Sunday, March 23, 2008

The Problem of Choice (Making Assumptions)

One of my all-time favorite professors once told our class, "ALL models are wrong, but some are useful." He was basically letting us know that as scientists and engineers we are going to rely on models to do our jobs, but we couldn't let the model muddy up what we could measure or observe. The Bohr (or shell) model of the atom is an example of a model that is clearly wrong but extremely useful. This is the model of the atom that you may remember from your high school chemistry class. Many of the problems in high school chemistry, Chemistry 101, and Chemistry 102 can be explained by falling back to the shell model for the electrons circling the nucleus of the atom, but the quantum mechanical description of particle wave functions (and their associated probability density functions) are much more reflective of the true situation at the atomic level.

Besides letting us know that the models themselves could prevent a full understanding of a problem, there was a second pitfall that he wanted to let us know about. This pitfall was the fact that when we choose a particular model to analyze a problem that we inherit all the assumptions built in to the model. This poses a serious problem when the analyst doesn't know or understand the assumptions that are built into the model. It can have a serious impact on the usefulness of any results that come from using the model.

Let's take a short trip back to 1922 to examine the havoc that a model choice can create when an entire field of study allows its assumptions to go unexamined. You remember 1922, right? Here is a quick summary: Prohibition, Al Capone, a HUGE lack of computers, and you had to solve extremely complex differential equations by hand. Well, because like every one else, physicists are lazy, this often caused them to look for short cuts (or assumptions) to simplify solving these tough problems. In most cases, the assumptions we are still taught to make (as of 12 years ago) for solving these problems will yield solutions that match reality quite well.

That brings us back to what happened in 1922. Arthur Milne, a fairly distinguished mathematician and physicist, was working out some of the differential equations for the greenhouse effect. He reached a point in solving the problem that required that the boundary conditions be satisfied, and he assumed an "infinitely thick" atmosphere to make the problem easier. While it is not clear whether or not he had been drinking in spite of Prohibition or if Al Capone ordered him to assume an infinitely thick atmosphere, one thing that is very clear is that all of the global circulation models (GCMs) and other climate models use this assumption with one exception. The one exception is the climate model produced by Ferenc Miskolczi. Miskolczi had noticed the assumption in a series of equations and decided to follow the road less traveled. For all you hippies out there, he questioned the assumptions.

What was the result? A new term popped out in the solution to the differential equations. This new term showed that "runaway" global warming is not physically possible because it contradicts the energy balance equations and models that show runaway temperatures are not reliable. Another result was that Miskolczi had to resign his position at NASA in protest because NASA would not allow his work to be published. His work was finally pu
blished and here is an excerpt from his abstract, "The long standing misinterpretation of the classic semi-infinite Eddington solution has been resolved. Compared to the semi-infinite model the finite semi-transparent model predicts much smaller ground surface temperature and a larger surface air temperature. The new equation proves that the classic solution significantly overestimates the sensitivity of greenhouse forcing to optical depth perturbations."

Miskolczi has received some vindication in the last couple of years as research from Brookhaven National Laboratory has presented statistical evidence that the earth's response to carbon dioxide is greatly overestimate. Anyway, I guess that assumptions can make an ass out of more than just you and me.


Anonymous said...

Very good "article", I must say. Belongs in a newspaper as a letter to the editor. Or, maybe the U of A newspaper?

Kritter Krit said...


I mean, um, good article. ;)

Lora Lee said...

Have to agree w/ Kristy on this one What? I do love to read though so glad you are blogging so I have something more to read, even if I don't understand it. Hope ya'll are good.

Love ya

Anonymous said...

yeah russ!!!! keep posting.

Anonymous said...

From one politically incorrect person to another: Woo-hoo! Thanks for the informative post. Love, Suzanne

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