Wednesday, May 7, 2008

It Doesn't Add Up

This post is a little different because I am going to take you guys with me as a wander around a problem that has been festering in the edges of my mind for quite some time. (For those not lulled into a coma, there's a reward at the end of this lengthy meander.) I am hoping for insights (in the form of comments) that might help clear the fog. Here is the list of related questions that has me bogged down in some cloudy thinking:

  • What is a global mean temperature?
  • How do you measure it?
  • If we don't measure it directly, how is it put together, inferred, or made up?
  • How would you validate that the method is correct?
There are more percolating, but my thinking is so muddled that I couldn't force the questions to make sense as I tried to put them onto electrons (paper for the old-fashioned out there).

When I hear the words "global mean temperature", my mind drifts back to my days in an undergraduate thermodynamics class where I learned that, physically, the temperature of a gas is the average kinetic energy (energy of motion) of the molecules in the gas. So, based on that definition, I would assume that the global mean temperature has to relate to how fast the atmospheric molecules are bouncing around. This makes sense if the atmosphere was well mixed and no temperature differences exist. We know this is not the case, so I am back to square one.

Another possible way to define the global temperature is to look at the blackbody radiation emitted by the earth and use Stefan's law (or Wien's displacement law) to define the temperature. There, we run into a couple of problems. First, the earth isn't really a blackbody. It is more of a gray body because it does not absorb all the radiation incident on it, but we can adjust for that. Second, Stefan's law tells us that the energy flux (energy emitted per unit area) of the blackbody radiation is proportional to the 4th power of the temperature in Kelvin. This is the sticking point for me.

Let's look at some "average" winter temperatures for the Arctic and the Tropics (I am making up these numbers to show the mathematics). Let's assume that the Arctic has a day where the air temperature is 250 K (-23 degrees C and -9 degrees F) while the same day the Tropics has an average air temperature of 300 K (27 degrees C and 81 degrees F). If I ratio the two energy fluxes that result from these temperatures, we get the following:
  • (250 x 250 x 250 x 250)/(300 x 300 x 300 x 300) = 0.48225
Here's the problem with this number: there is over twice as much energy flux in the Tropics compared to the Arctic, and this example is a relative moderate temperature difference. For example, I did not compare Death Valley in the summer to Antarctica in the winter (these happen at the same time). It also means that relatively small errors in measuring this global mean temperature (still don't know for sure what this is) can result in fairly large errors in the value of the energy flux from the earth.

So, I finally get to ask my first question, "What is this global mean temperature that I keep hearing about?" I have yet to receive an answer that satisfies my physical intuition about problems like this. This leads to my second question, "How do you measure a global mean temperature?" My humorous guess is that you stick a thermometer in the rectal cavity of the earth and read the value that shows up, but I don't really think that is the method.

That is the lead in to my third question, "If we don't measure it directly, how is it put together, inferred, or made up?" I am well aware that the UK folks take a temperature, the NASA folks take a temperature, and a few other groups do so as well. Will someone please tell me what calculation they have done when they tell me that the "temperature anomaly" from January was +0.002 degrees C?

Finally, we have arrived at my final question, "How would you validate that the method is correct?" I don't understand the numbers that these groups spit out each month and year, but without telling me their methods (NASA is famous for this) or giving me access to their data (in many cases), I am supposed to believe the numbers produced of each of these groups. For those of you who don't know me, I'm not a take-my-word-for-it kind of guy.

For those of you who have made it this far, you probably think I am joking. I SERIOUSLY don't know what any of these global warming numbers mean. I was trained as a physicist and I work with complex equations every day, but the metrics that are being provided make NO sense to me. I am hoping that one of you out there that stumbles across this post will be able to point me to some book, journal article, or presentation that will explain the physics of these numbers that I keep seeing.

Until someone can help me out, I am going to keep believing my thermometer theory. That, and the fact that these guys taking our planet's temperature don't want us to know about the wool they are pulling over the eyes of their funding agencies.


To end a torturous post with something funny, here's a clip that may show the fate of these temperature anomalies ten years from now (in case you miss what the woman says at the beginning, it's just a satellite):


Kritter Krit said...

We have had. An anomaly.

Love it! The poor video announcer goes from thrilled to "Uh. Oh, crap. Clean up on Aisle 7..." in the span of three seconds.

I have absolutely nothing to offer in terms of your problem, though. Sorry, Sweetness. But then, math and science. Yeah. Not really my gig.

Robert (Bob) English said...

She says " A problem with the vehicle on the pad". Ummm..yeah...just a little problem...sure. It blew up!

Otherwise, you raise all good points. I believe there is a conference every year where the nation's leading economists and scientists attend. They pull equations out of a box on their way through the front door, and that is the equation they use to generate whatever data it is that they generate. THIS IS WHY everytime I read something about Wallstreet or our nation's economy not matching expectations, they are ALWAYS WRONG! Their models never work! I mean, seriously, hardly ever work! They need a fudge factor to produce the opposite result, then they might get the answer right even if their "showing of the work" is inaccurate.

Josh & Margo said...

Here is what I do when I don't know the answer to something...ask wikipedia because they know everything and it is always true. Well, wikipedia did not have any answers about global mean temp. I did however find a journal type article about it but it has lots of big words in it (kind of like your post) that I don't understand so I will just give you the link and you can check it out, you may have already seen it. Smith-comparison.pdf

Anonymous said...

you need a hobby

Russ said...

"you need a hobby"

This is HILARIOUS coming from someone leaving an anonymous comment to a post made by an unknown blogger on an unknown blog located in the smallest corner of the vast internet.

Kritter Krit said...

Seriously, Anon. I'd venture to say you might want to look into getting one as well.

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