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Solar

Filed under: — stefan @ 4 May 2010

The new novel Solar by Ian McEwan, Britain’s “national author” (as many call him) tackles the issue of climate change. I should perhaps start my review with a disclosure: I’m a long-standing fan of McEwan and have read all of his novels, and I am also mentioned in the acknowledgements of Solar. I met McEwan in Potsdam and we had some correspondence while he wrote his novel. Our recent book The Climate Crisis quotes a page of McEwan as its Epilogue. And of course I’m not a literature critic but a scientist. So don’t expect a detached professional review.

In interviews McEwan describes his difficulties in approaching the topic of climate change: “I couldn’t quite see how a novel would work without falling flat with moral intent.”

One solution is that he makes his protagonist who tries to “save the world”, the Nobel laureate physicist Michael Beard, thoroughly pathetic and unlikeable. (Actually quite unlike any scientist I know, but certainly less boring than us at Realclimate.) The only redeeming feature of Beard is his sarcastic humor. When his business partner is worried that claims of global warming having stopped will ruin their grand solar energy scheme, Beard (after expertly refuting the “no warming since 1998” myth) retorts:

Here’s the good news. The UN estimates that already a third of a million people a year are dying from climate change. Even as we speak, the inhabitants of the island of Carteret in the South Pacific are being evacuated because the oceans are warming and expanding and rising. Malarial mosquitoes are advancing northwards across Europe… Toby, listen. It’s a catastrophe. Relax!

This is McEwan’s funniest book. The humour in it is another way around the moral gravity of the subject. In an interview he said:

The thing that would have killed the book for me, I’m sure, is if I’d taken up any sort of moral position, I needed a get-out clause. And the get-out clause is, this is an investigation of human nature, with some of the latitude thrown in by comedy.

Half-way through the novel Beard gives a riveting speech on climate change to an auditorium full of pension-fund managers (representing 400 billion dollars of investments) – a speech that I’d be almost tempted to steal and use verbatim myself at some occasion. But what could have been tedious – a whole lecture embedded in a novel – is turned into a hilarious scene where Beard is engaged in a losing battle with his bowels, trying to continue speaking while swallowing down “a fishy reflux rising from his gorge, like salted anchovies, with a dash of bile”.

McEwan showing off that he can write such a speech better than a scientist is reminiscent of his novel Enduring Love, to which he appended an entire scientific paper about a psychological disorder (De Clerambault’s Syndrome) that allegedly inspired the book. Later he admitted this “paper” was part of the fiction. He’d even submitted it to a journal, but one of the reviewers smelled a rat.

McEwan’s deep (and often playful) affinity to science is one of the hallmarks of his writing and of course one reason why I like his novels. The other is his stunning power of observation; he seems to be reading people’s minds, cutting right through their delusions to get to the deeper truths. In that, his analytic work as a writer resembles that of a scientist.

McEwan is a forceful rationalist and well-versed in science culture, and his witty observations on that are a big part of the fun of his books. In Solar, for example, he pokes some hilarious fun at the social constructivists. Beard chairs a government committee to bring more women into physics, and a social scientist on his committee introduces herself with a speech on how a particular gene is not discovered by scientists, but is rather a social construct.

Beard had heard rumours that strange ideas were commonplace among liberal arts departments. It was said that humanities students were routinely taught that science was just one more belief system, no more or less truthful than religion or astrology. He had always thought that this must be a slur against his colleagues on the arts side. The results surely spoke for themselves. Who was going to submit to a vaccine designed by a priest?

This develops into my favourite subplot. At a press conference of his committee, the journalists are “slumped over their recorders and notebooks” and “depressed by the seriousness of their assignment, its scandalous lack of controversy”, as “the whole project was lamentably worthy”. Beard makes some fairly harmless remarks about the efforts of bringing more women into physics perhaps reaching a ceiling one day, because they may have a preference for other branches of science. The social constructivist explodes (“Before I go outside to be sick, and I mean violently sick because of what I’ve just heard, I wish to announce my resignation from Professor Beard’s committee.”) Predictably, that makes the predatory journalists spring to life, and in the following McEwan spins a completely credible story how Beard’s remarks turn into a media storm where Beard’s love life is dragged into the tabloids and his “genetic determinist” views are linked to Third Reich race theories. One journalist, “more in the spirit of playful diary-page spite”, calls him a neo-Nazi.

No one took the charge seriously for a moment, but it became possible for other papers to take up the term even as they dismissed it, carefully bracketing and legalising the insult with quotation marks. Beard became the ‘neo-Nazi’ professor.

McEwan knows what he is writing about: he became subject to a media storm about his Islam-critical views a few years ago. I read Solar in February (thanks to an advance copy that the author had sent me), in parallel with the unfolding surreal, but real-world media campaign against IPCC, and found that McEwan dissects the mechanisms beautifully.

McEwan says that the idea to make a Nobel laureate the main character of his new book came to him in Potsdam, when attending the Nobel Cause Symposium organised by our institute in October 2007 (and on page 179 his hero Beard returns from a conference in Potsdam). At the time I discussed with him whether this wouldn’t be a good topic for a novel: humanity facing an existential threat that is well-understood by its scientists, but largely ignored by a population who prefers to delude itself in creative ways about the gradually unfolding disaster. McEwan responded: everything there is to say about this situation has already been said by Thomas Mann in his novel Death in Venice.

I’m glad he tackled the topic of climate change nevertheless. It’s McEwan at his best. Intelligent, funny, and full of insights. Read for yourself!

Link: Here is McEwan speaking about Solar (and about his views on climate change) in a TV interview.

726 Responses to “Solar”

  1. 701
    Completely Fed Up says:

    How about another tack?

    Martin, what would be the result if your theory that the half-life of CO2 in the atmosphere was 10 years.

    IF you’re right and the residency time for carbon as CO2 in the atmosphere was 10 year to reduce by 50%, what is the consequence?

  2. 702
    Completely Fed Up says:

    “I’ll sign off from Realclimate now and I won’t be back. ”

    We’ll miss you.

    “I’ll seek information from what you would probably call “denialist” blogs where, to be frank, I find the atmosphere more relaxed”

    relaxed about what would be considered a viable theory. More relaxed about what they’ll accept as truth.

    Martin’s mind is so open, his brain got up and walked off..

  3. 703
    Ray Ladbury says:

    Martin A.: “I’ll seek information from what you would probably call “denialist” blogs where, to be frank, I find the atmosphere more relaxed – and populated by the scientifically literate from many fields.”

    Ah, rather like the drunkard who loses his keys in the dark by his car, but decides to go over to the streetlamp to look for them because it is brighter. Anybody else smell the aroma of “tone troll”?

  4. 704
    Hank Roberts says:

    CFU, I think you arrived here after the person who posted as “Mark” left.
    May I suggest you study his posting style and consider if yours is better?

  5. 705

    CFU @ 701:

    How about another tack?

    Martin, what would be the result if your theory that the half-life of CO2 in the atmosphere was 10 years.

    IF you’re right and the residency time for carbon as CO2 in the atmosphere was 10 year to reduce by 50%, what is the consequence?

    More significantly, even if the entire annual variance could be “put to work”, reducing CO2 by any amount is pretty much limited to the ~7ppm difference from the annual high to the annual low.

  6. 706
    dhogaza says:

    CFU, I think you arrived here after the person who posted as “Mark” left.
    May I suggest you study his posting style and consider if yours is better?

    My hypothesis has been that if they’re not the same person, they’re identical twins separated at birth …

  7. 707

    Martin A 698: I’ll seek information from what you would probably call “denialist” blogs where, to be frank, I find the atmosphere more relaxed – and populated by the scientifically literate from many fields.

    BPL: I suggest that, by the same logic, you seek out information on biology from “Answers in Genesis,” information on archaeology from the Zechariah Sitchin and Erich von Daniken pages, and information on astronomy from the supporters of Immanuel Velikovsky and Oliver Manuel.

  8. 708

    #569 Bob (Sphaerica): I admire your fortitude in wading through all that CO2 “science” stuff. I usually give up when I find something obviously bogus. I really would like the mainstream science to be wrong because the consequences otherwise are so dire. Unfortunately violating the laws of physics isn’t a victimless crime. That an industry of the size of fossil fuel inc. can do no better makes me wonder how their execs sleep at night. Their own scientists must know all this stuff is garbage.

    Having gone to all this effort, maybe consider finding a space for your debunking at RC wiki?

  9. 709
    Completely Fed Up says:

    FCH, I would just like to know what MA thinks is the consequence of a system where atmospheric CO2 adjusts over a scale of ~10 years.

    The consequence is, of course, that anthropogenic sources accumulate for twice that period (20 years, 2x being the infinite sum of a series of powers-of-1/2). Therefore at an overestimate, humans have produced 40ppm CO2. Measurement shows that is off by about a factor of 2.5x.

    Actual measurement disavows a sequestration time of 10 years to remove 50% of extra load.

  10. 710
    Completely Fed Up says:

    “May I suggest you study his posting style and consider if yours is better?”

    I posted a long answer to you Hank, but it went awol.

    Suffice to say that I tried to teach MA but he refused. How he got my example that showed no change in the proportion of the 10 units of carbon among the two resevoirs, yet display a reduction in the C14 proportion to a theory that this somehow should mean that sequestration of carbon must happen on a scale of ~10 years shows he was not listening.

    Then he goes all Rita Hayworth on us and, just as JRB did before, proclaim that everyone here was closed minded and that was why we argued he was wrong (not that he was wrong, and that was why we argued he was wrong).

    Which I pointed out in another thread:

    http://www.realclimate.org/?comments_popup=3436#comment-174525

    He’s written before when RC trolls arguing the Arctic Ice Is Increasing went on and on. He didn’t seem to have read that, mind and was confused that the argument was being REbunked because it was the first time he’d argued it here.

    He was not an honest actor.

  11. 711
    Completely Fed Up says:

    “May I suggest you study his posting style and consider if yours is better?”

    I posted a long answer to you Hank, but it went awol.

    Suffice to say that I tried to teach MA but he refused. How he got my example that showed no change in the proportion of the 10 units of carbon among the two resevoirs, yet display a reduction in the C14 proportion to a theory that this somehow should mean that sequestration of carbon must happen on a scale of ~10 years shows he was not listening.

    Then he goes all Rita Hayworth on us and, just as JRB did before, proclaim that everyone here was closed minded and that was why we argued he was wrong (not that he was wrong, and that was why we argued he was wrong).

    Which I pointed out in another thread:

    http://www.realclimate.org/?comments_popup=3436#comment-174525

  12. 712
    Completely Fed Up says:

    [there was. we don’t have time to pick through posts to edit them. stick strictly to substance and all will be fine.]

    Comment by Completely Fed Up — 13 May 2010 @ 6:14 PM

  13. 713
    Hank Roberts says:

    from online bookseller abebooks.com (highly recommended, searches many small independent bookstores for you):

    AbeBooks April Bestsellers May 13th, 2010:
    Top 10 bestselling signed Books
    1. Solar by Ian McEwan …..

  14. 714
    Patrick 027 says:

    According to this:
    http://earth.geology.yale.edu/~avf5/teaching/ResourcesGG535/Lecture5.PotTemp.Thermodyn.LapseRate.pdf (p. 5),
    the adiabatic lapse rate in the ocean is 0.12 K / km

  15. 715
    Lawrence Coleman says:

    I’ve got a question that ive been puzzling over…. given the increasing amounts of CH4 emissions perculating up through the arctic waters, some of the methane is actually making it to the surface as intact bubbles but the majority I would still assume is diffusing back into seawater on the way up. My question is..is this diffusing of CH4 causing the arctic ocean specifically to become disproportionately acid (lower ph) compared to equitorial oceans due to increased carbonic acid?. If it is then it couldn’t happen at a worse location as it is the principal breeding ground of diatoms, planckton and krill. It has been found that certain micro crustations are losing size and shell thickness by up to 35% in these areas and the antarctic ocean as well.
    Could someone enlighten me on this point..thanks!

  16. 716
    Hank Roberts says:

    It’s been decades since I took chemistry, but I’d be surprised if dissolved methane changes the pH of water. CO2 dissociates and it’s the carbonic acid that changes pH.

    But, egad, we create new methane by erosion; imagine what’s been happening and what will happen with increased open water and open land surface and erosion around the Arctic, if this caution here is apt:

    “… Marine scientists have known for many years that biogenic methane (CH4) is generated in shallow seabed sediments on continental margins, especially in rapidly deposited muddy sediments with high organic matter content. Grassy sediments are found in river deltas, estuaries, and harbors, but also in deeper waters on continental shelves and slopes. Human activities can accelerate natural sea-floor gas generation by increasing the supply of sediments and organic matter from rivers through deforestation and intensive farming, and also by the disposal of human waste at sea. When this extra organic matter becomes buried to about one meter beneath the seabed, biogeochemical processes start to convert it to CH4. The impact of this extra CH4 could be felt within the next 100 years, assuming a one-centimeter-per-year sediment accumulation.”

    Title : Shallow Seabed Methane Gas Could Pose Coastal Hazard
    Corporate Author : NAVAL RESEARCH LAB STENNIS SPACE CENTER MS SEAFLOOR SCIENCES DIRECTORATE
    Report Date : 30 MAY 2006
    http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA464004

    Paging Peter Ward …. there’s a feedback from increased surface erosion to creation of new shallow sediment to production of new methane.
    With a _very_short_ timeline for trouble if this is correct.

  17. 717
    Cary Rymut says:

    Earlier, I was trying to get an feed for the RSS to the site and for some reason it ain’t displaying in Google Chrome. Any suggestions???

  18. 718
    Paul A says:

    I don’t think anyone has pointed this out yet, but Solar has won the Bollinger Everyman Wodehouse prize for comic fiction.

    http://www.guardian.co.uk/books/2010/may/25/ian-mcewan-wodehouse-prize

  19. 719
    MaryEllen Marucci says:

    I like to hedge my bets and plant trees such that some will survive the hot,cold, wet, dry or forever fog. As to the solar nightmare (Levenson #11)…been having that since 1974 when the Helois project predicted a dying and spastic sun in -10 to 10,000 years. I politely asked they revisit the data. Scientists too need some adjustment time.

  20. 720
    Thimbles says:

    Hi, got a bit of a post to go through here, and it’s on the topic of Solar forcing so I hope you won’t mind the clutter..

    Recently, a guy for the National Post wrote a truly stupid article:
    http://fullcomment.nationalpost.com/2010/05/21/its-the-sun-stupid/
    In the article he quotes a “solar scientist” by the name of Dr. Jeff Kuhn.

    So I tried to source his comments for context but all the Jeff Kuhn references traced back to the author.
    So I thought this might be a Carl Wunsch type swindle and I emailed him.

    I got a response back from Kuhn. (Which was nice because he’s a pretty busy guy and I’m not an important correspondent)

    Here’s what was said:

    I’m in the midst of organizing a large international meeting with many people needing my attention through the end of next week but I will append pieces of email I’ve sent to others that, I think, makes my position clear. I will try to respond further after SPW6 is completed next week if you have other questions.
    ——————————————————
    The politization of our science has been a destructive force for the truth. I appreciate your point about CO2 and agree with your overall perspective.
    Thanks for the email and encouragement.
    ——————————————————-
    Unfortunately the politization of this subject has obscured many clear facts. For example, the correlative relationship between solar variability and climate change is not disputable. The failings of [Global Climate Models] to reproduce measured climate change is also not disputable (for example the rapid temperature rise between 1910-1940 and the cooling period after 1940). My firm take on the data is that terrestrial climate models are fundamentally incomplete. To learn more about various models to understand the Earth-Sun variability connection you could read results from Gerald Meehl, K. Labitzke, H. VanLoon, W. Soon, S. Baliunas, and many others.
    ————————————————————
    In my opinion this debate has become politized beyond the realm of good science. Our research, in combination with many historical measurements suggests that there are long term climate trends that we believe are associated with the optical properties of the atmosphere.
    Best models suggest that the apparent changing solar diameter is due to stratospheric changes that affect optical “seeing.” Its difficult to understand the data without something like this. These changes appear to be correlated with known magnetic cycle changes in the Sun (i.e. sunspots). As far as I can tell this is one of the clearest and most significant ties between the Sun and the Earth’s atmosphere. The questions you raise about the direct sunspot/irradiance change and terrestrial weather is by no means resolved. I suggest you look up some recent results from Gerald Meehl (a member of the IPCC) who shows how UV and bolometric solar changes have sufficient “amplitude” to cause La nina and elNino effects. But this is not my research.

    I wish you good luck in attempting to separate the science from the
    religious/political zealotry.
    —————————————————-

    Back to Thimble here. So yeah, these were some snippets from other emails that he sent to other people’s inquiries that he thought would be relevant to my own.

    I wrote back:

    I appreciate the response and I agree with your points as an explanation of historical climate change. (Volcanism, tectonic movements, the occasional meteor, and solar variability have been the primary drivers of climatic change previous to the industrial age)

    I believe he is coming from the perspective that climate modeling is too focused on the optical characteristics of the emittee (what gasses are in the atmosphere and how their properties affect sunlight absorption and re-radiation) and not enough on the characteristics of the emitter (various sun cycles and sun variability). If I understand him correctly, he’s not discounting CO2 and other greenhouse gas’s roles, but he does not think that the models can be accurate if they assume solar invariability.

    If I am correct, then what the National post author did is take a desire for a tinker in the models and turn it into a repudiation.

    So first question, does it sound like I’m accurate? I don’t know Dr. Kuhn and he seems nice enough in email so I’m giving his statements a generous interpretation in spite of the “religious/political zealotry” language. Is that justified?

    Second question, does the critique have merit? I had thought that Nasa has people that measure year to year solar variability and that the climate modelers employ their data as an input. Also solar variability, though historically important and potentially very important in future as it gets more active, doesn’t seem significant to be a significant driver of recent climate trends, not significant enough to merit an “it’s the sun stupid” hit piece at any rate. Last I checked, the temperature trend has diverged from the influence of the recent solar minimum.

    Anyways, your thoughts?

  21. 721
    Completely Fed Up says:

    “Second question, does the critique have merit?”

    No.

  22. 722
    Thimbles says:

    Interesting bit on the ol’ sun.
    http://www.scientificamerican.com/article.cfm?id=solar-minimum-forecasting

    In very rough terms, the sun’s activity ebbs and flows in an 11-year cycle, with flares, coronal mass ejections and other energetic phenomena peaking at what is called solar maximum and bottoming out at solar minimum. Sunspots, markers of magnetic activity on the sun’s surface, provide a visual proxy to mark the cycle’s evolution, appearing in droves at maximum and all but disappearing at minimum. But the behavior of our host star is not as predictable as all that—the most recent solar minimum was surprisingly deep and long, finally bottoming out around late 2008 or so…

    “I think we’re almost in violent agreement that this is an interesting minimum,” said David Hathaway of the NASA Marshall Space Flight Center in Huntsville, Ala. By several measures—geomagnetic activity, weakness of polar magnetic fields, flagging solar deflection of galactic cosmic rays—the minimum was the deepest on record, Hathaway said, although some of those records contain just a few cycles.

  23. 723
    Completely Fed Up says:

    “In very rough terms, the sun’s activity ebbs and flows in an 11-year cycle, ”

    A cycle that over observed years has lasted between 9 and 14 years, the nominal most likely epoch length being 11 years.

  24. 724
    Ray Ladbury says:

    Thimble,
    From the sound of it, climate modeling is well beyond Kuhn’s expertise. None of the research he is citing would invalidate what we already know about CO2. There are climate scientists actively working on incorporating the solar cycle and other effects. However, I find it extremely difficult to explain a sustained rise in temperatures–let along stratospheric cooling–with a solar model.

    The “debate”, such as it exists in the scientific community is not over the role of CO2. The physics there are well known–at least among the experts.

  25. 725
    David B. Benson says:

    Thimbles — The claims have no merit. Here is a simple exposition as to why:
    http://www.realclimate.org/index.php/archives/2010/03/unforced-variations-3/comment-page-12/#comment-168530

  26. 726
    Patrick 027 says:

    Re John E. Pearson – sorry for the hiatus:

    (first, if I said somewhere above that the work done in adiabatic expansion corresponded to a decrease in enthalpy, that is incorrect; it’s the internal energy that is converted to work by expansion at pressure, although the thermodynamic equations can be algebraically manipulated to show a relationship between enthalpy and change in pressure.)

    PART III addendum

    PART III.

    “Considering some examples of what happens when atmospheric optical thickness at a particular LW frequency is increased from zero:”

    While keeping temperatures at each location unchanged.

    “3a. radiation to space: If the surface LW albedo is large enough and the atmosphere is warm enough relative to the surface, and absorption has a strong enough role in atmospheric optical thickness, the flux to space will initially increase as optical thickness increases from zero”

    Actually that’s always true, but with different requirements of temperature. For a perfect blackbody surface and no LW scattering by the atmosphere, the initial change in upward flux is an increase if the (optical thickness-weighted) average temperature of the atmosphere below is greater than the surface temperature; it is a decrease if it is less. If there were some LW scattering optical thickness, then the atmosphere would have to be warmer (averaged over absorbing optical thickness) than the surface by some additional amount to result in an initial increase in upward flux; if the surface had some nonzero LW albedo, then the atmosphere would have to be colder by some additional amount to result in a decreased flux with the initial introduction of LW optical thickness into the atmosphere.

    “However, as optical thickness continues to increase, eventually the flux to space starts to decrease, if”… “or if the scattering is concentrated toward the top of the atmosphere.”

    If the scattering optical thickness/absorption optical thickness ratio decreased with height within an upper layer, then the flux could start increasing again beyond some point with increasing total optical thickness.

    1a.
    “if the optical thickness is small, then any part of the atmosphere doesn’t absorb much of what the other part emits, so the emission weighting function that is in the atmosphere is distributed as optical thickness is distributed.”

    for 2 and 3, the emission weighting function is, for small optical thickness, distributed as the absorbing contribution of optical thickness; with greater optical thickness that includes scattering, scattering contributes to the concentration and redistribution of the weighting function, but the weighting function density will follow the concentration of absorption cross section over scales that are small relative to total optical thickness.

    ———

    To sum up:

    increasing opacity tends to bring the emission weighting function for a location closer to that location or otherwise distribute the function around the location, so that the centroid of the weighting function tends to get closer to that location. The radiant intensity from a direction is equal to the volume integral of the product of the blackbody intensity as a function of temperature and the density of the weighting function. Thus, if the temperature has some overall spatial trend over the scale of the bulk of the weighting function, then increasing the optical thickness per unit distance causes a trend in the brightness temperature away from the temperature at greater distance and towards the temperature nearer the location. The same tendency applies qualitatively to a flux per unit area (and the corresponding weighting function for a flux per unit area – which tends to straddle an ‘effective emitting altitude’ if the temperature varies smoothly with the dominant tendency being a spatial trend that doesn’t vary in sign, so that a position near the centroid (to a first approximation) of the weighting function can be found with a temperature equal to the brightness temperature of the flux per unit area that is emitted).

    The weighting function for emission of an intensity or flux reaching a location is equal to the distribution of absorption of an intensity or flux from the opposite direction passing through that location.

    A net intensity or flux per unit area is the difference between emitted intensities or fluxes per unit area in opposite directions. The corresponding pairs of weighting functions absorb each other’s emissions.

    (It is also true that for any two volumes sufficiently small to each be isothermal, the net flux (from emission to absorption) is from the higher temperature volume to the lower temperature volume.)

    Eventually, if the temperature doesn’t vary discontinuously, the net intensities and net flux per unit area approach zero as opacity increases beyond the point where the temperature variation per unit optical thickness gets small – because the pairs of intensities and fluxes approach the same value (same brightness temperature) when that happens.

    A location where the effective temperature may vary discontinuously or nearly so is at the ‘top of the atmosphere’, as the air temperature (in so far as there is one – or there may be several in the same volume corresponding to different populations of particles (?), or etc.) may never get as cold as the brightness temperature of space (near zero K except in the directions of some objects and in the frequency ranges where they are significant).

    (PS in the case that a single temperature can’t be well-defined for a location but can be defined seperately for different overlapping populations of matter, weighting functions can be divided into contributions from the different populations in the same space, and the brightness temperature of the resulting intensity or flux per area determined accordingly.)

    —————

    Part IV:

    Keeping the temperature distribution constant and just changing optical thickness or optical properties in general, the changes in fluxes that result are radiative forcings (if the changes in optical properties are feedbacks, than they’re effects could be called radiative feedbacks, but they can also be regarded as having radiative forcings in a context that doesn’t differentiate between forcings and feedbacks):

    For any sufficiently small change in a variable, a function of that variable, if smooth, can be approximated as a line.
    For a sufficiently small addition of optical thickness, a doubling of that addition will have double the effect on fluxes and net fluxes. This is true even if some amount of optical thickness is already present, so long as it is not the total that is being doubled but just the small addition. For example, whatever amount of water vapor and clouds, etc, are already present, adding a very small amount of CO2 will have the same radiative forcing as a doubling of that initial addition. Even when the forcing diverges from linear proportionality in total, it can be approximated as linear to sufficiently small perturbations (ie with the amount of CO2 present now, adding 1 ppm should have approximately half the effect as adding 2 ppm).

    This will be true at all frequencies and therefore true in total.