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Does positive feedback necessarily mean runaway warming?

What the science says...

Select a level... Basic Intermediate Advanced

Positive feedback won't lead to runaway warming; diminishing returns on feedback cycles limit the amplification.

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)

At a glance

Yet another climate change myth that has not aged well. As of early May 2024, all of the past 12 months had come in at more than 1.5°C above pre-industrial temperatures, so all of the first sentence is now tripe.

However, with regard to the rest of the myth, the evidence suggests it is extremely unlikely that Earth can enter a runaway greenhouse state.

Why is that? We have two good lines of evidence to support the contention. Firstly, we know an awful lot these days about the geography and climate of Earth in the past. Ancient geography can be determined by examining rock sequences on the continents and noting similarities in their fossil faunas, sedimentary environments and ancient magnetism.

So we know, for example, that around 55.8 million years ago, Ellesmere Island, off the NW coast of Greenland, was a lot warmer than it is today. The main geographical difference between then and now was that the Atlantic Ocean was narrower. The faunal difference was a lot more impressive. Where there are now glaciers and polar bears, back then tortoises, snakes and alligators thrived. Their fossils, along with those of redwood, ginkgo, elm and walnut, are to be found in Ellesmere Island's sedimentary rocks.

The time in question is known as the Palaeocene-Eocene Thermal Maximum. As the name suggests, it was probably the hottest climate experienced on Earth in the past 600 million years. To get temperate to subtropical temperatures in the Arctic is indeed impressive. But there was no runaway beyond that. Why?

Trapping of heat by CO2 and other greenhouse gases causes an energy imbalance on Earth. This imbalance gets amplified by positive feedbacks. A positive feedback happens when the planetary response to a change serves to amplify that change. For example, due to burning of fossil fuels, atmospheric CO2 has gone up by 50%. The resulting enhanced greenhouse effect is heating up the planet. The heating, among other things, melts arctic permafrost, releasing the CO2 and methane trapped within it. These gases amplify that initial change. The effect reinforces the cause, which will in turn further increase the effect, which in turn will reinforce the cause… and on and on.

So won't this spin out of control? The answer is almost certainly not. Feedbacks are not just positive. One very important one is that a warmer planet radiates more energy out to space than a cooler one. This feedback is not only negative but it is also strong.

Furthermore, positive feedback cycles will go on and on, but there will be a diminishing of returns, so that after a number of cycles the effects become insignificant. Thus, if we double the atmospheric concentration of CO2, the amount by which the response to that change - heating - can be amplified is approximately three times.

The creator and spreader of this particular myth is essentially putting words in people's mouths. No surprise there. But we do not need a runaway greenhouse effect to make life on Earth difficult. Just a few degrees of additional heating will do exactly that.

Please use this form to provide feedback about this new "At a glance" section. Read a more technical version below or dig deeper via the tabs above!

Further details

Some deniers 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 uninhabitable 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. In addition, negative feedbacks also occur due to warming, of which the powerful Planck response is particularly important. Put simply, the Planck response is a feedback that makes a warmer planet radiate more energy from the top of its atmosphere to space than a cooler planet, thereby reducing the energy imbalance.

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.

One topic along this theme, that you may have heard of in the media, concerns Arctic Permafrost. This is important because large amounts of organic carbon are stored in the permafrost - ground that remains frozen throughout the year. If large areas of permafrost thaw out as the climate warms, some of that carbon will be released into the atmosphere in the form of carbon dioxide or methane. That will certainly result in additional warming. A serious enough threat, for sure, but projections based on models of permafrost ecosystems suggest that future permafrost thaw will not lead to a ‘runaway warming’ situation. That's the conclusion from the FAQ regarding permafrost in the IPCC's latest Sixth Assessment Report (AR6) (PDF).

A final point regarding runaway global warming involves deep time. On several occasions in the geological past, Earth has recovered from the 'icehouse' climate state, going back into a Hothouse regime. The implication is that if such profound changes happened before without Earth entering a runaway warming state, it's highly unlikely to occur this time. That is no reason for complacency, though. A few degrees will be bad enough.

Those of a mathematical disposition will find additional interest in the Intermediate version of this rebuttal.

Last updated on 2 June 2024 by John Mason. View Archives

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Comments 26 to 50 out of 121:

  1. #24: "I worry that our "clathrate gun" and associated ice age relics might be cocked and loaded, so to speak. " It is, as with many other questions of climate change, a question of rate of change. Thus we do not know if the loaded gun has birdshot or a deer slug. Archer 2007 is an excellent summary of methane hydrate and their climate change potential. The hydrate reservoir is so large that if 10% of the methane were released to the atmosphere within a few years, it would have an impact on the Earth’s radiation budget equivalent to a factor of 10 increase in atmospheric CO2. ... Fortunately, most of the hydrate reservoir seems insolated from the climate of the Earth’s surface, so that any melting response will take place on time scales of millennia or longer. Acoustic images of real-time methane releases as in this example are dramatic evidence that such melting is indeed occurring, albeit in isolated places. As summer Arctic sea ice continues to dwindle in the coming few years, 'science experiments' such as this will no doubt become more frequent and widespread. In my days in the offshore O&G exploration, hydrates were a well-known drilling hazard; punch a hole in one and you cause it to go unstable very quickly. These guys are going looking for them. Combine that plan with another series of avoidable mistakes such as those leading to the BP disaster and you have given your loaded gun to a bunch of drunk teenagers. Here is a long, but quite thorough 2008 Scripps Institute video on the subject.
  2. It probably goes without saying, so I didn't bother saying this in my comment above. But obviously the consequences of a Venusian style runaway warming are so completely unacceptable, that even a very small probability of that outcome needs to be taken seriously. So I guess I'd characterize my position as "this is very unlikely to happen, but we should be investing a lot more in understanding the relevant processes (clathrates, etc.) just in case".
  3. Hi muoncounter- I've read one of Archer's papers, but it's been a few months and I'll reread it. I'd feel more confident in Archer's stuff if he hadn't written several joint papers with ExxonMobil chief scientist Kheshgi: ExxonMobil Contributed Papers on Climate Science
    17. Archer, D., Kheshgi, H., and Maier-Reimer, E. 1997. Multiple Timescales for the Neutralization of Fossil Fuel CO2, Geophysical Research Letters, 24: 405. 19. Archer, D., Kheshgi, H., and Maier-Reimer, E., 1998. The dynamics of fossil fuel CO2 neutralization by marine CaCO3, Global Biogeochemical Cycles, 12:259-276. 35. Kheshgi, H. S. and Archer, D. 2004. A non-linear convolution model for the evasion of CO2 injected into the deep ocean. Journal of Geophysical Research,109, C02007, doi:10.1029/2002JC001489. 13. Kheshgi, H. S., and D. Archer, 1999: Modeling the Evasion of CO2 Injected into the Deep Ocean, in Greenhouse Gas Control Technologies, edited by B. Eliasson, P. Riemer and A. Wokaun, pp. 287-292, Pergamon.
    I can see why an earth scientist might collaborate with ExxonMobil, or it's chief scientist. They undoubtedly have a monumental knowledge of geology, and an immense treasure trove of geological information. Having said that, though, Archer's estimate of the total amount of methane hydrates is on the low end of current estimates. It's a really important subject, and I'll get my information about it from sources with no known connection to ExxonMobil.
  4. #28: "Archer's estimate of the total amount of methane hydrates is on the low end of current estimates." As I said above, its the rate of release that's critical. Since clathrates are so well-distributed around the world's oceans, their volume is quite significant. But a methane release from an Arctic source may occur independently of one in the Gulf of Mexico. "information about it from sources with no known connection to ExxonMobil." Fair point. I note that Maier-Reimer was with the Max Planck Institute when those papers were written. Kheshgi also co-authored a paper with Bert Bolin, who I believe was Chair of the IPCC.
  5. Here's a quote from a 2008 paper, posted on the National Energy Technology Lab website, that uses the Tough +/Hydrate computer code for simulating methane hydrate dissociation. MODELING OF OCEANIC GAS HYDRATE INSTABILITY AND METHANE RELEASE IN RESPONSE TO CLIMATE CHANGE
    Two of the most recent studies, each accounting for the coupled contribution of organic matter decomposition and mass transport, have produced drastically different results. Klauda and Sandler [8] provide an upper estimate of 74,400 Gt of methane carbon in hydrate form (27,300 Gt along continental margins, while Buffett and Archer [9] used both compaction and advection in a 1-D methanogenesis/hydrate formation model to reach an estimate of 3,000 Gt of methane in hydrate and 2,000 Gt of gaseous methane existing in a stable state under current climate conditions.
    This paper seems to show increased levels of hydrate release for shallow hydrate deposits with less than a one degree C temperature increase. There are chemical reactions that oxidize the methane or transform it into bicarbonate that I was not aware of until recently. Still, the bigger the reservoir, the smaller the percentage that has to dissociate to cause the climate serious or catastrophic harm.
  6. Here are a couple other very interesting papers on methane hydrates, that Skeptical Science readers likely haven't seen yet: NETL Methane Hydrates Page
    The results generated through this project have lead to LBNL and LANL researchers publishing four papers in the peer-reviewed literature. (For more information, see the methane hydrate bibliography document.) The first paper, published in the Journal of Geophysical Research (Vol. 13, C12023, 2008) assessed the stability of three types of hydrate deposits and the dynamic behavior of these deposits under the influence of moderate ocean temperature increases. The results indicated that deep-ocean hydrates are stable under the influence of moderate increases in ocean temperature; however, shallow deposits can be very unstable and release significant quantities of methane under the influence of as little as 1 degree C of seafloor temperature increase. A second paper, published in Geophysical Research Letters (Vol, 36, L23612, 2009)here presented the first results of the 2-D slope-scale modeling, demonstrating that shallow hydrates in sloping systems may, alone, generate significant methane and lead to the formation of gas plumes at the seafloor. The results were consistent with the observation of methane venting along the upper limit of a receding GHSZ [Gas Hydrate Stability Zone- LP] off Spitsbergen. The third paper, published in Geophysical Research Letters (Vol, 37, L12607, 2010) and the fourth paper, in final revision for the Journal of Geophysical Research, present the first results of forward-coupled methane release, water column chemistry, and transport via ocean currents using a 1o version of the POP code. These establish a new paradigm for understanding the response of the oceans to methane release on a large scale. In particular, the work highlights the importance of resource limitations. Large and concentrated methane plumes may deplete the surrounding water of oxygen and other trace nutrients, reducing the ability of methanotrophs to consume the methane and increasing the chance of release into the atmosphere. This is in sharp contrast to previous assumptions of “99% consumption” of methane for all release scenarios.
    So, the news from these papers appears to me to be bad. The rate of release from hydrate deposits is limited by the endothermic nature of hydrate dissociation, and by fluid flow limitations, according to the second paper mentioned above, though. So - a crucial point - whether these deposits will lead to runaway warming may be very dependent indeed on their total quantity. An order of magnitude difference in estimates of their total quantity, with one of the estimates coming from Archer, who writes papers with ExxonMobil chief scientist Kheshgi, is just unacceptable.
  7. #31: "The rate of release from hydrate deposits is limited by ..." Nothing limited about these numbers: Gas escape features off New Zealand: Evidence of massive release of methane from hydrates Multibeam swath bathymetry data ... show gas release features over a region of at least 20,000 km^2. Gas escape features, interpreted to be caused by gas hydrate dissociation, include an estimated a) 10 features, 8–11 km in diameter ... If the methane from a single event at one 8–11 km scale pockmark reached the atmosphere, it would be equivalent to ∼3% of the current annual global methane released from natural sources ... Full paper, with graphics, available here.
  8. Thanks, muoncounter, it's a very interesting paper. Glaciations tend to start gradually, but end abruptly. Various people, referenced in the your paper and the Wikipedia article on the clathrate gun hypothesis, suspect that lower sea levels during those glaciations can cause pressure induced release of methane from hydrates, rapidly increasing atmospheric methane levels leading to an increase in temperatures and higher sea levels. If true, this does demonstrate one thing: large scale methane releases from oceanic hydrates can reach the atmosphere. This is supported by the carbon isotope data from events like the PETM and the End Permian- although direct intrusion of magma from the Siberian Traps volcanism into methane hydrate deposits may have been necessary to trigger the End Permian mass extinction. These carbon isotope data suggest that two to five or more trillion tons of isotopically light methane from the hydrates entered the active carbon cycle during those events. Can our greenhouse driven pulse of heat, which is working its way inexorably downward into the oceans, stimulate a similar rapid release of methane?
  9. I think the distinction between gain < 1 (no runaway even though feedback is positive) and gain > 1 should be explicitly stated early in the article. Climatology's use of "positive" (gain could be either > 1 or < 1) in regard to feedback is not the same as electronics's use of "positive feedback" (gain strictly > 1), IIUC. _That_ is why "positive feedback" has such a strong connotation of "runaway" for many newcomers to climate science. I think you need to jump on this early and explicitly in any discussion of "runaway", in order to cut down on misunderstandings. Don't bury the significance of _gain_ halfway down the article at the end of a paragraph ("and call the gain factor g").
  10. Here's another recent paper, which uses a state of the art atmospheric chemistry model to predict much stronger positive feedback from indirect atmospheric chemistry effects of large methane releases, than from the methane itself. They are talking about several hundred percent increases in stratospheric water vapor, for example, increased methane lifetime of roughly 100 percent for very large releases, and large increases of tropospheric ozone. The hydroxyl radical, by their modeling, decreases in the troposphere, where it is needed to oxidize methane, and increases in the stratosphere. The positive feedback factor that they calculate (eta) ranges from 1.5 for small releases, up to 2.9 for large ones. Strong atmospheric chemistry feedback to climate warming from Arctic methane emissions
    Here we apply a “state of the art” atmospheric chemistry transport model to show that large emissions of CH4 would likely have an unexpectedly large impact on the chemical compositioof the atmosphere and on radiative forcing (RF). The indirect contribution to RF of additional methane emission is particularly important. It is shown that if global methane emissions were to increase by factors of 2.5 and 5.2 above current emissions, the indirect contributions to RF would be about 250% and 400%, respectively, of the RF that can be attributed to directly emitted methane alone.
    It's a very important result, IMO, which could provide a bridge from mild CO2 based warming to runaway methane and atmospheric chemistry change based greenhouse heating. It's a very different atmosphere that they are talking about, with sustained methane release rates of 4 to 13 times those of today. Stratospheric water vapor and stratospheric hydroxyl radical increase, tropospheric hydroxyl radical decreases, and tropospheric ozone increases, leading to indirect warming several times that of the warming from methane itself. It's particularly worrisome because this appears to be an honest result, resulting from a fair query of a state of the art atmospheric chemistry transport model. If this work holds up, it may help explain the strong positive feedback of past apparent methane catastrophes including the Paleocene-Eocene Thermal Maximum and the End Permian mass extinction, I think.
  11. How do we know that the system is limited purely by the nature of its positive feedback? I'm trying to understand how the possibility of negative feedback being a limiting factor has been disregarded? There is a theory that the increasing levels of water vapour in the atmosphere due to increased temperatures might greatly increase cloud cover, increasing the earth's reflectance, reducing heat absorbtion into the system. As far as I know, the question of what the impact of increased atmospheric water vapour has on cloud formation and, therefore, albedo is still very open? So I wonder whether it isn't premature to assume that the system is self-limiting due solely to the reason given above? Particularly as the methane release issue casts further doubt on the idea that the system is self-limiting, without some other unconsidered factor coming into play. Thoughts?
  12. jpat A gain < 1.0 can still provide a several-fold amplification: Output = Forcing / ( 1 - gain ) A gain of 0.9 will result in an amplification of 10.0, as the sum will be 0.9 + 0.9^2 + 0.9^3 + ..., summing to 10x.
  13. True but irrelevant. The candidate system must be capable of power amplification. The output variance (power) in the passive system you describe (unit forward gain, attenuated feedback) can never exceed the input variance. In the system we are considering, the output variance due to Milankovitch forcing exceeds the solar variance from same.
  14. jpat - Not power amplification, that's a misunderstanding of the system. GHG's act as a throttle controlling energy flow out of the Earth climate, all said energy coming from the sun. Input energy inevitably gets dumped to space, the question is in what thresholds are in place in the mid-point of the system, driving internal energy levels so that the throughput can occur. You seem to be treating this as a limited system, rather than an open system with energy flows. I suggest more reading on your part. I would point you to The Discovery of Global Warming as a starting point. Not a passive system - a dynamic system. That's a serious error in viewpoint.
  15. rf -----^v---- ri | | -^v----*----|+\__| ? Vin --|-/ | _|_ |______| \ / Consider the circuit above. The op-amp is configured for unity gain. The feedback "gain" = ri/(ri + rf) < 1 and the feedback is positive. Since the forward gain is unity, the open loop gain (referred to as "gain" in #37) = feedback attenuation < 1. The claim in #37 is that this circuit will amplify. Not so much. The inverting input of the op-amp is wired to the output (Vo). The op-amp is ideal so the non-inverting voltage (v+) is equal to the inverting input voltage (v-) So Vo = v+ = v-. This means the voltage drop across rf = 0 which by Ohm's law means the current through rf (Irf) =0. But Irf = Iri. Thus the voltage drop across ri = 0. Thus Vo = Vi. The gain of this circuit is unity. Now suppose the op-amp is configured for a gain of 2 and the feedback divide ratio < .5 (again, so that gain as defined in #37 < 1). At first blush it appears capable of amplification. Now add the stability constraint that the input impedance > 0. We find that for stability, ri > rf. The open loop gain for the circuit can be shown to be 2-rf/ri which again must be <= 1 for stability. This doesn't disprove anything but rather shows that the feedback gain equation is subject to boundary conditions including conservation of energy. I really wonder whether one could devise a physical system capable of doing work using the formulation provided by KR.
  16. I guess my attempt at input a schematic got mangled by the html processor (block tags doesn't seem to work). KH - I posted before I saw your response. I take your point but am still struggling to understand how feedback amplifies the Milankovitch cycles. The system has to do real work, melting ice, heating the oceans etc. and I thought the argument was the system does more work with feedback than it could do without. That sounds like power amplification to me but I'll come back after I read up some more.
  17. jpat - A strictly electronic analogy will not work well with respect to the climate system. To some extent a transistor or op amp would correspond, but transistors are too non-linear. An operational amplifier could be used to build a corresponding circuit, with the Stephan-Boltzmann law providing the negative feedback, but not a bare op-amp. The S-B law indicates that thermal radiation to space scales as T^4 (in Kelvin), and means that excess energy accumulation in the climate, simply by heating/cooling the Earth, will rebalance the input/output levels. That's your negative feedback. There are fast energy state response elements (water vapor, clouds), slow response elements (ocean CO2, albedo from ice coverage, vegetation), and over and above this the forcings that drive those feedback items. In the ice age cycles a small amount of insolation variation (orbital changes shifting land/ocean exposure and polar insolation/albedo changes) acted as a forcing, with the temperature sensitive elements responding at various delays. Currently we are introducing a direct forcing with GHG's, and should expect to see water vapor levels, albedo, vegetation, and in fact CO2 levels from ocean solubility respond to the initial forcing with their own changes. All of these - forcings and feedbacks - act as throttles on the flow of energy from the sun into the climate and back out again, with rates dependent on the various states, gas concentrations, albedo, etc.
  18. KR - The op-amp is only their to provide the unity forward gain and ideal summing node required to implement the transfer function you gave in #37. I went through the exercise because I am pretty sure that a passive (i.e. forward gain <=1), physical implementation cannot provide variance amplification. I think this is a general result, imposed by boundary conditions and conservation of energy. Think of a step up transformer. True the voltage measured at the secondary will be higher than that at the primary but the variance (power) remains unchanged. I do think that climatologists use the term feedback in a different way than I am used to thinking about it. In this review, they state "S is proportional to 1/(1 − f)" where S is the sensitivity and f is the "net feedbacks". A control systems guy would call f the open loop gain, as in CL(s) = G(s)/(1-G(s)H(s)) where G(s) is the forward transfer function and H(s) is the feedback transfer function and s is the Laplace operator. I deduce from the above that climatologists model the forward gain as unity (which I find odd - if there were no feedback would all of the energy go into heat flux? Would some get reflected back immediately?) which is why the op-amp is configured for unity gain in my analogy. In any case I'm still trying to formulate a transfer function model for the radiant balance equations so that I can understand how it is that the CO2 could lag the temperature through the entire glaciation cycle, be responsible for the rapid interglacial rise and yet allow the small Milankovitch forcing to turn things around. Seems implausible but I've been fooled by intuition before.
  19. jpat - The Milankovitch forcings last for millenia, which allows time for various feedbacks to take effect. Just the Milankovitch forcings alone should change the average temperature of the Earth by a total of 1-2.5C; the 6-8C swings seen over the ice age cycles are due to the amplification of the forcing change by water vapor, CO2, ice retreat/advancement, etc. The Wiki on this is actually fairly reasonable. I would suggest caution in reasoning from electronics - that would be an analogy, and while providing an analogy is a useful way to explain something, you cannot reason from an analogy back to the original system, as analogies only resemble the original complex system in part. You will inevitably get tripped up on the differences - there is no substitute for actually studying the real thing. And the real thing includes multiple time lags, chaotic/non-linear variations, and lots of different forcing inputs
  20. jpat - I strongly suggest you take a look at the CO2 lags temperature thread in this regard.
  21. I think I have an analogy that maybe helpful to those like me who come from an engineering background and have trouble putting the feedback discussed here into a more familiar context. Consider a circuit comprised of a voltage source connected to a resistive divider. Assume the divided voltage is our output node. To this output node we connect the control port of a voltage controlled voltage source of gain b whose output is connected to the output node through a series resister. This is our feedback path. Assume all resisters are 1 ohm. If b is zero the output voltage is simply one third the input voltage. As b is increased from zero to 1, the output rises from vin/3 to vin/2. Thus we see a "gain" of 1.5 compared to the no feedback case but in both cases the forcing (vin) is attenuated. With b=0, the thevenin impedance looking into the output node is 1/3 and therefore the output power density is 4kT/3 W/Hz. With b = 1, the thevenin impedance rises to 1/2 and so too does the power density, to 2kT. This indeed we can see an increase in variance with feedback gain < 1. Finally note that b in my analogy is not the same as f in #37. In the example, b could actually vary between 0 and 3, (corresponding to 0<=f<1) before the circuit became unstable. However, to get actual gain (in the normal sense of the word, i.e. an output greater than vin), b must be greater than 2. That is, to get actual amplification requires active feedback, as expected.
  22. "The Milankovitch forcings last for millenia, which allows time for various feedbacks to take effect...The Wiki on this is actually fairly reasonable." From the Wiki: "Each glacial period is subject to positive feedback which makes it more severe and negative feedback which mitigates and (in all cases so far) eventually ends it." And yet in this tread (see #54), chris accuses me of making an "evidence free assertion" when I tried to make that very point. Which is it? Is climate sensitivity constant or does it vary as negative feedback(s) kick in at the extremes?
  23. jpat#47: "Is climate sensitivity constant or does it vary" Why does it have to vary? The sensitivity to any particular forcing may remain constant while the forcings themselves vary. For example, as more CO2 enters the atmosphere, that forcing increases with constant sensitivity. FWIW, I wonder if you've considered a circuit analogy from a simpler time: Hartley and Colpitts oscillators exploit feedback without necessarily running away.
  24. I think that climate sensitivity has to vary. Consider two extremes. If you melt all the ice pack, then the albedo feedback component practically disappears. Second consider an iceball earth with just enough solar input and CO2 start a melt the ice at the tropics. At point water vapour enters the atmosphere where it wasnt before. In this scenario, climate sensitivity has to be extreme. I think this is reason (beside the measurement errors) for the wide of range of sensitivities from paleoclimate studies. Carbon-cycle modelling still has a lot of uncertainty with many different ways to replicate known data. However, I dont think any of them would give a linear or log-linear response of atmospheric CO2 to temperature.
  25. "Why does it have to vary? The sensitivity to any particular forcing may remain constant while the forcings themselves vary." The Milankovitch forcing are very regular and of essentially constant amplitude. The sensitivity is determined by the sum of all the feedbacks so to the extent that one or more feedbacks depends on temperature or other dynamic variables in the climate, the sensitivity will change. I don't think it is controversial that the assumption of constant sensitivity is only valid over a few degrees. With regard to your other point, I think perhaps a more apt analogy would be a class of circuits called injection locked amplifiers. In and of themselves they are stable but have positive feedback. They don't oscillate because their complex poles have very low quality factor and are unable to remain on the jw axis for any period of time. However, if we inject a small periodic signal near the eigenvalue frequency, the circuit exhibits behavior very much like a phase-locked loop. Its phase trajectory tracks the input signal inside a bandwidth determined by the injection amplitude. Outside of this bandwidth, the phase trajectory variance falls as f^4. This makes them useful as filters but they are not widely employed because they have a tendency to exhibit chaotic behavior. The interesting thing about these circuits is that they behave much like oscillators in that each node in the circuit is a delayed version of the previous node (like the CO2 curve in the ice core is kind of a delayed version of the temperature). Another interesting thing is what happens when we add a constant forcing bias. The peak amplitude of the output does not change but rather the duty cycle is modified. It reaches equilibrium by modifying the symmetry of the output waveform. For instance with positive constant forcing the waveform adjusts to spends more time in the positive realm than in the negative realm but the peak amplitude remains unchanged. What got me thinking about this was a Fourier analysis I did of the Vostok ice core data. The phase noise power spectral density exhibits the same BW tracking fingerprint I saw when analyzing these injection locked amplifiers years ago. This doesn't prove anything but it is an interesting idea.

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