Does a Global Temperature Exist?
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.
25 March 2007 at 10:41 AM
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.
25 March 2007 at 10:44 AM
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.
25 March 2007 at 10:58 AM
It is also worth noting, that the activity of the sun is higher then ever in 8000 years:
http://www.canada.com/nationalpost/financialpost/story.html?id=67ac2d90-ec56-4460-a831-75aacc20670d
Maybe nobody here has noticed it?
Regards
[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]
25 March 2007 at 11:10 AM
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?.
25 March 2007 at 11:23 AM
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.
Correct?
[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]
25 March 2007 at 11:24 AM
Re: #3,
Lawrence Solomon is put in his place by DeSmogBlog:
http://www.desmogblog.com/irresponsible-solomon-at-it-again
25 March 2007 at 11:25 AM
Waitaminute. Do Essex et al. propose a more meaningful measure? If so, what’s the trend? If not, what’s the point?
25 March 2007 at 11:32 AM
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.
25 March 2007 at 11:36 AM
Anyone suitably motivated can read the preprint here:
http://www.uoguelph.ca/~rmckitri/research/globaltemp/GlobTemp.JNET.pdf
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…
25 March 2007 at 11:59 AM
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.
25 March 2007 at 12:17 PM
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]
25 March 2007 at 12:36 PM
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?
25 March 2007 at 12:36 PM
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:
http://www.realclimate.org/index.php/archives/2005/08/did-the-sun-hit-record-highs-over-the-last-few-decades/#more-180
http://www.realclimate.org/index.php/archives/2004/12/recent-warming-but-no-trend-in-galactic-cosmic-rays/
http://www.realclimate.org/index.php/archives/2005/07/the-lure-of-solar-forcing/
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.
25 March 2007 at 12:42 PM
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.
25 March 2007 at 12:44 PM
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.
25 March 2007 at 12:44 PM
Eli has five entertaining entries on this very subject on : http://rabett.blogspot.com/ starting back on March 15th.
Regards,
25 March 2007 at 12:51 PM
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!”
25 March 2007 at 12:56 PM
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
25 March 2007 at 1:37 PM
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 http://mathforum.org/dr.math/ ).
25 March 2007 at 1:42 PM
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.
25 March 2007 at 1:44 PM
Is this a scientific weblog or a cyber-prayer meeting? The comments indicate it is the latter.
25 March 2007 at 2:17 PM
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?
25 March 2007 at 2:40 PM
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.
25 March 2007 at 2:40 PM
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.
25 March 2007 at 3:01 PM
I found the comments in this post on Rabett Run (and links therein) rather illuminating:
http://rabett.blogspot.com/2007/03/open-book-test-in-comments-over-at.html
#14 SB: Thanks for the clarification, spuds now cooked and eaten
25 March 2007 at 3:55 PM
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.
25 March 2007 at 4:04 PM
Re #14 Not the John Gribbin of popular novel writing in the subjects of quantum physics, relativity and cosmology is it per chance ?
25 March 2007 at 4:20 PM
#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.
25 March 2007 at 4:52 PM
To Jim Cross #22
You could try Six Degrees of Warming by Mark Lynas.
http://www.marklynas.org/sixdegrees
25 March 2007 at 4:54 PM
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.
25 March 2007 at 4:54 PM
#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.
25 March 2007 at 5:13 PM
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!
25 March 2007 at 5:24 PM
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!
25 March 2007 at 5:37 PM
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).
25 March 2007 at 6:18 PM
>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.
25 March 2007 at 6:19 PM
> spectroscopically.
> Comment by John Gribbin
Triana!
25 March 2007 at 7:05 PM
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…”
25 March 2007 at 7:49 PM
“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.
25 March 2007 at 7:59 PM
Ross McKitrick is the guy who doesn’t know the difference between degrees and radians. Figures.
25 March 2007 at 8:17 PM
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?
25 March 2007 at 8:18 PM
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.
25 March 2007 at 8:18 PM
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.
25 March 2007 at 8:30 PM
You say celsius or kelvin to the majority of American politicians/voters and their brains take a pass.
25 March 2007 at 8:58 PM
http://rabett.blogspot.com/2007/03/bunny-still-has-pen-in-paw-cont.html#comment-2976390259195287901
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.
25 March 2007 at 9:07 PM
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.)
25 March 2007 at 9:31 PM
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 http://rabett.blogspot.com/index.html ).
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]
25 March 2007 at 10:01 PM
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.
25 March 2007 at 10:19 PM
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.
25 March 2007 at 10:45 PM
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)
info:doi/10.1029/2006gl028726
http://dx.doi.org/10.1029/2006gl028726
“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)
http://dx.doi.org/10.1029/2006gl027927
…”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)
http://dx.doi.org/10.1029/2006gl029068
…”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)
http://dx.doi.org/10.1029/2006gl028679
…”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)
info:doi/10.1175/jam2441.1
http://dx.doi.org/10.1175/jam2441.1
…”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)
http://dx.doi.org/10.1029/2006gl026358
“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)
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2006GeoRL..3305710H&%3Bdb_key=AST
…”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)
http://dx.doi.org/10.1029/2005jd006290
25 March 2007 at 10:49 PM
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.
25 March 2007 at 10:54 PM
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.
25 March 2007 at 11:53 PM
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
25 March 2007 at 11:54 PM
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
26 March 2007 at 12:26 AM
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
26 March 2007 at 1:34 AM
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.
26 March 2007 at 2:19 AM
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/
26 March 2007 at 7:17 AM
[[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.
26 March 2007 at 7:18 AM
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]
26 March 2007 at 7:21 AM
[[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.
26 March 2007 at 7:28 AM
[[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.
26 March 2007 at 7:33 AM
“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.
26 March 2007 at 7:51 AM
[[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.
26 March 2007 at 8:22 AM
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.
26 March 2007 at 10:56 AM
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.
26 March 2007 at 11:15 AM
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.
26 March 2007 at 11:35 AM
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
26 March 2007 at 11:37 AM
#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.
26 March 2007 at 11:47 AM
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?
26 March 2007 at 11:48 AM
Ola, good text, I am new in the space. automatiamente I automatiamente translated of the Portuguese English.
26 March 2007 at 12:24 PM
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.
26 March 2007 at 12:29 PM
[[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?
26 March 2007 at 12:49 PM
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…
26 March 2007 at 12:59 PM
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.
26 March 2007 at 1:25 PM
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.
26 March 2007 at 1:32 PM
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 March 2007 at 1:40 PM
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
26 March 2007 at 1:41 PM
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.
26 March 2007 at 1:41 PM
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.
26 March 2007 at 1:44 PM
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.
26 March 2007 at 2:24 PM
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.
26 March 2007 at 3:11 PM
#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.
26 March 2007 at 3:16 PM
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
26 March 2007 at 3:26 PM
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.
26 March 2007 at 3:29 PM
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.
26 March 2007 at 3:40 PM
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.
26 March 2007 at 3:54 PM
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.
26 March 2007 at 4:10 PM
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
26 March 2007 at 4:13 PM
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]
26 March 2007 at 4:51 PM
#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
26 March 2007 at 4:52 PM
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
26 March 2007 at 5:03 PM
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.
26 March 2007 at 5:28 PM
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
26 March 2007 at 6:03 PM
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
26 March 2007 at 6:51 PM
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.
26 March 2007 at 7:54 PM
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.
26 March 2007 at 7:56 PM
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.
26 March 2007 at 7:57 PM
#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.
26 March 2007 at 8:10 PM
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.”
26 March 2007 at 8:32 PM
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.
26 March 2007 at 8:59 PM
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…..
26 March 2007 at 9:25 PM
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.
26 March 2007 at 10:13 PM
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.
26 March 2007 at 11:13 PM
[[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.
27 March 2007 at 12:30 AM
#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.
27 March 2007 at 3:09 AM
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]
27 March 2007 at 4:54 AM
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.
27 March 2007 at 5:39 AM
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.
27 March 2007 at 7:20 AM
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?
27 March 2007 at 7:26 AM
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.
27 March 2007 at 7:27 AM
#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.
27 March 2007 at 7:35 AM
[[ 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.
27 March 2007 at 7:40 AM
[[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.
27 March 2007 at 7:43 AM
[[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.
27 March 2007 at 8:08 AM
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 …
www.sciencedaily.com/releases/1998/01/980129074316.htm
27 March 2007 at 9:59 AM
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:
http://www.ems.org/climate/pentagon_climate_change.pdf
But Grist archived it:
http://www.grist.org/pdf/AbruptClimateChange2003.pdf
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]
27 March 2007 at 10:18 AM
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 http://tinyurl.com/2abdbl (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 w