How well can we model pressure broadening?

The mice clamored for actual examples of pressure broadened lines and how well they could be fit. This is a fairly specialized area, and papers appear in a very small number of journals, principally the Journal of Quantitative Spectroscopy and Radiative Transfer, the Journal of Molecular Spectroscopy, Molecular Physics and Applied Optics. Eli went and downloaded some papers from JQSRT about line broadening in CO2.

These are two examples from a diode laser spectrum of L. Joly, et al., "A complete study of CO2 line parameters around 4845 cm-1 for Lidar applications. JQSRT (2007), doi:10.1016/j.jqsrt.2007.06.003. The spectrum and the fit are shown in the top panels the residuals are shown in the bottom two panels for Voigt and Rautian profiles respectively. In this case the Rautian is better than the Voigt. In both cases the P12 line of the (201) <-- (000) transition is shown, on the left at 70 mbar, 292 K, on the right at 564 mbar, 291 K. Note the different scales on the frequency axes. The scale for the spectrum on the right is four times larger than for that on the left. UPDATE: The full width at half maximum (FWHM) of the line on the right is about four times larger than that on the left. The x-axis scales in the two graphs are different.











Next we can look at an example from V. Malathy Devia, D. Chris Benner, M.A.H. Smith, and C.P. Rinsland, "Nitrogen broadening and shift coefficients in the 4.2–4.5-
m bands of CO2" JQSRT 76 (2003) 289–307 showing 20 calculated spectra (bottom panel) and the residuals between the calculated and observed spectra (upper panel). This includes self broadening and broadening due to N2. The cell has a mixture of 12C and 13C CO2. In this case Voigt profiles were used. The largest line is P(30) for the 12CO2 (001) <-- (020) band. There is also an R(28) line from 13CO2. The broadening depends on the rotational quantum number, the and the pressure. Details can be found in the paper and are included in HITRAN.

UPDATE: If you want to learn about temperature effects see here and for more on pressure broadening see here and here

Eli is on vacation

Eli is on vacation, a little surfing now and again.  Back eventually, till then there is this to ponder

Statistical mathterbation has broken out everywhere, Beenstock is back, Force X is out there, and Eli was reading Andrew Gelman who posted a useful comment from George Box on models

It is widely recognized that the advancement of learning does not proceed by conjecture alone, nor by observation alone, but by an iteration involving both. Certainly, scientific investigation proceeds by such iteration. Examination of empirical data inspires a tentative explanation which, when further exposed to reality, may lead to its modification. . . .

Now, since scientific advance, to which all statisticians must accommodate, takes place by the alternation of two different kinds of reasoning, we would expect also that two different kinds of inferential process would be re- quired to put it into effect.
The first, used in estimating parameters from data conditional on the truth of some tentative model, is appropriately called Estimation. The second, used in checking whether, in the light of the data, any model of the kind proposed is plausible, has been aptly named by Cuthbert Daniel Criticism.

In the comments, Corey refers to a paper which purports to show that Kepler's model was a worse fit to the data than the Ptolemaic model, however that paper had some problems

In brief, Spanos shows that the residuals of the Keplerian model fit to Kepler’s original n = 28 data set are indistinguishable from white noise, while the residuals of the Ptolemaic model fit to a data set of one Martian year (~2 Earth years) of *daily observations from the US Navy Observatory* (n = 687) show unmistakable autocorrelation. I don’t mind telling you that my jaw literally dropped when I realized that Spanos was checking the statistical adequacy of the two models on *two different data sets*.

 This, however, to Eli was unimportant, because physics, chemistry and increasingly biology are built upon the principle of parsimony, and this is something that need be made much more explicit in teaching science at all levels.  Realizing this, the epicycles were roadkill.  Kuhn, Popper and the rest never really came to terms with the two bedrocks of science, parsimony and consistency to understand the world.

The developments of the last thirty years have provided such models for biology and climate science, but the stamp collectors have not caught up.  Cladistics is useful when simplicity is lacking.  Pattern recognition can be powerful, but it also masks understanding.  Neural nets have no sense of guilt.

Enjoy

Kevin Vranes opens a new window in the Exxon AR4 advent calendar....

At first there was no consensus, then everyone knew that a scientific consensus is unimportant, now, the latest tactic is that the holders of the consensus are feeling guilty. The first gun fired in this direction was the misleading article in the Telegraph telling about how the fourth Assessment Report from the IPCC will downgrade the risks from climate change. Today Tim Lambert has a link to a posting by Kevin Vranes, as fine an example of blaming the victim as exists.

We tried for years - decades - to get them to listen to us about climate change. To do that we had to ramp up our rhetoric. We had to figure out ways to tone down our natural skepticism (we are scientists, after all) in order to put on a united face. We knew it would mean pushing the science harder than it should be. We knew it would mean allowing the boundary-pushers on the "it's happening" side free reign while stifling the boundary-pushers on the other side. But knowing the science, we knew the stakes to humanity were high and that the opposition to the truth would be fierce, so we knew we had to dig in. But now they are listening. Now they do believe us. Now they say they're ready to take action. And now we're wondering if we didn't create a monster. We're wondering if they realize how uncertain our projections of future climate are. We wonder if we've oversold the science.

This can be understood as the second leg in a campaign lead by reactionary industry and think tanks and politicians to discredit the scientific study of climate. The first effort was FUD based joining public relations firms, think tanks and a small group of denialists with scientific reputations, and sometimes just reputations of scientific reputations, and thin ones at that. Eli discussed the basis of that stage: (reproduced here in full for the link adverse)

Anyone who has come up hard and fast against reality understands that there is neither a theory or a model that explains everything. There are always residuals, unexplained anomalies and people on the fringes who will hold onto those for dear life, weaving webs of conspiracy theories that focus only on what remains unexplained. This throws the baby out with the bathwater: the fringe theories might explain the residuals, but they can't deal with the basic facts of the situation.

The best theories and models deal with the largest extent of the evidence available using intellectually valid and understandable ideas with predictive power. Those with no tolerance for ambiguity are doomed to a life of carping. The study of elephant droppings is not as interesting as the study of elephants. (Motivated by comments of Michael Sherman, editor of Skeptic Magazine on CSPAN)

However, if the elephant dropping salesman, is loud and insistent he can attract an audience, and if someone is paying him a lot of money to attract elephant dropping customers, why, as Barnum said, no one ever went broke underestimating the intelligence of the American public.

The elephant dropping salesmen, unfortunately were the ones talking to the public, indeed were the ones getting money to talk to the public through right wing think tanks and their supporters. When a few of the science types realized that the only way to get the gravity of the situation across to the public was to start to talk to the public, the push back was ferocious. The purpose of the attack was to force the scientists back to the lab bench. In many cases it was successful. If you want to understand this consider the ferocity of the onslaught against Jim Hansen and Michael Mann. Mann's case is particularly instructive. Mann was a post-doc when he was coauthor of the Mann, Bradley, Hughes papers. The other two are very senior scientists. Why was Mann attacked and NOT Ray Bradley and Malcolm Hughes? The simple answer is that the other two retreated from the confrontation, Mann met it.

Within the last few years, the public has become aware that there is a scientific consensus on global warming, first in the civilized world, lately among the population in the United States. Al Gore's Inconvenient Truth has played an important role, packaging the basic issues in a way that is understandable and entertaining for the public. The next tactic of the denialists was to deny that a consensus exists, then to deny that the scientific consensus had any meaning, and now, we have the Rovian tactic of attacking the opponents strength to discredit them, here, by claiming that the holders of the consensus are having second, guilty thoughts because there are outstanding issues, and, horrors, they have made clear to the public what the risks are.

Don't worry, Kevin, be happy

UPDATE: Great minds think alike, Andrew Dessler pretty much agrees with Eli.

The residual problem ....

Anyone who has come up hard and fast against reality understands that there is neither a theory or a model that explains everything. There are always residuals, unexplained anomolies and people on the fringes who will hold onto those for dear life, weaving webs of conspiracy theories that focus only on what remains unexplained. This throws the baby out with the bathwater: the fringe theories might explain the residuals, but they can't deal with the basic facts of the situation.

The best theories and models deal with the largest extent of the evidence available using intellectually valid and understandable ideas with predictive power. Those with no tolerence for ambiguity are doomed to a life of carping. The study of elephant droppings is not as interesting as the study of elephants.

However, if the elephant dropping salesman, is loud and insistant he can attract an audience, and if someone is paying him a lot of money to attract elephant dropping customers, why, as Barnum said, no one ever went broke underestimating the intelligence of the American public.

(Motivated by comments of Michael Sherman, editor of Skeptic Magazine on CSPAN)