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Simple physics and climate

Filed under: — rasmus @ 12 November 2013

No doubt, our climate system is complex and messy. Still, we can sometimes make some inferences about it based on well-known physical principles. Indeed, the beauty of physics is that a complex systems can be reduced into simple terms that can be quantified, and the essential aspects understood.

A recent paper by Sloan and Wolfendale (2013) provides an example where they derive a simple conceptual model of how the greenhouse effect works from first principles. They show the story behind the expression saying that a doubling in CO2 should increase the forcing by a factor of 1+log|2|/log|CO2|. I have a fondness for such simple conceptual models (e.g. I’ve made my own attempt posted at arXiv) because they provide a general picture of the essence – of course their precision is limited by their simplicity.

However, the main issue discussed in the paper by Sloan and Wolfendale was not the greenhouse effect, but rather the question about galactic cosmic rays and climate. The discussion of the greenhouse effect was provided as a reference to the cosmic rays.

Even though we have discussed this question several times here at RC, Sloan and Wolfendale introduce some new information in connection with radiation, ionisation, and cloud formation. Even after having dug into all these other aspects, they do not find much evidence for the cosmic rays plying an important role. Their conclusions fit nicely with my own findings that also recently were published in the journal Environmental Research Letters.

The cosmic ray hypothesis is weakened further by observational evidence from satellites, as shown in another recent paper by Krissansen-Totton and Davies (2013) in Geophysical Research Letters, which also concludes that the there is no statistically significant correlations between cosmic rays and global albedo or globally averaged cloud height. Neither did they find any evidence for any regional or lagged correlations. It’s nice to see that the Guardian has picked up these findings.

Earlier in October, Almeida et al., 2013 had a paper published in Nature on results from the CLOUD experiment at CERN. They found that galactic cosmic rays exert only a small influence on the formation of sulphuric acid–dimethylamine clusters (the embryonic stage before aerosols may act as cloud condensation nuclei). The authors also reported that the experimental results were reproduced by a dynamical model, based on quantum chemical calculations.

Some may ask why we keep revisiting the question about cosmic rays and climate, after presenting all the evidence to the contrary.

One reason is that science is never settled, and there are still some lingering academic communities nourishing the idea that changes in the sun or cosmic rays play a role. For this reason, a European project was estaqblished in 2011, COST-action TOSCA (Towards a more complete assessment of the impact of solar variability on the Earth’s climate), whose objective is to provide a better understanding of the “hotly debated role of the Sun in climate change” (not really in the scientific fora, but more in the general public discourse).

Oldenborgh et al. (2013) also questioned the hypothesised link between extremely cold winter conditions in Europe and weak solar activity, but their analysis did not reproduce such claims.


  1. T. Sloan, and A.W. Wolfendale, "Cosmic rays, solar activity and the climate", Environ. Res. Lett., vol. 8, pp. 045022, 2013.
  2. J. Krissansen-Totton, and R. Davies, "Investigation of cosmic ray-cloud connections using MISR", Geophysical Research Letters, vol. 40, pp. 5240-5245, 2013.
  3. J. Almeida, S. Schobesberger, A. Kürten, I.K. Ortega, O. Kupiainen-Määttä, A.P. Praplan, A. Adamov, A. Amorim, F. Bianchi, M. Breitenlechner, A. David, J. Dommen, N.M. Donahue, A. Downard, E. Dunne, J. Duplissy, S. Ehrhart, R.C. Flagan, A. Franchin, R. Guida, J. Hakala, A. Hansel, M. Heinritzi, H. Henschel, T. Jokinen, H. Junninen, M. Kajos, J. Kangasluoma, H. Keskinen, A. Kupc, T. Kurtén, A.N. Kvashin, A. Laaksonen, K. Lehtipalo, M. Leiminger, J. Leppä, V. Loukonen, V. Makhmutov, S. Mathot, M.J. McGrath, T. Nieminen, T. Olenius, A. Onnela, T. Petäjä, F. Riccobono, I. Riipinen, M. Rissanen, L. Rondo, T. Ruuskanen, F.D. Santos, N. Sarnela, S. Schallhart, R. Schnitzhofer, J.H. Seinfeld, M. Simon, M. Sipilä, Y. Stozhkov, F. Stratmann, A. Tomé, J. Tröstl, G. Tsagkogeorgas, P. Vaattovaara, Y. Viisanen, A. Virtanen, A. Vrtala, P.E. Wagner, E. Weingartner, H. Wex, C. Williamson, D. Wimmer, P. Ye, T. Yli-Juuti, K.S. Carslaw, M. Kulmala, J. Curtius, U. Baltensperger, D.R. Worsnop, H. Vehkamäki, and J. Kirkby, "Molecular understanding of sulphuric acid–amine particle nucleation in the atmosphere", Nature, vol. 502, pp. 359-363, 2013.
  4. G.J. van Oldenborgh, A.T.J. de Laat, J. Luterbacher, W.J. Ingram, and T.J. Osborn, "Claim of solar influence is on thin ice: are 11-year cycle solar minima associated with severe winters in Europe?", Environ. Res. Lett., vol. 8, pp. 024014, 2013.

35 Responses to “Simple physics and climate”

  1. 1
    Blair Dowden says:

    This is a nice supplement to professor Archer’s climate modelling course. However, I was not able to understand equation (1) in section 1.2 using unfamiliar concepts such as absorption line spacing and line width. More surprising is the conclusion that raising CO2 from 280ppm to 400ppm will cause a 6.6 degree C rise in temperature. I thought doubling CO2 gave 1.1 degrees, before feedbacks. It looks like he is assuming the entire long wave bandwidth is getting absorbed. Where do all the negative feedbacks to get the observed temperature reduction of 0.8 degrees come from?

  2. 2
    wili says:

    Blair wrote: “More surprising is the conclusion that raising CO2 from 280ppm to 400ppm will cause a 6.6 degree C rise in temperature.”

    Please explain more clearly where you are getting this statement. Links?

  3. 3
    Susan Anderson says:

    Gossip in the Princeton world has it that Dyson and Happer are planning to prove the opposite using the same basic physics. Should be interesting … but sounds like they got nuthin’

  4. 4
    Blair Dowden says:

    #2 Wili – I followed the first reference to this paper:

  5. 5
    Charles R Kiss says:

    I don’t think Cosmic Rays were ever as much about it [AGW], as say, what to do about it; if “it” were indeed happening, whether by anthropogenic causes or combinations or other field properties -nuclear power is NOT the way to go; humans will adapt and survive over shorter time periods in climate than over the half-lives of nuclear fission byproducts.

  6. 6

    “…humans will adapt and survive over shorter time periods in climate than over the half-lives of nuclear fission byproducts.”

    That doesn’t make a lot of sense. The more potent the by-product the shorter the half-life. Long lived radioactive isotopes have low levels of radiation.

    I’m agnostic on fission power but I’d prefer it to our present trajectory on fossil fuels. Coal and oil are an existential threat to the majority of the human race, fission is not.

  7. 7
    Charles R Kiss says:

    “…That doesn’t make a lot of sense.”

    Maybe you’re correct; maybe radioactive poisoning doesn’t exist.

    I would dare humanity to live in a world where are the fossil fuel energy is instead produced by nuclear power: our “date with destiny” would be just around the corner; in less than geologic time. IMHO

  8. 8
    HuntinHippy Bookmite says:

    I can see where some might believe that nuclear energy is all wrong considering the state of the current commercial implementation. However, there are materials which could be used, such as thorium, that not only to mitigates the super long half-life of the products of fission but also provides a cheap alternative to uranium. While the fission products in a thorium fuel cycle have a half-life of about 66 years; it is also so highly radioactive that it cannot be used to make bombs. If that thought is not enough, consider this, the current fission products from the uranium fuel cycle may be mitigated using some of the reactors that are capable of initiating the thorium fuel cycle.

  9. 9
    Charles R Kiss says:

    If you think Thorium is the answer read this:


    Using nuclear fuel of any type, on the scale where hundreds of thousands of megawatts in electricity are generated to significantly reduce CO2 emissions, human error will be inevitable, and statistically very, very relevant.

    This would include it’s transportation network, it’s security infrastructure; all subject to failure in it’s many possible, unpredictable forms.

    Thorium plants are also subject to explosions of their own: where in-line, high temperature and pressure “reprocessing” produces highly toxic radioactive fissile products.

    Most Thorium plants will contain, perhaps 10% Plutonium.

    At 1000MW production each (if they could ever be built so large), there would be thousands of these Thorium plants in the United States.

  10. 10
    Charles R Kiss says:

    It would be much easier to simply find a way of doing this:

    CO2 + 2*H2O + catalyst -> CH4 + 2*O2

  11. 11

    Another recent “simple physics” paper is by Caldeira and Myrhvold [1]. I got excited about it so blogged here:


  12. 12
    John Baez says:

    Blair Dowden – Sloan and Wolfendale’s paper says:

    “Such a temperature rise [of 6.6 °C] is much larger than the observed increase of 0.8 seen since industrialization. To explain this difference feedback mechanisms and all the other complications of the climate need to be invoked. Some of these complications serve to reduce the temperature increase and some to decrease it. Presumably the mechanisms which decrease the rise have a greater effect than those which increase it so that the actual rise in temperature is smaller than that predicted by the simple model.”

    But that’s a rather vague explanation of why their rough estimate is so large. If they’re assuming the entire long wave bandwidth is getting absorbed by CO2 that could do it. Their paper is not as clear on this point as I’d like, but maybe an expert could clarify.

  13. 13
    Carbomontanus says:


    In 2011, I decided to do something with it.

    And took up John William Herschels “Cyanotypie….Blåkopi..”

    The remedies are not for sale anymore , so I had to start from the bottom and from the beginning and found an iron strip on the street. Man tager, Man nehme… on prends…

    And was able to dilute it in strong HCl, iron in exess. Then oxidice it into Fe+++ by strong H2O2 and fall with 10% NH3.

    That substance could be washed 12 times over 12 nights at least with common water on a cofee machine, and dried into a deep brown chocolate like “knekk” in the glass.

    Which became a most magnificant “dodenkoop” when rubbed in the mortar. It is synthetic Goethit FeO(OH)

    Which is not easily soluble at all but it is a very pure Fe+++.
    I had it in a big test tube together with strong H2SO4 over a candle, for several hours giving a white substance probably Fe2(SO4)3, that is poorly soluble in strong sulphuric acid and tells us why that acid can be kept in iron bottles.

    But it dissolves easily in water, giving a pale yellow solution , which gives a quite superbe and sublime wine- red colour by the addition of Ammonia. Most probably the Fe+++ (NH3)n – complex.

    Ammonia is then added as long as one dares and before rust is falling out again.

    Then 4-5 drops of this superbe wine red liquid is given one or 2 crystals of citric acid. The colour disappers. One becomes the Fe+++ carboxyl complex with exess of NH4+, the fameous “Ferri- Ammonium Citrate”

    Then by adding 2 crystals of K2Fe(CN-)6, you have it, and give one drop of that solution on a filter paper, ……. under candle light….., and dry it.

    It exposes slowly under a Quarz Halogen- lamp , but dramatically faster in proper sunlight even in cloudy weather, even before sunrise.

    And not at all in clear weather with the milky way right in Zenith at night.

    This is John william Herschels method you see for rather short wave light, in order to repeat Bequerels experiment. Bequerel used AgBr.

    I did compute the “efficient voltage” Arbeidsspenning for light at 400 nanometer and found 31 volt. That voltage scratches allmost anything in the atmosphere exept for N2, giving free radicals.

    The rest is science…..

    If need for higher voltages to show, I would have used Uranium pitchblende like Bequerel did, instead of asking CERN for artificial teravolts.

    For scratching N2 in the atmosphere, do like Sam Eyde did and ask Professor Birkeland at The Royal Frederiks University.

    But Herschels Cyanotypie is impressive. It does not expose under a candle but it exposes outdoor at twilight allready. Because E = h.ny.

  14. 14
    Carbomontanus says:

    Correcture. Citric acid in exess!
    That gives the most photosensitive remedy. 2 sorts, brown and green are noted at Wikipedia of “Ammonium ferri citrate” brown and green. Green is ammonium and citric acid in exess.

    The mysterious pink colour og “Ferri ammonium alaun” could be cleared up. It is the Fe+++ NH3 Ligand. Not noticed in the books. The fameous “Mohrs salt” is the corresponding Fe++ ammonium ligand complex salt.

    CERN have been very clever producing (NH4)2 SO4 for Svensmark. That salt is not hygroscopic. And asked him how to explain further how it can grow into fogs and raintrops.

    Whereas the system SO3 .nH2O is extreemly hygroscopic giving acid rain. Katalysts are “NOx” and Ozone for SO2 into SO3.

    Moral: Better do discuss photochemical smog. Herschels cyanotypie throws evidence on the nature of sharp sunlight.

  15. 15
    MARodger says:

    Well bless my proton flux but it is heartening to know than there are “still some lingering academic communities nourishing the idea.” I find such nuanced language a pleasure to encounter. And indeed, the heat from that debate mentioned by TOSCA is but a gentle warmth within the science.

    Less edifying here is the puerile debate about nuclear power. Perhaps one of the commenters involved would care to explain its topicality.

  16. 16
    Jim Larsen says:

    10 Charles R Kiss describes a chemical perpetual motion machine:

    Sorry, but you’ll need more than a catalyst, you’ll need an energy source.

  17. 17
    Jon says:

    “It would be much easier to simply find a way of doing this:

    CO2 + 2*H2O + catalyst -> CH4 + 2*O2″

    Or it might be impossible since your nameless catalyst might not exist.

  18. 18
    Rob Quayle says:

    If you want a really really simple statistical climate model, try correlating global mean annual temperature &/or sea level with the CO2 data from Mauna Loa. The results look a lot like physical model results. Naive? Perhaps. But still, quite instructive. I’ll send you a copy if you like.

  19. 19
    SecularAnimist says:

    Have the moderators changed their policy that discussions of nuclear power are off-topic for this site?

    If such discussions are to be permitted, perhaps a new thread could be established for that purpose.

    For example a post regarding the recent open letter from Hansen et al, advocating more research on nuclear technology specifically to address GHG emissions from electricity generation, might be an appropriate place for such discussions.

    After all, the authors of that letter are all climate scientists, and a critical analysis of their arguments might help to reinforce why RealClimate is wisely NOT a place for “debating” energy policy — at least in part because that’s not a field to which climate scientists bring any particular expertise.

    Then at least there would be a place for nuclear advocates to go at it, rather than filling up unrelated comment threads with it.

  20. 20
    Charles R Kiss says:

    @16 and 17

    You’re both very funny! Your comments make me smile; yes, I took high-school chemistry, it was required. Today, there are photo catalysts, nanotubes, lots of research papers, etc. Looks fun; maybe even promising.

    I can’t imagine a worse solution than the nuclear one. It’s many of the climate scientists who are pushing it, that’s why it’s relevant here. I think it’s a horrible idea.

  21. 21
    Peter Roessingh says:

    Using simple physical laws to explain the basics of some mechanism is in principle very effective way to convince people of the validity of your argument. However, as Blair Dowden notes, it is disconcerting that the fairly rigorous first principle reasoning in the first part of the paper leads to a highly unrealistic answer. The authors deal with this result using a fair bit of handwaving, that contrast sharply with the preceding section

    It it really not possible to do a better job, and continue the type of reasoning used in the first section a bit further, to arrive at a temperature change of at least the right order of magnitude? That would make the argument a lot more convincing, especially for some of my more skeptical colleges that deeply distrust results from (in their view) overly optimized and complex General Circulation Models.

    I would be grateful for any pointers in the direction of such material.

  22. 22
    Aaron Sheldon says:

    Thank you for the back of the envelope reference. But wouldn’t a closer model be the first order ODE, where the difference between absorbed solar power and lost black body power has to equal the change in temperature with respect to time multiplied by the terrestrial and atmospheric combined heat capacity:

    S_solar(1 – A_earth)/4 – \sigma T_earth^4 = C_v dT_earth/dt


    S_solar is the solar constant
    A_earth Earth’s albedo
    \sigma is the Stefan Boltzmann constant
    C_v is the terrestrial and atmospheric combined heat capacity
    T_earth is the block body temperature of earth
    d/dt is the differential with respect to time

    In this context C02 affects the heat capacity not the albedo. The solution to this for an impulse change to the heat capacity is appropriately a saturation curve related to the hyperbolic tangent function.

  23. 23
    Aaron Sheldon says:

    Opps forgot the opacity of the atmosphere to long wave radiation lets say

    f_earth for the fraction of Black body radiation leaving the earth

    so the loss term is

    f_earth \sigma T_earth^4

    and C02 affects the opacity not the heat capacity, so the impulse function is in the change to opacity. Still results in a saturation curve related to the hyperbolic tangent.

    Damn you envelopes and napkins, they always get used to mop up the spilled beer which inevitably runs the ink.

  24. 24
    Aaron Sheldon says:

    …and one more thing. This little ODE also points out what was so troubling about the recent measurement of mid layer warming in the ocean. If we have underestimated the heat capacity then to account for the change in temperature the planet must have absorbed a lot more energy. This in turns implies we may have underestimated how much the opacity to long wave radiation has increased.

  25. 25
    Jim Eager says:

    “Today, there are photo catalysts, nanotubes, lots of research papers, etc.”

    But there is still no perpetual motion machine.

  26. 26
    Charles R Kiss says:


    Using energy X, a hypothetical black foil is made and spread across deserts and active volcanoes, continually absorbing heat, and/or light, scrubbing CO2 from the atmosphere for years to come producing energy 100000X of methane over it’s lifetime.

    Sheesh, have an imagination! There’s plenty of energy.

    “No, I’m going to perpetually circulate thousands of tons of extremely radioactive substances throughout the surface of the globe, poisonous for hundreds and thousands of years; because I believe in human infallibility, dammit!”

  27. 27

    #20: Some basic physical chemistry. Aa catalyst reduces the energy to start a reaction; it doesn’t remove the need for energy input. Even if your catalyst existed, you would need energy to drive the reaction.

  28. 28
    deconvoluter says:

    Rasmus says this:


    My initial and superficial reaction to this was to wonder whether such a simplified model needed to be in the paper, and if so whether it was the best choice:

    Yes the model looked quite nice at first until I arrived at this heading:

    1.2. Quantification of this model and the role of feedback.

    My italics.
    As the authors conclude, the uncorrected model is not a serious contender for estimating the magnitude of the warming.

    Considering all the contrarian propaganda about feedbacks it would be better not to introduce a new terminology here. The standard usage attributes physical meaning to the feedbacks which may be incompatible with the one implied here i.e. a sum of unspecified fudge terms to be added (or subtracted from) the estimated warming.

    The need for these fudge terms is probably nothing to do with feedbacks as usually defined, but with the need to correct for such simplifications as the one that supposes the greenhouse gases to cause the bulk of the atmosphere to be ‘black’ (authors usage) or grey at all infra-red wavelengths. Perhaps if the reviewers had been a bit tougher they could have encouraged the authors to produce a better paper.

  29. 29
    Jim Eager says:

    Re Charles @26, And plenty of imagination to match.

    We already know about natural materials that are very good at absorbing CO2 from the atmosphere, such as peridotite. The problem is the energy required to quarry it as solid rock, grind it into smaller particles to increase surface area, then transport and spread it around to expose it to the atmosphere. That and enough suitable vacant uninhabited land to spread it on; uninhabited because you are also going to release a lot of toxic heavy metals in the process. But first you need a suitable overthrust deposit that is not located in a national park (Gross Morne) or in a politically unstable region (Yemen).

    There is no free lunch, and there is no “free” energy.

  30. 30
    Hank Roberts says:

    > The problem is the energy required to quarry it
    > as solid rock, grind it into smaller particles
    > to increase surface area, then transport and
    > spread it around to expose it to the atmosphere.

    But our glaciers take care of that grinding, don’t they?

    Oh, wait …

  31. 31
    deconvoluter says:

    …doubling in CO2 should increase the forcing by a factor of log|2|..

    A small slip?

    If forcing F satisfies
    F = k log ([CO2])
    Each doubling of [CO2] produces the same increment of forcing k log(2)
    On the other hand the factor by which forcing is raised is given by
    F’ =k log(2[CO2])/ klog([CO2]) = 1 + log(2)/log([CO2])

    [Response: Right... It should be 1 + log(2). -rasmus]

  32. 32
    deconvoluter says:

    I’m sorry but I think we were and are both still wrong. My version should have started with a formula for a non zero forcing F(1) caused by an increase of the concentration from a reference level (0) to its present value denoted by (1).

    F(1) = k log([CO2](1)/[CO2](0))
    The awkward notation requires that each bracket has its partner somewhere.
    Now double the concentration, derive the new forcing F(2) and obtain:
    F(2)/F(1) = 1 + {log(2)/log([CO2)(1)/[CO2](0))}

    But who wants to know the factor by which the forcing will be raised? It rather throws away the simple properties of the log formula which shows that the forcing goes up by equal increments.

    [Response: Sure - fixed now. I was a bit too hasty. -rasmus]

  33. 33
    Patrick 027 says:

    re 21 Peter Roessingh – not much time to type right now, but…

    a simple explanation of radiative forcing, feedbacks, and response may suffice, even when the amount of number crunching implied is very large. For example, imagine what the atmosphere looks like in the terrestrial infrared, from different vantage points, in different directions, under different conditions, over different wavelengths (an incandescent inky fog, thick or thin, how far can you see through it?) … what you see is what you get, in energy flux (proportional to, anyway)… etc.

  34. 34
    Chris O'Neill says:


    You’re both very funny!

    Not half as funny as ignoring conservation of energy.

  35. 35
    Sean says:

    @ 8 & 9 China and SA seem to be advanicng well with high temp gas cooled pebble bed genIV reactor. China is now operating a power station now .. maybe 300MW the first full scale version. chinese nuclear scientists were pretty keen on this project. check it out is it very interesting for the long term future of nuclear (maybe) as it’s deemed safe incapable of a meltdown

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