My links to comments did not survive, so I added more information to help find the original comments in the original post.
The following comments are from Dr. Ronan Connolly and Dr. Michael Connolly. They are in answer to comments made on my review (see here) of their atmospheric physics papers. I’ve promoted the comments to a post because they are very enlightening and should be of general interest to our readers.
Dr. Michael Connolly’s comment below is in response to Dave (August 22, 2017 7:38AM and August 25, 2017 1:54PM).
In part, Dave says: “Two requests have already been made as to how this tetramer runs contrary to the law of mass action. A law that is best derived by a combination of the Gibbs free energy values for the reacting species. For the tetramer formation it is p (O8) = K p (O2)^4.”
The response also mentions a comment by Nick Stokes (August 22, 2017 10:34AM).
In part Nick says: “It seems that the data they are actually working from is measured pressure and temperature. So, they define molar density D = P/RT; the identification of that as density comes from the ideal gas law (which is ideal…).
So then, in Figs 4/5, they plot D against P. Is the slope of this not just 1/RT? And the “regime changes” just changes in T?”
Dr. Michael Connolly (I’ve edited this a bit for clarity) August 26, 2017 3:18AM:
I would like to thank Andy May for doing this blog post and all the participants for their interesting contributions. I am sorry that due to time constraints I could not contribute to the discussions as they were taking place. However, I have read all the contributions and I think the following observations might resolve many of the difficulties, but will also raise more problems (at least they do for me).
In paper 1 we reported that the slope of molar density (D = P/RT) plotted against pressure (P) is greater in the Tropopause – Stratosphere than in the Troposphere for all 13 million Radiosondes that we analysed.
Look at the video for Valencia that Ronan posted earlier in this thread (middle panel).
Link to video here.
This is a head scratcher, because according to the current theories of atmospheric behaviour, it should be the other way around (i.e. the slope should be smaller in the Tropopause-Stratosphere than in the Troposphere). As has been pointed out the slope should be 1/RT.
In the Troposphere T decreases with pressure. To increase the slope in the Tropopause –Stratosphere, T would have to decrease at a greater rate. (The slope is the reciprocal of T i.e. increasing T decreases the slope and decreasing T increases the slope). But the temperature does not decrease at a greater rate in the Tropopause, it stops decreasing all together, and in the Stratosphere it actually increases (See the top panel of the YouTube video Ronan posted).
The current explanation of the temperature profile in the Tropopause- Stratosphere region is that it is caused by UV heating of this region. But heating this region should decrease the slope of D versus P, which is the exact opposite of what happens. Therefore, a different explanation is required.
In paper 2 we suggest that a phase transformation from monomers to multimers, in the Tropopause – Stratosphere, if it took place, could explain the behaviour. An increase in the average molecular weight of the atmospheric gases in this region, would explain an increase in the slope of D versus P plot.
But is such a phase transition thermodynamically feasible? If not, then another explanation is required, and it may well be that another explanation will be found. However, now the only explanation we have come up with is the multimer hypothesis, and this is not without its own difficulties. For a gas phase reaction of the form nX2 ↔ (X2)n the value of the equilibrium constant (which is determined from the partial pressures of the reactants and products) can be used to calculate the direction of the reaction if the change in Gibbs free energy for the reaction is known.
For a closed system, it is sometimes possible to determine the value of the change in Gibbs free energy by experimentally changing the values of the state variables. However, in an open system this is not the case. In a closed system, the change in Gibbs free energy is a tradeoff between the heat of formation of the products and the change in heat capacity caused by changes in entropy(s) due to the reaction. However, in an open system, such as the atmosphere, where the value changes in the various components of Gibbs free energy (i.e. the heats of formation and changes in heat capacity of the reaction) are unknown; Gibbs is of no value.
This is very unsatisfactory, in section 2 of paper 2 we have attempted some heavily caveated “work arounds” but more experimental work is needed before the multimer hypothesis can be confirmed or rejected.
With respect to paper 3, in our day job we do a lot of work with heat pumps and heat exchangers and I have been awarded patents for novel designs of the same. For years a lot of our designs did not perform as theory predicted. It was only when we realized that we had had been neglecting through-mass mechanical energy transmission in fluids (as had everyone else) and that by taking this into account, that we could reconcile theory and performance. Steven Wilde (see here) in this thread said that there was no need to invent through-mass (non-acoustic) mechanical transmission which we call ‘pervection’. Well we did not invent it, nature did that all on its own. All we did was name it, measure it and now use it.
Dr. Ronan Connolly (also edited a bit) August 23, 2017 3:55PM:
Further research on our multimerization theory since our 2014 papers
Since those papers in 2014, we have been continuing our research into this phase change as well as into our multimerization theory. We have also been discussing our analysis with several prominent atmospheric physicists and chemists, and their comments have been generally encouraging.
Some commenters above (see Dave’s comment here) have wondered if our multimer theory could be tested under laboratory conditions. Yes, indeed, last year we carried out some preliminary experiments to reproduce tropopause/stratosphere temperatures and pressures in the laboratory. The results were suggestive of multimer formation, but the experiments were quite expensive and time consuming, and we don’t think we have collected enough data yet (in our opinion) to publish these findings. We do plan on completing these experiments at a later stage, but bear in mind we’re carrying out all this research in our spare time and at our own expense!
Still, in case you’re interested, we carried out a series of 8 experiments in which we evacuated dry air in a glass container to pressures down to about 20,000 Pa (200 mbar) and lowered the temperature using dry ice. We recorded the temperature and pressure of the air continuously throughout each experiment, and from these measurements we could also calculate the molar densities. Below about 200K we found that the molar density started to drop by a few percent, which is what we would expect from multimer formation. We also carried out several experiments using oxygen instead of air and found that the drop in molar density was about 5 times greater. Since air is only about 1/5 oxygen, this suggests that, if our multimer theory is correct, then oxygen is the main gas that is forming multimers.
We have also been in discussion with several groups about the possibility of analysing these experiments spectroscopically. In particular, we are looking at testing for changes in magnetism (monomeric oxygen is paramagnetic, but it is plausible that multimers could be diamagnetic), as well as testing for microwave emissions. [It has been reported by Spencer and Christy (1990) that the Tropopause is a source of unusual microwave emissions.]
Nick Stokes and Dave on plotting P vs. P/RT
When we first started analysing the weather balloon data, we expected it would be exactly how Nick Stokes and Dave described. We would have expected a plot of molar density (D=P/RT) vs. P to yield a simple linear plot of slope 1/RT. But, instead, the data consistently shows a bi-linear behaviour. We analysed over 13 million weather balloons (taken from over 1,000 stations with some data going back to the 1950s), and this bi-linear phenomenon occurred for all the balloons.
I showed this video in my reply yesterday, but in case anyone missed it, here are the plots for one year’s data for the Valentia Observatory station in Ireland. The D vs P plots are shown in the middle panels. For comparison, the top panels show the standard T vs P equivalents:
In all cases, the circular dots represent the experimental data. The two lines in the middle panels illustrate the change in slope. As Nick pointed out, this slope should in theory be constant (1/RT) for the entire plot. But, as Andy pointed out, it’s not.
I realise that many in the climate science field argue that if the data doesn’t match the theory, there must be something wrong with the data. However, we’re a bit more old-fashioned, so when we find an apparent conflict between the theory and the data, we try to consider the possibility that the theory might be wrong.
On our atmospheric temperature profile fits
For those who haven’t read this section yet, we point out there that, for a given balloon, after obtaining the linear fits for each of the two linear regions, you can then use the slopes and intercepts to estimate the atmospheric temperature profile. When you compare these estimates to the original observations, the fits are remarkably good (in our opinion), i.e., the residuals are very small. Andy has shown some of these plots in his post. We think it is striking that the entire atmospheric temperature profile can be described so well merely in terms of the fitting parameters of two (or sometimes three) straight line fits. To us, this suggests that using D vs. P plots could be a very powerful tool for meteorologists.