Wednesday, March 14, 2007

An open book test

In the comments over at Deltoid, note is made that Essex and McKitrick joined by one Bjarne Andresen have succeeded in getting their strangeness about temperature, Does a global temperature exist?, into the Journal of Non-Equilibrium Thermodynamics. This new candidate for the Chillingar and Khilyuk Cup is based on the same off the wall basic mistakes about thermodynamics and atmospheric temperature measurements that E&M put forth in their opus "Taken by Storm" and which was taken apart at Rabett Run(compare the figures to those the article), and at Deltoid and more Deltoid, and yet more Deltoid, and even MORE Deltoid (pay careful attention to Robert P's comments in the last one. Hopefully he has pen in hand at the moment to write to the journal with some of the folk over at NOAA). Still, they come back for more.

UPDATE: Hell's Handmaiden has some interesting comments on this

The test, dear mice, is to do the reading, and to explain why each of the following statements in the JNET article is a bowl of steaming crap.

To get you started, Eli will point out that there are no global temperature measurements, there are global temperature ANOMALY measurements. As is pointed out at the GISS website:

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

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

Eli is on deadline, feel free to join in. Best answers will be posted.
It is clear that there are many misconceptions about nonequilibrium temperatures fields. This paper serves to expose and identify them with specific reference to the measurement of climate change. They may be summarized by the following points, which are treated in detail later in the paper:
  1. Sums or averages over the individual temperatures in the field are not temperatures. Neither are they proxies for internal energy.
  2. Temperatures from a field (individually or averaged) neither drive dynamics nor thermodynamics. Instead dynamics are driven by gradients and differences, in temperatures and other variables.
  3. A global spatial average cannot be an index for local conditions, otherwise nonlocal dependence (i.e ”thermodynamics at a distance”) for local conditions would be required.
  4. The utility of any global spatial average of the temperature field as an index for global conditions has been presumed but not demonstrated.
  5. It is easily demonstrated that different spatial averaging rules over temperatures can have contrary trends in time (i.e. some increase while others decrease in time) when the two fields being compared have range-overlap, as they do in this context. This is demonstrated here in a basic example and subsequently with actual atmospheric temperature-field observations.
  6. No ground has been provided for choosing any one such statistic over the rest as the one proper index for global climate.
  7. If there are no physical or pragmatic grounds for choosing one over another, and one increases while the others decreases, there is no basis for concluding that the atmosphere as a whole is either warming or cooling.

41 comments:

Magnus said...

Other then the fact that I would have to redo my physic class I wonder if the fact that Bjarne Andresen is on the editor board have any thing to do with this... Not that I won’t to start speculations or anything.

http://www.degruyter.de/journals/jnet/272_5236_ENU_h.htm

Anonymous said...

"Temperatures from a field (individually or averaged) neither drive dynamics nor thermodynamics. Instead dynamics are driven by gradients and differences, in temperatures and other variables."

Unless you are talking about melting ice pack, that is.

Clearly, simply raising the air temp in Greenland or Antarctica above the melting point of water can have a quite dramatic dynamic effect, as anyone who has ever seen a calving glacier will appreciate.

jimbobboy said...

Wowie zowie!
These guys have been playing 3-card Monte for so long I'm not sure they remember where the Queen is! Here's the deal. Watch the lady ...
____________________________
"There is no global temperature. The reasons lie in the properties of the equation of state governing local thermodynamic equilibrium, and the implications cannot be avoided by substituting statistics for physics. Since temperature is an intensive variable, the total temperature is meaningless in terms of the system being measured, and hence any one simple average has no necessary meaning. Neither does temperature have a constant proportional relationship with energy or other extensive thermodynamic properties.
Averages of the Earth’s temperature field are thus devoid of a physical context which would indicate how they are to be interpreted, or what meaning can be attached to changes in their levels, up or down."
____________________________
Didja see where he picked up the Q and the J at the same time? It was pretty slick. Once again, in slow motion:
____________________________
"Neither does temperature have a constant proportional relationship with energy or other extensive thermodynamic properties."
____________________________
Hmmm ... I must have missed class the day they said that temperature and some extensive property -- oh let's just say internal energy, shall we? -- must be directly proportional for a change in one to be inferred from a change in the other. I do seem to recall that, even in mixed-phase systems, with sufficient information (like how much there is of what), system temperature as a weighted average does have an unequivocal physical meaning, and it is straightforward to calculate internal energy from it (or vice-versa). And, since in the case of the earth we do care about internal energy, and we do know how much there is of what, and we only care about functional dependence over a narrow range of conditions, it would seem that regional and global temperatures are ummm ... kind of meaningful.
Or perhaps I'm missing something that could have helped me out a lot when I was asked to calculate system internal energy from a set of constituents and temperature. "Bother me not with your fictitious example, ye white-haired muggins! There is no such thing as a system temperature, and I give you Ross 'Prince of Protractors' McKitrick as my authority! Now, if you'll excuse me, there's a cold one at the Student Union with my name on it."
I wonder how it would have worked.

Andrew Dessler said...

I sat next to Essex at a banquet following a meeting last summer and he told me about this. He truly believes it, and I decided that arguing was pointless. (it was an interesting table --- other members were Pielke Sr and McKitrick)

The main problem I had with it then (and still do) is their statement that the atmosphere is not in equilibrium. It is not clear what this means exactly ...

I suppose I should (as Eli would put it) RTFP, but I think I have better things to do ...

Anonymous said...

What is really being implied by the "global warming" claim, of course, is that the earth system is taking in more energy (from the sun) than it is emitting back to space.

There are many ways of gauging (tracking) this, of course. The one that has been chosen -- global average surface temperature anomaly -- is just one of them.

One really has to wonder what these people would find to complain about if "global warming" had instead been termed "Polar Warming"(or even broken down into the specific subsets "Arctic Warming" and "Antarctic Warming") -- since many of the potential future problems (eg, sea level rise) are linked in one way or another to temperature changes in the arctic and antarctic.

I'm sure they would find something to complain about -- probably say " 'Arctic Warming' is meaningless since you can't average the temperature in Nome and Anchorage" (that would be the temp in Fairbanks, right?).

There's really no way to win an argument with such people.

Anonymous said...

You gotta just love it when non-scientists try to sound scientific by bandying about buzzwords like they would a badminton birdie -- even inventing some cute terminology: "thermodynamics at a distance" (described by ME&B -- pronounced "Me and B" -- as "nonlocal dependence for local conditions" )

Kinda reminds you of "Bell's Inequality" don't it?

Nobel committee: Take note!

EliRabett said...

Following Essex, NOTHING is ever in equilibrium and all of equilibrium thermo has to be thrown out. Prigoginism to the nth.

Be that as it may, many of the statements he made are simply incorrect or based on false assumptions. This article really calls for a serious rejoinder.

Anonymous said...

The "no global temperature" argument can surely be applied at progressively smaller scales to deduce that there is no meaningful "temperature" in the UK, or in Lancashire, or in Manchester, or on my street, or in my back garden, or around this table, or in the bulb of my thermometer?

coby said...

It is easily demonstrated that different spatial averaging rules over temperatures can have contrary trends in time (i.e. some increase while others decrease in time)

Ugh, they're not still waving around that xls spreadsheet where they sometimes substitute missing measurements with 0 degrees and they sometimes don't, are they?

Anonymous said...

While it is certainly true that employing a broad spectrum of averaging methods and being inconsistent about their application can lead to a broad spectrum of results, this does not speak to what was actually done by NASA in this case.

By diving (and subdividing) into small regions (and representing the temp change within each small region with the average temp change over the region), NASA has already accounted for the "extensive vs intensive" issue that ME&B harp on.

But NASA has done much more in the process. They have compiled information about and then tracked how each region and subregion has behaved. This information is used as a cross check on what the mean global anomaly is doing.

If we tracked surface air temperature over time from every square inch of the earth's surface, few would argue that we could not then draw conclusions about whether the air at the surface of the earth was warming or cooling as a whole.

For example, if all the temperatures went up, we could conclude it was warming. If all went down, cooling.

But we could do much more because, since the temperature measurement at each location correlates directly with the average translational energy of air (N2, O2, etc) molecules in the "parcel" of air above the surface, each temp measurement would represent the same "extensive" thing (in this case translational energy).

A change in the temp of each parcel (temp anomaly) would represent the amount of translational energy lost or gained by each parcel.

The total obtained by summing all these together would represent an actual physical quantity -- the amount of energy lost or gained as a whole (ie, by all the parcels)

So dividing this total by the number of measurements (ie, simple arithmetic average) would also mean something physical (the average change in the translational energy of a parcel of air above the earth's surface).

So, the ME&B argument basically boils down to the following claim: "there is no way of using averaging to 'fill in the gaps' in order to come up with a reasonable estimate for the changes occurring in those gaps" (in this case, parcels of air above small "patches" of the earth).

They have claimed something that is clearly false. Any good engineer knows this (and regularly does it, though not necessarily for the earth's surface) -- and so does NASA.

Anonymous said...

"Following Essex, NOTHING is ever in equilibrium"

...especially in the "Climate Auditosphere", the paragon of "far-from-equilibrium systems".

Ian said...

I propose an experiment.

Let's place Essex, McKitrick and Andresen in a large pot (much like the one depicted in those old cartoons about cannibals).

We light a fire under the pot.

Clearly if they're correct it is meaningless to talk about an average temperature of the pot since it is a non-equilibrium thermodynamic system.

That being the case, they should easily be able to spend a few hours in the pot.

bigcitylib said...

Their argument proves too much. You might say that the average price of a home in the U.S. is a meaningless figure, since people don't by a home in the U.S. but in cities like Miami or New York. But then the average of a home Miami is a useless figure, because people don't by in Miami, they by in a particular neighborhood.

Also the claim these guys make (which I can find in several news stories but not in the paper) that the calculation of the average planetary temperature is "political" is clearly false. The concept has been in use forever in, among other things, scientific popularizations of planetary astronomy. How do you get across that Venus is hotter than Mars? The concept does not have its roots in the GW debate.

EliRabett said...

Big City has a good point, but it becomes an excellent point if you realize that what GISS and the Hadley center do to measure temperature anomolies is average changes in temperature at locations.

This would be the same as looking at the average change in prices in Miami and New York and Columbus or the changes in prices in all the neighborhoods in Miami. Comparing, or averaging the differences are much more informative than the absolute prices themselves (OK the absolute prices say that NY is more expensive than Columbus, but Miami is hotter than NY.....

Anonymous said...

World breaks temperature records


Staff and agencies
Friday March 16, 2007
Guardian Unlimited
http://www.guardian.co.uk/weather/Story/0,,2035667,00.html
"The world experienced its warmest period on record during this year's northern hemisphere winter, the US government said today.

The National Oceanic and Atmospheric Administration report said the globally averaged combined land and sea surface temperature for December to February was the highest since records began in 1880.

During the three-month period, known as boreal winter, temperatures were above average worldwide, with the exception of Saudi Arabia, Iraq, and areas in central United States."
[end quotes]
////

But as everyone knows, all the energy that boosted the air temperature over the vast majority of the world's surface was "taken" from Saudi Arabia, Iraq, and areas in central United States.

Anonymous said...

Funny that the temperature went down in Iraq. I would have guessed the opposite.

Perhaps they were measuring in a cold spot -- Condi Rice's hotel room on her last visit to Baghdad.

Anonymous said...

The thing that I find most puzzling (amazing, really) about this is that the Journal of Non-equilibrium Thermodynamics would publish a paper that does not even focus on non-equilibrium thermo and that talks about something (averaging) most people learn about in junior high school.

They must be really hurtin' for submissions. That's the only explanation I can come up with.

Joel Shore said...

I've been looking at Figures 2 and 3, which I suppose they would say are the real "meat" of the paper in the sense that they show how the temperature trend in their 12-city data set depends on the way that they average.

In particular, in Fig. 2, they do it by essentially taking different "moments" where the r=1 case corresponds to a regular arithmetic average and r=2 is what one would call the root-mean-square. They plot the temperature trend per decade that results as a function of r for r values ranging from -125 to 125. It is true that you see the trend depend significantly on r...but this is only so dramatic because they are using such a huge range of r's. What I think they are doing, essentially, is detecting just the trend of the highest-temperature station in the limit of large positive r and of the lowest temperature station in the limit of large negative r.

Their graph actually shows, to the degree one can see it, that as long as r is in some reasonable range, say 0 to 3, the temperature trend will differ very very little from what you get by conventional r = 1 averaging.

I have no idea how you would justify using an r very different from 1. It seems completely silly to me.

Anonymous said...

It's somewhat curious that an economist (McKitrick) would claim that "there is no such thing as an average global temperature", given that his own field of economics calculates and uses something analogous -- "average global per capita income".

"Temperature" is measure of (directly proportional to) the "average translational kinetic energy per molecule (or atom)" (in a volume of gas, for example).

"Per capita income" is a measure of the "average income per person" (in a country or region, for example).

So, McKitrick apparently sees no problem with the World Bank's (and other economists') calculation and use of a global average for the "per capita income", but when it comes to climate scientists' calculation and use of a global average for "surface air temperature", he has a hissy fit.

McKitrick has directly demonstrated how much physics he knows (very little), with his use of Celsius in the Stefan-Boltzmann equation. But he has also demonstrated (at least indirectly) how much economics he knows.

John A said...

Not really much of an answer is it Eli?

After Lambert getting his pasty white arse kicked for claiming that irreversible thermodynamic changes in equilibrium systems don't involve anything like entropy and that cold flows to hot, he still tries for a title of "Most Useless Uninformed Critic on the Blogosphere" by attacking McKitrick once again.

I note that Lambert, being a terminal coward, doesn't bother tangling with Andresen or Essex but instead goes for McKitrick in yet another desperate attempt to rehabilitate the Hockey Stick or the miscreants who perpetrated it.

At least Essex, Andersen and McKitrick managed to get through peer-review which is more than can be said for you or the wretched Lambert. I suppose we wait in vain for a Rabett/Lambert paper refuting the paper point-by-point?

I guess that you'll like to extend your sphere of ignorance by working out what the difference between equilibrium and non-equilibrium systems are, we can start the intellectual and public arse-kicking that you desperately require.

Oh and we'll take on "anonymous" first:

It's somewhat curious that an economist (McKitrick) would claim that "there is no such thing as an average global temperature", given that his own field of economics calculates and uses something analogous -- "average global per capita income".

No that's exactly the sort of thing that McKitrick would point out as an example of a statistical composite that has no fundamental meaning. Economists create and use statistical metrics all the time - they don't go around claiming that these constructs really exist except as a way to measure change within an economic system.

For example, inflation is a statistical composite that is used to measure the general rise in prices of commodities, but there is no fundamental theory that says it must be a simple weighted average rather than a geometric mean.

Similarly the "global temperature" is a statistical composite of a simple weighted mean with no fundamental mathematical or physical theoretic reason why it should be calculated in one way rather than another other than by convention.

Of course subtleties like fundamental theory fail to spark the interest of the desperately ignorant, preferring insults to thinking.

Anonymous said...

For those not familiar with use of the "global average per capita income" (referred to above), it's basically used as a baseline to which per capita income for a particular country (or region) is compared, as in this example.

Anonymous said...

John A claims (with no proof other than ME&B's nonsensical paper that uses Celsius instead of Kelvin temperatures in the Stefan Boltzmann radiation equation)

"Similarly the "global temperature" is a statistical composite of a simple weighted mean with no fundamental mathematical or physical theoretic reason why it should be calculated in one way rather than another other than by convention."

Have troubles with reading, John A? or just comprehending (or just with physics in general)?

"Temperature" is measure of (directly proportional to) the "average translational kinetic energy per molecule (or atom)".

Anonymous said...

And by the way, John A, if you actually read what I said above (that means "translating the little squiggly lines"), it was about per capita income, not inflation.

John A said...

Oh dear, anonymous puts his foot in it again.

"Temperature" is measure of (directly proportional to) the "average translational kinetic energy per molecule (or atom)".

I'll have to use large letters and type slowly....

ONLY IF THE SYSTEM IS IN THERMODYNAMIC EQUILIBRIUM.

There that's difficult to understand isn't it? Now I assume that "anonymous" is a recent graduate of the "Lambert School of Physical Ignorance" and doesn't know what thermodynamic equilibrium is, which means I'll have to type even slooooooower next time.

How slow can I go? It all depends.

John A said...

Anonymous said...

And by the way, John A, if you actually read what I said above (that means "translating the little squiggly lines"), it was about per capita income, not inflation.


and what I wrote in reply was:

No that's exactly the sort of thing that McKitrick would point out as an example of a statistical composite that has no fundamental meaning. Economists create and use statistical metrics all the time - they don't go around claiming that these constructs really exist except as a way to measure change within an economic system.


Oh dear, this is much too easy. It must be my day for "Whack an Idiot"

Anonymous said...

It's your day all right, John.

Today and every other day.

John A said...

I must be one lucky guy to have such opponents who make me look so good.

Anonymous said...

John, now that you have satisfied yourself with the self-flagellation, perhaps you might address some physics?

For example, why do your physics heroes (Neinsteins all) use Celsius instead of Kelvin temperatures to illustrate temperatures "appear[ing] in connection with blackbody radiation" (ie, from Stefan Boltzmann radiation Law)?

Why dey do dat, John?

John A said...

John, now that you have satisfied yourself with the self-flagellation, perhaps you might address some physics?


You haven't responded to my points about thermodynamic equilibrium or statistical composites.

I'm waiting for a response to those things first.

Anonymous said...

Johnboy, Johnboy, Johnboy,

As they say in computer science: garbage in (Celsius in Stefan Boltzmann) garbage out.

bigcitylib said...

John A wrote:

"Economists create and use statistical metrics all the time - they don't go around claiming that these constructs really exist except as a way to measure change within an economic system."

Actually, I have never heard of an economist claiming that "average global per capita income" does not exist. Can you point to an example. Otherwise, check-mate, matey.

Anonymous said...

John A knows some of the buzzwords, to be sure: "statistical composites", "non-equilibrium thermodynamics", and seems to use them at every opportunity (mixed in with a healthy helping of the usual hackneyed insult: "ignoramus", etc, etc), but that seems to be as far as he can take it.

He apparently is oblivious to the fact that using Celsius temperatures in the Stefan Boltzmann equation is nonsense equaled only by the Mad Hatter's statements in Alice in Wonderland.

Or then again, perhaps he is aware of this and that is the very reason he so quickly changed the subject when pressed to explain why ME&B made such an elementary error (and why the referees failed to catch it).

Anonymous said...

John A (from above) "After Lambert getting his pasty white arse kicked...

and more John A:

"I note that Lambert, being a terminal coward,...
and yet more John A:

"...which is more than can be said for you or the wretched Lambert...


What brought on the rant about Lambert here anyway?

I thought we were talking about "average global temperature" and then this guy comes in and immediately heads off into the far corner of left field: "Lambert this and Lambert that.."

Anonymous said...

John A:

In case you don't look on the other thread, here's my response to the false claim made by yourself and friends McKitrick, Essex and Andresen that one is not warranted in assuming [Local] 'thermodynamic equilibrium' for air near the surface of the earth (ie, Local Thermodynamic Equilibrium).

The condition for local thermodynamic equilibrium (LTE) is that

"the mean free path of the atom is very small compared to the distance over which the temperature changes,"

From "Thermodynamic Equilibrium, Local and otherwise"
Copyright © Michael Richmond.


Under such conditions, "the atom will collide many times with other atoms, all of the same temperature, before it can possibly reach some region with a different temperature. In this case, the speed of atoms within some small region may very well be described by a Maxwell-Boltzmann distribution with a definite temperature."

http://spiff.rit.edu/classes/phys440/lectures/lte/lte.html


So, to determine whether the air at the surface of the earth is in LTE, we must determine whether the mean free path of an "air" molecule (Oxygen or nitrogen, for the earth's atmosphere) is small compared to the distance over which temperature changes significantly.

or, what is equivalent: determine how much the temperature changes for an elevation gain that is equal to the mean free path of an oxygen (or nitrogen) molecule at temperature and pressure (1 ATM) typical near the earth's surface.

If this temperature change is very small over the mean free path in question, then we can be confident that we have met LTE.

So, is this temperature change very small over the mean free path in question?

For O2 (oxygen)at one atmosphere and 25 °C, the Mean free path is only 9.7 × 10^(–6)cm

or about 10^(-5)cm

where the ^ means "raised to the power"

http://www.iupac.org/goldbook/M03778.pdf.
For nitrogen (N2) it’s of the same order

So, how much does the temperature of the atmosphere change if we move upward over a distance equal to the mean free path of Oxygen gas at 1 ATM and 25 deg C? --ie, if we move up by 10^(-5)cm

For that we need the adiabatic lapse rate, defined as the negative of the rate of change in temperature with height observed while moving upwards through an atmosphere.

Dry adiabatic lapse rate
The DALR is a constant + 9.78 °C/km
Moist adiabatic lapse rate
MALR 4.9 °C/km

http://en.wikipedia.org/wiki/Lapse_rate

Using the larger of the two values above (dry lapse rate), gives 9.78x10^(-5) deg C per cm rise in elevation

or roughly 10^(-9) deg C per every 10^(-5)cm rise in elevation

so, in other words, for dry air at the earth's surface, the temperature changes only by 10^(-9) deg C (1 billionth of a deg C!) for a rise in elevation that is equal to the mean free path of Oxygen at the surface, when the temperature at the surface is about 25C.

Or we can look at it the other way:

Suppose we assume that we gain just enough elevation that the temperature changes by 1/10,000th of one percent (0.000001) of an assumed starting value of 25 deg C at the surface or by 0.000025 deg C.

How much elevation elevation gain will that take?

0.000025 deg/ (9.78 deg / km) = 2.6 x 10^(-6)km = 0.26cm

How many times the mean free path is this?

0.26cm/ (mean free path of O2 at 25C and 1 ATM) = 0.26/(9.7 x 10^(-6)cm) = 26000 times!

or in other words, the change in elevation that produces a temperature change of 1/10,000th of one percent is equal in length to 26,000 times the mean free path!



So, in the above case, the mean free path is a tiny fraction of the distance over which the molecule would have to move to experience a temperature change of 1/10,000th of one percent (a tiny fraction of the initial temperature!)

If one calculates the distance the molecule would have to move upward to experience a temperature change that is 1% of the above starting value (25 deg C), it comes out 260 million times the mean free path, or, the mean free path is 1/260,000,000 this distance.

In other words, the average distance the (Oxygen or nitrogen) molecule actually moves in air at 25 C at the earth's surface before it collides with another gas molecule (mean free path) is vanishingly small in comparison to the distance the molecule would have to move to find itself in a region of higher temperature.

Recall the criterion for satisfying Local Thermodynamic equilibrium:
"the mean free path of the atom is very small compared to the distance over which the temperature changes,"

To a very high degree of accuracy, the criterion for local thermodynamic equilibrium as described above is met for air at the earth's surface.

Anyone who claims otherwise is either blowing smoke in your face or inhaling it himself (and it sure as hell ain't cigarette or cigar smoke!)

Anonymous said...

I'm still waiting for the inevitable question about the above analysis , which uses vertical variation in air temperature (vertical gradient) to show that local thermodynamic equilibrium is applicable for air at earth's surface.

Since no one asked -- and probably never will, since there were undoubtedly only a few people reading at the start (if that), and that may have dropped to just a couple (or less)--, I'll ask the question (of myself?):

What about horizontal air temperature gradients (variation over distance) at the earth's surface? Can't they be even greater than the 9.78 deg C/km given above for vertical gradient?

Well, glad I asked.

The answer is "Yes, in some cases."

But, in most cases, not by much and even in the extreme cases, it has no impact on the conclusion of the above analysis that "air at the surface of the earth is in local thermodynamic equilibrium."

Even though in most cases the vertical temperature gradient is greater than the horizontal, nonetheless, in some cases, the opposite is true.

For example, along a sea coast at night the gradient might be slightly higher in the horizontal direction (than the 9.78C/km given for the vertical) as a result of the land's having cooled more quickly than the water (and thereby producing a "land breeze", by the way), as described here.

In the Land breeze example given in the link the temp gradient was 12 deg C/km (typical for such cases), slightly higher (though not by much) than the 9.78C/km vertical (dry adiabatic lapse rate) value.

But except in very extreme cases, the horizontal temperature gradients to be expected in air at the surface of the earth are still going to be of the same order of magnitude as the 9.78 deg C/km vertical gradient.

If the temperature varied by as much as 100 deg C over a 1km distance, for example (which would be an order of magnitude change over the 9.78 deg C/km vertical variation), and one started in air at 0 deg C, just moving 1000m would cause water to boil!

While that might be convenient for cooking your dinner, it ain't going to happen, at least not outside the crater of an active volcano (and perhaps papers published in Journal of Non-Equilibrium Thermodynamics)

So the numbers obtained in the above analysis are not going to change by even a factor of ten -- which itself would not mean diddly- squat to the conclusion that "air at the surface of the earth is in local thermodynamic equilibrium".

By the by the way, "wind" (in the case of the land breeze, for example) does not appreciably affect the above analysis for two reasons.

First, the speed of the molecular constituents of air (nitrogen and oxygen, essentially) near the surface of the earth due to their temperature is normally much greater (an order of magnitude or better in most cases) than the wind speed (speed of translation of the molecules as a large group)

Compare the mean speed of nitrogen molecules in a container at 0 deg C, for example (455m/sec) to even a 60 mph wind (about 27m/sec) -- an order of magnitude difference.

But that's not all or even the most important thing: "winds" are comprised of large numbers (ie, large volume) of molecules moving together as a group, so the conditions still exist for local thermodynamic equilibrium within the volume of air that comprises the wind.

This illustrates very well the source of confusion among some with the concept of "local thermodynamic equilibrium".

Some look at the atmosphere and say that "the air is almost constantly moving, so how can the condition of 'equilibrium' (thermodynamic or any other kind) ever possibly apply?"

The very question is based in common sense ideas of what the word "equilibrium" means: balanced, motionless.

"Local Thermodynamic equilibrium" means something very specific (see above), and like other common sense notions (eg, about adding speeds of things in relative motion) applying the "common sense" idea of "equilibrium" in this case is simply incorrect.

ankh said...

So, um, the journal's title uses the word.

"the Journal of Non-Equilibrium Thermodynamics. "

What sense is that?

Chris O'Neill said...

""Temperature" is measure of (directly proportional to) the "average translational kinetic energy per molecule (or atom)".

ONLY IF THE SYSTEM IS IN THERMODYNAMIC EQUILIBRIUM."

In that case which formula for "average" do we use?
According to Essex et al, any formula for average is just as good as another (nth root of mean of nth powers where n is anything you like). Trouble is, they all give different answers. According to the logic in Essex et al, this means there is no such thing as average translational kinetic energy per molecule in an equilibrium system either.

Anonymous said...

In the case in question (for which climate scientists take and average temperature anomalies) -- for air at the surface of the earth -- local thermodynamic equilibrium does hold, notwithstanding the contrary claim of John A (and the paper's authors) made without any evidence whatsoever.

See the two detailed comments/analyses regarding that very issue just above.

Chris O'Neill said...

""Temperature" is measure of (directly proportional to) the "average translational kinetic energy per molecule (or atom)".

ONLY IF THE SYSTEM IS IN THERMODYNAMIC EQUILIBRIUM."

A thermodynamic system doesn't have a unique "temperature" if it is not in equilibrium (according to http://en.wikipedia.org/wiki/Temperature ). But that doesn't preclude defining an "average temperature" with practical and meaningful physical properties for such a system. i.e. systems in equilibrium have a "temperature" while systems out of equilibrium have an "average temperature".

Anonymous said...

That may be, but it actually does not matter in this case because the air at the surface of the earth is in local thermodynamic equilibrium and therefore does have a corresponding temperature -- and this temperature actually is directly proportional to the average translational kinetic energy of the molecules.

John A's (and the paper author's) implication that air at the surface is not in thermodynamic equilibrium is simply false.

And actually, practically speaking every measured temperature is an average temperature because every means of measuring temperature takes some amount of time and therefore involves averaging over time.

Anonymous said...

For those who are not convinced by physical arguments (calculations) like those above and need the authority lent by credentials, here's what the people at the National Radio Astronomy Observatory have to say on the subject of thermodynamic equilibrium:

"The [earth's] atmosphere is not in full thermodynamic equilibrium, but it is in local thermodynamic equilibrium (LTE)."


From course notes on Radiative Transfer put out by the Radio Astronomy Observatory, U o f Virginia


The upshot:
Because a small parcel of air at the surface is in LTE, it does have a unique temperature (contrary claims notwithstanding).

This temperature can be (and is) measured and is proportional to the mean translational kinetic energy of the "air" (N2, O2) molecules within that parcel.