### Does a Global Temperature Exist?

Filed under: — rasmus @ 25 March 2007 - ()

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. 1
Paul Higgins says:

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.

2. 2
Bob Reiland says:

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.

3. 3
Hedwig Braun says:

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

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]

4. 4
Nick Riley says:

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?.

5. 5

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

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

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

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]

6. 6
Stephen Berg says:

Re: #3,

Lawrence Solomon is put in his place by DeSmogBlog:

http://www.desmogblog.com/irresponsible-solomon-at-it-again

7. 7
Pat Cassen says:

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

8. 8
Hank Roberts says:

“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.

9. 9
SomeBeans says:

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…

10. 10

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

11. 11
George K says:

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]

12. 12
pete best says:

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?

13. 13
Peter Houlihan says:

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

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

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

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

14. 14
John Gribbin says:

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.

15. 15
Chuck Booth says:

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.

16. 16
Fergus Brown says:

Eli has five entertaining entries on this very subject on : http://rabett.blogspot.com/ starting back on March 15th.

Regards,

17. 17
Alexander Ac says:

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!” :-)

18. 18
FatBoy says:

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

19. 19
Dick Veldkamp says:

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/ ).

20. 20
Vern Johnson says:

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.

21. 21
W F Lenihan says:

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

22. 22
Jim Cross says:

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?

23. 23
Steve Bloom says:

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.

24. 24
Jason DeRoche says:

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.

25. 25
SomeBeans says:

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

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

26. 26
Rod B. says:

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.

27. 27
pete best says:

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

28. 28
Richard Ordway says:

#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.

29. 29
Ed Sears says:

To Jim Cross #22

You could try Six Degrees of Warming by Mark Lynas.
http://www.marklynas.org/sixdegrees

30. 30
Tim McDermott says:

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.

31. 31

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

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

32. 32
Joel Shore says:

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!

33. 33
David B. Benson says:

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!

34. 34
Timothy says:

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).

35. 35
Hank Roberts says:

>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.

36. 36
Hank Roberts says:

> spectroscopically.
> Comment by John Gribbin

Triana!

37. 37

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

38. 38
Ellis says:

“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.

39. 39

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

40. 40

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

41. 41
joel says:

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.

42. 42
P. Lewis says:

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.

43. 43
J.C.H says:

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

44. 44
Ken Williams says:

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.

45. 45
P. Lewis says:

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.)

46. 46
James Annan says:

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]

47. 47
Mark A. York says:

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.

48. 48

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

49. 49
BarbieDoll Moment says:

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 1Â°â??2Â°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)
…”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

50. 50

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

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

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