasing, r/t absorbing GHGs, & reducing albedo), we’re done for.

    Anyway, the extreme off-season cold snap much of the U.S. underwent in late Jan & Feb I’m thinking of as a weird GW effect. It was a short, but very cold winter.

    Also, if we do get greater and more frequent storms & hurricanes, then there will be more times when heat energy get translated into kinetic energy. So you go from very hot & sultry to a quick cool down during & after the storm.

    OTOH, I do know that GW entails a narrowing of the difference between daytime and nighttime temps (due to the GHG “blanket” effect at night, I think). That’s apparently why there were so many heat deaths in Europe in 2003, because people could not recouperate during the night from the heat stress during the day.

    This is all just speculation from a non-scientist (or perhaps nonsense).

    Comment by Lynn Vincentnathan — 4 Apr 2007 @ 11:35 AM

  165. Tamino, I’m not sure that is quite right. Say we have a mass of air at 0 degrees C over a mass of ice. Start adding energy to the air–the temperature will stay the same, but ice will melt. Now say we have a mass of wet air moving over a mountain range. The air cools adiabatically as it rises, and eventually the water drops out as snow or rain. Now the air moves downslope, heating adiabatically, except the adiabatic heating rate for the dry air is higher than the adiabatic cooling rate for wet air. Net result: A high-temperature gravity-driven wind like a chinook. Have we added energy to the air?
    So maybe to first order, but I think you will systematically undercount the added energy if you do so. After all, one of the favorite arguments of the denialists is that 0.6 degrees is insignificant. Yet, one need only look in polar regions to put the lie to that misunderstanding.

    Comment by Ray Ladbury — 4 Apr 2007 @ 11:49 AM

  166. Re: #163, #164 “As such, the only average which is appropriate is the arithmetic average, regardless of the distribution of temperatures.”

    Having originally trained a a physicist, that makes sense, but from a statistics sense, I sill want to know the shape of the distribution. For some problems, one *expects* to find lognormals, and thus use Geometric Means. [Computer benchmark sets expressed as sets of performance ratios work that way.] Sometimes datasets happen to be fit better by lognormals, for no obvious reason. I don’t know of any reason why temperature data should be lognormal, but people mentione Gemoetric Means, inciting my post.

    I simply never like averages alone without some sense of the shape of the distribution [skew, dispersion], because I remember the old adage about someone drowning in a river whose depth averaged 6 inches. In any case, if somebody tells me data is normally distributed with a modest std. deviation, from then on, I’ll happily just use the average.

    Comment by John Mashey — 4 Apr 2007 @ 12:32 PM

  167. Re: does a global temperature exist

    The Wall Street Journal’s editorial page continued as usual, with a Holman Jenkins Jr opinion piece called “Climate of Opinion”, which includes:

    “And that’s without considering whether a planetary ‘average’ temperature is even a meaningful datapoint (some have likened it to averaging all the phone numbers in the phone book.)” Hmmm, I wonder where that came from?
    {A: the Essex/McKitrick article that started this]

    Comment by John Mashey — 4 Apr 2007 @ 12:50 PM

  168. > The air cools adiabatically as it rises, and eventually
    > the water drops out as snow or rain.

    Ray, the “heat of condensation” at that point goes into the surrounding molecules — the _gas_ picks up heat from the molecules of water as they condense; the water molecules have lost energy so they can stick together in droplets. On the far side of the ridge, the now much drier air warms up as it descends. There’s no fog it, so the heat stays in the air rather than turning mist into humidity.

    This is also what makes a towering cumulus cloud go boiling up into colder air once it starts to form, if the air above the condensation height is colder than the air in the rising thermal column as the water condenses out.

    One example: pyrocumulus (lots of moisture coming off a forest fire; once it condenses, it becomes a cumulus cloud and gets tall fast)

    On a lower or cooler ridge, where you don’t lose most of the humidity falling out as rain, the condensing cloud/fog rises over the top and falls down the far side, and is available to absorb heat again as the droplets of water disassociate into molecules again, so the air doesn’t warm as much.

    Comment by Hank Roberts — 4 Apr 2007 @ 1:10 PM

  169. John, Correct me if I’m wrong, but the distribution we’re interested in here is the distribution of temperatures at every point on Earth’s surface at a given moment in time. Since we are interested in whether the center of the distribution is changing, it makes sense to look at the arithmetic mean. I mean, after all, since we’re looking at temperature, the distribution will be bounded above and below, right, so really, it’s neither lognormal nor normal. Now, I believe that the arithmetic mean will significantly underestimate the energy going into the system–it doesn’t take into account increased evaporation, ice melting, etc. However, other estimators will probably do an even worse job. So, as an intuitive measure of increasing energy density, it may be as good as we’ll get.

    Comment by Ray Ladbury — 4 Apr 2007 @ 1:24 PM

  170. Re 168: Hank, my point is that that temperature doesn’t reflect energy absorbed or released in a phase change, or heating of the ocean, etc.–thus, it tends to underestimate warming in a warming climate or cooling in a cooling climate. You get a damped picture of what’s going on. Thus, I think it can be misleading to look at temperature alone. I don’t, however, liken it to averaging the numbers in a phone book. If you see a change in temperature, it is a real indication of change in the climate.

    Comment by Ray Ladbury — 4 Apr 2007 @ 1:57 PM

  171. Re: 169
    “distribution we’re interested in here is the distribution of temperatures at every point on Earth’s surface at a given moment in time.”

    Well, that’s one of the distributions that might be useful, but I think, when looking at the yearly plots, people have averaged across:
    – geography (doing their best to derive homgeneity from heterogenous sources)
    – across the year [unless doing season-season comparison]
    – across time-of-day [unless doing daytime/nighttime studies]

    Of course, weather stations are where they are, and many daily temperatures are not real averages across 24 hours, but .5* (min + max).

    Thought experiment:
    Consider the *ideal* distribution that we’d love to have, if we wanted to compute exactly one temperature for a year/month/day/minute

    – Pick a random minute from the year/month/day/minute
    – on the Earth’s surface, pick a random location [not just at stations]
    – Measure the temperature then and there.

    If one does it N times, as N gets larger, the resulting datasets would better and better approximate the continuous probability distribution function for the chosen time-period’s data.

    NCDC has a nice chart on recorded extremes:
    which range from -129F to 136F [i.e., the outliers are not pleasant weather!]

    The existence of bounds on temperature ranges doesn’t stop them from being well fit by normal, lognormal, or other distributions: the only way to know is to actually look at the data:

    – quick check: do histograms and eyeball the data
    – compute Skew and excess Kurtosis, and if those are close to 0:
    – run Normality tests, as for example:
    (I haven’t found one simple reference, but people seem to use such techniques often on various climate datasets: Google Scholar: climate temperature normality test
    gives 15K hits,and in general, the words “normal” and “distribution” have multiple meanings, so I haven’t yet located the sort of reference I’m looking for, although I’ve tried many queries.)

    If the data sort of looks normal, but is right-skewed, perhaps it can be better modeled as lognormal, in which case one computes the logs, and then goes back through the above. Of course, it might be something else.

    I have no idea whether the distribution, say for 5000 samples as above, for a year, is normal, lognormal, or some left-skewed distribution. Can anybody point me at a paper or website that has such? I’ve looked at USHCN, various NOAA websites, etc.
    Ideal would be histograms, with the key statistical metrics for datasets that approximate the thought experiment above for sometime period.

    I would be perfectly happy if the resulting distributions were ~normal, or at least symmetric, as the arithmetic mean (which does seem to fit the physics) would also be in the intuitive “center” of he distribution.

    Comment by John Mashey — 4 Apr 2007 @ 4:29 PM

  172. RE #167, well that would be something if the average of all the phone numbers in the book were going up over the years, over the decades. You’d think something might be causing it…..I.e., it probably wouldn’t just be due to random fluctuations.

    Comment by Lynn Vincentnathan — 4 Apr 2007 @ 7:26 PM

  173. Just a note: the normal distribution has 0 skewness, but not 0 kurtosis; for the normal distribution the kurtosis is = 3.

    Comment by tamino — 4 Apr 2007 @ 7:39 PM

  174. John, I agree, a Normal or lognormal will do fine in the center–not in the tails. A bounded distribution looks Weibull in the tail (Extreme Value Type III, I believe). Now I agree that we probably don’t care too much about the extremes–though you might expect to see trends there, too. The reason the lognorm or normal look reasonable is because of the CLT. BTW, the common Weibull is the only distribution I know of that is skewed left (for shape parameters above a certain value). Moreover, if the probability in the tails is sufficiently small, the skews won’t matter–guess that would be ~normal for our purposes. However, even for a skewed distrubution, arithmetic mean approximately tracks central tendency–that is, if the center of the distribution shifts, so will the mean, unless you get some really freaky cooperation from the other moments.

    Comment by Ray Ladbury — 4 Apr 2007 @ 7:49 PM

  175. Just for laughs, I took the daily mean temperature for Geneva, Switzerland (from the European Climate Assessment and Dataset Project) and subtracted the seasonal pattern to define temperature anomaly. Then I did a histogram of the anomalies, and superimposed a normal distribution with the same mean (0, by definition) and standard deviation (3.0527 deg.C). I’ve posted the graph on my blog, and you can go straight to the graph here:

    Comment by tamino — 4 Apr 2007 @ 8:36 PM

  176. re: #173: Tamino
    Sorry I was a little sloppy earlier, but in #171, I was precise, and said if the “excess Kurtosis” were 0… Excess kurtosis = kurtosis – 3.
    See: OR
    as far as I can tell, people are sometimes imprecise as to which they’re using.

    re: #174, Ray: yes, we agree, and in particular, with the numbers of data points usually available in climatology, one doesn’t get weird results from a few outliers (unlike computer benchmarking, which often has small datasets from which people draw more conclusions than they ought) and the arithmetic mean is likely to be fine. In any case, I’d guess the real issue is the motion of some mean, calculated in a consistent way. [I’ve never used Weibull, not having done reliability studies.]

    As always, one hopes to end up with something ~normal [as Tamino’s #175 certainly looks: thanks!], in which case Life Is Good, but I still think:

    a) One should never just assume normality, one should look at the data and see, and if it is, it’s nice to be able to say: data is normal, and be done with it.

    b) One may gain insight from noticing outliers or multi-modal data.

    c) We’re probably deeper into the stat than most people want to go, but the great John Tukey’s pithy observations seem relevant and memorable:

    “Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made more precise.”

    “The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data.”

    [I overlapped with Tukey 10 years at Bell Labs. He was associate executive director of a division that contained Joseph Kruskal, John Chambers (S), and Paul Tukey, among other star statisticians. Bell Labs required that when someone wanted to publish a paper outside, it had to be first reviewed by several departments outside their line of management. Of course, anything in which statistics was important went to these folks, and I understand that their comments could be acerbic, a not-uncommon effect amongst statisticians. That meant that other people learned to get help from the statisticians earlier, not later, and also to treat data with suspicion, by default.]

    Comment by John Mashey — 4 Apr 2007 @ 10:43 PM

  177. While I only understood the introduction and the conclusion, I agree with the bottom line of what is being said. But that does not change the fact that a statistical measurment can be useful in seeing patterns, as many here have stated.

    So did this paper change anyones mind one way or the other. :)
    I must say that when I saw the title my first thought was, “Here we go again.” I have to constantly re-ground myself from what “I already know”, and from what is being added to the pool of knowledge by new data.
    I am a bad scientist.
    Not that this paper added anything really useful in my laymans understanding.

    Comment by Eric — 5 Apr 2007 @ 1:42 PM

  178. How can the IPCC use temperature data with three significant figures? How can they be confident that the temperature at any point on the earth in 1000 A.D. was 32.1 degrees C rather than 32.2 degress C? If the data were reliable to two significant figures the profile would be a flat line with a possible step change of 1 degree C around 2000. Am I wrong?

    Comment by peter — 6 Apr 2007 @ 8:47 AM

  179. Okay, re the need for more than the mean (we’re all agreed we need the mean, elsewise how could we calc the s.d.)…

    I read today that the AR4 IPCC said in re to N. America, “In the short term, crop yields may increase by 5 to 20 percent from a longer growing season, but will plummet if temperatures rise by 7.2 F.”

    I’m not even sure there will be such increases. I’m thinking there may be these wild fluctuations in weather so we get some fluke late spring and early fall killing frosts, and it only takes one of these to do in a crop. So while the AVERAGE may be a warmer & longer summer, the fluky outliers may increase (I have no idea, but this could be a possibility).

    Not to mention those killing heat spikes (outliers in the hot direction) that kill much of the crop mid-summer.

    So from that POV, we really do need much more than the mean.

    Comment by Lynn Vincentnathan — 6 Apr 2007 @ 9:04 AM

  180. Nor is temperature the only factor in crop yields, or even the most important one. There’ve been several news articles in the last couple of days on a study predicting that the southwestern US and northern Mexico will be much drier in the future as a result of AGW. Since the area’s mostly desert now, with crops being grown only with irrigation, that doesn’t bode well for future productivity.

    Looking back at the warming at the end of the last Ice Age, we see the whole western half of the US becoming much drier. It seems reasonable to think that further warming would only intensify this, which would seem to indicate that the northwest (east of the Cascades) and Great Plains might become too dry for agriculture as well. So perhaps we’d better start hoping that those areas which still retain enough moisture do become more productive, else we all may be getting a bit hungry.

    Comment by James — 6 Apr 2007 @ 11:51 AM

  181. Re #170: “If you see a change in temperature, it is a real indication of change in the climate.”

    Perhaps…in some subset of the measurements, or perhaps overall.

    Or…perhaps not…it is known the summing of even spatially independent but temporally correlated series can produce spurious breaks or trends (long-memory) in the averaged series.

    I find the Essex paper interesting, and agree with their conclusions for the reasons above. I would not rely upon globally averaged temperature as an indicator of climate change.

    Comment by Tom Boucher — 12 Apr 2007 @ 5:16 PM

  182. [[I find the Essex paper interesting, and agree with their conclusions for the reasons above. I would not rely upon globally averaged temperature as an indicator of climate change. ]]

    You would seem to be wrong on both counts. The average temperature of the atmosphere is a measure of how much energy the atmosphere is holding, via the old H = m cp T relation where H is heat content (in Joules in the SI), m is mass (kg), cp is constant-pressure specific heat or heat capacity (J kg-1 K-1), and T temperature (K). I would guess that the more energy in the climate system, the more energetic the weather, on average.

    Comment by Barton Paul Levenson — 13 Apr 2007 @ 10:17 AM

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