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Does positive feedback necessarily mean runaway warming?

What the science says...

Select a level... Basic Intermediate Advanced
Positive feedback means that a system reacts to a stimulus by reinforcing that stimulus, so the stimulus builds up, and the output builds up, and the stimulus builds up... However, this only leads to a "runaway" instability if the reinforcement is strong enough. If it's not, as in the case with the enhanced greenhouse effect, the feedback can give rise to a definite, but stable, increase over the original stimulus.

Climate Myth...

Positive feedback means runaway warming

"One of the oft-cited predictions of potential warming is that a doubling of atmospheric carbon dioxide levels from pre-industrial levels — from 280 to 560 parts per million — would alone cause average global temperature to increase by about 1.2 °C. Recognizing the ho-hum nature of such a temperature change, the alarmist camp moved on to hypothesize that even this slight warming will cause irreversible changes in the atmosphere that, in turn, will cause more warming. These alleged "positive feedback" cycles supposedly will build upon each other to cause runaway global warming, according to the alarmists." (Junk Science)

Note: Breaking with custom, we will discuss some math in this rebuttal, because the argument is about a mathematical topic: the implications of positive feedback. But we'll try to keep it light.

One of the problems about understanding the extent of global warming (the question of climate sensitivity) is that the total average temperature increase due to CO2 is greater than the first guess: Climatologists must also take into account "second-order" effects which add to the initial estimate of the warming. It is not easy to calculate these effects, but the general consensus is that, overall, they magnify the temperature increase by about a factor of 3. These second-order effects work as a form of "positive feedback."

An example of this: Imagine the pre-industrial world, with the Earth, land & sea, in rough thermal balance. Then add a dollop of 35% more CO2 to the atmosphere (by burning fossil fuels): Due to the enhanced greenhouse effect (EGE), the outgoing radiation of infrared energy is inhibited, and this reduction in radiative cooling raises the global average temperature. But the increase in temperature has the effect of increasing even further the amount of atmospheric CO2, because the heated ocean will hold less CO2 (think of a can of warmed Coke), and the warming Arctic tundra will reveal formerly frozen biomass that will decompose and release more CO2. So you get even more CO2 in the atmosphere, which gives rise to even more warming, which gives rise to even more CO2...

But this is where the suspicions of the skeptics are aroused: "If more CO2 gives rise to higher temperature, and higher temperature gives rise to more CO2, and this additional CO2 gives rise to even higher temperature, doesn't this go on forever? Doesn't that mean that the Earth would turn into an oven? If the greenhouse effect REALLY has positive feedback, why hasn't this happened already? Something is wrong with this picture!"

This line of thought is partly right and partly wrong:

  1. Yes, in a sense this cycle does go on forever; but
  2. No, the Earth will not turn into an oven!

How can these both be true? Well,

  1. The cycle does go on forever, like the reflections between two facing mirrors; but
  2. At each step in the cycle, the incremental increase gets smaller and smaller. After a few cycles, the increase is negligible.

When does positive feedback lead to a "runaway"?

To understand this, consider first the "classic" example of positive feedback: The output of an amplifier is plugged back into its own input. This can lead to a sustained shriek. How does it work? Starting at input level Io, the output of the amplifier is Io multiplied by the gain factor, g; this gets plugged back into the input, and comes out multiplied by another factor of g; and so on. If we plot the output as a function of the number of cycles of feedback, it looks like this:


We have used three different values for g:

- for g < 1, the output fades towards 0;

- for g = 1, the output remains unchanged; and

- for g > 1, the output grows larger and larger

So if the gain factor is > 1, and only in that case, the system is described as "runaway": Any input leads to an output that grows beyond bounds. (In the real world, the system becomes limited by factors not included in the original mathematics, so the output does not really go to infinity, but saturates at a high value. So when an audio amplifier gets into the range of runaway positive feedback, the sound system doesn't explode, it just produces an ear-shattering shriek.)

Why doesn't the enhanced greenhouse effect run away as well?

The nature of the positive feedback is different than for the case of the simple amplifier: In the case of the amplifier, the increase in output is proportional to the input; but in the case of the enhanced greenhouse effect (EGE), the increase in output is less than proportional to the input: It is logarithmic. The result is that when we plot a (highly simplified) model of the temperature increase due to the EGE against the number of feedback cycles, we get:

In these plots, we use three different values of the feedback parameter, f:

- Due to the feedback, the temperature does indeed rise beyond the initial jump (due to the dollop of 35% more CO2).

- However, after several (3 to 10) iterations, there is no further significant change.

- The terminal value of the temperature increase depends on the value of the feedback parameter f: The stronger the feedback, the larger the terminal value.


- When you add CO2 to this model system, there is indeed positive feedback, so even more CO2 will end up in the atmosphere than you dumped in from the burning of fossil fuels.

- However, this does not give rise to a runaway scenario: Eventually, the impact of that dollop of CO2 comes to an end.

- Now, in the real world, that end will not be an ultimate end until we stop adding more CO2 ourselves: Every time we add another dollop of CO2 through the burning of fossil fuels, we kick off another round of significant feedback cycles. Currently, we are still adding small dollops all the time...

Note: A more detailed explanation is provided here.

Last updated on 20 October 2010 by nealjking.

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Comments 1 to 25 out of 121:

  1. So Dr. Hansen is wrong?
  2. I believe Hansen has said that it might be possible for Earth to get to runaway greenhouse warming if we burned all fossil fuels on the planet. Nothing in the article above speaks to such a scenario.
  3. In fairness, this is not just something that skeptics fail to understand, many environmentalists don't get it either. The media (in the UK anyway) really got addicted to talking about 'runaway climate change'. I am not sure where it came from because I've hardly ever seen the term used in the science. I am aware that a lot of climate scientists are very uncomfortable about the use of this phrase. But there are different ideas bound up in it- if there is a low probability of carbon cycle feedbacks doing something extreme and becoming very nasty even if not becoming self-perpetuating, then is that 'runaway'? How much does something have to run away before it is 'runaway'?
  4. I am uncomfortable about the soda pop analogy for CO2 in seawater. The naysayers get confused by this and cone up with all kinds of wrong arguments based on it. The ocean is not saturated with CO2. It would be better to describe the temperature dependance if the distribution coefficient. But even that would be wrong because I am not sure that the system is in equilibrium.
  5. The interesting thing about feedbacks is that to some extent we can get "runaway" feedback. The earth receives a certain power from the sun. For an earth in equilibrium, all that power must be radiated back out to space. The rate of radiation is proportional to T^4, where T is the temperature in degrees Kelvin (about 290 at the moment). For a simple analysis of feedbacks, we model the T^4 dependency by a linear one with matching slope at our current temperature. Over a small temperature range (and compared to 300, 1 or 2 degrees is small), the T^4 curve and the linear model will be almost identical. With the linear model we can now get "runaway" feedback. That is, each iteration of temperature in the spreadsheet analysis above leads to a bigger temperature jump than the one before, so instead of converging on a new value, the temperature just get bigger and bigger. Of course in this situation, the linear model is not accurate. What happens though is that we jump to a different part of the T^4 curve - a place where the slope is great enough so that the local linear model won't produce runaway feedback. To summarise. If feedbacks are small (or negative), you will get a multiplier effect - a small temperature change might get (say) doubled by feedback. If feedbacks are big, you may end up jumping to a different part of the T^4 curve. If one looks at the recent ice-age/interglacial temperature movements, it does look possible that feedbacks are kicking us from one temperature regime to another and then back again. Maybe I should try and post this with graphs and stuff.
  6. 3, Josie: I see it as runaway if the system goes to an extreme that is stopped only by a lack of resources of some sort: in the case of the amplifier, limits to power; in the case of the Venusian atmosphere, exhaustion of water. In this model, the feedback is positive but decreasing, so it just stops adding up. I consider it self-limiting, as opposed to runaway.
  7. 4, Lazy Teenager: - I don't quite get your point: The solubility of CO2 in water declines with increasing temperature. Last I heard, the uptake of CO2 has dropped in recent years, although up til now it has absorbed about half the CO2 produced by fossil fuels. - I don't understand the issue regarding equilibrium.
  8. 5, John Brookes: The carbon-cycle aspect has a positive feedback, because the increase in T => increase in CO2 => increase in greenhouse effect => increase in T. The T^4 radiated power has a kind of negative feedback, because the increase in T => increase in cooling => reduction of the increase in T. (But actually, T^4 behavior is not really the way the system works: If it did, we wouldn't be talking about the greenhouse effect.)
  9. I'm sorry, but I think this post (I'm looking at the intermediate one) is very confused and does more harm than good. It should be pulled until it can be improved. First, it ignores the fast feedbacks (water vapour, snow) and goes straight to carbon cycle feedbacks, which is slow and relatively uncertain. Second, the logarithmic nature of the greenhouse effect is a red herring, at least for small perturbations. Chris Colose's recent guest post[*] on RealClimate explains the primary reason that positive feedbacks don't *necessarily* cause a runaway: "Feedback behavior The ultimate constraint on climate change is the Planck radiative feedback, which mandates that a warmer world will radiate more efficiently and therefore provide a cooling effect. For a blackbody, the emission goes like the fourth power of the temperature. So the question of how the other feedbacks behave is really of how they modify the Planck feedback." [*] http://www.realclimate.org/index.php/archives/2010/09/introduction-to-feedbacks/ Now, when I stated the same thing on another comment thread on SkepticalScience recently, I was told I was wrong because the Earth is not a black body. This is true, but it is still an object in space that can lose heat only by infrared radiation, and this radiation depends strongly on its temperature. Or, more precisely, on the temperatures of a whole range of different levels in the atmosphere and/or at the surface, each of which affects a different IR frequency band. Mark
  10. 9, hadfield: The intent of the post is to address a specific logical question: "How can there be ANY positive feedback if the Earth hasn't done a temperature runaway already?" To that end, a mathematical model is given as an example of a system displaying both positive feedback and non-runaway behavior. This post does not propose to describe the full picture of the dynamics of global warming. You might take a look at the "Advanced" version for more perspective.
  11. 10, nealjking In the introductory paragraph (Advanced version) you say "Climatologists must also take into account "second-order" effects which amplify the initial estimate of the warming. It is not easy to calculate these effects, but the general consensus is that, overall, they magnify the temperature increase by about a factor of 3." This seems to be a reference to fast feedbacks, the ones that increase the warming due to an increase in radiative forcing of 1 W/m2 from about 0.3 C to about 0.8-1.0 C. The remainder of the article appears to describe a carbon-cycle feedback: CO2 affects temperature; temperature affects CO2. Forgive me if I have misunderstood, but if I haven't, don't you think it is a little confusing to conflate the two?
  12. hadfield: This article is intended to illustrate a mathematical fact, not to describe the dynamics of the real atmosphere. Please read the Note that has been there from the beginning: "Note: This model incorporates a number of features of the actual feedback mechanism for the enhanced greenhouse effect, in particular the dependence of radiative forcing on the logarithm of CO2. However, it is definitely not intended as a full model for the effect. It's only intended to illustrate the point that there is no contradiction for a system to have positive feedback, while maintaining self-limiting behavior. "
  13. It illustrates a mathematical fact that is irrelevant to the action of the fast feedbacks, which are what the introduction suggests the article is about. So what's the point?
  14. hadfield: The argument in the intro is: "These alleged 'positive feedback' cycles supposedly will build upon each other to cause runaway global warming, according to the alarmists." That is what is being controverted.
  15. OK. The trouble with addressing "sceptic" claims is that they are often rather incoherent, so it can be damned hard to work out they are in the first place. If you have any examples of the claim you are addressing, that would help focus the discussion. In the absence of that, I can think of two versions of the "sceptic" claim. The first is that a system with positive feedback is by definition unstable. "Alarmists" are always pointing to positive feedbacks, some of them with short time scales like the water vapour feedback and ice-albedo feedback. But the climate is clearly not unstable so the positive feedbacks must not exist, or must be outweighed by negative feedbacks. The answer to this is that there is a large negative feedback that is fundamental to the Earth system and that is not usually identified as a feedback, namely the Planck feedback as I've discussed earlier (see also the recent article by Chris Colose on Realclimate). That feedback on its own dictates that the Earth's climate sensitivity will be fairly low. The evidence is that there are several fast positive feedbacks that act to increase the sensitivity, but nowhere near enough to make the system unstable. A second version of the claim might be that "alarmists" are saying the carbon cycle feedbacks will cause runaway warming a la Venus. The problem with this claim is that no "alarmists" are actually saying this, except Jim Hansen who has suggested it as a very remote possibility, but obviously one with huge consequences. Your discussion of the logarithmic dependence of the greenhouse effect on greenhouse gas concentrations tells us one reason why this runaway warming is not easily triggered. The fact that the Earth has not done so in the past also shows us it's hard to set off. Neither of these things indicate that it's completely impossible. To be of any help in avoiding confusion, your article needs to be clear about what claim it is addressing. At the moment it's not. Specifically, it conflates fast and slow feedbacks.
  16. hadfield - Your statement "a system with positive feedback is by definition unstable" is incorrect, a system with a gain < 1 is stable, as discussed at some length here, and in better detail on the advanced version of this page. Total stable increase for a particular gain (g<1) and forcing (f) is, if you work the math: V = f / (1-g) The oft-quoted 3oC increase for a doubling of CO2 (forcing = 1oC) represents a gain of 0.666. This, incidentally, works for negative feedbacks as well - gains with an absolute value < 1.0 are always stable. Differing time constants may cause some oscillation before settling, but systems with |g| < 1.0 are always stable. Gains > 1 don't tend to exist in natural systems (as they would require infinite energy!); they're pretty common in electronics, amplifying values until you hit the limits of the power supply.
  17. KR, the statement that "a system with positive feedback is by definition unstable" is not mine, it is my paraphrasing of a sceptic claim. What this set of articles needs to do is clarify that the existence of positive feedbacks in the climate system does not imply |gain| > 1, because the Planck feedback dictates that the the Earth's climate sensitivity is low. It doesn't do that, it goes off onto a tangent about a toy model of a carbon cycle feedback.
  18. 17, hadfield: The statement you are trying to promote is different from what I am trying to do. Sorry.
  19. OK, I'm happy to leave it there.
  20. Climate senitivity must be lower than the IPCC calculates. The ice age was ended by slight changes in the earth's orbit and rotation which melted some ice which enhanced the initial warming. Also a warming ocean gave up more carbon dioxide to the atmosphere further reinforcing the warming. These feedback loops continued until the present interglacial began. What I'm curious about is why did the warming stop. Wouldn't the warming have continued to feed on itself until all the ice sheets were gone and when the ocean ran out of carbon dioxide to emmit? Because of this there must be a negative feedback that we don't understand that well. Please explain this.
    Response: Try reading the "Advanced" tabbed page here. Is there some particular part of that, that you have a question about?
  21. Karamanski@20: The exchange of CO2 between the ocean and atmosphere isn't governed only by temperature, it is also governed by the difference in partial pressure of CO2 between the atmosphere and the surface oceans. Loosely speaking CO2 leaving the oceans has to push against the partial pressure of CO2 in the air, so as more CO2 is added to the atmosphere the comes a point where the increased partial pressure balances the effect of increased ocean temperature, and you get a new equilibrium. If the climate did not have equilibrium states formed by the balancing of positive and negative feedbacks, it is unlikely we would be here to see it! HTH
  22. This is a very interesting and informative article, and I thank the author for it. Respectfully, however, I think that readers might jump to a false or questionable conclusion reading this article, because CO2 is only a piece of the climate change problem. What Hansen envisions, I think, in his runaway climate change scenario is a series interlinked positive feedback effects which in total might be sufficient to tip the earth into runaway warming. He very specifically mentions destabilization of the methane hydrates as part of his runaway scenario, for example. I can't speak for Hansen, but what I worry about is the scenario below. Increases in fossil fuel produced CO2 cause warming, which activates the following positive feedback processes: The Arctic sea ice/ albedo feedback. The permafrost decay feedback. The forest wildfire feedback. The ocean CO2 release feedback. The destabilization and release of methane from the shallowest methane hydrates including the Siberian yedoma and thermokarst. Atmospheric increases in water vapor. The combined effect of all of these processes destabilizes the oceanic methane hydrate deposits starting with the shallowest ones first. Most methane from this release ends up dissolved in the sea water, and oxidized into CO2. Increasing amounts are able to vent directly to the atmosphere through sudden releases. Destabilization of the hydrates also results in associated deposits of natural gas venting directly into the atmosphere. Most of this takes place in the Arctic, while the Antarctic continues almost intact. Due to the fact we are coming out of an ice age, large inventories of methane hydrates are available. As methane releases accelerate, concentrations of the hydroxyl radical in the atmosphere plummet, leading to longer residence times for methane in the atmosphere before it is oxidized into CO2, and increased warming as a result. About this time, CO2 based warming is approaching a first plateau, as this article predicts, due to diminishing positive feedback returns and saturated absorption bands. So, we get maybe 10 degrees C of temperature increase due to maybe 3000 ppm of atmospheric CO2. But methane impact on global heating has its own diminishing returns curve, and that curve is in its steepest part. Water vapor concentrations continue to increase, and the diminishing returns curve of water vapor is also near its steepest point at this time. The diminishing returns curve of CO2 is at a plateau. When the diminishing returns curve of methane and water vapor plateau, the earth is perhaps another twenty degrees C warmer, on top of the ten degrees C caused by CO2 alone. At this point many inland lakes lose their water to the atmosphere. Evaporation is greatly increased, from the landmasses. About this time, the oceans have heated enough to release most of the methane from hydrates. The oceans become anoxic, and hydrogen sulfide starts to evolve from the oceans, killing most land organisms. The hydroxyl radical has been overwhelmed, and atmospheric oxidation times for methane have become hundreds of years. The oceans begin to boil, and transfer their water into the atmosphere. Soon, most of the water in the oceans has transferred to the atmosphere. As ground temperatures increase, carbonate begins to convert to CO2. Plate tectonics, driven by the temperature difference between the mantle and the surface slows and stops. So the rock weathering cycle and subduction of carbon containing sediments also stops. Eventually, with all of the water, CO2, and methane in the atmosphere, the earth becomes another Venus, but hotter at first because we still have all of our water, while Venus has lost its water due to light induced dissociation of water into hydrogen and oxygen, and loss of the hydrogen into space, as happened on Venus. How likely is all of this? Well mass extinction events such as the Paleocene-Eocene thermal maximum have apparently taken us part way down this path, according to isotope ratio records. And the sun is hotter, now.
  23. Leland Palmer writes: How likely is all of this? You've written that very coherently, and it's not by any stretch of the imagination a "crackpot" scenario. But I would say it's very unlikely, even under a BAU emissions scenario. Lord knows I'm no expert on the PETM, but achieving that kind of CO2 pulse would seem to require burning more fossil carbon than would be projected even under an extreme scenario. And my understanding of the benthic methane hydrate issue is that it's likely to kick in only very slowly (on a global scale, ignoring local exceptions). The PETM was certainly nasty, and we wouldn't want to subject ourselves to anything like it. But it didn't lead to the kind of Venusian runaway warming you describe, despite involving much higher temperatures than AGW is likely to produce (remember that in addition to the large magnitude of the warming, the PETM was starting from a warmer point). Yes, the sun is hotter now, but the PETM-Holocene difference in TSI isn't that large (a couple of percent?). Perhaps most importantly, there have been other periods in the past (not just the PETM) when the planet was much hotter than today (think crocodiles and azolla blooms in the Arctic) and no Venusian runaway occurred. On very long timescales (tens of millions of years), the earth has been gradually cooling. We're going to be unwinding that process by at least a couple of degrees C in a geologically very short time ... but I think the dangers more involve disruption of our agricultural system, expensive and painful impacts from sea level rise, and loss of biodiversity (esp via ocean acidification). I don't think the Venusian runaway is remotely likely unless our descendants tried really hard to bring it about. (E.g., massive production and release of CFCs). Again, though, paleoclimate isn't really my area of expertise, so this is just one person's amateur understanding.
  24. Wow, thanks for the quick and thoughtful response. Any thoughtful person would be thankful to be wrong about such a scenario, of course. The fact that we are coming out of an ice age, and starting from a cooler starting point might not save us from such a scenario, though. Our methane hydrate deposits are in equilibrium at ice age temperatures. The speed at which we are introducing CO2 is absolutely unprecedented, so far as I know. Also, the forcing from fossil fuel use is entirely non-random, unlike most past naturally occurring events. So, our methane hydrates could be particularly susceptible to disruption, and have had no chance to gradually lose methane, and have it safely oxidized into CO2 and sequestered via the rock weathering cycle over many thousands of years. Yes, there were warmer periods in the past, but we may have gotten to those warmer periods in a safer manner, more gradually, allowing harmless oxidation of methane at reasonable rates. The permafrost decay positive feedback is a similar concern. If this permafrost loses its frozen plant matter to decay into CO2 and methane gradually, there is no problem. If the accumulated frozen plant matter from thousands of years of ice age conditions decays within a century, though, this might add to warming in an unprecedented manner. The yedoma and thermokarst of Siberia are a similar concern. These ice age accumulations of methane and methane hydrate could also be susceptible to anomalously rapid dissociation. The PETM is worrisome, but the event that really worries me is the End Permian. As you point out, the PETM was nasty, but the End Permian mass extinction was the big one, extinguishing on the order of 90 percent of species existing at that time. Direct intrusion of the Siberian Traps volcanism into methane hydrate deposits may have been necessary to cause that one, but we don't know this for sure, so far as I know. So, I worry that our "clathrate gun" and associated ice age relics might be cocked and loaded, so to speak. Some things that might save us, as you point out, are the logarithmic nature of the greenhouse effects from the various greenhouse gases, and the diminishing returns positive feedback phenomenon. Also in favor of stability are the endothermic nature of methane hydrate dissociation, and the Planck radiation feedback. One thing that really worries me is the unpredictable nature of positive feedback phenomena. I frankly doubt the ability of anyone to predict the outcome of such a complex interlocked series of positive and negative feedbacks. If anyone could do it, it would be someone like Hansen- and Hansen is worried, too. Another thing that worries me is that estimates of the total quantity of methane hydrates differ by at least an order of magnitude. The sun is a couple of percent hotter than it was during the PETM, but several percent hotter than during the End Permian, I think. If we take the End Permian event, and add in a more rapid triggering event, a buildup of ice age methane hydrates, and a sun that is five percent or so hotter, what do we end up with?
  25. Re: Leland Palmer (24) Recent evidence supporting the clathrate gun hypothesis exists:
    "Evidence that massive quantities of methane gas have been released from the sea floor during past ice ages has been reported. The discovery supports the hypothesis that huge releases of ocean methane contributed to the rapid warmings of the Earth that have ended past ice ages."
    As reported in Reporting Climate Science .Com Free copy of the study available here. I agree with Ned in that, to the level of understanding we have currently, the possibility of a methane clathrate/hydrate release sufficient to trigger a hydrogen sulfide release and/or leading to a Venus-style runaway situation is remote. What is disturbing, however, is that such a possibility even exists. More disturbing is that future conditions may not be a good analog for anything in the paleo record other than the PETM. Without being able to establish an upper bound to the risk, we may find out that we we didn't know was more relevant than what we did. That should be of concern to all, as this is an experiment to be run once only. The Yooper

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