Posted on 03/19/2007 2:11:10 PM PDT by Daffynition
Science Daily — Discussions on global warming often refer to 'global temperature.' Yet the concept is thermodynamically as well as mathematically an impossibility, says Bjarne Andresen, a professor at The Niels Bohr Institute, University of Copenhagen, who has analyzed this topic in collaboration with professors Christopher Essex from University of Western Ontario and Ross McKitrick from University of Guelph, Canada.
It is generally assumed that the atmosphere and the oceans have grown warmer during the recent 50 years. The reason for this point of view is an upward trend in the curve of measurements of the so-called 'global temperature'. This is the temperature obtained by collecting measurements of air temperatures at a large number of measuring stations around the Globe, weighing them according to the area they represent, and then calculating the yearly average according to the usual method of adding all values and dividing by the number of points.
Average without meaning
"It is impossible to talk about a single temperature for something as complicated as the climate of Earth", Bjarne Andresen says, an an expert of thermodynamics. "A temperature can be defined only for a homogeneous system. Furthermore, the climate is not governed by a single temperature. Rather, differences of temperatures drive the processes and create the storms, sea currents, thunder, etc. which make up the climate".
He explains that while it is possible to treat temperature statistically locally, it is meaningless to talk about a a global temperature for Earth. The Globe consists of a huge number of components which one cannot just add up and average. That would correspond to calculating the average phone number in the phone book. That is meaningless. Or talking about economics, it does make sense to compare the currency exchange rate of two countries, whereas there is no point in talking about an average 'global exchange rate'.
If temperature decreases at one point and it increases at another, the average will remain the same as before, but it will give rise to an entirely different thermodynamics and thus a different climate. If, for example, it is 10 degrees at one point and 40 degrees at another, the average is 25 degrees. But if instead there is 25 degrees both places, the average is still 25 degrees. These two cases would give rise to two entirely different types of climate, because in the former case one would have pressure differences and strong winds, while in the latter there would be no wind.
Many averages
A further problem with the extensive use of 'the global temperature' is that there are many ways of calculating average temperatures.
Example 1: Take two equally large glasses of water. The water in one glass is 0 degrees, in the other it is 100 degrees. Adding these two numbers and dividing by two yields an average temperature of 50 degrees. That is called the arithmetic average.
Example 2: Take the same two glasses of water at 0 degrees and 100 degrees, respectively. Now multiply those two numbers and take the square root, and you will arrive at an average temperature of 46 degrees. This is called the geometric average. (The calculation is done in degrees Kelvin which are then converted back to degrees Celsius.)
The difference of 4 degrees is the energy which drives all the thermodynamic processes which create storms, thunder, sea currents, etc.
Claims of disaster?
These are but two examples of ways to calculate averages. They are all equally correct, but one needs a solid physical reason to choose one above another. Depending on the averaging method used, the same set of measured data can simultaneously show an upward trend and a downward trend in average temperature. Thus claims of disaster may be a consequence of which averaging method has been used, the researchers point out.
What Bjarne Andresen and his coworkers emphasize is that physical arguments are needed to decide whether one averaging method or another is needed to calculate an average which is relevant to describe the state of Earth.
Reference: C. Essex, R. McKitrick, B. Andresen: Does a Global Temperature Exist?; J. Non-Equil. Thermod. vol. 32, p. 1-27 (2007).
These people are discussing facts, that has nothing to do with Gorebal Warming.
Does a Global Temperature Exist
Christopher Essex, Department of Applied Mathematics, University of Western Ontario
Bjarne Andresen, Niels Bohr Institute, University of Copenhagen
Ross McKitrick, Department of Economics, University of Guelph
Journal of Non-Equilibrium Thermodynamics, Volume 32 No. 1
Physical, mathematical and observational grounds are employed to show that there is no physically meaningful global temperature for the Earth in the context of the issue of global warming. While it is always possible to construct statistics for any given set of local temperature data, an infinite range of such statistics is mathematically permissible if physical principles provide no explicit basis for choosing among them. Distinct and equally valid statistical rules can and do show opposite trends when applied to the results of computations from physical models and real data in the atmosphere. A given temperature field can be interpreted as both "warming" and "cooling" simultaneously, making the concept of warming in the context of the issue of global warming physically ill-posed.
Apparently there's a little problem with the proper units to use in the Stefan-Boltzmann equation, and the reviewers didn't notice it. Anonymous at 12:15 AM really goes to town.
I'm still trying to wrap my feeeble brain around the idea that scientists should uphold the same standards for their theories, which is what I get from this article.
So simple a cave man could understand it! Great explanation. Thanks for posting it.
And the combined, global, land-sea temperature anomaly record DOES show warming. There is less in the Southern Hemisphere; partly due to the thermal inertia of the major mass of the southern Pacific Ocean, I would think.
similar:
Is there an average global temperature?
American Thinker | March 18, 2007 | James Lewis
Posted on 03/18/2007 6:58:21 PM EDT by neverdem
http://www.freerepublic.com/focus/f-news/1802940/posts
Ross-Lempriere benchmark
http://www.john-daly.com/deadisle/index.htm
Apparently there's a little problem with the proper units to use in the Stefan-Boltzmann equation, and the reviewers didn't notice it.
Interesting, I have no problem demonstrating similar relationships using absolute temperatures and appropriate temperature values for the Newtonian cooling example, within the range of current arctic/tropical saltwater temps with ambient temperature set at the current global surface average.
http://home.earthlink.net/~a_geezer/Climate/Fig1Kelvin.gif
I would say for demonstration purposes, the distinction is without significance, being only a matter of scaling and setting up the conditions to demonstrate the principle.
LOL...
I had a strong suspicion that cogitator's civilians who were criticizing the example were a bit less reliable than the researchers and reviewers. When I looked at the data and graph, I didn't see anything wrong with them at first blush.
Thanks for your quick refutation.
"The global temperature statistic is also described as the average, as if there is only one kind of average. Of course there is an infinity of mathematically legitimate options. Indeed over one hundred different averages over temperatures have been used in meteorology and climate studies [7] with more appearing regularly. For the case of temperature, or any other thermodynamic intensity, there is no physical basis for choosing any one of these from the infinite domain of distinct mathematical options. The international standards organization ISO tried to choose one but failed [8]. The problem is not a mere absence of a convention for selecting one from among many mathematically different but physically-equivalent measures for a single underlying property. The problem is that there is no single underlying property, because there is no global temperature. But this does not stop averages from being made.
There is no experimental or theoretical way to falsify any particular choice of averaging rule, if averages are (falsely) proclaimed to be temperatures. Proclaiming them to be temperatures leads to a paradox, as any two ad hoc choices applied to a particular outof- equilibrium field can have mutually contradictory behaviors: the system can seem to be both warming and cooling simultaneously. Paradoxically, whether the system is “warming” or “cooling” becomes a property of the choice of average — a choice which is independent of the system.
The resolution of this paradox is not through adoption of a convention. It is resolved by recognizing that it is an abuse of terminology to use the terms “warming” and “cooling” to denote upward or downward trends in averages of temperature data in such circumstances. Statistics might go up or down, but the system itself cannot be said to be warming or cooling based on what they do, outside of special circumstances."
"[7] Peterson T. C., Vose R. S., An Overview of the Global Historical Climatology Network Temperature Database, Bulletin of the American Meteorological Society, 78 (12) December 1997, 2837–2849.
[8] Boehmer K., ISO and climate change: Delivering on the promise, ISO Bulletin, August 2002, http://www.iso.org/iso/en/commcentre/isobulletin/comment/2002/August2002.html "
The example more amply and accurately demonstrates the problem of why ISO could not set a standard to represent global climate change that would be accurate or statistically meaningful in a dynamic system such as that of earth's climate.
http://www.climateaudit.org/?p=1150
Next here is a comparison of the USHCN 2000 version (digital data downloaded from John Daly, but matched to figure in contemporary press release) to CRU. The CRU comes as monthly data - I made an annual average and then zero-ed on 1951-1980 to match GISS 1951-1980 centering. (In passing, CRU is supposed to have 1961-1990 centering, but I couldn’t replicate this at all!) The blue histogram shows the difference between HadCRU3 and GISS 2000. The maximum negative delta in the 1930s is -0.35 deg C and the maximum positive delta is 0.28 deg C. In HadCRU3, the record year remains 1934.
So as between CRU and Hansen’s crowd, it looks like Hansen’s crowd is adjusting things more. It would be nice to see what CRU is doing differently. But hey, they’re the Team and I guess we’ll never know.
When "there is no physical basis for choosing any one of these from the infinite domain of distinct mathematical options." Everything is fair game and grist to feed the propaganda mill.
When "there is no physical basis for choosing any one of these from the infinite domain of distinct mathematical options." Everything is fair game and grist to feed the propaganda mill.
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Yup. This really IS the problem.
I suspect that given a few days, even I could think of several very legitimate methods of computing "average temperature" that have never even been suggested, and have people argue that my methods were as good or better than any of those currently being used.
I don't mind metrics being suggested, but for someone to believe that there is a single value that can be all-encompassing for "global temperature" is demonstration that they are incapable of deep thought. The disparity of those metrics currently in use, and the vast number of possible methods that have been invented, in itself demonstrates that there is no obvious solution, and proves the point.
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