Posted by Peter Morcombe, April 2014
“Climate Science” is a strange discipline that makes all kinds of claims that lack any valid mathematical basis. For example, the Arrhenius hypothesis:
“The selective absorption of the atmosphere is……………..not exerted by the chief mass of the air, but in a high degree by aqueous vapor and carbonic acid, which are present in the air in small quantities.”
I write about “Climate Science” because it is used to justify a political agenda that aims to “mitigate” CO2 regardless of negative impacts on billions of people. Even though most “Climate Scientists” get their pay checks from governments they are reluctant to engage with members of the public who express doubt about the need to reduce the atmospheric concentration of carbon dioxide.
Before making a post I reach out to experts in the field. For example, Tom Peterson (GHCN), Albert Klein Tank (KNMI), Richard Alley (Penn State) and several scientists at the DMI helped with my posts on Greenland (here and here). When I wrote about the Unified Theory of Climate (here and here) Ned Nikolov provided many helpful comments. Scott Denning took an interest in my doubts about the Arrhenius theory (here and here). I think of these folks as “Good Sports” who don’t get offended when their ideas are challenged. They behave as real scientists should.
I was building a model of planetary atmospheres using FEA (Finite Element Analysis) when I came across this letter in “Nature”:
Robinson and Catling (R&C) have constructed physical models to explain temperatures at all heights for bodies that have significant atmospheres. Furthermore they have made their model available to the public. There are many possible uses including predicting temperatures on exo-planets.
I wrote a draft post and sent it to David Catling for comment. He was kind enough to answer in detail and with such effect that this post had to be completely rewritten. My expectation is that this is the first of many that will be based on the Robinson & Catling model. Enough of the preamble, let’s go kick the tires!
The R&C model is designed to run in “IDL” a powerful program marketed by the Exelis corporation. At first this seemed like a show stopper as my wife insists that her kitchen upgrade comes before my hobbies. Fortunately there is a freeware alternative so it was just a matter of minutes to install GDL (gnudatalanguage) that comes with my operating system (Linux “Mint”). I followed the instructions included in these files published by R&C:
AN_RC_MOD.pro and EXAMPLE.pro
The output was a plot of temperature vs. pressure in Titan’s atmosphere. Fortunately I had a copy of the HASI probe data handy so I compared the EXAMPLE model output with it and also with my calculations based on Nikolov & Zeller’s equations [=”N&K” in the chart below, vj].
The blue curve marked “HASI” is the published data from the Huygens probe. The R&C model matches the probe data really well whereas the N&K plot does not. So how does the R&C model work? It uses eight parameters to calculate the temperature against pressure. A critic might say he could match any curve given eight parameters to play with but most of R&C’s parameters are not under the modeler’s control:
- Ttoa Temperature at top of atmosphere (assumed as stratopause) [K]
- F1 Flux absorbed in channel ‘1’ (assumed to be “stratosphere”) [W/m2]
- F2 Flux absorbed in channel ‘2’ (assumed to be “troposphere”) [W/m2]
- F20 Flux absorbed in channel ‘2’ down to reference level p0 [W/m2]
- Fi Internal heat flux [W/m2]
- gamma Ratio of specific heats, Cp/Cv (see Eq. 8 of RC12)
- alpha Empirical adjustment to dry adiabatic lapse rate (see Eq. 10 of RC12)
- n Scaling parameter that relates tau ~ pn, where tau is gray thermal optical depth
(see Eq. 6 of RC12)
The only fudge factor I can see is the “alpha” used to tweak the lapse rate. Clearly this is necessary on Earth with oceans of water and on Titan with oceans of methane.
The R&C model is a fine achievement that provides a mathematical basis for gaining insights into atmospheric physics. The model shows three regions namely the stratosphere where radiative processes dominate, a transition region that occurs at a pressure of ~0.1 bar (tropopause) and below that a convective region (troposphere) where the lapse rate is defined as -g/Cp or less when vapors are present. It appears to correspond well with observations on all seven bodies in our solar system that have significant atmospheres.
The model also includes the effect of internal heat sources that are important in the case of the gas giants and it provides an explanation for the anomalous (negative) lapse rate in the upper Venusian atmosphere. When time allows I plan to become proficient enough in its use to be able to understand the work that R&C have already done, with the aim of applying the model to some questions that have puzzled me over the years. I hope that other amateurs will do the same.