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Does a Global Temperature Exist?

Filed under: — rasmus @ 25 March 2007 - (Portugu√™s)

Does a global temperature exist? This is the question asked in a recently published article in Journal of Non-Equilibrium Thermodynamics by Christopher Essex, Ross McKitrick, and Bjarne Andresen. The paper argues that the global mean temperature is not physical, and that there may be many other ways of computing a mean which will give different trends.

The common arithmetic mean is just an estimate that provides a measure of the centre value of a batch of measurements (centre of a cloud of data points, and can be written more formally as the integral of x f(x) dx. 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 arithmetic 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). Thus the choice may not need a physical justification, but is part of a scientific test which enables us to get a clearer ‘yes’ or ‘no’. One could choose to look at the global mean sea level instead, which does have a physical meaning because it represents an estimate for the volume of the water in the oceans, but the choice is not crucial as long as the indicator used really responds to the conditions under investigation. And the global mean temperature is indeed a function of the temperature over the whole planetary surface.

Is this paper a joke then? It is old and traditional knowledge that the temperature measurements made in meteorological and climatological studies are supposed to be representative of a certain volume of air, i.e. the arithmetic mean. Essex et al. argue that it is not really physical, but surely the temperature measurements do have clear practical implications? Temperature itself can be inferred directly from several physical laws, such as the ideal gas law, first law of thermodynamics and the Stefan-Boltzmann law, so it’s not the temperature itself which is ‘unphysical’. Even though the final temperature of two bodies in contact may not be the arithmetic mean, it will still be a weighted arithmetic mean of the temperatures of the two initial temperatures if no heat is lost to the surroundings. Besides, grid-box sizes for numerical weather models often have a minimum spatial scale of 10-20km, and the temperature may be regarded as a mean for this scale. Numerical weather models usually provide useful forecasts.

And what distinguishes the mean temperature representing a small volume to a larger one? Or do Essex et al. think the limit is at greater scales. For instance at the synoptic spatial scale (~1000 km)? The funny thing then is that the concept of regional mean temperature would also not be meaningful according to Essex et al. And one may also wonder if the problem of computing a mean temperature is meaningful in time, such as the summer-mean temperature or winter-mean temperature?

Essex et al. suggest that there are many different ways of computing the mean, and it is difficult to know which make more sense. But when they compute the geometric mean, they should not forget that the temperature should be in degrees Kelvin (the absolute temperature) as opposed to Celsius. One argument used by Essex et al. is that the temperatures are not in equilibrium. Strictly speaking, this applies to most cases. But in general, these laws still give a reasonable results because the temperatures are close to being in equilibrium in meteorology and climatology. The paper doesn’t bring any new revelations – I thought that these aspects were already well-known.

Update: Rabett Run has a very detailed set of posts pulling apart this paper more thoroughly.


182 Responses to “Does a Global Temperature Exist?”

  1. 51
    Chuck Booth says:

    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.

  2. 52
    Eli Rabett says:

    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

  3. 53
    Hank Roberts says:

    Then say degrees above absolute zero, for the politically impaired.
    And for the UK, surely the Scots will know him:
    http://scienceworld.wolfram.com/biography/Kelvin.html

  4. 54
    Edward Greisch says:

    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.
    Join lifeboat.com

  5. 55
    Robin Johnson says:

    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.

  6. 56
    Dick Veldkamp says:

    Re #39 (Dave Rado)

    While you’re at the site provided by Dave ( http://timlambert.org/2004/08/26 ), check out some other posts by Tim Lambert on how McKittrick handles temperatures (about one page down from the top), for example: http://timlambert.org/2004/07/mckitrick5/

  7. 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.

  8. 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]

  9. 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.

  10. 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.

  11. 61
    Alex Nichols says:

    “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.

  12. 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.

  13. 63
    Alan says:

    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.

  14. 64
    Eli Rabett says:

    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.

  15. 65
    Webster says:

    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.

  16. 66
    kroganchor says:

    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?
    TIA
    Krog

  17. 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.

  18. 68
    Daniel C. Goodwin says:

    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?

  19. 69
    Iara Nunes says:

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

  20. 70
    Mitch Golden says:

    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.

  21. 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?

  22. 72
    Mark Frank says:

    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…

  23. 73
    Figen Mekik says:

    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.

  24. 74
    Chris O'Neill says:

    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.

  25. 75
    John D. says:

    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.
    http://www.oism.org/pprojects/s33p357.htm

  26. 76
    Hank Roberts says:

    Oh, right, check them out, if anyone doesn’t already know about them:
    http://www.sourcewatch.org/index.php?title=Oregon_Institute_of_Science_and_Medicine

  27. 77
    Benny says:

    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.

  28. 78
    Dick Veldkamp says:

    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.

  29. 79
    Mitch Golden says:

    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.

  30. 80
    El Cid says:

    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.

  31. 81
    John D. says:

    #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.

  32. 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:
    http://adamant.typepad.com/seitz/2007/03/no_wonder_its_w.html

  33. 83
    tamino says:

    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.

  34. 84
    Harold Ford says:

    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. :? :?

  35. 85
    Dick Veldkamp says:

    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.

  36. 86
    Chris O'Neill says:

    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.

  37. 87
    Ike Solem says:

    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: http://news.bbc.co.uk/2/hi/science/nature/5134022.stm

  38. 88
    Rob says:

    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]

  39. 89
    Richard Ordway says:

    #75 Red Herring, John D.

    [[http://www.oism.org/pprojects/s33p357.htm]]

    Your link is to a well-known fossil-fuel funded website: The Oregon Institute of Science and Medicine
    http://en.wikipedia.org/wiki/Oregon_Petition

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

    http://www.ucsusa.org/global_warming/science/skeptic-organizations.html

  40. 90
    kroganchor says:

    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?
    Krog

  41. 91
    Hank Roberts says:

    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.

    http://news.bbc.co.uk/2/hi/science/nature/5134022.stm

    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.

  42. 92
    Jim Dukelow says:

    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

  43. 93
    Figen Mekik says:

    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

  44. 94
    Jim Cross says:

    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.

  45. 95
    Hank Roberts says:

    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.

  46. 96
    Eric Swanson says:

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

    http://www.uoguelph.ca/~rmckitri/research/globaltemp/globaltemp.zip

    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.

  47. 97
    John D. says:

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

    #89
    Thanks for the heads up. I will look into that.

  48. 98
    Lynn Vincentnathan says:

    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.”

  49. 99
    Dave Rado says:

    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.

  50. 100
    Rod B. says:

    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…..


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