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Why positive feedback doesn't necessarily lead to runaway warming

Posted on 13 September 2010 by nealjking

Some skeptics ask, "If global warming has a positive feedback effect, then why don't we have runaway warming? The Earth has had high CO2 levels before: Why didn't it turn into an oven at that time?"

Positive feedback happens when the response to some change amplifies that change. For example: The Earth heats up, and some of the sea ice near the poles melts. Now bare water is exposed to the sun's rays, and absorbs more light than did the previous ice cover; so the planet heats up a little more.

Another mechanism for positive feedback: Atmospheric CO2 increases (due to burning of fossil fuels), so the enhanced greenhouse effect heats up the planet. The heating "bakes out" CO2 from the oceans and arctic tundras, so more CO2 is released.

In both of these cases, the "effect" reinforces the "cause", which will increase the "effect", which will reinforce the "cause"... So won't this spin out of control? The answer is, No, it will not, because each subsequent stage of reinforcement & increase will be weaker and weaker. The feedback cycles will go on and on, but there will be a diminishing of returns, so that after just a few cycles, it won't matter anymore.

The plot below shows how the temperature increases, when started off by an initial dollop of CO2, followed by many cycles of feedback. We've plotted this with three values of the strength of the feedback, and you can see that in each case, the temperature levels off after several rounds.


So the climatologists are not crazy to say that the positive feedback in the global-warming dynamic can lead to a factor of 3 in the final increase of temperature: That can be true, even though this feedback wasn't able to cook the Earth during previous periods of high CO2.

Note: this is a new rebuttal written by Neal J. King to the skeptic argument "Positive feedback means runaway warming", a sentiment sometimes expressed in comments on this website. In a first for Skeptical Science, Neal actually wrote all 3 levels of this rebuttal in one fell swoop. So as well as the Basic Rebuttal (which is used in this blog post), those seeking a little more meat can opt for the Intermediate Rebuttal which goes into more detail about gain factor. For the climate tragics (you know who you are), the Advanced Rebuttal lets you dive into the equations Neal used to derive his results.

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Comments 51 to 73 out of 73:

  1. This isn't a tricky concept and the heat doesn't "disappear", its radiated out to space. Compare this to the ocean under ice that cant radiate its heat anywhere. Nobody can answer with any certainty whether all the energy gained during Summer will be radiated but I remind you again that the expectation from scientists is that the arctic will freeze over during winter so its entirely reasonable that all the energy and possibly more than was gained over summer is radiated for a possible net loss of earth's heat. Once you see that, your second question is also answered.
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  2. The reason that the various positive feedbacks in the climate system (eq. water vapour, ice and snow) are acting against a very strong negative feedback produced by the Stefan-Boltzman Law for radiative balance of the Earth as a whole emitted radiation = sigma T^4 where T is a suitably defined effective absolute temperature, somewhat lower than the surface temperature, because the greenhouse effect. This isn't usually called a feedback, but whatever you call it, the exponent 4 for temperature means that a small change in temperature produces a large change in emitted radiation. The positive feedbacks would to be really large to overcome this and cause a runaway. At least that's the way I like to look at it.
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  3. 52, hadfield: The Stefan-Boltmann T^4 law does not apply to this case, because the Earth is not a blackbody: specifically in the frequency region of interest for greenhouse-effect considerations. There is no one "effective temperature". What matters in a particular frequency region is the altitude of the photosphere for that frequency. For frequencies that are transparent to the atmosphere, the photosphere is at ground level, and so the radiant emission reflects ground-level temperature. For frequencies that are absorbed by greenhouse gases, the photospheres are at various altitudes, depending on the absorption coefficients of those gases for the frequency, and on the distribution of the gases in the atmosphere. Thus the effective temperature at each frequency reflects the temperature at the altitude of the photosphere for that frequency. The way that the enhanced greenhouse effect works is that adding more greenhouse gas raises the altitude of some frequencies' photospheres, thus cooling them (higher altitude implies lower temperature, due to the adiabatic lapse law) and reducing the radiated power from the photosphere. Reduced power radiated => reduced cooling => heating. How does this relate to feedback? - When the ground-level temperature increases, all the temperatures of the different photospheres increase by the same amount (to first-order consideration), because they all shift upward: again, this is due to the adiabatic lapse rate of temperature with altitude. - The heating may introduce changes (probably mostly increases) in the greenhouse gases: methane, CO2, water vapor) which will adjust the photosphere levels again. This is a second-order consideration. - Sea ice will decrease: Most of what I have seen suggests that the dominant effect will be due to reduced albedo: More absorption of radiant energy, particularly in the Arctic. - There will be more clouding: What exactly this will do is a hot topic of discussion.
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  4. 48, 51, TimTheToolMan: Yes, radiated thermal power depends on temperature difference. More power flows from warmer to cooler than the reverse.
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  5. Thermally radiated energy depends on the temperature of the object and its emissitivity. You're confusing thermal radiation with thermal conduction of energy which does depend on temperature differences. What were you saying about the photosphere? That sounds fascinating.
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  6. 55, TTTM: 1) Yes, the amount of thermal radiation power in a frequency range depends on the emissivity; but the overall balance of heat transfer is going to be driven by the direction of the temperature difference. It will always be from warmer to cooler; and if there is no temperature difference, there will be no net transfer. If you have two objects of different emissivities facing each other, they still drive towards an equilibrium with the same temperature, because their absorption at that frequency range is proportional to their respective emissivities: one of Kirchhoff's laws on blackbody radiation. At equilibrium, they don't have to emit the same amount, and they don't have to absorb the same amount; but there is a match between what they emit and what they absorb, individually. So when the two objects are at different temperature, the hotter object will be losing more heat to the colder, on net. And when the temperatures are the same, there will be no net transfer. 2) The full explanation of the way the greenhouse effect works depends on an understanding of how radiation works in the atmosphere, specifically on radiative transfer theory. The best concise explanation I have seen is in a book (which I got in early preview version by softcopy) by Pierrehumbert: http://geosci.uchicago.edu/~rtp1/ClimateBook/ClimateBook.html . It is likely that I will attempt an explanation in another post I agreed to write, on why CO2 can be an effective greenhouse gas even though it represents such a tiny percentage of the atmosphere. But it will be tough: definitely harder to make clear than this feedback model. To try to give some general answer to your specific question: The source of IR radiation in the atmosphere is the ground. Let's consider photons of a particular frequency range, say about 4 micron wavelength. They are emitted from the ground in an upward direction; but because of the greenhouse gases (specifically, in the case of 4-micron IR, CO2), some of them are absorbed. After being absorbed, the CO2 molecule is in an excited state for awhile, and then re-emits a similar IR photon in some random direction. So you can think of it like this: The IR photon headed up, got stopped by a CO2 molecule, bounced into a different direction. It travels awhile, hits another CO2 molecule, bounces into yet a different direction. Basically, each photon is doing a random walk around the atmosphere; but the length of each step in the walk depends on the likelihood of hitting another CO2 molecule. The higher the altitude, the fewer the CO2 molecules, so that means that a photon starting off high up will take a longer step than one starting low down. There is a point where the concentration of CO2 molecules is so low that there is a good chance (more than 50%) that the IR photon will never hit another CO2 molecule: It will be emitted and keep going - it's escaped! That specific escape altitude defines the photosphere for that frequency of photon. A visible example: Ever seen a photograph of the Sun? You get a sense of a visible sphere of substance, with a well-defined surface. But that surface is the photosphere for the frequency of light which was used to make the photograph: If you take the picture with X-rays, you get a completely different picture, with a far smaller radius, because the X-ray photosphere of the Sun is different. This reflects the temperature profile. Anyway, the point is that the IR photons can be considered to escape when they are emitted from the level of the photosphere, whereas when they are emitted from lower altitudes they're still bouncing around. OK, so what is the rate of emission from the photosphere? It depends on the altitude there: the higher up it is, the colder it is, and the lower the emission power. Thus, the higher up the level of the photosphere is, the less emission there will be, the less escaping of the IR photons, and the less the cooling of the atmosphere through that particular frequency band. So when you add more CO2 to the atmosphere, you are increasing the altitude of the 4-micron band IR photosphere, so you are reducing the cooling. Hence, warming of the atmosphere. (Note: I've made a few simplifications: - The photon path is not completely random: I am ignoring some stimulated-emission effects. To do this right, we need to go into radiative transfer theory. Let's not. It doesn't change the overall picture, and it is A LOT of math & physics. - I defined the photosphere as the 50% escape point; a better definition would be when the escape probability is 1 - 1/e = 1 - 1/2.78 = 0.632. It doesn't make much difference. - Probably lots of others; as I said, this is very complex, so to even jump into it, I'm making all sorts of assumptions that would have to be justified in a real exposition.)
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  7. >"I really can't make sense of the rest of your >argumentation, no one else seems to be paying >much attention, and it clearly does not derive from >the relevant scientific literature so I'm just going to >take it as an ill-supported opinion and leave it at >that." If you have a specific question, I will gladly answer it. >For those who can't access this in press article, >this is the abstract: [re "Dessler and Davis in JGR"] Thanks for the link. This paper does provide some evidence of alternate humidity estimations that indicate increasing trends in water vapor aloft. That differes from the trends than the NCEP analysis, the ICCSP analysis, and the NVAP analysis: http://www.google.com/url?sa=t&source=web&cd=6&ved=0CC0QFjAF&url=http%3A%2F%2Fams.confex.com%2Fams%2Fpdfpapers%2F84927.pdf&rct=j&q=nvap%20paper%20von%20der%20haar%20water%20vapor&ei=x_SQTKf8M4OesQOv0cGyDg&usg=AFQjCNGSAZn3mjAW50coTgiXDs1bVnC4VQ&cad=rja The exceptions I would take to the paper are: 1. The focus on El Nino fluctuation to validate long term variation is not relevant - El Nino is a known internal DYNAMIC variation. It could easily be that the DYNAMICs which change the temperature also change the humidity and not the thermodynamics. In other words temperature and humidity are both forced by dynamic changes and are just co-variants. 2. The differing periods of the various analyses. 3. The analysis which indicates the greatest increases in humidity, the MERRA, is the high outlier, with the greatest variance from not just the NCEP, but the JRA as well. That doesn't mean it is not correct, but it bears watching. 4. The statement: "And finally, we point out that there exists no theoretical support for having a positive short-term water vapor feedback and a negative long-term one." I take this as saying: The observations must be wrong because they don't match the theory.
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  8. Tim The Tool Man, I'll try another way. Imagine you are looking down at the planet from outer space and you are wearing some sort of glasses which allow you to see in the infrared. Furthermore, you also have the ability to distinguish between different wavelengths of infrared radiation. Just for the thought experiment we'll ignore water vapor and other greenhouse gases and focus on CO2. What you'll see if the planet has no greenhouse gases (from space) is all of the infrared radiation emanating from the surface and being received by your glasses. For a no greenhouse atmosphere, this radiation will roughly correspond to the surface temperature (as given by the Stefan-Boltzmann law). Now if we bump up the CO2 amount to, say, 10 ppmv then from space still you will see a lot of Earth's radiation from space coming up from the surface. These are the window regions where CO2 is a poor absorber. But in regions where CO2 absorbs strongly, you will see some radiation coming from near the top of the atmosphere. It is much colder here and so the emission you are seeing is "weaker" than the surface radiation. The dominant CO2 feature for Earth is actually the 15 micron region, not 4 (The 4-micron region is actually a stronger band, but this really can't be that crucial because Earth's Planck-weighted emission at this wavelength is very small, although it matters more for a planet like Venus). If you keep the temperature fixed, the Earth is now emitting less radiation to space, because now the OLR is the original minus the "bite" in the spectrum due to the CO2 band. The Earth's goal is radiative balance, and so the only way to get the original back (to compensate for the loss due to CO2) is to increase the temperature, which increases the whole area under the curve of a Planck radiation plot. This means the decrease in emission from the 15 micron spectral flux is compensated by an increase from window regions such as at 10 microns. This spectral selectivity is also key to understanding stratospheric cooling by the way. Eventually (at relatively low concentrations) at the center of the CO2 band, the emission from space is coming from as high as you can really get. In fact, at current concentrations of CO2 near the band center right at 15 microns, your glasses are seeing emission from the lower stratosphere. So, generally the OLR is greatest for regions of a warm surface that is overlaid by a dry, cloudless atmosphere and least in the polar regions or regions where you have cold cloud tops. Outside of the 15 micron center (but still within where CO2 strongly absorbs, at the edges) you are seeing emission somewhere between the surface and tropopause. This height of emission will clearly increase as you add more and more CO2. This "height level of emission" is what neal is referring to as the photosphere (it's not generally a term you'll see in the literature or conversation, but I don't suppose there's anything wrong with it...it's usually applied to the outer layer of the sun when climatologists talk). The key to the saturation arguments out there are that there's always more absorption waiting out in these wings, and depending on the wavelength you can always have an impact by increasing the height of emission to space, which reduces the OLR for a given temperature. So if you're doing government work and don't need super-fancy science you can model the emission from a planet with a greenhouse effect as something like T to the 3.9th power or whatever. To summarize, the best way to think about the greenhouse effect without getting into all the subtle spectral details is that for a given temperature, the outgoing radiation to space is reduced when you add GHGs. So if you don't change the incoming part of the radiation from the sun you need to warm up by a certain amount to get back in that radiative equilibrium. Note that a lot of the basic internet descriptions focus on the enhanced downward infrared emission to the surface but this is not really a good way to think about it because it's not necessarily inevitable more CO2 will directly increase the downward emission (like if you have a lot of water vapor in the boundary layer so it's already a blackbody at a given temperature) so most of the increased downward emission will actually come from increased temperature. Then, the surface energy budget is also linked to evaporation and other fluxes, so the enhanced CO2 problem is really a top of atmosphere centric focus. I've done a more complete post on this here (and if neal wants help with his future guest post I will be glad to!)
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  9. Chris, - I used the 4-micron band for illustration, because CO2 doesn't share it with H20, unlike the 15-micron band. So it's a conceptually clearer example to discuss. - I started to use the term photosphere to describe the (radial) altitude level at the "atmospheric edge" for a specific frequency, because of seeing solar-physics photos. I'm not against using standard terminology; but I don't particularly care for "height level" because it sounds so "flat-Earthish", whereas I want to convey the mental image of a photon doing a random walk through a spherical space (well, a spherical space with a big rock in the middle! 3-dimensional equivalent of an annulus). - Yes, when I write something up, I may run it past you. In the meantime, maybe you would know the answer to this question: It's my impression that CO2 is quite significant up to 100 km, whereas H20 vapor quits at around 10 km. Is this true? And at about what altitude does the optical path length = 1 for the 15-micron band? (Where is the 15-micron "photosphere"?)
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  10. ClimateWatcher: I'm not really following the discussion on Dessler & Davis, but I did notice your following remark: "4. The statement: 'And finally, we point out that there exists no theoretical support for having a positive short-term water vapor feedback and a negative long-term one.' "I take this as saying: The observations must be wrong because they don't match the theory." I think it's perfectly reasonable for a paper to point out that a certain set of observations doesn't make any sense within current theory. First, it raises the stakes for the cited paper - which is not a bad thing for the authors, provided they're professional enough to know that their results were going to raise some eyelids. Other readers will focus a little more attention on it, see if it's compatible with their own experience. This is good. Second, it not infrequently happens that the experimental data ARE wrong. The UAH measurements on tropospheric warming/cooling were discrepant with ground-level temperature measurements for over 10 years, and all the climate community could say for sure was that it didn't make any sense - until the UAH team finally figured out their data analysis was in error. Likewise, I remember talking to Richard Feynman about evidence for solar neutrino oscillations, and he pointed out that the question of whether there was a real question had to do with the size of the error bars on some optical solar measurement, and if the uncertainties were just a bit more than the experimenters thought, the whole thing would be a non-issue. He said that part of the game of theoretical physics was knowing whose error estimates you could rely on.
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  11. The scale height for water vapor is quite small, about 2 km so abundance-wise you are correct. This is one reason why water vapor doesn't overwhelm the CO2 greenhouse effect, as water vapor is relatively leaky high up. CO2 has a very little effect in an atmosphere that is really wet up into the stratosphere, as you might get prior to a runaway scenario, but Earth is quite far from this regime. CO2 is pretty well-mixed until the stratosphere or so; I'm not sure how the CO2 mixing ratio changes once you get above the stratosphere (clearly water vapor is not really existent here) but for radiative transfer purposes there isn't really much greenhouse influence this high anyway because the air is so thin. One you get above the so-called "photosphere" at a given wavelength you become pretty optically thin, and below it pretty absorbing. If you use David Archer's model (which I plotted a few example diagrams in my link in the last comment) you can convince yourself that right at 15 microns the CO2 emission comes from the stratosphere (and in the wings, closer to the surface), since there appears to be an upwards blip inside the ditch in the spectrum itself (this becomes really obvious if you put like 100,000 ppm of CO2 into the model). The reason for this is that the temperature of the stratopsphere becomes isothermal or increases with height. Numbers of a spectrally averaged "photosphere" is about 5 km, since 288 ~ 255 K +(5 km)(6.5 K/km) Hope that helps
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  12. 61, Chris: - Your first paragraph confirms the conclusion I had come to about why CO2 is so important despite being only about 4% of greenhouse gases. The height of the 15-micron photosphere is most significant from this perspective, since CO2 and H20 share this band: It would make most sense if the 15-micron photosphere would be well above the point at which there is significant H20 vapor: Otherwise, the abundance of H20 (on average) is 25X that of CO2; and the absorption coefficient looks to be only about a factor of 2 smaller. So if H20 and CO2 were competing at the same altitude, H20 would have an advantage of a factor of about 13, and indeed it would be hard to credit a major role for CO2. - I guess 6.5-degK/km is the lapse rate assumed, for "typical" humidity? The figure I'm used to is 10-degK/km (for dry air). - You refer to the scale height for H20. How useful is an exponential model, given that temperature is dropping with altitude? I would have thought that an adiabatic model would be more appropriate.
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  13. Chris: Also, I saw some place some folks talking about detecting water vapor at 11+ km recently. Have you heard anything about this? Obviously, if that's a significant amount, it would screw up the picture.
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  14. >>>"I take this as saying: The observations must >>>be wrong because they don't match the theory." > >I think it's perfectly reasonable for a paper to >point out that a certain set of observations doesn't >make any sense within current theory. Of course, if water vapor is providing positive feedback, one can still question why the warming rate is below the best estimate for the low end of IPCC projections. >The UAH measurements on tropospheric >warming/cooling were discrepant with ground-level >temperature measurements for over 10 years, and >all the climate community could say for sure was >that it didn't make any sense - until the UAH team >finally figured out their data analysis was in error. Well, for the MSU era, the MSU-LT (of both RSS and UAH ) track pretty well with the Land/Ocean indices (both CRU and GISS). The difference was the observations subsequent to the last big el nino, and not the corrections, however. Both RSS and UAH, with recent corrections, indicate cooling trends in the pre 1998 data. Also lost in that tale is that the -middle- troposphere, where models predict the greatest warming, indicates much less warming for both RSS and UAH.
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  15. ClimateWatcher #64, "Of course, if water vapor is providing positive feedback, one can still question why the warming rate is below the best estimate for the low end of IPCC projections." Only if they are living in a fantasy world where the statement above ISN'T nonsense. Observed warming is within the range of IPCC projections, not below the low end. Have you been listening to Monckton's fictional accounts of 'IPCC projections' which don't actually appear anywhere in the IPCC reports? "Both RSS and UAH, with recent corrections, indicate cooling trends in the pre 1998 data." Oddly the people who actually produce the RSS and UAH data all say that their results show long term warming trends... both pre and post 1998. "Also lost in that tale is that the -middle- troposphere, where models predict the greatest warming, indicates much less warming for both RSS and UAH." Source?
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  16. "So if you don't change the incoming part of the radiation from the sun you need to warm up by a certain amount to get back in that radiative equilibrium." Or increase cloud cover (albedo) or increase convection, surely.
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  17. TTTM: - Increasing albedo would indeed reduce the radiation absorbed by the Earth, and would help curb the radiative imbalance. Lindzen suggests that this may be happening; as far as I can tell, right now the bulk of the evidence seems to be against him. It's not a crazy idea; it just doesn't seem to be what's happening. - Increasing convection wouldn't actually do anything to cool off the planet. Convection can only carry warmth as far as the atmosphere goes, whereas to cool the planet the warmth must depart into space. Analogy: You can depopulate the planet with space ships but not with airplanes: They don't go far enough.
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  18. #67 : "No Increasing convection wouldn't actually do anything to cool off the planet." Convection takes water vapour from the surface high into the atmosphere where it condenses back into water losing a significant amount of latent heat which is then radiated away. Its one of the most important heat transfer mechanisms in our atmosphere.
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  19. 68, TTTM: It's true that the immediate effect of convection is to move heat upwards. However, the problem remains that the altitude at which the water vapor condenses is still far below the photosphere for the relevant IR photons, so those photons have to try for their chance at escape just like all the other IR photons. That rate of escape is set by the temperature of the surface of the IR photosphere. This in turn is set by: a) the temperature at ground level; and b) the adiabatic lapse rate. Now, actually, it occurs to me that you might have a point: The adiabatic lapse rate is reduced by increased humidity; so if the humidity increases, the temperature at the photosphere will be increased, so it will radiate more. Of course, increased humidity also means more greenhouse gas in the atmosphere - but if it's below the photosphere, it shouldn't matter. I'll think it over...
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  20. High level Cirrus clouds make a large difference to keeping the long wave energy within the atmosphere. Your ideas that the (15um) long wave energy is literally trapped within the atmosphere isn't supported by evidence (or the science)
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  21. TTTM: After some thought, I come back to the same point of view: - Increasing convection, in itself, wouldn't change the radiative forcing budget, so it wouldn't affect the global average temperature. Additional mixing would probably stir things up a bit more, spreading the heat around: So you would get "more weather". Not surprising: weather is pretty much driven by convection anyway. - The ground-level heating should increase the absolute humidity, which should result in a smaller lapse rate (rate of temperature drop with altitude): Dry air has a lapse rate of about 10-deg-C/km, whereas saturated moist air drops at about 5-deg-C/km. What this implies is that the ground-level temperature will not need to rise as much to make the radiative forcing imbalance go away. This effect can never be big enough to result in a net cooling, but it will moderate (to some extent) the warming due to the enhanced greenhouse effect. So, never let it be said that I denied ALL negative feedback loops in global warming!
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  22. 70, TTTM: I'm not sure what you mean by "literally trapped". What is pretty clear from the radiative transfer theory is that the intensity of IR power reflects the temperature at the photosphere; so the higher the altitude, the lower the radiated power, the smaller the amount of cooling. I don't see any conflict with cirrus clouds: Just because you use a blanket doesn't mean you can't wear pajamas.
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  23. Further search of previous research of the temperature limiting factors of biosphere... From http://www.dbio.uevora.pt/Micro/Brock.pdf ("Life at high temperatures", review on prior research, unfortunately it doesn't include much on terrestrial vascular plants.) "We found visible algal growth (of the unicellular blue-green Synechococcuts) at temperatures up to 73° to 75°C, but not at higher temperatures (24)" and "Quantitative studies of the algal mats along thermal gradients in hot springs have shown a definite correlation between the temperature and the algal biomass (33). In the Yellowstone hot springs, maximum algal biomass was found at albout 55°C, and it falls off sharply as the temperature increases above 55°C (34)." So one limit of inhibition for high (too hot for humans) temperatures is 55°C and photosynthesis ends at 75°C. Above this temperature all photosynthecic life will decompose and photosynthesis needs to be born or moved to the area again. Geological processes will eventually bury the decomposed carbon. further: "Thus, it is surprising that eucaryotic algae are not common at temperatures above 40°C, whereas eucaryotic fungi are found up to 60°C (14)." So 40°C is about the maximum limit when oceans will turn into carbon emitters. lastly: a point on scientific inertia... "Most of the surface of the earth has a moderate temperature, with an average of 12°C (15)." checking this up, it turns out this was an approved value in 1955: "15. H. F. Blum, Time's Arrow and Evolution (Princeton Univ. Press, Princeton, N.J., 1955)."
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