Seen at a meeting yesterday:
Grant us…
The ability to reduce the uncertainties we can;
The willingness to work with the uncertainties we cannot;
And the scientific knowledge to know the difference.
(Drawn from a white paper on the use of climate models for water managers).
Discuss.
An “uncertainty” I have after reading Hansen’s storms book and also reading about the snowball earths, is where does Hansen’s pessimism about a Venus style runaway greenhouse come from? I read (can’t remember where) that CO2 reached atmospheric concentrations of ~10% in order to melt the snowball 600mya. Given that this did not lead to the oceans boiling why does Hansen say he believes that it’s a “dead certainty” if all tar sands etc are exploited? I know his view is not the consensus, but is the increase in solar output over the intervening 600my enough to make the difference? Or is it that there was something different about the post snowball world (e.g. weathering rates vastly increased by abundance of ice-ground rocks in post snowball period?)
The views of a few experts on this puzzle would be appreciated. Thanks.
It’s good to see that someone is looking to the future in the course of their jobs, and taking the climate scientists seriously.
I guess I should say someone *else* – the DoD and other groups have been looking at all sorts of climate instability for years.
I only read the summary of the document, but it’s also heartening to get the attitude of “clearly there could be a serious problem, and we need some help in better predicting just how much of a problem it will be *right here*”.
On a more pithy note, changing our climate and praying to the Divine for assistance is probably not a very healthy measure:)
Science is always contingent.
dcomerf: cites please. I haven’t heard “~10% CO2” anywhere before. I’ve heard “10 times more”, maybe even 10,000 ppm, but that’s 1%, not 10.
I don’t think the sun has gotten that much stronger in 600 million years.
I also think you’re vastly over-simplifying things in your thinking. IE, I believe you posit that if we had 10% CO2 with the snowball earth 600 mya that 1000 ppm now couldn’t possibly drive us to the Venus syndrome.
During the snowball Earth event, volcanoes kept erupting under the ice, but weathering of rock to silicates didn’t happen because the newly exposed rock was a) under all the ice and b) cold. Temperature speeds up chemical reactions, and removing the ice exposed the rock to high levels of CO2. Eventually a combination of orbital changes and increased CO2 levels took us out of the snowball state and they did indeed lead to a “hothouse Earth”.
The Earth of 600 million years ago was a very different place; continental configuration was different, ocean circulation was different, plant and animal life totally different. You can’t just make a simple comparison between now and then. The sun was cooler too, but I can’t say how much.
What Hansen says in his book is that as little as 10-20 W/m^2 could drive us into the Venus syndrome with sufficient time, so the real question is how much we can do before crossing that threshold.
It’s not just about CO2. Methane also needs to be considered, especially in a runaway event.
Indeed, methane still seems to me the BIG uncertainty–how much will be emitted how fast. In the last week, the Arctic melt has gone into hyperdrive–rates and levels never seen before.
On the general issue of uncertainty, denialists always point to any kind of uncertainty (of which there is always some) as a sign that there is nothing much to worry about, since it might be much less harmful than predicted. But of course the uncertainty cuts both ways, and, IIRC, the fat side of the tail is on the not-so-benign side of things.
Also, there are two kind of uncertainty–uncertainty about future global average temps and uncertainty about effects in particular locations. Obviously the latter uncertainties are much higher, but people actually live in particular localities, so the certainty they most want is the certainty modelers are least able to give.
Any comparison of Earth to Venus is disingenuous…Venus’ atmosphere is made up of 97% CO2 while Earth’s is 36/100ths of 1%. Apples and oranges people.
[Response: not really. Venus is good example of a) a demonstration that very high amounts of co2 lead to very high greenhouse effects, and b) what happens when all the water evaporates, which will happen to the Earth in a few billion years. On a more technical level, the atmospheric physics on Venus has a lot of analogies with aerosol, chemistry, and cloud processes on Earth. – gavin]
Gavin: <…what happens when all the water evaporates, which will happen to the Earth in a few billion years.
Uh-oh. I hear a new argument: “Nature will evaporate all the water on Earth in a few billion years, humankind’s contribution to global warming is insignificant, and by the way I have a lot of coal to sell you.”
With regard to the uncertainty prayer, the older I grow the more often I find myself answering questions with “It depends.”
I read (can’t remember where)
Then perhaps you should do more reading.
An alternative explanation seems reasonable to me
Cut the philosophy and pass me another snowball
I enjoyed the prayer almost as much as I enjoyed Schmidt and Wolfe’s definition of a greenhouse gas in Climate Change: Picturing the Science. I had always thought that acceptance should come before serenity in the original version, and this seems to circumvent that nerdy quibble while having a good scientific spin to it.
As for the discussion that has quickly evolved…The question of at what threshold does the Earth succumb to the runaway greenhouse is fundamentally a question of at what point does the greenhouse effect of water vapor (and the corresponding increase in the saturation vapor pressure by increasing temperature) wins the race against condensation. The history of runaway greenhouse studies has shown that individual infrared-active substances have associated with it a critical point that depends on the solar flux, and whether a planet is above or below that threshold determines whether the water (or whatever else) primarily exists as a liquid ocean or as vapor in the atmosphere. Ingersoll (1969) was one of the first to clearly point out that the outgoing radiation flux has a maximum value when water vapor becomes a significant constituent in the atmosphere (the argument doesn’t need to apply specifically to water vapor, but it is most common). If the incoming solar flux exceeds the limiting outgoing radiation term, then the planet must continue to warm up because it has no way of getting rid of the imbalance and the oceans boil away. When the oceans are evaporated and the atmospheric mass becomes fixed again, the OLR becomes free to increase again (particularly if temperatures are hot enough for the planet to radiate significantly in the visible and near-infrared where water vapor opacity is relatively low).
The question of at what limit the OLR vs. T curve flattens out depends also on the acceleration due to gravity, but uncertainty in clouds preclude confident estimations of where this threshold actually exists. However, it does not appear to lie much lower than about 1.4 times the current solar constant (see Kasting, 1988) and so even if one were to lower the albedo quite a bit, it seems we would be quite safe from the prospect of a runaway greenhouse. Note that the limiting OLR (also known as the Kombayashi-Ingersoll limit) is only weakly dependent on the CO2 concentration. CO2 has only a minor effect on temperature anyway once water vapor becomes a dominant constituent in the atmosphere, and actually, it’s possible to get a wet stratosphere and lose lots of water vapor to space through photodissociation even prior to the full runaway. Thus, even if we did burn all the coal today, there is no physical way that we could really kick in a runaway greenhouse (unless, I suppose, clouds did something really weird to dramatically accelerate the warming).
By the way, just as a matter of clarification for the comments so far: The evolution of solar luminosity with time can be roughly fit by the equation (Gough 1981):
L(t)=L_o*[1+(2/5)-(2t/5t_o)]^-1
where L(t) is the luminosity at time t, and L_o is the modern luminosity at the current age of the sun, t_o . If the ratio of t/t_o is about 0.87, as it would have been in the neoprotezoic, then it follows that the luminosity would have been 95% of today’s value. The luminosity is directly related to the solar insolation at Earth by a constant if the distance to the sun does not change, and so the solar constant at the neoprotezoic would have been 0.95*1370 W/m2 = 1300 W/m2. As I’ve stated before though, the Earth is comfortably below any incoming radiation threshold in the present to get a runaway greenhouse, regardless of what happens with CO2. It will take some billion years or so of star evolution to kick in a runaway.
We could perhaps add “the wisdom to know what these uncertainties mean in practical terms.” But that gets us to (or beyond) the frontiers of science and politics, doesn’t it? Wili’s comment (#6) is particularly apposite in that regard.
Decomrf, I’m not expert, but as I recall, Hansen’s worst case scenario is a triple-whammy of 1) a stellar luminosity increase (he cites the 2% increase in luminosity since 250 million years ago as equal to a doubling of CO2), 2) uncertainty in CO2 proxies from 250 million years ago (2000 ppm was safe then under the dimmer sun, give or take 1000ppm), and 3) saturation of natural carbon sinks foiling the Earth’s capacity to absorb emissions.
Added to these, he descibed methane hydrates as having built up since their last big release 55 million years ago, and being primed for another release should ocean currents warm and or change their paths. He also suggested that there is a possibility that ocean currents reorganized 55 mya with deepwater forming in the Pacific. Such an event today could warm vast stores of methane hydrates.
I would add that if I accept his argument that uncertainty in proxies from 250 million years ago doesn’t provide a safe limit, then guesses about snowball earth conditions farther back are also suspect.
After reading his book, I summarized his worst case scenario in an illustration here: http://brightstarswildomar.blogspot.com/2010/01/on-reading-hansons-storms-of-my.html
thanks,
jg
I know one thing is sure from reading that white paper – if you live in the areas cited your water bill is going up.
Regardless of what else happens.
dcomerf: Roughly speaking the sun has been increasing its output by about 1% every 100 my. That means that it is about 5% to 10% hotter now than it was 600 mya. That is really quite a lot. What’s keeping the Earth from being very warm is the relatively low concentration of CO2 in the last million years or so.
We really don’t need high CO2 concentrations to go along with a warmer sun.
How can you work with uncertainties you can’t reduce? Sounds like Donald Rumsfeld talking to me.
Michael
[Response: People do it all the time. It’s uncertain whether your house will burn down. You buy insurance. It’s uncertain whether it will rain next weekend. You pack an umbrella. etc. Indeed, if you think about it, very few of the decisions you make about dealing with future events are made because it is certain what will happen. – gavin]
Unless the water managers live as long as Yoda, I can’t see how the models are useful.
From Chris Colose 11, I take it that to the best of our knowledge run away green house cannot be triggered currently by burning fossil fuels. From JG 13, I understand that Hansen argues that the best of our knowledge is uncertain, and if we are in error in the wrong way, run away greenhouse could be triggered by burning fossil fuels. This leads me to two questions.
First, does Chris Colose (or the consensus of opinion) agree with Hansen that our knowledge is still that uncertain?
Second, presumably if our error in estimates paleo CO2 concentrations where in error in the opposite direction to which Hansen allows, then the sceptics would be right (or nearly so) in their conclusions if not their methods. So what is the relative probability of an error sufficient that runaway greenhouse is a real possibility, compared to probability of an error sufficient that business as usual will result in greenhouse warming of less than 2 degrees C? In essence, who is wackier – a “warmist” who thinks that runaway greenhouse is probable in the next few centuries with business as usual, or a sceptic who thinks we need to nothing to avoid significant adverse impacts from greenhouse gass emissions?
Phew, I thought this was going to be: “Grant me certainty and conviction over AGW, but not yet!”
BTW, there’s a confusion in terminology that crops up once in a while: in this thread, “runaway greenhouse effect” has been taken to mean “running away to extremely high temperatures,” such that, as Chris writes, the oceans basically evaporate.
However, you also see this phrase used to describe a scenario in which natural feedbacks come to dominate the warming process such that mitigation of human GHG emissions becomes essentially insignificant–that is, the greenhouse effect becomes a “runaway” from (potential) human control. I can’t recall for sure if he used the phrase or not, but this scenario is envisioned in Gwyn Dyer’s Climate Wars.
Caveat lector.
dcomerf, Google the Faint Sun Paradox. Sol is a main-sequence yellow star–it burns hotter with age.
I love it, great words, great thoughts, and very true. This is what guides me polar cities work, which nobody wants to discuss in public for fear of having their PHDs and careers ruined. SIGH. But polar cities are coming, in fact, as one brave PHD told me, they are already here. Think about what he meant!
http://pcillu101.blogspot.com
Kevin McKinney, the thing about the distinction you draw in comment currently #17, is that once the second meaning of “runaway greenhouse effect” is realized — and “feedbacks come to dominate the warming process such that mitigation of human GHG emissions becomes essentially insignificant” — there is no way at present to be confident that the result will not be realization of the first meaning.
Thanks Gavin, Chris Colose and JG for interesting stuff.
No thanks Danny Bloom, your polar bunker is NOT impenetrable. Murmansk, Russia already exists. So what?
Re 11 Chris Colose – Very nice post. An important point: it isn’t actually necessary to reach a runaway water vapor feedback and sustain it for the oceans to be removed (and leave CO2 with no geologic sink*?*); maintaining some lesser warmth can over time allow ocean removal by increased stratospheric H2O leading to enhanced H escape to space. Of course, regarding AGW, is there any way that CO2 and feedbacks could sustain such warmth for long enough to destroy the geologic CO2 sink*?* before the geologic CO2 sink prevents that fate – I’d guess no at this point, though I haven’t gone through those calculations.
** – more rapid (globally) inorganic geologic CO2 sequestration is favored by a coexistance of warmer wetter conditions (with more CO2) with sediment/debris containing silicate minerals with certain ions. However, the process can switch from reactant-favored to product-favored at sufficiently high temperatures (depending on the cations/minerals involved and the partial pressure of CO2) – which of course is why there are inorganic geologic CO2 emissions.
Of course, geologic organic C burial requires photosynthesis with incomplete oxidation – can happen to some of the organic C sinking within the oceans, on relatively flat land regions depending on climate.
PS how much would the methane residence time in the atmosphere increase as atmospheric methane is increased?
PS much much much much less than a Venus-like scenario is plenty enough justification to reduce CO2,etc emissions.
… But about ocean removal – it isn’t just the mass of water in the oceans (and groundwater, surface water, ice, vapor and clouds) – there is also water in the mantle which may tend to replenish the ocean if water is removed by H escape (James Kasting did a paper on a (proposed?) mechanism that may act as a negative feedback to changes in ocean depth over geologic time). Not an infinite well, though.
Let me put a different twist on the “Uncertainty Prayer.” The problem is that it is simplistic in seemingly assuming that we can identify all the important uncertainties. So, my twist:
Grant us…
Ability to reduce uncertainties that science identifies;
Willingness to work with those we cannot reduce;
Wisdom to anticipate unknowns that we can’t possibly imagine;
Awareness to leave an ample margin of safety for all of them; and
The Strength to do so very fast.
We are engineering the structure of our climate incrementally both through our daily global actions and the diplomatic and legislative steps of policy making. No professional engineer would design a structure without an ample factor of safety. This is not just about the science, it is about how to apply the science we have now as well as the science we have yet to gain, safely. If we don’t do both, we can expect to fail.
This is especially critical regarding climate, where to be successful our mitigative actions must be taken years or decades in advance of clear indicators. When we have the clear indicators, it’s too late for action then.
What this entails is – as a society – distinguishing between wants and needs, and then reevaluating some of our needs. Especially so with our population projected to climb to 9 billion over foreseeable decades, which is both a problem that must suppress wants and is one of said “needs.”
Gavin, it looks like the appeal to God has been made more, er, implicit this time than is usually the case in climate change discussions. This is progress! I’d say that all we need now is a “Dear Lord” at the beginning and we’re done. ;-) Best, Alex
There is always uncertainty in scientific thought so the third point is what really matters. Every now and again there is a paradigm shift in knowledge when issues that were uncertain become clear. Was it Debye (or Hildebrand) who said that if something was not yet simple it was not yet right? So we persevere – and wait for those paradigm shifts!!
“Response: People do it all the time. It’s uncertain whether your house will burn down. You buy insurance. It’s uncertain whether it will rain next weekend. You pack an umbrella. etc. Indeed, if you think about it, very few of the decisions you make about dealing with future events are made because it is certain what will happen. – gavin”
You do not remodel economies and civilisations based on uncertainties. There is a big difference between an umbrella and a whole economy.
[Response: Perhaps you are being deliberately obtuse – but you will find that many economic decisions are made in spite of uncertainties. Do all investments work out? No. Yet people continue to invest. Did the TARP program guarantee the future functioning of the financial system? No. But it was tried anyway. Did the stimulus packages provide for certain economic recovery? No. etc… – gavin]
22
Danny Bloom says:
29 June 2010 at 9:25 PM
“I love it, great words, great thoughts, and very true. This is what guides me polar cities work, which nobody wants to discuss in public for fear of having their PHDs and careers ruined. SIGH. But polar cities are coming, in fact, as one brave PHD told me, they are already here. Think about what he meant!
http://pcillu101.blogspot.com”
And not a single low or mid or high latitude city has been abandoned in the last century or so due to climate.
Richard Steckis writes: “You do not remodel economies and civilisations based on uncertainties. There is a big difference between an umbrella and a whole economy.”
That’s funny. You’re willing to remodel the atmosphere and the climate based on uncertainties, but not the economy.
Some might say that’s a strange set of priorities.
By the way, to whom is The Uncertainty Prayer addressed?
The Cosmic Schrodinger Wave perhaps?
Actually, Steckis’s comment is nicely illustrative of something that’s all too common.
Let’s say you’re thinking about some action to take in the future. You have two possibilities: you can do A or you can do B. You also have uncertainty about the costs and benefits of each action.
One way of making that decision is to weigh the various costs and benefits in light of their respective uncertainties, and come up with a best guess about whether A or B would most likely lead to a better outcome. That’s the approach we’d use in almost all circumstances.
Another approach would be to say “There’s a lot of uncertainty, so no one really knows which would be better. Therefore, I’ll do A.” That’s essentially Steckis’s approach.
Somehow, the existence of uncertainty becomes a justification for not making any changes to our economy and infrastructure, but it isn’t a justification for not adding hundreds of gigatons of CO2 to the atmosphere.
31 Richard Steckis: “And not a single low or mid or high latitude city has been abandoned in the last century or so due to climate.”
And we all know what happened in an area of the world which ignored the warnings of a meteorologist, even threatened him with physical violence, who had discovered (through examining the historical record) thatthe area could be hit by a large tsunami any time soon: Boxing Day 2004.
http://riskman.typepad.com/perilocity/2005/01/tsunami_smith.html
“You’d really have to go digging into very old historical records and the scientific literature and extrapolate from what’s there to find that yes, there could be effects (leading to tsunamis) in Thailand,” says Phil Cummins, a seismologist who studies the region at Australia’s national geological agency. “But he was correct.”
There are no pockets in shrouds.
28 Alex Harvey: “Gavin, it looks like the appeal to God has been made more, er, implicit this time than is usually the case in climate change discussions.”
Tell that to a Deist or spiritual atheist. ;)
jg (#13),
Thank you for your graphical summary but it doesn’t tell me how a runaway H2O greenhouse is supposed to happen in the first place. As I understand it, the scientific consensus has long been that a few thousand ppm of CO2 would not materially affect the theoretical Kombayashi-Ingersoll limit which depends on the gravity of the planet and tells us how much non-reflected solar radiation is necessary to make a runaway greenhouse possible for a particular molecule. And we’re not supposed to be close to the limit. I suppose that an unknown cloud regime might possibly make the limit irrelevant… is that what Hansen’s arguing? Or is he arguing that the reasoning behind the limit is bunk? Or something else entierly?
To put it in the terms of Gavin’s prayer, it’s not rational to be willing to work with ANY risk of such a runaway. It’s effectively an unacceptable, uninsurable infinite risk. You simply don’t go there. Life on Earth isn’t a limited liability corporation. ANY chance higher than zero of a runaway happening would be much worse than, say, a 99% chance of 6C global warming and would justify ANY means of stopping this trainwreck. All these consensual climate summits would go out of the window for one thing because thermonuclear weapons would come into play. These are the tools which have been designed to deal with existential threats.
I’ve been led to believe the risk is zero. But Hansen has been saying it isn’t zero for a while… and it’s past time for his colleagues to tell us in no uncertain terms if he’s making any sense.
#31 Richard Steckis:
That is what the farmer said when his cow died. “Wow, he never did THAT before!”
Scott A. Mandia, Professor of Physical Sciences
Selden, NY
Global Warming: Man or Myth?
My Global Warming Blog
Twitter: AGW_Prof
“Global Warming Fact of the Day” Facebook Group
> great words, great thoughts, and very true.
> This is what guides me polar cities work
— Danny B
You fallout shelter seller
Can’t get in my door,
Not now or no other time.
— Bob Dylan
Survivalist/bunker types love haunting science sites with their predictions of doom and self-promotions. ‘Revere’ over at Effectmeasure took them down for trying to use that public health discussion site to sell their ideas. Recommended. http://scienceblogs.com/effectmeasure/2009/07/swine_flu_how_not_to_report_a.php#comment-1783939
Tom Curtis,
Uncertainties on CO2 sensitivity are asymmetric. Our confidence that CO2 sensitivity is not below 2 degrees per doubling is equal to that of it not being above 4.5 degrees per doubling. However, we are still in trouble if it is 2 and in deep kimchee if it is 4.5. Uncertainty is not the friend of the complacent here.
Richard Steckis wrote: “And not a single low or mid or high latitude city has been abandoned in the last century or so due to climate.”
If you don’t understand that the climate of the next century or so will be significantly different from the climate of the last century or so, then you have not been paying attention.
I’ve been led to believe the risk is zero.
You’ve been led to believe by the scientific impact community that the risk of a catastrophic impact is zero as well, and guess what. It’s not zero.
30, Richard Steckis: You do not remodel economies and civilisations based on uncertainties.
that’s an odd comment. Economies and civilizations are continuously reinvented based on entrepreneurs’ (and other’s) assessments of calculated risks and benefits, all of which have always been uncertain. Right now, China (among others) is refashioning its economy and civilization by expanding renewable energy supplies based on the uncertain calculation that fossil fuel-based energy production is unsustainable — it leads the world in biofuels-related patents. Back when no one could imagine a Boeing 747, or even a P-51 Mustang, inventors and entrepreneurs started building the aircraft and airline industries.
At best, you must have meant something different from what you wrote.
33, Secular Animist: The Cosmic Schrodinger Wave perhaps?
Nice. Very Nice.
Chris Colose: Please give an equation for the Kombayashi-Ingersoll limit. How is it derived?
RC: Is he correct? I am looking at:
http://chriscolose.wordpress.com/2008/03/10/physics-of-the-greenhouse-effect-pt-2/
About the responses to dcomerf:
No one mentioned albedo. I assume the huge albedo had a very important role in keeping snowball Earth cold while CO2 was slowly building up. Right?
Whenever there are uncertainties, going forward to determine a course of action, most scientists develop pilot projects; usually a series of pilot projects to answer a number of questions. In error, a less well experience researcher attaches importance to a pilot project yielding looked for results. This fixation upon “preliminary results” most times leads scientific inquiry “down the garden path.” Not seen nor accounted for, as dictated by uncertainties, are the pilot projects that answer other questions. There seems to be this rush to winow away all conflicting information from what appears to be a winning idea. The history of science is littered with such “golden boy” projects, when we have not listened to critics who say: “not so fast.”
#31 Richard Steckis: “And not a single low or mid or high latitude city has been abandoned in the last century or so due to climate.”
It wasn’t a discreet city. It wasn’t 30 years, although it was damned persistent. And the weather at least wasn’t anthropogenic. Still it wouldn’t hurt to read this.
http://en.wikipedia.org/wiki/Dust_Bowl
12 Steps of Recovery For Climate Change Skeptics
1. Admit we are powerless over global warming — that our climate has become unmanageable.
2. Come to believe that climate scientists more knowledgeable than ourselves can restore us to sanity.
3. Make a decision to turn our will and our lives over to the care of climate scientists as we understand them.
4. Make a searching and fearless inventory of our climate change skepticism.
5. Admit to God, to ourselves, to another human being the exact nature of our climate change skepticism.
6. Be entirely willing to have climate scientists remove all these defects of character.
7. Humbly ask climate scientists to remove our shortcomings.
8. Make a list of all the climate scientists we have harmed, and become willing to make amends to them all.
9. Make direct amends to such people, wherever possible, except when to do so would injure them or others.
10. Continue to take personal inventory and when we were wrong promptly admit it.
11. Seek through prayer, meditation, and research to improve our knowledge of and conscious contact with climate scientists, as we we understand them, praying only for knowledge of their will for us and the power to carry that out.
12. Having had a scientific awakening as a result of these Steps, try to carry this message to other climate change skeptics, and practice their principles in all affairs.
— Adapted from the 12 Steps of Alcoholics Anonymous
Re #23–
Exactly, SA. I was taking it as a given that relinquishing the partial control we (potentially) have over global climate would not qualify as a Good Idea.
For Edward G:
http://scholar.google.com/scholar?q=Kombayashi-Ingersoll+limit
will lead you to:
http://geosci.uchicago.edu/~rtp1/papers/InsightHydrology.pdf
The hydrologic cycle in deep-time climate problems
Raymond T. Pierrehumbert
where you can read, among much else
“… a value known as the Kombayashi–Ingersoll limit. This is the limit to how fast a planet with a moist atmosphere can lose energy by infrared radiation…. The precise value one obtains for the limit depends on the treatment of infrared absorption properties of water vapour at high temperature and pressure…. we have sketched in the value from ref. 42 (about 320 W m–2), and the reader is referred there for further details.”
Their Ref. 42 is:
Kasting, J. F. Runaway and moist greenhouse atmospheres and the evolution of Earth and Venus. Icarus 74, 472–494 (1988).
http://www.geosc.psu.edu/~kasting/PersonalPage/Pdf/Icarus_88.pdf
Remember, always read the citing papers for subsequent work.