Control of methane, soot, and other short-lived climate-forcing agents has often been described as a cheap way to "buy time" to get carbon dioxide emissions under control. But is it really?
Expectations for the outcome of the Cancun climate talks seem to be running low, and the suggestion has emerged that maybe we should forget about controlling CO2 emissions for now, and instead do something with short lived climate forcing agents like methane or soot. This is often described as "buying time" to put CO2 emissions controls into place. For example, in a recent New York Times Op-Ed, Ramanathan and Victor write:
"Reducing soot and the other short-lived pollutants would not stop global warming, but it would buy time, perhaps a few decades, for the world to put in place more costly efforts to regulate carbon dioxide." — Ramanathan and Victor
The idea that aggressive early action to control short-lived climate forcing "buys time" to do something about CO2 has often been pushed in the past, e.g. in various newsletters and press releases associated with the UNEP Atmospheric Brown Cloud program, for example
"The BC reduction proposal is not proposed as an alternative to CO2 reduction. At best, it is a short term measure to buy a decade or two of time for implementing CO2 emission reduction strategies." — Ramanathan, writing in the UNEP Black Carbon Newsletter.
To be fair, it should be acknowledged that such pleas for more attention to short-lived climate forcing are almost invariably accompanied by a salutary reminder that it is really CO2 that needs to be gotten under control, as in the quote above. Achim Steiner, writing in the same issue of the Black Carbon Newsletter writes "Paying attention to black carbon should not distract people from the real issue at hand, carbon dioxide." A similar sentiment is expressed in the Ramanathan and Victor op-ed. While emphasizing the central importance of CO2, Penner et al. argue that "…to provide short-term relief from climate warming, the short-lived compounds that induce warming need to be brought under control within a timescale of a few decades." (They also make the intriguing suggestion that doing so might provide a global experiment that could help constrain climate sensitivity.) Writing in Science, Stacy Jackson concludes that "… a focus on CO2 may prove ineffective in the near term without comparable attention to pollutants with shorter lifetimes"
All of this is well-intentioned stuff, none of it denies the central importance of CO2, and I’m sure there are many benefits to be had from reducing soot emissions sooner rather than later. Given the large agricultural component of methane emissions, keeping these emissions from growing in the face of a the need to feed a growing number of people is a serious challenge that must ultimately be met. But still, these proposals tend to convey the impression that dealing with the short-lived forcings now will in some way make it easier to deal with CO2 later, and that’s wrong. In this post, I will explain why.
To get a feel for the issues in play, we’ll first take a look at methane vs CO2. This provides a clean example, because methane has a straightforward, well-characterized warming effect which is easy to compare with that of CO2. If you’re just looking at the concentration of methane and CO2 at a given time, the methane/ CO2 equivalence is pretty easy to figure, since you can turn them both into the common currency of top-of-atmosphere radiative forcing. For example, doubling CO2 from 300 ppm to 600 ppm yields a clear-sky radiative forcing of 4.5 W/m2. Doubling methane from 1ppm to 2 ppm yields a radiative forcing of 0.8 W/m2, but since we started from such a low concentration of methane, it takes many fewer molecules of methane to double methane than to double CO2. Per molecule added, methane yields about 54 times as much radiative forcing as CO2. Note that most of this effect has nothing much to do with any special property of methane, but arises simply because the radiative forcing for most greenhouse gases is logarithmic in concentration, so you sort of get the same radiative forcing for everybody upon doubling their concentration — but if you start with somebody whose concentration is low, it takes many fewer molecules to double. That means that the CO2 equivalent of methane depends on what concentration you are starting with. If you started from a concentration of 10ppm, then the equivalence factor drops to 10. If you start out with equal amounts of methane and CO2 (300 ppm), then the equivalence factor drops further to 0.5. In that sense, methane is, intrinsically speaking, a worse greenhouse gas than CO2, though the crossover is at values that are so high they are only relevant (at most) to the Early Earth. ( I ran these calculations with the Python interface to the NCAR radiation model, provided in the Chapter 4 scripts of my book, Principles of Planetary Climate. They are done using an idealized clear-sky atmospheric profile, so the numbers are a bit different from what you’ll find in the IPCC reports, but it’s nice to have a calculation simple enough you can re-do it yourself.)
Things get a lot trickier when you try to bring time into the problem, because methane and CO2 have vastly different atmospheric lifetimes. Methane oxidizes to CO2 in about 10 years, and since we are dealing with so little methane, that extra ppm of CO2 you get after it oxidizes adds little ongoing warming. That means that the methane concentration in the atmosphere is determined by the methane emission rate averaged over the previous ten years, and the methane component of warming disappears quickly after emissions cease. In contrast, about half of CO2 emitted disappears into the ocean fairly quickly, while the other half stays in the atmosphere for thousands of years. Therefore, the atmospheric burden of CO2 in any given year is determined by the cumulative emissions going back to the beginning of the Industrial Revolution, and the warming persists for thousands of years after emissions cease. Over the long term, CO2 accumulates in the atmosphere, like mercury in the body of a fish, whereas methane does not. For this reason, it is the CO2 emissions, and the CO2 emissions alone, that determine the climate that humanity will need to live with for a time that stretches into the future at least as long as the time since the founding of the first Sumerian cities stretches into the past. The usual wimpy statement that CO2 stays in the air for "centuries" doesn’t begin to convey the far-reaching consequences of the amount of CO2 we decide to pump out in the coming several decades.
As a reminder of that, here’s a graph from the NRC Climate Stabilization Targets report (of which I was an author) summarizing how cumulative carbon emissions set the climate thermostat for the next 8000 years and more.
The numbers on each curve gives the total cumulative carbon emissions (in gigatonnes) during the time when human activities continue to emit carbon. These results are based on calculations by Eby et al using the UVIC coupled carbon/climate model, and they are really just a reprise of what Dave Archer has been telling all of us for years (e.g here, here and here). It turns out that it matters little to temperature whether all the CO2 is emitted in a carbon orgy near the beginning of the fossil fuel era, or spread out over a few hundred years. It’s cumulative carbon that counts, and pretty much it is the only thing that counts. A cumulative emission of a trillion tonnes of carbon just might keep the Earth below a warming of 2ºC, in line with earlier estimates equating the European Union target warming threshold with cumulative carbon (see our Trillion Tonne post). The peak warming scales approximately linearly with cumulative emissions, and the warming you get at the peak is pretty nearly the warming you are stuck with for the next millennium, with only slight declines beyond that. We are currently about halfway to our first trillion tonnes, but given the miracles of exponential growth, we are going to get there pretty quickly if nothing changes. If you go beyond, and dump 2355 gigatonnes into the atmosphere before kicking the fossil fuel habit, then the global mean temperature will still be 3ºC warmer than pre-industrial in the year 8000. That gives plenty of time for bad stuff to happen, including deglaciation of Greenland, loss of the West Antarctic Ice Sheet, or a destabilizing PETM-type soil carbon release. Note further that these calculations were done with a model designed to have a climate sensitivity similar to the IPCC median. Therefore, even if you hold the line at a trillion tonnes, there is still about a 50% chance that warming will exceed 2ºC.
Let’s suppose, however, that we decide to go all-out on methane, and not do anything serious about CO2 for another 30 years. To keep the example simple, we’ll think of a world in which methane and CO2 are the only anthropogenic climate forcing agents. Suppose we are outrageously successful, and knock down anthropogenic methane emissions to zero, which would knock back atmospheric methane to a pre-industrial concentration of around 0.8 ppm. This yields a one-time reduction of radiative forcing of about 0.9W/m2. Because we’re dealing with fairly short-term influences which haven’t had time to involve the deep ocean, we translate this into a cooling using the median transient climate sensitivity from Table 3.1 in the NRC Climate Stabilization Targets report, rather than the higher equilibrium sensitivity. This gives us a one-time cooling of 0.4ºC. The notion of "buying time" comes from the idea that by taking out this increment of warming, you can go on emitting CO2 for longer before hitting a 2 degree danger threshold. The problem is that, once you hit that threshold with CO2, you are stuck there essentially forever, since you can’t "unemit" the CO2 with any known scalable economically feasible technology.
While we are "buying" (or frittering away) time dealing with methane, fossil-fuel CO2 emission rate, and hence cumulative emissions, continue rising at the rate of 3% per year, as they have done since 1900. By 2040, we have put another 573 gigatonnes of carbon into the atmosphere, bringing the cumulative fossil fuel total up to 965 gigatonnes. By controlling methane you have indeed kept the warming in 2040 from broaching the 2C limit, but what happens then? In order to keep the cumulative emissions below the 1 trillion tonne limit, you are faced with the daunting task of bringing the emissions rate (which by 2040 has grown to 22 gigatonnes per year) all the way to zero almost immediately. That wasn’t very helpful, was it? At that point, you’d probably like to return the time you bought and get a refund (but sorry, no refunds on sale items). More realistically, by the time you managed to halt emissions growth and bring it down to nearly zero, another half trillion tonnes or so would have accumulated in the atmosphere, committing the Earth to a yet higher level of long-term warming.
Suppose instead that you had focused all efforts on reducing the growth rate of CO2 emissions from 3% to 2%, averaged over 2010-2040, forgetting about methane until the end of that period. In this scenario, the cumulative carbon emitted up to 2040 is only 713 gigatonnes, giving more time to avoid hitting the trillion-tonne threshold. The warming from CO2 in 2040 is about 1.2C, but we have to add in another 0.4ºC because we haven’t done anything to bring down methane emissions. That brings the warming to 1.6C, which will increase further beyond 2040 as the cumulative carbon emissions approach a trillion tonnes. However, since methane responds within a decade to emissions reductions, we still get the full climate benefit of reducing methane even if the actions are deferred to 2040. The same cannot be said for deferral of action on CO2 emissions.
The following cartoon, loosely based on Eby’s calculations shows two illustrative scenarios: one in which early action is taken on methane, at the expense of allowing cumulative CO2-carbon emissions to rise to around 1.7 trillion tonnes, and another in which action on methane is delayed until 2040, allowing cumulative emissions to be held to a trillion tonnes. The curves can be diddled a bit depending on how much short term warming you get from controlling additional short-lived gases, and how much extra cumulative carbon emissions you assume goes along, but it is really hard to come up with any scenario where you come out ahead from acting early on the short-lived forcings instead of going all-out to reduce the rate of CO2 emissions.
There are a few greenhouse gases other than CO2 that have lifetimes sufficiently long to lend some urgency to their control. That would include HFC23 with a lifetime of 260 years, CFC13 with a lifetime of 640 years and SF6 with a practically unlimited lifetime. Most of the rest are more like methane than they are like CO2 (e.g HFC31 at 5 years)
Absorbing aerosols — soot, loosely speaking — have a number of complex regional effects that make it difficult to treat their climate impact on an equal footing with that of well-mixed greenhouse gases. Soot falling on snow or ice has an unambiguous warming effect, manifest particularly strongly at high latitudes and high altitudes. For airborne absorbing aerosols, though, it is hard to even know whether they have a warming or cooling effect on surface temperature, or leave it more or less unchanged. Except over high albedo surfaces, airborne aerosols mainly heat the atmosphere by direct solar absorption, at the expense of reduced solar absorption at the surface. When the shading is not too strong, the main consequence is a reduction of the convection that would ordinarily carry solar energy from the ground to the atmosphere. This profoundly influences precipitation, and the atmospheric circulation, especially in the tropics. In extreme cases, the atmospheric absorption can even shut down convection completely, leading to stabilization of the tropospheric lapse rate and a severe surface cooling, as in the Nuclear Winter limit (see also the more elementary discussion of this limit in Chapter 4 of Principles of Planetary Climate).
A further consideration is that most activities that emit soot also emit precursors to reflecting aerosols which cool the planet. It is unlikely (and probably undesirable) that one would be able to limit one without also limiting the other. Hence, the net implication of the black carbon component is probably that it will help offset some of the warming caused by eliminating sulfate aerosols. That’s good, but it’s not what you bargained for if you were expecting a cooling for your money. The main thing about soot and the stew of toxic emissions going into the Atmospheric Brown Cloud , though, is that there are compelling human health, agricultural, and regional climate reasons to eliminate them, regardless of the side effect on global temperature. These are things that need to be done regardless of the climate implications (positive or negative), just as there is a need to supply the developing world with reliable clean water. It is pointless to make an already complicated climate negotiation yet more complicated by wrapping such things into the mix. It is nonetheless worth noting that many of the things one would do to reduce soot emissions, such as substituting natural gas for coal, or burning coal in cleaner, more efficient power plants, also would tend to reduce CO2 emissions, and such double-wins are of course to be sought and pursued ardently (note Gavin’s op-ed on co-benefits of CO2 reduction).
IPCC-style Global Warming Potentials attempt to trade off radiative forcing against lifetime in a Procrustean attempt to boil all climate forcings down to a single handy-dandy number that can be used in climate treaties and national legislation. In reality, aerosol-forming emissions, short-lived greenhouse gas emissions, and CO2 emissions are separate dials, controlling very different aspects of the Earth’s climate future. CO2 emissions play a distinguished role, because they ratchet up the Earth’s thermostat. It’s a dial you can turn up, but you can’t turn it back down. CO2 is a genie you can’t put back in the bottle. Climate forcings should not be aggregated. Each category should be treated in its own right. Otherwise, there are perverse incentives to do too much too soon on short-lived forcings and too little too late on CO2.
#90 raypierre
I can attest to this on a small scale. I painted the roof, hood and trunk of my Honda. I used to be afraid to touch the steering wheel in the summer. Now life is good :)
Benefits:
– Car is cooler
– Less heat stress on dashboard and interior
– I rarely need to turn on the AC, even on very warm days
– Saves on gas mileage because I’m not using AC as much.
Let’s just say it’s cool ;)
in the response to post #90 about solar radiation:-
“As an earlier commenter noted, the solar energy is just reflected back to space, and doesn’t reappear anywhere on Earth.”
Surely this is not quite true? just as solar energy heats up air, gas and water molecules going down to the surface of the planet, the same will happen on the way up? look into a bright illuminated mirror and feel the warmth! (or stare at a white wall in the sun)
Is it possible that this extra “return trip” energy is significant, especially as the atmosphere above urban areas is relatively “thicker” with CO2 and particulates etc? Effectively doubling the opportunity for energy to be transferred into the atmosphere at sympathetic wavelengths of infra-red. In short Atmospheric density is not uniform so why should it’s ability to absorb energy be? (see clouds..)
A specific question if anyone interested in answering it?
As a tremendous amount of deforestation and biomass burning occurs at equatorial regions, and this is where the sun warms the atmosphere most.
If the contents of the atmosphere above these regions is enriched with CO2 and other gases and particles then surely more energy will be absorbed into the atmosphere here than would have otherwise been the case with cleaner air?
The question is, as this “enriched atmosphere” rises through the air column and displaces the normal water vapor does it have a significantly higher ability to absorb and transport energy than the “normal” atmosphere it displaced?
Having watched satellite water vapor images for years I can say that “normal” atmospheric displacement patterns appear to have changed, especially over oil, gas and biomass burning sites.
Feh, a typo in my #89, if anyone still cares:
“numerous, often not especially well-founded questions” should read “numerous, often not especially well-founded assertions.“
Welcome back, Raypierre.
[Response: Nice to have time to be back, now that the Planetary Climate Book and other major time sinks are more under control. –raypierre]
AL 40,
Natural sources are matched by natural sinks, which is why CO2 was stable at about 280 ppmv for thousands of years. It’s the artificial addition that’s the problem, since the natural sinks are only handling about half of it. That’s why CO2 is up 38% since the industrial revolution started.
EG 50: The [Chernobyl] “disaster” was mostly hype.
BPL: 56 people died and thousands of kids got thyroid cancer. That’s a disaster by any rational standard.
[Response: Enough please. Let’s not re-start the nuclear power flame wars. –raypierre]
GS 77: Christopher, can you please explain where the rejected heat [from painting his driveway white] goes?
BPL: Back out to space, if we’re talking about sunlight. Otherwise it would be absorbed and the driveway would be hotter. Higher albedo DOES cool the Earth, or pretty much anything else.
Vendicar 88,
The GOP is very much opposed to science in general, even when they claim to be defending it. Too often these days scientists are finding reasons to put taxes or regulation on certain big businesses. To stop that, they have to stop science. Then there’s the problem of “teaching our kids they come from monkeys.” And it all fits together. You can’t throw out large areas of science without affecting all the other areas.
Keith Kloor, Again, I would suggest that we have to make political reality correspond to physical reality, as I do not know of a way to do the opposite.
The fact is that while we know the effects of climate change will be severe, we do not know at what temperature they will transform from severe to devastating. We do not know even now how much warming we are committed to in the pipeline as it were. These uncertainties are what make such incrementalist plans risky–that and they give the illusion that people are actually doing something.
People need to stop being petulant children and accept the reality that lies before them. THAT is the political reality.
#101, David Painter–
A couple of things. First, the atmosphere is pretty transparent to visible light (that’s presumably why we evolved eyes optimized for those frequencies of light.) So light is reflected at the ground (or roof), it mostly escapes the atmosphere quite easily. Yes, there will be some absorption by particulates like soot, but I think that is not large on a global scale compared to the greenhouse effect. (Corrections welcome if I’m wrong about that.)
What happens when light reaches the ground and is absorbed is that that energy is thermalized. That’s what one feels on one’s face, upturned on a sunny day. That energy will also be re-emitted as near IR, which you mention–and that’s what the CO2 and other GHGs absorb. Reflective surfaces cause this whole process to be avoided.
Second, you speak of “enriched” atmosphere “displacing water.” I know of no reason to think that additional CO2 or particulates would displace water vapor. (Though particulates encourage condensation, don’t they? But the water is still present, albeit liquid rather than gaseous.) And if it did, the effect on energy absorption might well be negative–since, as both “warmists” and (most?) “denialists” agree, water vapor is a powerful greenhouse gas!
None of that means that your observations of satellite water vapor are wrong; but there may be other reasons for what you see. (Lessened transpiration seems likely to me.)
Second,
Ray L,
I don’t think Keith K disagrees with the necessity to do so. He disagrees about *how* to best start doing so, given the geopolitical situation. You’re attacking a strawman.
I repeat my question:
“The integral of fossil carbon is the most important problem for our future climate.
So, it is incomprehensible that there is no serious work, in my knowing, on the question of carbon (coal) availability and IPCC itself says nothing about this in AR4.
You cited Lackner:
“but when I ran this by Klaus Lackner recently, Klaus thought that hydrocarbon extraction would get so good that we’d probably start running out of oxygen before we ran out of coal.”
Is this sustained by a publication or another serious work, or is this a joke?”
[Response: As far as I am concerned, no estimate of coal above a trillion tonnes or so is supported by any credible published analysis. You can find lots of arguments for there being a lot less that 5 trillion tonnes, but we just don’t know when it will run out. Klaus was not joking, but the general idea is that there are a lot of dilute hydrocarbons in sediments, and it is quite possible technologies will emerge to allow deep, dilute deposits to be tapped. Klaus pointed out that Rogner’s review article of about a decade ago didn’t include much gas from hydrofrakking, since it wasn’t thought to be an economic technology at the time. But I’m way out of my depth here, so don’t take anything I say as authoritative. But don’t be so quick to take what the experts say either. It’s an important issue that needs to be resolved. –raypierre]
re: 108.
It goes even further than that when the GOP (and deniers/skeptics) start claiming that science is a “religion”. As we have seen from some of the regular denier posters here.
[Response: Getting a bit off-topic here. Kloor’s site might be a better place for political discussions. Though I do understand that it is hard to discuss the issue at hand without getting involved with the realities of what can actually be done in the present US political climate. –raypierre]
Re 99#
thanks for response
“Location of soot and other aerosol emissions is important, but CO2 can be considered (for purposes of radiative forcing) well mixed on account of its long lifetime. It doesn’t matter where the CO2 is emitted”
If this is true then how is the effect of localized (country sized) biomass and hydrocarbon burning taken into consideration when massive air columns rise up to the outer edge of the atmosphere carrying large amounts of heated gases? (also see volcanic)
Is it true 200ppm of CO2 at sea level is as damaging as 200ppm of CO2 at 100,000ft?
(when temperature, pressure and exposure to unattenuated solar energy are massively different)
Standard weather balloons displace more volume at altitude, so other gases should if injected there behave the same, heavier elements like CO2 should fall back to earth unless heated by unattenuated solar energy surely? Like a sort of minature Roziere balloon? (possibly remaining at altitude)
http://en.wikipedia.org/wiki/Rozi%C3%A8re_balloon
M. Tobis @49 says: “At some point climate change may well become so severe that per capita wealth will begin a long term, accelerating downturn. At that point, no mitigation at all will be affordable.”
Exactly! Economists (e.g., Nordhaus and Tol) argue over what’s the appropriate number for the discount rate regarding future environmental impacts – but they assume as an article of faith that the discount rate MUST BE POSITIVE. There is no basis for this assumption – it is not some sort of immutable natural law. Under a scenario of future decline in societal wealth the discount rate can become NEGATIVE and in that scenario it makes more sense to invest NOW in crucial infrastructure that society can afford now and that will be essential later (when that society won’t be able to afford to construct new equivalents of such infrastructure) – as opposed to current spending on lattes and Hummers (ephemeral goods that don’t add future societal value). (Similar to the story of “The Ants and the Grasshopper” and all that.)
[edit – please don’t bother to post abusive comments directed at other commenters]
David Painter,
The way to think of this is as follows:
Unless the atoms/molecules of gas have energy states that can be excited by the light, the atmosphere will be transparent to that wavelength. Millimeter waves, radio, etc. can excite rotational states. IR tends to excite vibrational states in some molecules (notably ghgs). UV and x-ray can excite electronic excitations (which is why we can’t do astronomy with these on Earth). However, the fact that you can tell the colors of stars, planets, etc. shows that the atmosphere is pretty transparent in the visible. You do get scattering, but that doesn’t impede energy transport much. It’s the same reason melting snow winds up giving a positive feedback by changing albedo or black carbon gives a forcing by changing snow albedo (and then melting the snow).
86, Walter Pearce: Re: SM #85 — What, other than the climate, would you expect to be different in 20 years that would enable coal to be taxed?
new paragraph
Fiscally, this is the best time in 60 years for the U.S., at least, to begin taxing fossil fuels. As this chart from Reutersshows, payroll taxes could be cut, carbon taxes instituted, and the overall tax burden remain relatively low.
Second point first, this is the best time in 60 years, I agree. I think that a concerted effort focusing on the environmental degradation caused by coal, and not emphasizing CO2, might produce a tax sometime in the next 10 years. Recall that this is a complex democracy and almost nothing both simple and good happens very rapidly. More on politics below. For now remember that lots of people earn their livings around coal, and their representatives are in the House and Senate. Something can be worked out. Maybe sooner: I think Chu, Vilsack and Salazar (an exceptionally good team) have the moxie to work something out with Congressional leaders of both parties, should they focus on coal for at least a year.
First question, in 20 years ( I think more like 10) the production techniques to replace the electricity from coal will be cheaper, so it will be clearer to everyone that the coal-fired power plants can be readily phased out without sacrificing the electricity and putting lots of people out of work.
About politics. Al Gore’s “An Inconvenient Truth” and the Kyoto Treaty that preceded it stimulated a huge public policy debate that for now has been won by the people who oppose a rapid end to CO2. Concomitantly, more Americans have become aware of the challenges of maintaining America’s liquid fuel supply and are more willing to subsidize all alternative sources of energy (these are not exactly closely related logically). My recommendation to you guys would be to emphasize alternative energy production for the next 10 years (as a matter of policy), and focus on the science of CO2 related global warming but go lightly on CO2 reduction (as a matter of policy.) Politics is a “long game”, a “marathon not a sprint”, “a full 4 quarters” etc, and we are in the “early innings”. After being ahead for a while, you are now behind (afaict), so you need a strategy that will pull you ahead in the future. There will be a future, so prepare for it. Also, since this is a democracy, you might need to develop a style of speech more along the lines of “Here are things we can work on together” instead of “You are all corrupt, ignorant and stupid.” (and avoid extravagant Cancun-like parties.) Lots of AGW opponents are equally strident and insulting, and you’d like to marginalize them instead of marginalizing yourselves. FWIW
I wrote in response to an earlier comment that I’d like to reemphasize: the reason for going slow now (“doing nothing” isn’t what’s happening, to clarify that detail) is that all the replacement technologies are declining in price.
As to California, I’d hate to see the whole US do to its economy what Californians have done to theirs. I’d recommend you study Iowa and Texas instead: Texas overtook California in producing electricity from wind; Iowa is number 2 and has a large state-of-the art turbine factory. Even Nevada, but not California, has permitted the construction of a new turbine factory. California law AB32 will enrich suppliers in Nevada, Arizona, and China while producing continued economic decline here by raising the cost of electricity. California is a most ambiguous example.
Since people frequently recommend stuff for me to read, I thought I’d mention that I have ordered Raymond Pierrehumbert,s new book from CUP. Enjoy my few bucks in royalties Raypierre!
#114–
David, air columns don’t make it to “the outer edge of the atmosphere”–stratospheric levels are pretty much the limit, and most don’t nearly get that far. See:
http://en.wikipedia.org/wiki/Earth%27s_atmosphere#Structure_of_the_atmosphere
I’m going to duck the question of CO2 efficacy at different altitudes, but I will say that CO2 is not much inclined to sink in the atmosphere due to the effects of turbulence, not heating per se. You can actually see this when CO2 fog is used in a stage production; the fog hangs low, but disperses upward and mixes with even relatively sedate motions by the performers onstage.
[Response: This is a very nice example of a useful ‘visual’ to use when explaining mixing in the atmosphere — thanks!–eric]
re #99
This is a minor nit. Certainly, for this study, location of CO2 emission is irrelevant, but in a few cases, the location actually does matter.
See Mark Jacobson testimony to Congress, the oral testimony is probably enough.
Basically, while CO2 is generally well-mixed, some urban areas have noticeably higher CO2 levels, and if they are already polluted, the higher temperatures a) make pollution worse and if it is warm enough to want air conditioning, b) they want more, which uses more power, which may mean more Co2 emissions somewhere.
Los Angeles is the obvious example, but it’s also true of the CA Central Valley, and some parts of the SF Bay Area, i.e., like San Jose.
Im wondering if someone might be able to help me fully understand this.
If methane oxidizes to Co2 in about a decade, why would we not address methane first? If the higher warming factor of methane lasts for a decade before it turns to Co2, which then lasts for thousands of years, should we not eliminate methane first to get rid of that initial extra warming potential? From my understanding its seems like emitting methane is pretty much the same as emitting Co2, except in the first 10 years of its life it has a greater warming potential than Co2.
Not touching methane would mean we get its initial short term warming effects plus its long term Co2 warming effects. So in that sense reducing methane initially would be a better approach.
So what part am I missing here, since this is the opposite conclusion the author draws?
No, Kloor’s repeated insistence that no political effort based on climate change mitigation is possible is a strawman, and he bases his entire argument for giving up on mitigation as a political goal on this strawman.
We saw that in CA during the last election, when an effort to block CA’s ambitious emissions reductions law went down by 21%.
What is true is that *certain* political approaches are off the table. The Republican Party will ensure that no coordinated federal-level effort will be put into place for the next two years, at least. That’s not stopping states like CA and OR (and others) from moving forward.
What’s also true is that the UN international effort that depends on consensus agreement among over a 100 countries appears dead in the water. But that’s really been true since Kyoto, since the US didn’t ratify that treaty and it’s been clear that no other overarching treaty would have much chance of ratification here, either.
That doesn’t block agreements from individual countries, such as the talks between China and the US that appear to be moving forward in Cancun suggests.
There’s really nothing in the global political environment to support Kloor’s “let’s give up on mitigation and hope that efforts that lead to CO2 reductions as a side-effect rather than goal are sufficient” portrayal of reality.
Kloor also has this odd POV where he seems to insist that raypierre’s technical assessment of the benefits of an OTF approach doesn’t respect the political situation, i.e. that somehow the physical science should reflect the political environment, which is just weird (you have to read what he writes at his own blog and elsewhere to fully appreciate this).
Hugh @ #98 – Thank you for the link, I read the whole thing and am going to repost the link in a couple of places. Scary indeed, as is your email … even having read about the problem, I had not realized the coral would die so quickly in such a wide area.
I mentioned some of Sterman and Sweeney’s work at Kloor’s as an example of the basic misconceptions that the public has on “flow” problems versus “stock” problems. I think it is worthwhile considering this in the current discussion.
As I understand it, methane is characterized more as a “flow” problem, while CO2 is clearly a “stock” problem. And you can not substitute solving one for dealing with the other.
As with most “human” analogies for physical problems, there are shortcomings, but this is one that I have been mulling since the Ramanathan/Victor piece was published.
Suppose you are hurtling towards personal bankrooptsie*. You have some relatively easy-to-cut expenses, say a golf course membership. And you have some honking huge amount of personal credit debt, that is accruing interest at roughly the same annual rate as the excess personal expenses.
If you elect to cut the country club membership, and defer dealing with the debt for a decade until it is more politically personally palatable, you have not really bought yourself extra time. More likely, you’ve just exacerbated your situation so that the debt is now truly an intractable problem.
You were not able to trade the one-time “flow” problem off for the inexorably deteriorating “stock” problem.
Sure, at least you were doing something!. And perhaps the “heat” of inbound telephone calls abated for a while as the golf course kollekshun* department eased off, and you used the time to you wait patiently to win the lottery or somesuch, but you really have not made yourself better off.
In fact, you almost certainly would have been far better off to have found a way to reduce the golf course membership in half while using the savings to pay off half of the accumulating interest on the debt. Or even keeping the membership and using any extra funds to keep the debt constant…
There are inevitable weaknesses in the analogy, but it may resonate better with some.
As Sterman and Sweeney say, the public’s and policy-makers’ flawed understanding of stocks versus flows: “These beliefs… support wait-and-see policies but… violate fundamental physical constraints including conservation of mass.”
I really think whenever we can we should be framing the CO2 dilemma in the “budget” concept that Meinhausen et al, Allen et al, TrillionTonne.org and others do. In fact, I think we should emphasize the concept of “a one-time emission endowment amount that we are depleting” rather than “an accumulated emission amount that we want to stay below”, because the idea of “running out” seems – to me, anyway – as more naturally intuitive to most people.
(I suspect, as well, that black carbon tends more towards the characterization of a “stock” problem, at least as far as ice goes, but that’s just off the top of my head…).
*I am making some deliberate bizarre misspellings here, because my previous submission got rejected as spam, and I don’t want to have to retype a third time!
[Response: This is a very nice example of a useful ‘visual’ to use when explaining mixing in the atmosphere — thanks!–eric]
Most welcome, Eric! Just for clarity, though, there are other substances used for stage “fog” as well, not all of which behave exactly as described–just another complication to bear in mind. (Sigh.) I did witness this effect recently in a production of “The Nutcracker,” where I happen to know that CO2 “fog” was indeed used.
#121–Because the hugely overwhelming proportion of CO2 is emitted directly; if we eliminated methane emissions, it wouldn’t much affect CO2 concentrations 10 years later.
You know, I’m beginning to notice a common theme running through the arguments of the complacent–it is “Anything but CO2”.
First, they are saying that warming is due to ANYTHING BUT CO2–cosmic rays, land use, fraud, Martian heat rays…. Then when they are confronted with the incontrovertible evidence that CO2 is responsible for current warming, they say we must mitigate ANYTHING BUT CO2.
The thing is that it is CO2 that is the dominant source of the problem. Addressing everything else is going for the capillaries rather than the jugular.
This is one of the best articles I have read on Real Climate. It goes to the heart of the matter and shows that any delay (by almost any means) in stopping CO2 emissions is a very wrong approach. We have to face several realities that all of us seem to avoid to a certain extent. Let me just give one example.
I have a friend here in Calgary who has invested CD$35,000 to install a PV and water heating system on his house at our latitude (51 degrees north) and altitude (1000 meters). The investment is totally irrational by any economic standards and is in his and my opinion absolutely necessary.
Even after this investment he still has to purchase electricity and natural gas in our local climate of extremes i.e. our daily temperatures (currently very cold) and other climatological measurements are very mercurial to say the least. This makes switching from CO2 technologies to other technologies very difficult and painful.
Recently his solar panels were completely covered by snow and ice for days at a time and rendered utterly useless.
I am afraid that many of our non-CO2 energy producing options will become less and less effective and efficient as global warming proceeds. Hence any delay in drastically decreasing CO2 emissions is extremely harmful.
Calgary is known as the sunniest city in Canada with over 2400 hours of sunshine per year. This is the average sunshine per year over a number of years. I have the distinct impression that this is changing rapidly and that increased humidity and cloud cover will steal the sunshine hours that we need so desperately. Increased humidity and cloud cover is a prediction by our climate scientists and will proceed inexorably as global warming fueled by increasing atmospheric CO2 content proceeds.
If we are worried by what global warming may do to our climate and environment how much more should we be worried by what it will do to the efficacy of our available technical solutions to this very dire predicament?
SM #118 — Thanks, lots of food for thought. On California, btw, I was referring to politics not strategy. We may be closer to a tipping point in favor of change — not only in public opinion but also within the business community — than you or I might have thought.
#121 eric
ppm vs. ppb
Atmospheric methane (CH4) is measured in parts per billion. So when it does break down, it is not adding much CO2.
The fossil fuel emissions however are the 800 pound gorilla on the block and need more attention. So comparatively speaking, when the CH4 breaks down, it’s not adding that much CO2 to the overall mix.
I’m a little fuzzy tonight due to a flu bug. If I have this wrong, would someone please correct me.
Sheesh, I’m sorry I wrote so much in 118. It was in response, but still overlong.
Here is another process already under way that will make a big difference in 10 years’ time:
http://www.theglobeandmail.com/report-on-business/commentary/neil-reynolds/north-america-the-new-energy-kingdom/article1828896/
Would you be willing to support the conversion of coal-fired plants to natural gas while the non-fossil energy sources (including recovery of methane from feedlots, sewage, and landfills) are growing? Would you support substantial tax credits to finance the conversions?
According to WUWT, senator David Vitter (R-LA) has filed the “Public Access to Historical Records Act, S. 4015.” WUWT reports that according to Bryan Zumwalt, Legislative Counsel for U.S. Senator David Vitter, “The bill would force NASA to release their original raw historical temperature data and post it online for anyone to see and use.”
Any comment?
First, excellent work tackling this issue. Very topical, and your post has helped to make very clear that parallel strategies are needed for both SLCFs and LLGHGs.
I have one suggestion to make, and that is that your readers might benefit from being directed further to the NRC report on Climate Stabilization Targets. I found section 2.3 on Short-Lived Radiative Forcing agents extremely useful, in particular the argument that the most appropriate way to think about the impact of measures to reduce SLPFs is in terms of ‘peak trimming’. This section of the Climate Stabilization Report also emphasizes the fallacy of thinking in terms of ‘buying time’ through emission reductions of SLCFs. Figure 2.8 is very effective in conveying the ‘peak trimming’ message. Perhaps a follow-up post would be warranted to make this additional point.
[Response: A lot of what I wrote about in this post came from the background reading I did in the course of helping to write that section of the NRC report. Thanks for pointing readers in that direction. I will be standing by the NRC poster to answer questions on Thursday at AGU, so if any of you are around, please stop by. These cartoon sketches of the various climate futures need be turned into precise calculations based on simulations, and that’s something I hope to get done in the next few months. I do encourage everybody to read the NRC report, and especially the section on Anthropocene Climate. –raypierre]
I also have a request for clarification of much of paragraph 5 in this post, which I found very confusing. In particular, the statement about “getting the same radiative forcing for everybody upon doubling their concentration” seems to conflict with the very different values provide for doubling CO2 and CH4 at the top of the paragraph. Also, the text lower in the paragraph about the forcing equivalence of CH4 and CO2 and how it changes with concentration is also unclear to me. You state that “the equivalence factor drops further to 0.5.” and then follow that statement with the following sentence “In that sense, methane is, intrinsically speaking, a worse greenhouse gas than CO2” but if the equivalence were 0.5 then that would make CH4 less effective than CO2 and not a worse GHG (which we know is not the case). Something is not clear here. Could you take another crack at clarifying the concepts you try to describe in this paragraph? Thank you.
[Response: I was being a bit folksy there, so I could see how somebody new to this subject might be confused. Here’s the same thought in more straightforward language. For most greenhouse gases, you get a fixed increment of radiative forcing each time you double the concentration. The increment differs for different greenhouse gases. For methane, you get about 1 watt per square meter each time you double, and for CO2 it’s about 4 watts per square meter each time you double (in round numbers). If you start out with just 1 ppm of methane, you still get 1 watt per square meter for doubling, which is fully a quarter of what you get from doubling CO2 (starting from 300 ppm of CO2). However, it only takes 1/300 as many molecules to double methane, since you are starting from a low concentration. If you start from 300 ppm of methane and 300 ppm of CO2, though, you only get 1 watt per square meter from adding 300ppm of methane, whereas you get 4 watts per square meter from adding the same amount of CO2. That would make methane worse as a greenhouse gas than CO2 by a factor of 1/4. In the example I gave in the article, it actually works out to more like 1/2, because it turns out that when you increase methane that much you do start to get some deviations from the rule-of thumb of a watt per square meter for each doubling. (CO2 shows a similar effect when you get to enormous concentrations). -raypierre]
[Response: Looking this over again, I realize that the source of confusion is actually my use of the word “worse.” This is a good lesson in how easy it is to be misunderstood. When I said “worse” greenhouse gas, I meant that at high concentrations methane was not as effective as CO2 as a greenhouse gas, in that you got less radiative forcing for the same number of molecules. What you evidently thought I meant by “worse” was “worse for the climate,” in the sense of “more dangerous.” That’s not what I meant, but I can see that normative words like “worse” are perilous in scientific communication. I’ll definitely try to keep that in mind for the future. Thanks for pointing that out. –raypierre]
SM #131 — No worries here…appreciate your thoughts.
tamino:
I thought NASA’s GISTemp uses the GHCN data, which is already online, and which among other things allows you to order DVDs of digital scans of the original data sheets in their archives, etc (which is about as raw as data gets)?
Huh?
raypierre, you say, “In contrast, about half of CO2 emitted disappears into the ocean fairly quickly, while the other half stays in the atmosphere for thousands of years.”
There has to be something missing in this statement.
I ask facetiously, “How do the ocean destined molecules know they must scurry into the depths?”
As to the basis of this article which would involve the ‘control of methane’, the NYT times article wherein this notion reached our attention should be questioned. The authors of that piece seem to think that by tweeking up natural gas pipelines a bit and, uh well, controlling what coal does, we might have an opportunity to do something. However, a bit of examining of this could have saved the trouble of all this discussion.
Much of the natural gas industry involves big natural gas wells, but a lot of natural gas is present in the typical oil well. Where electricity is hard to access, it is common to run engines on self produced natural gas to pump up the oil. But in the more common case where electricity is available, the natural gas is simply allowed loose. When the price of natural gas goes up a lot, there is reason for the additional effort and equipment to capture and pipe the natural gas to a central collection system. I suggest it is mythical that pipeline leaks are the main source of natural gas leaking into the atmosphere.
As to the coal field naivety, it would be good for those interested to look at the open pit coal mine operations of the Powder River Basin.
I stand ready to be awed by quantified descriptions of landfill operations to collect methane.
So let’s get back to CO2 going into the oceans. That needs some real attention. If half the CO2 goes into the oceans in a quick time ‘T’ then half the remaining half should go into the oceans at 2xT. This does not sound like ‘thousands of years’. Unless of course, maybe we are talking about varying rates of absorption?
[Response: The “half and half” soundbite is an oversimplified sound bite meant to provide a sound bite (for those who demand sound bites) that is better than the oversimplifeed (but much more misleading) sound bite that the CO2 lifetime is “centuries.” The latter is a meaningless average. If you want an actual understanding of what is going on, you should read Dave Archer’s, “The Long Thaw,” followed by the section on carbonate/bicarbonate equilibrium in Chapter 8 of my book. The accompanying software to do a simplified version of the calculation of air fraction is available for free under Chapter 8 ChapterScripts in the Planetary Climate Book web site. Susan Solomon’s PNAS article on “irreversible” warming also provides a very concise and readable introduction to the subject. The quick (but mathematical) response to your confusion is that you are thinking in a too Markovian (i.e. history independent) way. The “easily accessible” CO2 sinks get used up first, and then you rely on progressively slower processes to take care of the remainder. –raypierre]
[Response: Another thing to keep in mind is that the “half and half” part of the sound bite is also an approximation, most appropriate up to cumulative emissions of about a trillion tonnes carbon. As one increases the cumulative emissions beyond that, the proportion of emitted CO2 that stays in the air for millennia increases. It is that increase which cancels out the negative curvature of the logarithmic radiative effect of CO2, and leads to the peak warming being approximately linear in cumulative carbon emissions. This property was pointed out nicely in Matt Damon’s Nature paper on cumulative carbon, and is discussed at length in the NRC Climate Stabilization Targets report. The calculation of the increase of air fraction with cum. carbon is also included as one of the problems for Chapter 8 of my Planetary Climate Book. –raypierre]
Re #133: That’s pretty funny, Tamino. When it comes to science, it’s as if politicians like Vitter are still in diapers… oh wait.
“I ask facetiously, “How do the ocean destined molecules know they must scurry into the depths?”'”
I think there is a communication issue here: rather than “In contrast, about half of CO2 emitted disappears into the ocean fairly quickly, while the other half stays in the atmosphere for thousands of years”
I would prefer the phrasing “In contrast, about half of the increase in atmospheric CO2 concentrations due to a given amount of emissions is reduced on a short timescale (due mainly to ocean uptake), while the other half of the increase lasts for thousands of years”
It may be subtle, but the CO2 molecules themselves don’t necessarily stay in the atmosphere that long… but the state of the atmosphere stays changed for centuries. As a very rough example, think of two bathtubs linked by underwater channel. Add 1 liter of colored dye to bathtub #1. You’ll see two things: 1) dye spreading slowly between bathtubs. 2) Bathtub #1 will originally increase in volume by 1 liter, but eventually the two bathtubs will reach an equilibrium of 0.5 liters each. Note 1: The rate at which dye exchanges in not directly related to the rate at which the volume changes. Note 2: some percent of the volume increase is permanent.
-M
[Response: Scientific communication to a broad audience is a matter of which way and by how many, you expect to be misunderstood. The worst thing is to be not understood at all, and that involves some compromises. Fussing too much about whether we are talking about individual molecules or the anthropogenic CO2 concentration anomaly is pretty pointless in my opinion, because the number of readers who are likely to confuse themselves on this score is a lot less than the number that would be confused by an awkward circumlocution. Fussing about this point is a lot like this: I’m at a bus stop, I say to my buddy, “The Number 173 bus is running late,” and he looks puzzled and complains, “Which bus were you talking about? There are all sorts of different vehicles that run this route. Did you mean that the current bus that was slotted to be here right now is somewhere it shouldn’t be?” A reasonable person wouldn’t get hung up on that. Buses are fungible, just like CO2 molecules, so the natural intuitive thing is to refer to fungible things by a mass noun, as being equivalent. –raypierre]
RC,
So its a trillion tonne carbon race and not a CO2 one ?
Re 132 ScepticMatthew.
“Natural Gas vs Coal: Undoubtedly, high efficiency natural gas-fired power stations can produce up to 70% lower greenhouse gas emissions than existing brown coal-fired generators, and less than half the greenhouse gas emissions of the latest technology black coal-fired power stations. Notice the distinction between black and brown coal, however, exactly how much less CO2 also depends upon the type of gas-fired station”.
Quoted from http://www.global-greenhouse-warming.com/gas-vs-coal.html
So yes I would love to see all coal fired power plants converted to natural gas in North America and everywhere else for that matter.
It was largely conversion to natural gas that allowed Britain to meet Kyoto agreement requirements.
This conversion may allow our friends in the USA to meet the Kyoto protocol requirements without signing the agreement and for at least my province Alberta meeting the Kyoto requirements, Canada having signed the agreement and not lived up to it.
I live in Alberta where the tarsand companies burn beatiful natural gas to recover oil from the dirty tarsands while other companies simultaneously burn dirty coal to produce electricity. Talk about irony or is it tragedy? My guess would be stupidity.
137, Jim Bullis: I stand ready to be awed by quantified descriptions of landfill operations to collect methane.
chuckle
Landfills, feedlots, meat processing plants, municipal solid waste, sewage: I think I read that collectively these might produce more than 5% of America’s energy budget. Not much chance of awe. Still, that’s 5% of a large amount, and it’s all domestic.
142 SM
That 5% you assert is sort of quantitative. The missing numbers are how much this would cost per kWhr. I am not a snob, so anything that makes it as a sound financial proposition, great. But let’s not skip the burden on the public like the recycling folks do it (A study I read long ago said that sorting of cans and paper etc. was cost free since it was left to the homeowner – I am sure they do not count storage space, containers, etc. and I wonder if they count the extra trucks needed for pickup.).
Coal is also domestic, by the way.
Feedlots? Have you ever seen a feed lot? Meat processing? This sounds like a pleasant place to collect stray bits of methane. Chuckle.
In #137 Jim asks:
So let’s get back to CO2 going into the oceans. That needs some real attention. If half the CO2 goes into the oceans in a quick time ‘T’ then half the remaining half should go into the oceans at 2xT. This does not sound like ‘thousands of years’. Unless of course, maybe we are talking about varying rates of absorption?
That might be almost, kind of, right if there were a chemical reaction occurring to bind the carbon, and there were plenty of the reactants in the ocean.
That’s not what’s happening. The CO2 is mainly dissolving into the ocean, increasing the amount present there and lowering the pH in the process. It’s a partial pressure thing.
The rate of absorption should be closely proportional to the difference in partial pressures between the air and water.
141 Joseph Sobry
You bring interesting things to the discussion.
It does not matter what the color of coal is; no energy-significant amount of carbon is left unburned in even the worst power plant, and those putting out unburned carbon should be hunted down by the EPA without mercy.
The color of coal is somewhat confusing in the matter. The specific coal from Powder River Basin is said to be low in sulphur but also low in heat value. It looks fairly black. No matter, a BTU of heat comes from coal depending on how much carbon is there to burn. And thermal efficiency varies consistently with your statement about ‘existing’ versus ‘latest technology’ in coal systems. So it is the difference in CO2 emitted per BTU produced and the relative thermal efficiency that matters.
Natural gas is important as a fuel, but it should be used in ways that it is most effective. Burning it up in central power plants that use two to three times as much energy in heat as the energy produced in electricity form is unconscionable. In complete cogeneration systems, no heat is thrown away, since the heat that has to be thrown away by the heat engine is subsequently used for other purposes. Natural gas is distributed in such a way that this could be done.
Beyond the direct energy considerations, it should also be noted that a large increase in use of natural gas should be expected to cause a large increase in price of that fuel. Thus, using it for power production or for driving trucks is likely to be a very bad thing, since it will rapidly reduce the so-called reserves presently estimated.
One should look carefully at the UK achievement in reducing CO2 by using natural gas. Yes, check the reserves now and you will find they are nearly gone. The great North Sea boon in natural gas made for a clean England, but it seems likely to soon turn out to be a foolish England.
Not to worry, we in the USA are fully capable of stepping up and matching their foolishness, blow for blow.
143, Jim Bullis: The missing numbers are how much this would cost per kWhr
True enough. Municipalities that are adopting the technologies reduce their purchases of electricity and sell their surpluses. The technology is spreading.
It’s the decaying offal from the meat packing plants that generates the methane and other pollution. Like feedlots, they are places you don’t want to live near.
You’re absolutely correct on this “buying time” issue. Not that we shouldn’t be reducing BC as it is. It simply sidesteps the underlying problem. And that is the anthropogenic production of GHG’s.
So now that a study by Lahouari Bounoua concludes that the increase in vegetation growth due to a doubling of CO2 will have a cooling response of -0.3 degrees Celsius (C) (-0.5 Fahrenheit (F)) globally and -0.6 degrees C (-1.1 F) over land, do we all run out and plant a tree. Well sure it will help a little, but there is still that nagging underlying problem that either won’t go away or as some feel — can’t go away.
> coal
By the way, one of the little side effects of burning vast amounts of coal is destroying an enormous fossil record.
I’ve always wondered if that could have something to do with the overlap between people who vehemently disbelieve in evolution, and people who are most eager to keep burning coal.
Take a look, it’s pretty amazing how aggressively people argue against the validity of the fossil record found in coal: http://www.google.com/search?q=coal+bed+fossils+plants+animals+insects
Thanks for this posting. I have long had the opinion that the Kyoto protocol, by including methane and forest sinks, has introduced major complexity and uncertainty into dealing with global warming, and has allowed countries and corporations to manipulate the figures which they use to justify their actions/inactions.
What you are writing here about methane / CO2 seems to justify my opinion about the relative unimportance of methane, and perhaps indirectly in regard to forest sinks, as you point out so well that the only way we’re really going to deal effectively with global warming is to rapidly phase out our use of fossil fuels.
Are there atmospheric scientists around of sufficient stature to persuade the world that Kyoto 2, or whatever replaces it, should for the moment forget about methane and forest sinks, and concentrate entirely on CO2? Do you think this could or is likely to happen?
Sorry if this has already been asked… I notice the first graph (temperature evolution for different total CO2 emissions) has small bumps on top of the overall pattern; the smaller warmings have more delayed bumps; the largest warming doesn’t have the bump (perhaps it blends into the larger earlier warming?), and for the smallest warming, after some cooling, their is a small sharp cooling with some rebound. One thing I can think of which might cause that behavior is albedo feedback from an ice sheet, where the feedback is stronger as the ice sheet gets thin in the center so that a smaller mass loss causes a larger areal decline (or maybe that’s not what would happen?) … but I wouldn’t have thought it would be that distinct and sharp, so I’m wondering what it is.