The two-degree delusion?

Ted Nordhaus, of Breakthrough Institute fame, has a recent article in Foreign Affairs called [t]he two-degree delusion. Basically, it argues that we cannot possibly achieve this target without harming the poor, and that continuing to try and do so also makes it more difficult to focus on viable alternatives (adaptation, for example).

There’s a great deal one could say about Ted Nordhaus’s arguments, but there was one thing that I wanted to highlight, that I think he gets largely wrong. He says:

Such calculations are further complicated by the substantial lag between when we emit carbon and when we experience the climate impacts of doing so: because of the time lag, and because of the substantial amount of carbon already emitted (atmospheric concentrations of carbon today stand at 407 parts per million, versus 275 prior to the start of the Industrial Revolution), even an extreme precautionary approach that ended all greenhouse gas emissions immediately would not much affect the trajectory of global temperatures or climate impacts until late in this century at the earliest.

This is – I think – a commonly held view, but it is mostly a misconception. In fact there is a paper by Ricke and Caldeira (that I discussed in this post) that finds that

the median time between an emission and maximum warming is 10.1 years, with a 90% probability range of 6.6–30.7 years.

In a sense the issue is that there is a difference between stabilising emissions, stabilising concentrations, and halting emissions. If we stabilise emissions, concentrations will continue to rise, and we will continue to warm. Stabilising concentrations will require – on decadal timescales, at least – substantial emission reductions and will lead to continued warming for many decades. This is because of the inertia in the climate system.

If, however, we actually halt emissions, then there may be little in the way of committed warming. Also, see this Realclimate post. It does depend somewhat on the mixture of long-lived greenhouse gases (GHGs), short-lived GHGs, and aerosols, but it’s not true that what we do now will have no impact until late this century, at the earliest. In many respects, the inertia is really societal, not climatic.

As for the 2C target itself; yes, it does seem likely that we will not keep warming below 2C. Current emission reduction committments will probably only keep us below 3.5C. I also agree that we should be willing to consider the implications of attempts to drastically reduce emissions. However, I still think there are reasons for maintaining something like a 2C target; even if we do miss it, there’s likely to be a vast difference between just missing it, and missing it by a lot.

Also, if people are concerned about the impact of trying to reduce emissions now so as to potentially keep warming below 2C, they might want to also consider what would happen if we do not try to reduce emissions now and then discover that the climate impacts are a severe as some people expect. We’d either then have to accept further warming with even more severe impacts emerging, or we’d have to plan for even more drastic emission reductions than would be required today. This would also not reverse the changes that had already occurred; without some kind of technological intervention, climate change is likely irreversible on human timescales.

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73 Responses to The two-degree delusion?

  1. John Hartz says:

    ATTP: You warote:

    This is because of the inertia in the climate system.

    Where can I find a good explanation of why this is so?

  2. The Very Reverend Jebediah Hypotenuse says:


    Basically, it argues that we cannot possibly achieve this target without harming the poor…

    Every time I come across a deeply-held, Lomborgian, Ridleyian, first-world concern for the poor, I cannot help but be reminded of:


    Take up the White Man’s burden —
    Send forth the best ye breed —
    Go bind your sons to exile
    To serve your captives’ need;
    To wait in heavy harness,
    On fluttered folk and wild —
    Your new-caught, sullen peoples,
    Half-devil and half-child.

    Comes now, to search your manhood
    Through all the thankless years
    Cold, edged with dear-bought wisdom,
    The judgment of your peers!

    The poor are not children.
    The poor can decide their futures all by themselves, without any help from columns in ‘Foreign Affairs’ magazine.

    When Ted Nordhaus says:

    Meanwhile, we need to stop trying to balance the increasingly parsimonious carbon emissions budgets entailed by a two-degree target on the backs of the global poor. There is no moral justification for denying those populations the benefits of fossil-fuel-driven development.

    I have to wonder:
    who is this “we”, ke-mo sah-bee?
    – and who among the global poor asked for your permission, much less your moral justification, Ted?

  3. Jai Mitchell says:

    I believe that TN is speaking primarily about his work with IAMs that downplays the future impacts of climate change, artificially extends the cost of those impacts toward the latter half of the century (mostly sea level rise) and includes an amoral pure-time of rate multi-generational discount rate that reduces the value of lives lost in 70 years to 4% of today’s value.

    Coming from someone who has consistantly downplayed the risks of global warming, who has even argued that the global economy in 2100 will be 8X that of today under RCP 8.5 scenarios, I take NO stock in his ability to evaluate future (or even present!) reality!

  4. M&S says:

    Jai – you’re thinking of William Nordhaus, not Ted.

  5. John Hartz says:

    Until I read Nordhaus’ Foreign Affairs article, I did not know that he is William Nodhaus’s nephew. Has the elder Nordhaus publicly opined about his nephew’s work?

  6. The inertia in the climate system is due to the slow diffusional sequestration of CO2 into the ocean and the slow diffusional uptake of heat into the ocean. Diffusion naturally produces lags with fat tails

    “Where can I find a good explanation of why this is so?”

    It’s actually difficult to find good explanations of this behavior in the literature. What you often find is an approximation called the 2-Box model for heat update and the Berne model approximation for CO2 sequestration, which are both heuristic models for diffusional processes. The 2-Box model is poor as a heuristic as it does not generate a fat tail, while Berne is better as it generates a heuristic via a sum of 3 damped exponentials (IIRC), with the slowest exponential providing the fat-tail.

    Moreover, there is a dispersion in the diffusion properties that to some extent enhances the fat-tail nature of the response.

    The reason that the diffusional models are not routinely used is because they are computationally ugly to work analytically, often expressed in terms of transcendental erfc (error function) expressions. The 2-Box model makes it easier to come up with a closed-form solution so that it can guide the intuition — but this of course misses the fat-tail.

    But the GCM models do describe better the diffusional process, mainly by the inclusion of a multiple-layer or multiple-slab computational model. In principle, diffusion operates over an infinite number of layers, which is far from the 2-Box or 2-layer model used in the approximations.

    I have a couple of chapters submitted describing the modeling of diffusion.

  7. While the Berne model approximation is a heuristic, IIRC the Berne model itself is not, it is a multiple-box model of the carbon cycle and the transfers between reservoirs, attempting to model the physical processes.

  8. Nordhaus is right….and wrong. You see, the optimum green house gas reduction path should be estimated in steps, starting with a “base pathway” which yields a time series A of worldwide GDP. The first “reduction case” should assume a slight reduction in emissions versus the “base pathway”, which can be carried out using different approaches. If this first reduction case has five alternatives then we have R (for reduction) 1.1, 1.2, 1.3, etc. which yield a series of GDPs R1.1….to R1.5.

    This has to be repeated for a steeper reduction case which also has say 5 alternatives. Rinse and repeat.

    But Nirdhaus disconnects because he doesn’t have quality inputs for fossil fuel resource distribution and how much they will cost in the future. And this is a HUGE deal which both political sides are unable to accept. I happen to know that oil companies are having a difficult time finding new oil reserves by exploring for new fields, that fracking for oil is overhyped, and that most forecasts you are seeing are spurious, because they include liquids such as ethane (used for plastics) and biofuels. I’m told the picture is similar for coal by people in that business.

    So the models gave to include both a fossil fuel cost module, whereby oil, gas, a and coal require a growing amount of inputs per joule delivered to the end user. A similar curve has to be prepared for nuclear, wind, solar, geothermal, biofuel, etc. This curve should hopefully have decreasing costs. And these curves are somewhat unknown, so we gave to run say 20 combinations. Thus we end up with hundreds of cases. These can also be repeated for variable TCR/ECS. In the end we have a cloud of tine series which can be discounted using all sorts of alternatives. And this means the results cloud can have 5000 curves.

    With these in hand you start seeing that Nordhaus is right, the really fast reductions are not as sensible as the gentler ones. And when we factor the future higher cost of fossil fuels the optimum seems to be say between 550 and 650 ppm. Which could be slightly above 2 degrees C.

    If you do want a rational solution you real,y have to get into this type of logic and stop the cognitive dissonance. Accept there’s some things you don’t know, go try to figure out how to fill the gaps.

    By the way, if emissions are reduced by 40% from slightly above today’s value the end result is really decent. And it’s much more achievable.

  9. Willard says:

    > If you do want a rational solution you real,y have to get into this type of logic and stop the cognitive dissonance. Accept there’s some things you don’t know, go try to figure out how to fill the gaps.

    An important ClimateBall move that may not be reducible to an appeal to ignorance. There are things unknown, but there are also things Fernando has the privilege to know. If only everyone knew as much as Fernando. However, this:

    With these in hand you start seeing that Nordhaus is right, the really fast reductions are not as sensible as the gentler ones.

    could very well be classified as handwaving.

  10. Windchaser says:

    And when we factor the future higher cost of fossil fuels the optimum seems to be say between 550 and 650 ppm. Which could be slightly above 2 degrees C.

    “Could be”

    For the life of me, I can’t understand why we’d want to build our plans around planning for the best possible scenario, instead of looking at either the most realistic scenario or the entire range of scenarios from good to bad.

  11. The Very Reverend Jebediah Hypotenuse says:

    fernandoleanme:

    the optimum seems to be say between 550 and 650 ppm. Which could be slightly above 2 degrees C.

    Speaking of results clouds with 5000 curves, cognitive dissonance, and what the optimum seems to be:
    Hansen and Sato (2011):
    “goals of limiting human made warming to 2°C and CO2 to 450 ppm are prescriptions for disaster”.

    But don’t worry too much – In the long run, sea-level rise, droughts, famines, floods, and the ensuing wars, will effectively take care of the problem.

  12. While the Berne model approximation is a heuristic, IIRC the Berne model itself is not, it is a multiple-box model of the carbon cycle and the transfers between reservoirs, attempting to model the physical processes.

    The heuristic for the Bern model only has 3 exponentials and the slowest exponential is only 200 years, which means it does not match a true diffusional process, which has a 1/sqrt(t) tail.

    You can see this on my plot below, which only shows the response to 100 years. The diffusional tail will extend way beyond that, which is shown by the realistic formulation for dispersed diffusion. My point is that this is a better model than a mix of exponentials because it is simpler and follows the physics better.

  13. Mal Adapted says:

    Ted Nordhaus:

    There is no moral justification for denying those populations the benefits of fossil-fuel-driven development.

    The moral justification for denying them the benefits of fossil-fuel-driven development is that the social cost of fossil-fuel-driven climate change exceeds the social benefit of fossil-fuel-driven development. There is no moral justification, OTOH, for delaying the build-out of carbon-neutral energy to drive economic development for Nordhaus’s global poor. Front-end cost will be higher, but the total cost will be much less.

  14. Everett F Sargent says:

    The linked article is paywalled (or some such at my end) … But I found a full read copy here …
    http://eng.majalla.com/2018/02/article55255534/two-degree-delusion

  15. If I thought that all climate mitigation dollars were coming directly out of helping poor people, then, yes, I might have second thoughts about aggressive climate mitigation.

    Of course, I don’t think that. In fact, a well designed tax and rebate system can be a net plus for the poor even before the reduced climate impacts are taken into account. At the low low cost of having the rich take fewer plane flights and buy less energy intensive houses (depending on to what extent one believes that low-carbon energy sources are actually more expensive than fossil fuels once on a level playing field).

  16. Clive Best says:

    Looks like

    “the median time between an emission and maximum warming is 10.1 years, with a 90% probability range of 6.6–30.7 years.”

    directly contradicts the arguments in

    Guest post: A ‘new’ measurement of climate sensitivity?

    Either there is a long tail of inertial warming or there isn’t.

  17. JCH says:

    It’s apparently too complicated for some physicists.

    But, there was a subsequent paper that argued large emissions (pulse?) take longer to reach max warming.

  18. Francis says:

    This — “the optimum green house gas reduction path should be estimated in steps, starting with a “base pathway” which yields a time series A of worldwide GDP” — alone should be enough to result in the poster being shunned in polite society.

    Worldwide GDP as the measure of all things? I guess that mean that the entire continent of Africa plus a good chunk of southeast Asia, home to billions of people, can be sacrificed to the desire of Americans never, ever, to pay the true cost of their lifestyles. Those areas, after all, generate very little worldwide GDP.

    And speaking of worldwide GDP, didn’t the first Tol analysis come out far enough in the past so that the accuracy of the analysis can be measured? Has the hotter world actually raised GDP?

    (A further point: Last I checked, destruction of wealth — whether through war, flood, drought or hurricane — isn’t measured in GDP because GDP only measures current economic activity. California’s spending on the repair of Oroville Dam will show as an increase in GDP. If I’m correct on this point, GDP is even less useful as a measure of how to determine greenhouse gas reduction rates.)

  19. Clive, That link you provided says it’s a one-box model, which lacks a fat-tail as you can see in Figure 1 with the fitted black lines. The curvature there looks like a single damped exponential asymptotic response, not a Fick’s law type response as the blue lines show (which are more realistic for a diffusional process).

  20. Willard says:

    Speaking of the GDP, I’m sure auditors will appreciate:

    About one fourth of countries in the IMF’s database have no data on GDP; almost half of countries in the World Bank’s database either have no data on poverty or have it for only one year. It’s difficult to speak about a reduction in poverty (or an increase in GDP) when you don’t have a comparison point, and even more difficult when you don’t have any data at all.

    Source: https://medium.com/@UnlearningEcon/seeing-like-a-neoliberal-part-1-blinded-by-the-data-a134a7026d87

  21. All the evidence I’ve seen so far – and there’s been a lot of it recently – is that “the poor” are already suffering from pollution, much of it due to fossil fuels and associated activities. The death estimates are staggering, and air quality is a real problem even in the poorer neighborhoods of oil country in Texa. I looked it up and it was even worse than I remembered. Here are a few links:
    http://time.com/4989641/water-air-pollution-deaths/
    “Pollution kills 9 million people each year, new study finds” – https://www.washingtonpost.com/news/energy-environment/wp/2017/10/19/pollution-kills-9-million-people-each-year-new-study-finds/

    Then there’s this: https://www.nytimes.com/interactive/2017/12/21/world/asia/jakarta-sinking-climate.html

    Not a benefit to “the poor” by any measure

  22. izen says:

    Stages of Denial.
    1)It is not warming.
    2)It is warming, but it is Natural, not us.
    3)It is warming and it is us, but it is not dangerous or costly.
    4)It is warming and it is us and may be dangerous and costly, but it would be more dangerous and costly to reduce emissions.
    ———————————————- Recovery from Denial.
    5)It is warming and it is us and is dangerous and costly, it will become more dangerous and costly unless we reduce emissions to as close to zero as possible.

    Nordhaus has reached stage 4.

  23. JH,

    This is because of the inertia in the climate system.

    Where can I find a good explanation of why this is so?

    This is because if we were to lock atmospheric CO2 concentrations, we would still not be in equilibrium and so would continue to to warm and we reached equilibrium. This would take decades/centuries.

  24. I wrote “While the Berne model approximation is a heuristic, IIRC the Berne model itself is not, it is a multiple-box model of the carbon cycle and the transfers between reservoirs, attempting to model the physical processes.

    paul pukite wrote “The heuristic for the Bern model only has 3 exponentials and the slowest exponential is only 200 years, which means it does not match a true diffusional process, which has a 1/sqrt(t) tail.”

    No, as I said, that is only an approximation of the Bern model which is obtained from the impulse response of the Bern model, it isn’t the Bern model itself. The approximation is a heuristic, but the Bern model itself is not, it is a physical model (in the same way that the carbon cycle modelling in a GCM is a physical model).

  25. verytallguy says:

    Dikran, I’ve never seen a good description of the Bern model.

    Can you point me at one (or maybe you can feel a guest post coming on?)

  26. I don’t think there is a single source as there seems to have been many versions of the Bern model, where components have been changed/upgraded over time. I think Siegenthaler and Joos is the reference for the HILDA ocean component in the BERN SAR model. Having said which, I’ve just found a paper on an open-source reimplementation of a basic form of the BERN model, which may be what you (we) are looking for. I was hoping to develop some more complicated carbon cycle models than the very simple model in my residence time paper, but I read enough to realise it was well beyond my time/energy budget. 😦

    The main thing I learned was how little I really knew about it! ;o)

  27. There are several variations of the the Bern model. One is apparently a 4-box model instantiation of the HILDA model, which stands for High-Latitude Exchange/Interior Diffusion-Advection

    http://unfccc.int/resource/brazil/carbon.html

    As I said before, the mathematical ideal for diffusion requires an large (infinite) number of layers, which is how the erfc solution arises. For every box in the Bern model, one gets essentially an additional heuristically-fitted damped exponential. So a 4-box Bern model by association is approximated by 4 damped exponentials. Only by having an infinite number of boxes, can one truly approximate the erfc solution, which is the transcendental solution to a random walk between an infinite number of layers.

    Maybe it helps to know where I am coming from, which is semiconductor material science research, where one has to characterize the diffusion process precisely to have any chance of producing a device. The erfc solution is the starting point at understanding how a dopant diffuses into a semiconductor material. It’s not like I am going to unlearn that aspect just to fit in with the heuristics that I see in climate science. To me, a dopant diffusing into a layer of semiconductor material is no different than a molecule of CO2 diffusing into the ocean, the differences being in the values for the diffusion coefficient, and the fact that there is also additional drift going on there, which is rare in a fabrication setting.

    I don’t mind discussing this, because I have the topic covered in the book, which is going through a review process in any case.

  28. “To me, a dopant diffusing into a layer of semiconductor material is no different than a molecule of CO2 diffusing into the ocean, the differences being in the values for the diffusion coefficient, and the fact that there is also additional drift going on there, which is rare in a fabrication setting. ”

    is the layer of semiconductor material thermally stratified? Does it have physical turbation in the upper layers? One should be wary of shoehorning a physical system from some other field into the framework used in your own. Sometimes there are good reasons for things to be done differently.

    The point I am making is that it is important to distinguish between the BERN model and the approximation to the impulse response of the BERN model, especially when talking about heuristics.

  29. That’s the reason that I have made improvements on the diffusion model to incorporate dispersive aspects. There is not a single diffusion coefficient in the ocean, but a range of coefficients that I model as a maximum entropy spread. Applying this to the diffusion equation one can get a compact fat-tailed expression that’s actually much simpler than the erfc solution. Modeling of dispersion is also common for semiconductors, as these are often not homogeneous (think multi-layer structures), or are imperfect, such as amorphous materials loaded with defects. This approach is often referred to as superstatistics (due to C. Beck) and also described by Sornette in his book on disorder.

    The original question is on explaining the inertia of the climate system, and all this math does is explain the random walk wander of CO2 as it tries to sequester. There are an infinite number of pathways that a molecule can take, and you have to determine the best stochastic model to describe the path.

  30. The point I am making is that it is important to distinguish between the BERN model and the approximation to the impulse response of the BERN model, especially when talking about heuristics.

  31. I agree that the BERN model approximation is missing the fat-tail that Archer and others suggest can lead to a CO2 adjustment time that can extend to thousands of years. As David Archer put it, “The lifetime of fossil fuel CO2 in the atmosphere is a few centuries … plus 25 percent that lasts essentially forever.”

    That’s some inertia !

  32. “That’s some inertia !”

    except that thermal equilibrium would be reached earlier than that, so I don’t think (but could be wrong) it is relevant to the question in this case:

    on decadal timescales, at least – substantial emission reductions and will lead to continued warming for many decades. This is because of the inertia in the climate system.

    [emphasis mine]

  33. Dikran,

    except that thermal equilibrium would be reached earlier than that, so I don’t think (but could be wrong) it is relevant to the question in this case:

    Yes, if we could reduce emissions so that atmospheric concentrations stop rising, or rise slowly, then we would end up pretty close to equilibrium within decades/centuries.

    If we manage to get emissions to zero, then (as others have mentioned) some fraction (about 25%) of our emissions will remain in the atmosphere for thousands of years, and it would probably take more than 100 thousand years to return to pre-industrial levels. This is different to the timescale over which we would reach thermal equilibrium. In fact, once the slow carbon sinks start to draw down atmospheric CO2, we would start to cool back towards pre-industrial levels.

  34. Apart from sea level rise, I suspect most of the costs are due to change in the climate, rather than it being in a generally warmer state, so it is the thermal equilibriation time that seems more of a problem than the long tail of CO2 (which would keep the climate warmer, but steady, for a long time). However that is just my intuition and rising sea levels are a big problem in the very long term.

  35. Mal Adapted says:

    climatemusings:

    If I thought that all climate mitigation dollars were coming directly out of helping poor people, then, yes, I might have second thoughts about aggressive climate mitigation.

    Yep. Lukewarmers will consider AGW a problem only when it directly harms them or the few people they care about. They’ll delay internalizing their marginal climate-change costs as long as possible. Meanwhile the poorest of the world’s poor, who’ve always lived on the edge of survival, will fall over it as GMST rises.

    To be fair, there’s abundant precedent for privatizing benefits and socializing costs while shouting “won’t someone think of the poors?”

  36. You’re getting there. There’s also thermal diffusion of heat which has the same 1/sqrt(t) fat-tails as diffusion of CO2 into the ocean. These are separate processes with different average diffusion coefficients. I don’t know if there’s an equivalent Bern model for the thermal diffusion model, but it is certainly incorporated into the GCMs.

    That’s why it takes so long to equilibrate. The differences in temperature may not be great, but as long as there is a thermal gradient, the thermal energy will continue to redistribute via random walk diffusion.

  37. “You;’re getting there” – LOL!

  38. Getting there is combining the thermal diffusive fat-tail with the CO2 sequestering fat-tail, which has not been explicitly acknowledged

    Perhaps a good analogy is attaching a huge heat sink with a fan to a CPU. Plenty of heat capacity and thermal conductivity to disperse the heat away from the source, but without the fan to eventually dissipate the heat, it will gradually overheat. The analogy is that the ocean acts as a heat sink and the CO2 is preventing the fan from operating efficiently.

    Two types of inertia going on here — one for the thermal inertia and one for the inertia due to a missing dissipative factor.

  39. Everett F Sargent says:

    I think I’m interested in the Bern Model …
    http://unfccc.int/resource/brazil/carbon.html
    (SAR and TAR)
    http://www.ipcc-data.org/observ/ddc_co2.html
    (TAR?)
    The Bern Simple Climate Model (BernSCM) v1.0: an extensible and fully documented open source reimplementation of the Bern reduced form model for global carbon cycle-climate simulations
    (Kuno Strassmann(1),(a) and Fortunat Joos(1) (1) University of Bern, Switzerland (a) now at: Federal Institute of Technology, Switzerland)
    https://www.geosci-model-dev-discuss.net/gmd-2017-233/
    (discussion paper starting 2017-11-02, still under discussion)

    I kind of want to play with this type of model in my personal sandbox, so any other references/links (right off the top of your heads) would be greatly appreciated. THX

  40. lerpo says:

    the median time between an emission and maximum warming is 10.1 years, with a 90% probability range of 6.6–30.7 years.

    That covers global temperatures, but would climate impacts largely lag temperatures, possibly by much more than a few decades?

  41. lerpo,

    but would climate impacts largely lag temperatures, possibly by much more than a few decades?

    Possibly. Also, I think one should bear in mind that even though it make only take about a decade to reach maximum warming, there would be some re-balancing between the northern hemisphere (NH) and the southern hemisphere (SH) because the NH contains more land than the SH, and the SH contains more ocean than the NH. So (IIRC) the NH would initially warm more than the SH and then if we halted all emissions the SH would continue to warm, while the NH would cool slightly.

  42. PP “Getting there is combining the thermal diffusive fat-tail with the CO2 sequestering fat-tail, which has not been explicitly acknowledged”

    as I said, that is irrelevant to the question at hand, hence my amusesment at the “you’re getting there”. Any sensible person would just have agreed that it was irrelevant (or shown why it was relevant) rather than digging the hole ever deeper. I’ve no doubt you will respond with some more digging, but I’ll leave you to it.

  43. Hyperactive Hydrologist says:

    Lerpo,

    It will probably take at least 50-100 years to full understand the extent of future impacts due to internal variability and by the fact that extreme events/impacts are by definition rare. I would argue that 30 years is far too short a time frame to define climate particularly when considering impacts at the local and even regional level.

  44. I started on this thread because John Hartz was wondering about the origins of inertia in the climate system.

    It’s generally acknowledged that diffusivity is a way to quantify thermal inertia. Somebody even thought to add that to the Thermal Diffusivity Wikipedia page

    In a sense, thermal diffusivity is the measure of thermal inertia.

    Digging a hole deeper is a good metaphor, since doing experiments with boreholes is one way to evaluate thermal diffusion models. The following figure came out of a book that will be published at the end of this year. The context is of evaluating heat exchange models and simplifying the formulations to make them more convenient. The point to get across is the inertia in even this simple a system. What looks like an initially fast damped exponential transient continues on with a fat asymptotic tail that creeps along. That’s a significant fraction of the inertia, as diffusion provides the lag in the system. Solved closed-form analytically with an infinite-box diffusion model.

  45. I had also forgotten that I had cited this neat paper co-authored by noted climate scientist Nathan Myhrvold (!)

    “Projections of the pace of warming following an abrupt increase in atmospheric carbon dioxide concentration” http://iopscience.iop.org/article/10.1088/1748-9326/8/3/034039

    The best model is arguably the full diffusional model, which incidentally is likely a variation that Hansen used in his groundbreaking 1981 paper where he assumed a single diffusion coefficient of 1 cm^2/s.

  46. Paul,
    It would seem that you’ve jumped in and conflated the timescale over which we would tend to equilibrium if we fixed atmospheric CO2 levels, and the timescale over which atmospheric CO2 would return to pre-industrial levels if we stopped emitting CO2 into the atmosphere. These timescales are – as far as I’me aware – independent.

  47. Willard says:

    > I started on this thread because […]

    However you start, Web, we can predict where you’ll end up. Chief does the same at Judy’s. Don’t be like Chief.

  48. It’s not as if I am working out a precise solution, but I did say:

    combining the thermal diffusive fat-tail with the CO2 sequestering fat-tail, which has not been explicitly acknowledged”

    Both of these are independently fat-tail, so combining a fat-tail with another fat-tail gives a fatter tail. Convolving thin-tail distributions will tend to narrow the relative variance of the result, ala the central limit theorem, but when convolving fat-tail distributions, the CLT assumption is not valid and it remains fat. This is also intuitive, imo.

    I don’t know exactly what I have conflated here. The two are on equal footing, afaiac.

  49. Paul,
    They’re essentially independent, and operate on quite different timescales.

  50. As compared to this near tautology:

    This is because of the inertia in the climate system.

    Where can I find a good explanation of why this is so?

    This is because if we were to lock atmospheric CO2 concentrations, we would still not be in equilibrium and so would continue to to warm and we reached equilibrium. This would take decades/centuries.

    I didn’t think that really explained the why of the question. Perhaps my answer was more detailed than John Hartz wanted, but since he is a mainstay at Skeptical Science, I assumed he would appreciate at least a deeper take than that.

  51. JCH says:

    Well, I do not think it explains the “why”, which I suspect was the point of the question. I think I understand why, but I also understand why JH is asking. Because the explanations of why are poor explanations.

    Maximum warming from an emission of CO2 takes an average ~10 years. Equilibrium takes a whole lot longer and there’s even more maximum warming. Sounds weird. ? Diffusion. Huh?

  52. JCH,
    The key difference is between the warming due to a single pulse (which reaches a maximum after about a decade) and the warming that we will occur if we fix atmospheric CO2 concentations. The latter requires continued emissions and hence, we will continue warming for much more than a decade.

  53. JCH says:

    If the layers of a stratified ocean become respectively warmer, they will support a warmer ocean surface.

    That is what takes decades to centuries to occur?

  54. Steven Mosher says:

    long ago when tasked with calculating collateral damage from dropping bombs,we had a way of dealing with uncertainty.

    let god sort them out.

    ya the innocent might get harmed, the guilty too. just take action, let god sort it out.

    we wont act optimally except as a stroke of luck. so take the action you can take. like biofuels. opps. youll know youve hurt the poor when they scream. Then dont do that thing again.

  55. Diagonally opposite the Foreign Affairs article the Rev Hypotenuse deplores, is another on climate and policy in an earlier issue that begins:

    “Apocalyptic predictions require, if they are to be taken seriously, higher standards of evidence than do those on other matters where the stakes are not so great”

    By essays end it was apparent the author had none to offer and had staked his apocalyptic rhetoric on what he oxymoronically termed ” a sophisticate one dimensional model.

    I objected in correspondence in the following issue, and two years later FA duly ran Steve Schneider’s “Nuclear Winter Reappraised.” Maybe Gavin should follow Steve’s example and ask Gideon Rose for space to reply.

  56. Paul the long tail of CO2 update is the interia of the carbon cycle, but it isn’t the long tail of climate (particularly warming), as I pointed out repeatedly. The climate will effectively equilibriate long before the carbon cycle will.

  57. typing too fast, “update” should of course be “uptake”

  58. Yes, the first comment I made on this thread was exactly that:

    “The inertia in the climate system is due to the slow diffusional sequestration of CO2 into the ocean and the slow diffusional uptake of heat into the ocean. Diffusion naturally produces lags with fat tails”

    I bolded the and now because I didn’t think it was necessary then.

    Eddy diffusion is the main factor that drives the mixing to-and-from the ocean surface, and this is similar for both dissolved CO2 and thermal energy, so the fat-tails may be similar to first-order.

    Incidentally, this is in clear distinction from the diffusion process that I cut my teeth on. For semiconductors, the substrate (i.e. ocean equivalent) is clearly at a high-temperature equilibrium, so all that mattered is the dopant impurity (i.e. CO2 equivalent) diffusion rate. The latter is significantly elevated at the high annealling temperatures but is still very small, which allows a precise process control. That of course is all done under laboratory-controlled conditions, whereas with the climate we are are still somewhat winging it with interpretation, since we suffer from the lack of experimental controls.

  59. Paul,
    One day you might actually read what other people say (or, actually spend some time thinking about it if you do). This is clearly not that day.

  60. Dave_Geologist says:

    As you can perhaps guess from my newly-minted name, Paul, my idea of the long tail removing CO2 is (A) dissolve some in rainwater, (B) dissolve some rocks with the rainwater, flush some HCO3 into the sea, let critters turn it into their skeletons, let them die and sink to the bottom of the sea, bury, rinse and repeat for 100k years. Then (C) carry across the ocean to a subduction or collision zone expose, erode, rinse and repeat starting at (B), largely bypassing the atmosphere for 100M years. Or subduct and cook the limestone, belch CO2 out of a volcano, rinse and repeat starting at (A). (A) and (B) is how we’ll get back to 280ppm, not diffusion.

  61. dikranmarsupial says:

    PP your first comment on this thread was not that the long tail of CO2 is irrelevant to the inertia of the climate system, so it evidently was not “exactly that”. As ATTP suggest, you appear not to be paying attention to what is being said to you.

  62. Willard says:

    > Diagonally opposite the Foreign Affairs article the Rev Hypotenuse deplores, is another on climate and policy in an earlier issue that begins: […]

    I suppose you could refer to your own stuff more obliquely, Russell:

    http://adamant.typepad.com/seitz/2006/09/blast_from_the_.html

    The list of but but buts:

    – Al Gore
    – nuclear winter
    – WMDs
    – Cold War
    – teh stoopid modulz
    – Ehrlich
    – an uncertain Mr. T (under the form of we know very little)
    – ordinary people

    The Club of Rome seems to be missing.

  63. Dave_Geologist,
    What is interesting is that the Bern model impulse response also has an infinite half-life factor, which means that they think that a fraction of the CO2 will never sequester. As I recall, they set that fraction to about ~20%.

    My question is whether this is a way of approximating the “really long” tail of the diffusion impulse response, or whether this is the result of applying a different diffusion model, such as Ornstein-Uhlenbeck random walk, which essentially bounds the extent of the random walk.

    If the 20% value is constant to infinite times, it means that ~20% of the CO2 will forever be wandering, i.e. randomly walking in a kind of “no-mans zone”, trying to find a sequestering location without any success. This is an interesting premise, supported by Archer’s statement that “The lifetime of fossil fuel CO2 in the atmosphere is a few centuries … plus 25 percent that lasts essentially forever.”, without any way to verify that it is happening.

  64. Paul,
    Yes, the Bern model does have a residual term that is about 20%. However, that’s not because it’s thought that 20% will remain forever. It is because a residual of about 20% is expected to remain for thousands of years, which is longer than is probably regarded as relevant for the Bern model. The residual is related to the Revelle factor which, like most who critique carbon cycle modelling, you probably haven’t bothered to understand.

  65. Yes, the Revelle Factor is similar to a partial pressure factor with a dissociative rate law attached. The equivalent is well known in dopant processing for semiconductors. At a given annealing temperature, the initial uptake of dopants is balanced by the dopants that also simultaneously out-gas from the substrate, according to Arrhenius rate laws. The key concept to getting a net downward flow is the random walk diffusion that occurs once the atoms (or molecules) enter the substrate. They essentially get captured at the surface and start a downward migration (i.e. diffusion) before they can get ejected from the surface. The kinetics are why we can create doping profiles in semiconductor devices. But since the dopants are atomic, there is no dissociative rate law attached to it as with a reactive molecule such as CO2 (at least with standard processes).

    Yet, if this balanced partial pressure incorporation is throttled by some mechanism that prevents CO2 from entering the ocean, such as dissociative rate laws factored in with the partial pressure of the impinging molecules, the uptake could be gradually clamped, and certainly more excess would remain in the atmosphere. That definitely would make the problem a lot worse! Thus even fatter tails than I am modeling.

    But should we be seeing an increase in the “airborne fraction” of CO2 year-after-year if this is the case? Hansen had a chart where he is showing the fraction is decreasing back in 2013. Perhaps if we wait long enough, where the dissociative saturation starts kicking in much more strongly along with positive feedback Arrhenius effects. But that has nothing to do with an impulse response curve, which is the basic transient model.

    Ricciuto in ‎2008 said this, and currently the GCMs are using models of variable latitudinal diffusivity:

    “Sarmiento et al. [1992], who show that thermocline diffusivity is key in controlling the magnitude of oceanic uptake of anthropogenic carbon on annual timescales.”

    Interesting stuff.

  66. JCH says:

    Equilibrium Climate Sensitivity Obtained from Multi-Millennial Runs of Two GFDL Climate Models

    Abstract
    Equilibrium climate sensitivity (ECS), defined as the long-term change in global mean surface air temperature in response to doubling atmospheric CO2, is usually computed from short atmospheric simulations over a mixed layer ocean, or inferred using a linear regression over a short-time period of adjustment. We report the actual ECS from multi-millenial simulations of two GFDL general circulation models (GCMs), ESM2M and CM3 of 3.3 K and 4.8 K, respectively. Both values are ~1 K higher than estimates for the same models reported in the Fifth Assessment Report of the Intergovernmental Panel on Climate Change obtained by regressing the Earth’s energy imbalance against temperature. This underestimate is mainly due to changes in the climate feedback parameter (−𝛼) within the first century after atmospheric CO2 has stabilized. For both GCMs it is possible to estimate ECS with linear regression to within 0.3 K by increasing CO2 at 1% per year to doubling and using years 51-350 after CO2 is constant. We show that changes in −𝛼 differ between the two GCMs and are strongly tied to the changes in both vertical velocity at 500 hPa (𝜔500) and estimated inversion strength (EIS) that the GCMs experience during the progression towards the equilibrium. This suggests that while cloud physics parametrizations are important for determining the strength of −𝛼, the substantially different atmospheric state resulting from a changed SST pattern may be of equal importance.

  67. Michael Hauber says:

    fernandoleanme:


    But Nirdhaus disconnects because he doesn’t have quality inputs for fossil fuel resource distribution and how much they will cost in the future.


    the optimum seems to be say between 550 and 650 ppm. Which could be slightly above 2 degrees C.

    Seems rather contradictory. We don’t know what the cost of fossil fuel is in the future. And our best estimates of climate sentivity range from 1.5 to 4.5. And so many unknowns on future impacts (will we have breakthroughs breeding new agricultural species resistant to heat/drought, or will some pest explode due to changed ecological condiitons?) I call nonsense on claiming we have enough knowledge to determine a range as narrow as 550-650 for optimum amount of future fossil fuel usage.

  68. Dave_Geologist says:

    Paul and ATTP
    From the BernSCM preprint, they recognised the long-term geological drawdown I referred to above but choose to ignore it “CaCO 3 compensation by sediment dissolution and weathering
    (Archer et al., 1998) are not considered here, but could be described using analogous elimination processes with time scales on the order of 10 4 to 10 5 kyr (Joos et al., 2004).” From the human impact and policy viewpoint, we can debate whether not caring what happens after 2100 is fair to future generations, or whether committing to 20m of sea level rise is OK if it takes 1000 years but not if it takes 100 years, while agreeing that “Mother nature will fix it in 100kyr” is functionally equivalent to “essentially forever”.

  69. Dave,
    Yes, that is my understanding. It’s not suggesting that the residual has an infinite lifetime, they simply do not model the very slow weathering that will draw it down on thousand year timescales (probably > 100kyr in total).

  70. BBD says:

    After all, been there, done that: PETM.

  71. Willard says:
    February 19, 2018 at 6:36 pm
    > Diagonally opposite the Foreign Affairs article the Rev Hypotenuse deplores, is another on climate and policy in an earlier issue that begins: […]

    I suppose you could refer to your own stuff more obliquely, Russell:

    Hardly more than your link- it doesn’t connect to my writing in Foreign Affairs , or for that matter Schneider’s, and the present point is less teh Cold War or teh Gore than the persistence of views framed by promitive models in policy debates.

  72. Pingback: Climate Hawks | …and Then There's Physics

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