Arguments
Explaining how the water vapor greenhouse effect works
What the science says...
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Increased CO2 makes more water vapor, a greenhouse gas which amplifies warming |
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Climate Myth...
Water vapor is the most powerful greenhouse gas
“Water vapour is the most important greenhouse gas. This is part of the difficulty with the public and the media in understanding that 95% of greenhouse gases are water vapour. The public understand it, in that if you get a fall evening or spring evening and the sky is clear the heat will escape and the temperature will drop and you get frost. If there is a cloud cover, the heat is trapped by water vapour as a greenhouse gas and the temperature stays quite warm. If you go to In Salah in southern Algeria, they recorded at one point a daytime or noon high of 52 degrees Celsius – by midnight that night it was -3.6 degree Celsius. […] That was caused because there is no, or very little, water vapour in the atmosphere and it is a demonstration of water vapour as the most important greenhouse gas.” (Tim Ball)
At a glance
If you hang a load of wet washing on the line on a warm, sunny day and come back later, you can expect it to be dryer. What has happened? The water has changed its form from a liquid to a gas. It has left your jeans and T-shirts for the air surrounding them. The term for this gas is water vapour.
Water vapour is a common if minor part of the atmosphere. Unlike CO2 though, the amount varies an awful lot from one part of the globe to another and through time. Let's introduce two related terms here: 'non-condensable' and 'condensable'. They set out a critical difference between the two greenhouse gases, CO2 and water vapour.
Carbon dioxide boils at -78.5o C, thankfully an uncommon temperature on Earth. That means it's always present in the air as a gas. Water is in comparison multitalented: it can exist as vapour, liquid and solid. Condensed liquid water forms the tiny droplets that make up clouds at low and mid-levels. At height, where it is colder, the place of liquid droplets is taken by tiny ice-crystals. If either droplets or crystals clump together enough, then rain, snow or hail fall back to the surface. This process is constantly going on all around the planet all of the time. That's because, unlike CO2, water vapour is condensable.
CO2 is non-condensable and that means its concentration is remarkably similar throughout the atmosphere. It has a regular seasonal wobble thanks to photosynthetic plants - and it has an upward slope caused by our emissions, but it doesn't take part in weather as such.
Although water vapour is a greenhouse gas, its influence on temperature varies all the time, because it's always coming and going. That's why deserts get very hot by day thanks to the Sun's heat with a bit of help from the greenhouse effect but can go sub-zero at night. Deserts are dry places, so the water vapour contribution to the greenhouse effect is minimal. Because clear nights are common in dry desert areas, the ground can radiate heat freely to the atmosphere and cool quickly after dark.
On the other hand, the warming oceans are a colossal source of water vapour. You may have heard the term, 'atmospheric river' on the news. Moist air blows in off the ocean like a high altitude conveyor-belt, meets the land and rises over the hills. It's colder at height so the air cools as it rises.
Now for the important bit: for every degree Celsius increase in air temperature, that air can carry another 7% of water vapour. This arrangement works both ways so if air is cooled it sheds moisture as rain. Atmospheric rivers make the news when such moisture-conveyors remain in place for long enough to dump flooding rainfalls. The floods spread down river systems, causing variable havoc on their way back into the sea.
Atmospheric rivers are a good if damaging illustration of how quickly water is cycled in and out of our atmosphere. Carbon dioxide on the other hand just stays up there, inhibiting the flow of heat energy from Earth's surface to space. The more CO2, the stronger that effect.
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Further details
When those who deny human-caused global warming use this argument, they are trying to imply that an increase in CO2 isn't a major problem. If CO2 isn't as potent a greenhouse gas as water vapour, which there's already a lot of, adding a little more CO2 couldn't be that bad, they insist.
What this argument misses is the critical fact that water vapour in air creates what scientists call a 'positive feedback loop'. That means it amplifies temperature increases, making them significantly larger than they would be otherwise.
How does this work? The amount of water vapour in the atmosphere has a direct relation to the temperature in any given region and the availability of water for evaporation. Heard the weather-saying, "it's too cold to snow"? There's more than a grain of truth in that; very cold air has a low capacity for moisture.
But if you increase the temperature of the air, more water is able to evaporate, becoming vapour. There's a formula for this, the figure being 7% more moisture capacity for every degree Celsius of warming. All you then need is a source of water for evaporation and they are widespread - the oceans, for example.
So when something else causes a temperature increase, such as extra CO2 emissions from fossil fuel burning, more water can evaporate. Then, since water vapour is a greenhouse gas, this additional moisture causes the temperature to go up even further. That's the positive feedback loop.
How much does water vapour amplify warming? Studies show that water vapour feedback roughly doubles the amount of warming caused by CO2. So if there is a 1°C upward temperature change caused by CO2, the water vapour will cause the temperature to go up another 1°C. When other demonstrable feedback loops are included, and there are quite a few of them, the total warming from a 1°C change caused by CO2 is as much as 3°C.
The other factor to consider is that water evaporates from the land and sea and falls as rain, hail or snow all the time, with run-off or meltwater returning to the sea. Thus the amount of water vapour held in the atmosphere varies greatly in just hours and days. It's constantly cycling in and out through the prevailing weather in any given location. So even though water vapour is the dominant greenhouse gas in terms of quantity, it has what we call a short 'atmospheric residence time' due to that constant cycling in and out.
On the other hand, CO2 doesn't take an active part in the weather. It does hitch a lift on it by being slowly removed from the air as weak solutions of carbonic acid in rainwater. These solutions are key weathering agents, affecting rocks on geological time-scales. Weathering is a key part of the slow carbon cycle, with the emphasis on slow: CO2 thus stays in our atmosphere for years and even centuries. It has a long atmospheric residence time. Even a small additional amount of CO2 thus has a greater long-term effect - and in our case that additional amount is far from small.
To summarize: what deniers are ignoring when they say that water vapour is the dominant greenhouse gas, is that the water vapour feedback loop actually amplifies temperature changes caused by CO2.
When skeptics use this argument, they are trying to imply that an increase in CO2 isn't a major problem. If CO2 isn't as powerful as water vapor, which there's already a lot of, adding a little more CO2 couldn't be that bad, right? What this argument misses is the fact that water vapor creates what scientists call a 'positive feedback loop' in the atmosphere — making any temperature changes larger than they would be otherwise.
How does this work? The amount of water vapor in the atmosphere exists in direct relation to the temperature. If you increase the temperature, more water evaporates and becomes vapor, and vice versa. So when something else causes a temperature increase (such as extra CO2 from fossil fuels), more water evaporates. Then, since water vapor is a greenhouse gas, this additional water vapor causes the temperature to go up even further—a positive feedback.
How much does water vapor amplify CO2 warming? Studies show that water vapor feedback roughly doubles the amount of warming caused by CO2. So if there is a 1°C change caused by CO2, the water vapor will cause the temperature to go up another 1°C. When other feedback loops are included, the total warming from a potential 1°C change caused by CO2 is, in reality, as much as 3°C.
The other factor to consider is that water is evaporated from the land and sea and falls as rain or snow all the time. Thus the amount held in the atmosphere as water vapour varies greatly in just hours and days as result of the prevailing weather in any location. So even though water vapour is the greatest greenhouse gas, it is relatively short-lived. On the other hand, CO2 is removed from the air by natural geological-scale processes and these take a long time to work. Consequently CO2 stays in our atmosphere for years and even centuries. A small additional amount has a much more long-term effect.
So skeptics are right in saying that water vapor is the dominant greenhouse gas. What they don't mention is that the water vapor feedback loop actually makes temperature changes caused by CO2 even bigger.
Last updated on 23 July 2023 by John Mason. View Archives
Very briefly for Old Sage @250, the "entrapment" of heat by CO2 never ceases. However, following an increase in CO2 concentration, and as the temperature increases, the IR radiation from the surface and atmosphere also increase, thereby increasing the amount of radiation to space. After the temperature has increased a certain amount the amount of radiation to space returns to the the amount which balances incoming solar energy, at which point the temperature increase ceases. The temperature increase required to do that is a function not only of the reduction in radiation to space as a result of the increase in CO2 but also any further changes to the energy balance that result from the increased temperature.
This is so basic to understanding the greenhouse effect that it is stated, in one form or another, in any serious exposition of the greenhouse effect (other than those by some AGW deniers). If you did not know this, you do not understand the theory at even the most schematic level. Playing 'devil's advocate' requires actually understanding, and criticizing the theory being discussed. It also requires accepting the basic observational data. Old Sage does neither. Rather, his verison of 'devil's advocaccy' is the intellectual equivalent of a child putting their fingers in their ears, and shouting "Nah, nah, nah, nah nah-nah - can't hear you." Nobody mistakes that child for playing devil's advocate, and nor does such a response result in stimulating discussion.
Tom Curtis - Typo? An increase in CO2 leads to a _decrease_ in IR to space, an energy imbalance that causes an accumulation of energy, an increase in temperature, until the warning climate once again emits an amount of energy equal to that coming in.
KR @252, the initial decrease in IR with the increased CO2 is the "entrapment" that Old Sage refers to. I mention it again in the last sentence of the first paragraph. The rise in IR radiation to space that I mention in second sentence of the first paragraph is a consequence of the rise in surface temperature. So, not a typo, but that second sentence was poorly, and confusingly worded. Specifically, I mention that the rise in IR radiation follows the increase in CO2 (meaning in terms of time sequence) and follows on from the rise in temperature (meaning as a direct causal consequence). Clearly that makes the sentence ripe for confusion. Thank you for seeking clarrification.
old sage @250:
"I repeat, what physical process shuts down the alleged entrapment of heat by CO2 insulation after it has reached its target temperature per concentration thickness. If you can show that, you will see the rise is snuffed out from the outset and T does not rise whatever the concentration thickness."
Ergo: Insulation has no impact on temperature, and all the producers of house insulation, thick winter clothes and so on are just making profit from a hoax.
BTW, furry mammals started that hoax about 200 million years ago, followed by feathered dinosaurs and birds, so it has obviously been going on for a very long time!
From a previously snipped comment by old sage:
"...radiation from gases at STP, they scatter, they absorb, but most definitely they do not spontaneously radiate from their translational kinetic energy to any significant extent. All they do is convey energy from one place to another in an energy neutral fashion."
Here in a nutshell is where old sage doesn't understand what he is talking about. For his statement is correct, but incomplete. They don't radiate as a consequence of their translational kinetic energy; in fact they don't absorb in a way that impacts the translational kinetic energy either.
They radiate 'from' their rotational and vibrational energy. This is the entire basis of the field of Molecular Spectroscopy which deals with emission and absorption by entire molecules as a result of rotational and vibrational transitions, in contrast with Atomic Spectroscopy which deals with electron energy level transitions within individual atoms.
Before commenting again old sage needs to do some research into the topic of Moelcular Spectroscopy. If he comments again without evidence that he has first done that research then he will have shown that he isn't interested in learning.
Glenn Tamblyn @255, while CO2 molecules emit IR photons by giving up the energy stored in either one of three of their four possible vibrational states (see below), and microwave photons by giving up rotational energy; the energy of vibration and rotation is, on average in a gas, equal to the energy of translation along any of the three mutually perpendicular axis. That is a direct consequence of the equipartition theorem. That in turn is a consequence of the fact that any collision between two molecules can result in transfer of translational energy to rotational or vibrational energy, or the reverse. It follows that the amount of energy stored in a given vibrational state is a function of the temperature of the gas, ie, of the average translational energy of the gas.
I think this means that CO2 molecules do spontaniously radiate energy from their translational kinetic energy, but they do so through a mediated process. A hot CO2 gas sealed in a IR transparent case in a cold environement will gradually bleed away its translational energy (ie, drop in temperature) as collisions replenish the vibrational energy that is lost by spontaneous emission. It is that which Old Sage seeks to deny.
I know that we disagree on this only on whether that mediated loss of translational energy counts as "spontaneious radiation of translational kinetic energy", ie, on wording. But I think it is important to clarrify, both because Old Sage does not (I think) interpret the phrase "spontaneously radiate from their translational kinetic energy" as you do; and because readers unfamiliar with the process, or only casually familiar may be confused by that statement if the full relationship is not stated.
Agreed Tom. They don't radiate directly from translation. But their translational energy does constitute a pool of energy that can be transferred into/out of vibrational or rotational modes and thus radiated/absorbed via those modes.
The interactions go even further. Vibration of molcules, especially in the stretching modes of vibration, will actually alter the Moment of Inertia of the molecule. In order to conserve angular momentum the rotational velocity of the molecule will be constantly changing as the molecule vibrates and the MoI varies. To conserve energy as well as angular momentum there will be a continuous interchange of energy between the vibrational and rotational modes, coupling them together to some extent. And collisions can exchange energy, momentum and angular momentum, as any snooker player can tell us.
Its fascinating how all these concepts - degrees of freedom of action, equipartition, Moments of Inertia and Quantum mechanics - all come together to give us a solid understanding of the reasons why different gases have the Specific Heat Capacities they do. And the basics of why molecules radiate and absorb.
This for me is the great strength of science; the theories interlock so well and build a coherent picture.
"This for me is the great strength of science; the theories interlock so well and build a coherent picture."
It is also for me, and it is worth saying again and again.
Your request for references and data for what is basic text book physics is rather like asking for a reference when I say the sun will rise tomorrow. Do you seriously require a reference for the water cycle and the way clouds form? As for the work of Ramanathan, it starts using the radiative convective model - one which could hardly be better designed to exclude the constant hunting for equilibrium in the contest between sunshine and cloud cover. Take it from me, his findings - and he admitted not considering clouds or aerosols in the paper I read - is just an exercise in mathematical sophistry. There is only one way CO2 can raise earth's energy content - and I've tried to find justification for the GHG theory - is that by increasing the atmosphere's opacity, it increases the cross-section presented to the sun. I haven't bothered to calculate how much difference it would make, but it is at least a thermodynamically sound possibility. Energy neutral transfers within one thermodynamic system being able to raise the system's energy content is not sound.
[PS] Hand-wavy dismissal of observation/model match and of papers you continue to misconstrue is more sloganeering.
Please note that posting comments here at SkS is a privilege, not a right. This privilege can and will be rescinded if the posting individual continues to treat adherence to the Comments Policy as optional, rather than the mandatory condition of participating in this online forum.
Consider a thin plate on earth's surface. You can isolate it in glass box with near-vacuum if preferred to minimize conductive effects. What is the temperature of that plate a/ when sun is shining. b/ at midnight? Textbook answers that match actual observations require use of the GHG effect. Please show us how your understanding of physics will give the correct answer for observed temperature of the plate without the GHG effect. I see little point in further comments from you on this forum from you till you have answered this question.
Old Sage: Your most recent comment was deleted itn its entirety because it violated a number of prohibitions set forth in the SkS Comments Policy.
You are now on the cusp of relinquishing your privilege of posting comments on this site.
[PS] Old sage needs to answer the question above. He instead asks questions readily answered in a text book and by people here (see Postive feedback = runaway greenhouse) but seems utterly incapable of understanding the answer. Answering how he understands the temperature of a surface to be determined is best way to sort out misunderstanding/misapplications of physics.
This blog states: "The other factor to consider is that water is evaporated from the land and sea and falls as rain or snow all the time. Thus the amount held in the atmosphere as water vapour varies greatly in just hours and days as result of the prevailing weather in any location. So even though water vapour is the greatest greenhouse gas, it is relatively short-lived."
S. Stanley states "Agricultural irrigation is so widespread that it accounts for about 4% of the total evapotranspiration of water from Earth’s surface." (Eos.org: Research Spotlights, August 2016). Further, De Vrese et al [1] show that Asian irrigation causes a large increase in precipitation in East Africa. And Lo et al [2] and others show that California irrigation affects precipitation in the US mid-west. Considering that irrigation is fairly continuous and constitutes a fairly large source of evapotranspiration, the resulting atmospheric water vapour flows might be fairly significant in terms of their effect on atmospheric temperature, even if a particular droplet might be short lived. My question is whether you can point to a study that has quantified the effect of irrigation water vapour flows on the temperature of the atmosphere, including over the last 100 years.
[1] de Vrese, P., S. Hagemann, and M. Claussen (2016), Asian irrigation, African rain: Remote impacts of irrigation, Geophys. Res. Lett., 43, 3737–3745, doi:10.1002/2016GL068146.
[2] Lo, M.-H., and J. S. Famiglietti (2013), Irrigation in California's Central Valley strengthens the southwestern U.S. water cycle, Geophys. Res. Lett., 40, 301–306, doi:10.1002/grl.50108.
TonyLambert @261, the effect of irrigation on temperatures has been studied a number of times. In chronological order we have Boucher, Myhre and Myhre (2004), who find a 0.03-0.1 W/m^2 global greenhouse forcing from irrigation, but a surface cooling of 0.8 K over irrigated lands. That equates a 0.02 K increase in global temperature, assuming a Transient Climate Response of 2 K per doubling of CO2, and weighting the regional cooling by area.
In contrast, Puma and Cook (2010) find an overall cooling effect from irrigation in tropical latitudes (NH winter) and tropical and NH mid-latitudes (NH summer) once all factors are included, but for land surface only:
Boucher et al also show a slight cooling for land surface only according to Puma and Cooks' table 1.
Finally, Vresse, Hagemann and Claussen (2016), which you cite, shows a cooling effect from irrigation both in Asia and Africa, but do not give global figures.
Clearly from the tables in Puma and Cook, this listing is not exhaustive.
I have read through most of the SkS posts, but I have seen no mention of the very limited bandwidth of the CO2 absorption spectrum in the region of 250 K radiation. It seems that CO2 will be transparent to most of the outward radiation from water at the top of the troposphere. Comment, please.
Technical Question about Water Vapor
1. SPECTRALCALC has an "atmospheric browser" which will give the user the volume molecular ratio of water vapor in the atmosphere as afunction of altitude for the U.S. Standard Atmosphere. If one plots that output versus altitude it matches closely the corresponding curve on Modtran Infrared Light in the Atmosphere (MILA).
2. The SpectralCalc data, (and I suspect also the MILA data) are based on the1976 U.S.Standard Atmosphere.
3. I would think it would be informative if "they" would "just" do whatever they did around 1976 once more in the present day to update the U.S. Standard atmosphere. (Lot of weather ballons, maybe?) Then you would have a direct measurement of the water vapor concentration now compared directly to 1976 obtained by the same procedures as 1976.
4. Another way of putting this: We now know that CO2 is world wide at a 400 ppm level, whereas in 1976 CO2 was at 330 ppm; therefore for a current SpectralCalc calculation involving a present day atmosphere, the scale factor is 1.212 instead of 1 for CO2. What should be the present day scale factor for water vapor?
If water vapor is just an "amplifier" and co2 (within the current climate system) is the most important driver of current global warming does this also implicate that temperatures will go down in the future if we succeed in lowering atmospheric co2-levels? And will water vapor then also act as an 'amplifier' in lowering the temperature and if so, were will the cooling in that case stop?
LinkeLau.
Broadly yes. In a cooler world, due to less CO2, water vapor levels will drop, adding to the cooling. Where it stops depends broadly on two things. If nothing else has changed then on returning CO2 levels to where they were in the past, pre-industrial levels for example, we would expect climate to return to that pre-industrial state.
If... the reflectivity of the Earth hasn't changed. The Earth only absorbs around 70% of the sunlight that strikes it, the rest is reflected. Sunlight is relected by clouds, snow & ice mainly and to a much lesser extent by the land and ocean surface.
If the reversal of CO2 levels happens quickly enough, before the coverage of ice particularly can change, then we would go back to a past climate. However if the reversal is slow and the ice cover has contracted, then the earth would still be somewhat warmer because it is absorbing more sunlight and a full return would require enough time for the ice to expand again.
I'm afraid I disagree with the rebuttal presented here. The explanation of how the water vapor feedback works is that the carbon dioxide greenhouse effect warms the atmosphere and enables it to absorb more water vapor. At the same time, the CO2 greenhouse heating causes more evaporation from the oceans and other liquid H2O sources. Since H2O vapor is the stronger greenhouse gas and there is much more of it, the small amount of greenhouse heating from CO2 is then amplified by this H2O vapor feedback. In this manner, the relatively small amount of greenhouse heating from CO2 nevertheless controls the much larger H2O feedback.
This argument, unfortunately, neglects the much larger greenhouse heating term resulting from the H2O vapor feedback being driven by the H2O vapor greenhouse effect itself. As was stated earlier, the greenhouse effect for H2O vapor is much stronger than that for CO2. At this point, climate change believers point out the very short residence time of H2O molecules as water vapor in the atmosphere as compared with CO2 molecules. In other words, H2O vapor may be the strongest greenhouse gas, but it is much more "short-lived" in the atmosphere that CO2. The greenhouse effect, however, does not depend explicitly on atmospheric lifetimes of the molecules, but only on the concentrations and IR spectral profile of the greenhouse gas. A greenhouse gas molecule will contribute to the greenhouse heating with a strength determined from its IR spectrum for as long as it is in the atmosphere. If it drops out of the atmosphere (due to condensation or precipitation), then it does not participate in the greenhouse effect until it re-evaporates. The frequent precipitation and re-evaporation of H2O does introduce short-term fluctations into the temperature profiles, but does not affect the longer term greenhouse heating.
Therefore, I must disagree with the "control knob" theory of carbon dioxide driving the water vapor feedback. It is the greenhouse heating from water vapor driving the water vapor feedback that actually dominates the greenhouse effect.
[TD] You misunderstand the explanation, by focusing on "residence time." The residence time of individual molecules is irrelevant. Warmer air retains more total molecules of water vapor, regardless of how often individual molecules swap out. See the relevant post.
JeffDylan @267 , as the moderator has indicated, you seem to have misunderstood the rebuttal presented here. Permit me to expand the discussion :-
The authors pointed out that H2O vapor has a larger greenhouse effect (than CO2 does) at current ambient temperatures of the planet. And you agree with that. However, when the authors pointed out the "fragility" [if I may call it that] of H2O levels existing in vaporous & cloud-droplet form in the atmosphere, they were not suggesting that the "fragility" (i.e. rapid large amplitude variations in levels) detracted in any way from the important H2O greenhouse effect. And that's because those fast changes would be too brief to have more than a relatively momentary effect on the planetary surface temperature — as I am sure you were already aware.
Nor were the authors suggesting that the often extremely transient residence time of any one particular H2O molecule in the atmosphere would have any relevance either. Since at any one time it is the total amount of vaporous or cloud form, which produces the effect. Likewise with the somewhat longer residence time of an individual CO2 molecule (compared with the centuries/millennia duration of CO2 molecules en masse at a certain overall level).
You will note how I emphasized H2O's role at current ambient temperatures (say roughly minus 30 to plus 50 degreesC temperature range).
Where it gets interesting , JeffDylan, is if you do this thought experiment :- (a) picture all H2O suddenly removed from the atmosphere — result: within days "new" H2O has evaporated from land & sea, and the status quo is restored. Essentially nothing has changed (other than a brief blip of coolness from evaporation). Now (b) picture all CO2 suddenly removed from the atmosphere — result: a strong rapid negative feedback. Temperatures plummet, with widespread snow & frost precipitation on land and a fast-spreading layer of ice on the sea [with further sunlight reflection and further spread of sea-ice, to 100% coverage]. Ultimate result: a frozen world (and with minimal H2O in the atmosphere).
As you see — whichever way you look at it, CO2 (not H2O) is the temperature "control knob".
[TD] Lest Jeff misunderstand your accurate statement about total H2O in the atmosphere: Clouds comprise liquid water ("cloud-droplet")--condensed water--not water vapor. Liquid water in the atmosphere interacts with infrared radiation (IR) differently than water vapor does. Notably, liquid water reflects IR in addition to absorbing it.
Yes, my apologies TD.
I spoke with clumsy brevity, and was thinking of the H2O's interchange between vaporous and droplet form while remaining in the atmosphere.
Eclectic @268 — Thanks for your response. Understand however that the "answers" I get about the dominant greenhouse gas are generally incomplete or don't make sense at some point.
I did some pondering on your thought experiment, and I believe your prediction in part (a) is correct. Since energy balance is maintained in the long term and the supply of liquid H2O for water vapor is virtually limitless, it makes sense that the earth would tend to return to that state if the atmospheric H2O vapor is somehow removed.
In part (b), however, I believe your prediction is erroneous. The "frozen world" you mention is an unstable equibrium. Although there is no greenhouse effect due to the fact that the CO2 was removed and H2O exists as a solid instead a gas, any minor perturbation of the system that causes some heating will drive H2O molecules from the ice to the atmosphere, thereby causing greenhouse heating which in turn causes more H2O molecules to leave the ice and enter the atmosphere, which causes more greenhouse heating. In this manner, the H2O content of the atmosphere increases until a new equilibrium/energy balance state is obtained. This new state may be somewhat cooler than the old state that included CO2, but it certainly would not be a long-term frozen world.
JeffDylan @270 ,
we should await better brains than mine, to give some quantification to the scenario you have proposed!!
As I picture it, a minor perturbation (in the warming direction) would only release a tiny amount of H2O vapor, which would promptly fall back as snow & frost — i.e. it would not meet the threshold to achieve current ambient temperatures (to maintain enough vapor to give positive feedback).
I am not sure of what cause of perturbation you were thinking about. If it was of ("Milankovitch") alterations of planetary tilt or orbital shape, then these would produce only very tiny changes in solar heat flow into the planet. Volcanoes? — they would produce both a "sooty" coating to surface ice [positive] and atmospheric reflective particles/aerosols [negative] : but their real cumulative warming effect would come from the CO2 emitted. Which brings our discussion back full circle!
Without CO2, it is difficult for a fully frozen world to "escape".
JeffDylan: Positive feedback whose gain is less than one converges (peters out). The smaller the gain, the faster it converges. See the post about runaway (though I understand you did not claim it would run away). Note there are Basic, Intermediate, and Advanced tabbed panes.
By "perturbation", I mean any event that releases heat into the atmosphere. It could be forest fires, volcanoes, lightning, or even a solar flare. The purpose of part (b) of my posting @270 is to show that the "frozen world" scenerio described by Eclectic @268 is not stable even though it is an equilibrium, and to analyze stability of a system in equilibrium, we ask the general question "Will some small deviation (or perturbation) in the system from equilibrium grow?". In this case, the answer is "yes". As I argued in 270, a tiny amount of heat applied to the ice leads to big changes in the greenhouse heating which means the system is unstable. Therefore, we really can't use this frozen world scenerio to conclude anything.
As per Tom Dayton - "unstable" implies feedback with gain > 1.0. Maybe there is a some configuration with this level of unstability but I am unaware of any evidence from observation or models for such a strong gain. Certainly in the modern climate, water feedback gain is small (0.3-0.4 from memory).
JeffDylan, if the instability of the sensitivity you described existed, it would exist for all configurations of the Earth, not just frozen Earths. Think about it--all of them. Empirically that simply is not the case. Please read the "runaway" post I pointed you to.