A faster rotating early-Earth may have compensated for reduced Sun output
Guest post submitted by Ian Schumacher
The ‘faint young sun’ paradox states that according to star models, billions of years ago the Sun would have only been about 70% as bright as it is today. Given the same environment as today this would result in most water on Earth being frozen making early life difficult to exist. However, geological history does not show such a frozen Earth period and early Earth is thought to have been quite warm.
Most solutions to this problem relying on an enhanced greenhouse effect or on cosmic rays and clouds. To me these solutions, while possible, ignore much the simpler explanation of a shorter Earth day.
The Stefan-Boltzman law/equation states that, at equilibrium, the outgoing radiation from a black-body equals incoming radiation (from an external source) and is proportional to the fourth power of the temperature of a black-body.
S=σT⁴
From our perspective, what is important here is that outgoing radiation increases quickly with temperature. The average temperature is highest when temperatures are evenly distributed. The average temperature is less than or equal to the fourth root of the average of the fourth power of temperature:
≤ ()1/4
The more uneven the temperature distribution, the lower the average temperature. For example, consider the set of numbers:
{2, 2, 2, 2, 2}
The average of this set is 2. The fourth root of the average of the fourth power of these numbers is 2. Now consider the set of numbers:
{1, 2, 4, 2, 1}
The average of this set is also 2. The fourth root of average of the fourth power of these numbers is 2.75. In order to have the same fourth power average we would need the set of numbers:
{0.72, 1.45, 2.90, 1.45, 0.72}
which only has an average of 1.45; significantly less than 2 from the more even distribution.
A fast spinning Earth distributes temperatures more evenly allowing for a significantly higher average temperature than a slow spinning Earth. The faster the Earth spins, the higher the average temperature.
Billions of years ago, the Earth was rotating up to twice the rate it is today (it has slowed over time due to tidal friction). All else being equal, this would have distributed temperatures on the Earth’s surface more evenly and resulted in a higher average temperature. Since the Sun was also weaker the two effect may have roughly canceled each other out.
The Earth is not a black-body, but reflects a significant amount of light. Reflected light is not available to heat up the Earth’s surface and therefore has a large effect on Earth’s temperature. The reflection coefficient is also known as albedo. Water in solid state (snow, ice) has a very high albedo compared to water in liquid state or soil. A small increase in temperature can cause some snow to melt, reducing albedo and causing temperatures to increase further. In this way water provides a strong positive feedback; amplifying small changes in temperature. It is this effect that likely drives the Earth into and out of ice-ages by amplifying an otherwise small external forcing factors such as changes in Earth’s orbit. Similarly this positive feedback mechanism could work to amplify the increased average Earth temperature due to faster Earth rotation of an early Earth.
More here: http://blog.vzv.ca/2012/10/a-simple-resolution-to-faint-young-sun.html
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Also a note. 30% fainter sounds like a lot (and it is), but again, because of the T4 relationship, temperatures would not be 30% less, but only about 1/4th that or 7.5% less.
dS/S = 1/4 dT/T
Whoops, that should be
dS/S = 4 dT/T
@Ian Schumacher
Early life could have existed if they were mainly primitive forms of extremophiles during this period, but then there wouldn’t be a paradox. 🙂
I used the 30% fainter estimate because I read it was a figure the late Carl Sagan came up with, their are probably more up to date estimates.
The dim sun paradox is really the “how can people be so stupid as to believe in climate forcing” paradox. What the dim sun paradox tells us is that you cant really force the climate – or, more precisely, that even a “forcing” of a change of 25% of solar output fails to force the climate – something more than this would be needed. Climate is robust and negative feedbacks keep its temperature within a life-supporting range.
“””””…..agimarc says:
October 17, 2012 at 9:33 am
Granted that clouds are a cooling mechanism during times of sunlight in the tropics and temperate regions. But they are also a warming mechanism at the higher latitudes when there is little to no sun. Warmest times in the winter up here are cloudy days and nights. Coldest are when it is crystal clear, at which time God sucks all the heat out and deposits it somewhere in the vicinity of Saturn (/sarc). Cloud cover is more complex than a simple reflection of incoming or outgoing energy. Cheers -…..”””””
Here we go again !!…..”””””…..Coldest are when it is crystal clear, …..”””””
NO !!! HELL NO !!! Crystal clear is when it is coldest. When it is cold, there is no evaporation to form those clouds; THAT’S WHY IT IS CRYSTAL CLEAR !!
Now when it is HOTTER during the day (and humid) you get evaporation which will condense as clouds WHEN IT COOLS DOWN AT NIGHT; and it WILL cool down at night.
So agimarc why don’t you wake us all up; from “up there” if and when you have a nice cold low humidity day and no winds, AND IT WARMS UP AND FORMS CLOUDS AFTER SUNDOWN.
Otherwise think about what is CAUSE and what is EFFECT. Clouds don’t cause warm; warm causes clouds (when it cools after warm.)
“””””…..Ian Schumacher says:
October 17, 2012 at 12:14 pm…..”””””
Ian, my apologies for misspelling your name; I should be more careful. And I hope you don’t feel set upon. I think if you had kept the average Temperature of your two cases, exactly the same, one having a greater spread than the other, and pointed out that the greater spread case is going to radiate more in toto, as a consquence of the S_B law, you would be on the right track; but you see everything else is simply not going to stay the same; and changes in cloud feedback is just one of the things that is going to screw up any simple situation.
Don’t forget, since we had any weak young sun (so far as I’m aware) all of the continents have shifted all over the place. No way could the climate stay the same.
George
Ian Schumacher says:
October 17, 2012 at 5:17 pm
“Agreed, temperature variability probably not important for the ocean. Presumably ocean temperature changes so little because of evaporation, which create clouds. A faster spinning Earth would most like then have fewer clouds. Fewer clouds, hotter Earth. Maybe?”
No, it changes so little because sunlight penetrates to a depth of about a hundred meters to heat it spreading the energy out through a lot of mass. The temperature of that whole column has to fall at night because of convection i.e. if the surface cools a little it sinks and is replaced by warmer water from below. So you have a water column a hundred meters deep that is resisting change in temperature. On the other hand rocks and soil don’t convect and sunlight can’t penetrate below the surface so you only have a column less than a meter deep resisting diurnal temperature change.
The idea of a more massive sun and major changes in planetary orbits is not a factor, as the period being discussed takes place millions of years apart and after the formation of the early solar system. And depending on how the earth and moon formed, whether the Earth and moon formed together or if they formed separately as two planetary bodies that collided to form the Earth and moon.
Actually, the period being discussed ranges from roughly 4.5 to 5 Bya (when the sun ignited and the Earth coalesced and cooled) to ballpark 600 Mya when complex life forms started to emerge. See article here:
http://en.wikipedia.org/wiki/History_of_the_Earth
especially the timeline. The faint sun paradox addresses the hadean through the archean and proterozoic, but especially the archean. Life appeared at the beginning of the archean, at least some 3.5 Bya (there is some speculation that it is even older).
See: http://en.wikipedia.org/wiki/Faint_young_Sun_paradox
The “paradox” is simple: The Earth “should” have been frozen solid, assuming its current orbit and a sun with an output that is only 70% of its current output. Yet there is abundant evidence of liquid water dating back to the beginning of the Archean (that’s what defines its boundary, in fact) and life kicked in almost immediately in terms of geologic time once there was liquid water. Since that point, there has always been liquid water, meaning the the planet never froze solid when it “should” have, given stellar evolution of the sun that is consistent with what we observe in astronomy. Hence the paradox. The timescale of the problem isn’t millions of years, it is billions of years, across major changes in the composition of the atmosphere (when life first appeared there was little free oxygen in the air).
Of course astronomical observations have a hard time being precise about things like the rate at which young stars cast off material, so we have no more than estimates of the rate at which the early sun lost mass, hence we do not know very accurately what its original mass was, hence we do not know either what the early orbits of the planets were relative to the Sun or how bright the Sun really was. The stellar evolution sequence considers stars of similar mass and their progression, but it has to make assumptions about how a star cuts across the http://en.wikipedia.org/wiki/Hertzsprung%E2%80%93Russell_diagram as it evolves. In particular, it is assumed that a star like the Sun starts out on the main sequence, then moves up and to the left along the main sequence during its lifetime (ending eventually as a red giant). However, this assumption might be mistaken — it might start up on the main sequence and sit there without significant changes in its luminosity (or with slower, smaller changes), casting off mass to partially cancel what would have been progress up and to the left.
There are a variety of other “stellar” scenarios that could explain and resolve the faint young sun paradox — infalling matter as the new sun swept up and ate that portion of the surrounding interstellar medium above the critical size threshold where light pressure pushes it away, a process surely much stronger in the first 2-3 billion years after formation than it is today, as evidenced by the lunar surface and the fact that moon itself resulted from a planetary scale collision. I would rather expect that entire planetary objects fell into the early sun more or less intact during the first billion years (out through the archean). Perhaps some fraction of solar variability in the present is leftover “ringing” from just such a collision, given that the sun is so dense as to nearly be “rigid” in much of its interior. Or, perhaps mercury began its existence as a gas giant — we have plenty of evidence that stars often have very large gas giants in very close orbits — and the sun was continually fed by that gas giant outgassing until it depleted it a Bya or so. We’d have to visit mercury to even think of finding evidence for that, but it is a perfectly plausible core for a gas giant that has lost its entire atmosphere, some of which was blown away as solar wind, some of which spiralled in to feed the young sun.
And then there are atmospheric composition theories — early atmosphere largely greenhouse gases (and much denser) sufficient to keep it warmer than one expects assuming Earth then is “like” the Earth now. It probably wasn’t. There are leftover heat of formation/moon collision theories — a more geologically active Earth stayed hotter. Tidal heating theories — the moon (half the distance away) would have produced tides 8 times stronger than they are today, causing much greater deformation of the crust and a lot more heat. More radioactives. Basically, there is no lack of possible explanations of the “paradox”; there is a lack of data to help choose between them, and several of them might have all contributed anyway.
rgb
o agimarc why don’t you wake us all up; from “up there” if and when you have a nice cold low humidity day and no winds, AND IT WARMS UP AND FORMS CLOUDS AFTER SUNDOWN.
Actually, it sometimes does something very close to this, because humidity is relative humidity. It can be a nice, clear day with a relative humidity that is low but a higher absolute humidity, the sun can go down, the air cools and clouds form, and as they precipitate they release the heat of vaporization into the surrounding air. The same thing happens on the ground as dew forms — the droplets warm the air as they precipitate out. The clouds thus formed also form a greenhouse canopy and at night slow the flow of surface heat out to space.
That’s one thing that several posts above have ignored. Clouds aren’t “simple” — they don’t always (net) cool, they don’t always warm. During the day in the tropics through the temperate zone, they tend to net cool by reflecting sunlight before it hits the ground or ocean and is absorbed (high albedo). During the night and near the poles they tend to net warm by greenhouse trapping of heat — I learned all the way back in boy scouts when CAGW wasn’t even a twinkle that cloudy nights are rarely as cold as clear nights, and humid nights are rarely as cold as dry nights with or without clouds. There is further variation on net warming/net cooling according to WHERE the clouds form in the troposphere. It’s a major problem with the presumed strong positive water vapor feedback in the IPCC catastrophic warming scenarios — clouds are so complex that we don’t really know that we have the SIGN of the feedback right (and the sign might change with macroscopic drivers like the global oscillations or variations in oceanic heat flow!) let alone that water vapor increases will more than double the presumed all-things-equal CO_2 doubling warming of a degree K or so.
Note that I don’t pretend to know the answer here either. I don’t find any of the descriptions of how the water cycle (including oceanic heat uptake and loss and redistribution via currents with timescales and turnovers up to a thousand years long) affects global climate particular convincing. It’s an insanely difficult problem, and we probably don’t even have the instrumentation to take the data that would help us figure out the solution yet.
rgb
Joe Doe:
Yes that makes sense [Sunlight penetration combined with huge heat capacity of water means small variation]
george e smith:
Cloudy areas do seem the warmest – true. What about a desert though? They are cool at night also and would have an increased average temperature with a shorter day.
It seems tremendously complicated for sure and if this was Myth Busters I would say that my theory was ‘busted’ 😉 Still, ‘maybe’ more people are now thinking about the importance of variability then they were before and the fallacy of equating and ()^1/4
Cheers.
Oh the < > are filtered out. Should be:
equating avg(T) with (avg(T^4))^1/4
Re: george e smith – “So agimarc why don’t you wake us all up; from “up there” if and when you have a nice cold low humidity day and no winds, AND IT WARMS UP AND FORMS CLOUDS AFTER SUNDOWN.”
I think we are having a glass half empty / half full sort of argument. My poorly made final point was: Cloud cover is more complex than a simple reflection of incoming or outgoing energy.
Altitude of those clouds is also important. For example, there are times in the northern climes with very cold temps and very high relative humidity. You end up with ice fogs, fogs and hoarfrost (which nicely glazes the local roads). In this case, the clouds are right at the surface and not particularly thick, neither reflecting anything much from the sun (mainly due to low incoming incidence angle of sunlight) nor keeping surface radiation from escaping.
And none of that complexity is ever reflected in any of the models. Cheers –
“””””…..See: http://en.wikipedia.org/wiki/Faint_young_Sun_paradox
The “paradox” is simple: The Earth “should” have been frozen solid, assuming its current orbit and a sun with an output that is only 70% of its current output. ……”””””
What was it Richard Feynman said: something like; if your theory disagrees with experiment, then it is wrong.
So since the earth was not (apparently according to experimental data) “frozen solid”, then the theory that it should have been, is clearly WRONG under the Feynman doctrine.
Ergo the earth should not have been frozen solid, since it was not.
“””””……o agimarc why don’t you wake us all up; from “up there” if and when you have a nice cold low humidity day and no winds, AND IT WARMS UP AND FORMS CLOUDS AFTER SUNDOWN……”””””
“”””””……AND IT WARMS UP AND FORMS CLOUDS AFTER SUNDOWN……”””””
“””””…..WARMS UP AND FORMS CLOUDS ……”””””
“””””…..AFTER SUNDOWN……”””””
So the day is cold and low humidity ergo low atmospheric water content.
The sun sets. ergo it is then “AFTER SUNDOWN”
And THEN the TEMPERATURE RISES (AKA warms up) AND clouds form. (so they say )
Presumably the formation of those clouds resulted from the surrounding upper atmosphere (cold) having extracted LATENT HEAT from the water VAPOR in the atmosphere. Gee I guess the “heat” flowed from warmer (higher Temperature) to cooler (lower Temperature) just as the Second Law predicts.
I can see how “heat” is transported from near the surface to a greater altitude which is colder, and to an even colder higher altitude, if the near surface humidity was lower (during the sunlit day); but I’m having difficulty figuring out how the near surface Temperature continues to rise after the sun has shut down its source of energy.
But that’s why I’m here; to learn these things.
For the near surface Temperature to RISE after sundown, some form of “heat” energy has to arrive there from somewhere else. Convection is out; no winds, so no moving mass of hotter air coming in from somewhere else. The moisture in the air is rising, specially if the surface Temperature is rising; and this is REMOVING “heat” energy from near the surface to be deposited higher up. Even if ALL of it returned to the surface by some as yet unexplained process (zero losses), it couldn’t raise the surface Temperature above what it was before that energy first left the surface. It CAN’T ALL return as “HEAT” without special dispensation from the keeper of the Second Law; and it can’t ALL return as radiation, since any upper atmosphere source of such radiation would of necessity be essentially isotropic , so only about half could return. Ergo it can’t bring the surface Temperature above what it was at sundown.
But I’m happy to learn how this can happen.
“””””……agimarc says:
October 18, 2012 at 10:13 am
Re: george e smith – “So agimarc why don’t you wake us all up; from “up there” if and when you have a nice cold low humidity day and no winds, AND IT WARMS UP AND FORMS CLOUDS AFTER SUNDOWN.”……”””””
I think we are having a glass half empty / half full sort of argument. My poorly made final point was: Cloud cover is more complex than a simple reflection of incoming or outgoing energy……”””””
YOU maybe having such an argument; I am NOT.
I’m saying quite succinctly, that the 6PM weather reports that say “it is going to be a high cloudy evening; so it will be warm and muggy” have it completely backwards.
BOTH the CLOUDS and the MUGGY WARMTH are a direct CONSEQUENCE of the simple fact that it WAS HOTTER AND MUGGIER during the daytime BEFORE that high cloudy muggy evening. The Temperature WILL go down after the sun sets.
I agree the height of the clouds that form, whether zero or 50,000 feet is a function of the Temperature and humidity profile.
The text books all say that the higher the clouds the more the warming; NO ! the more the warmth near surface , the higher the moist air has to rise to get down to the dewpoint so clouds can form.
And the higher the (relative) humidity near surface the lower will be the dew point, and hence cloud formation; but the clouds ARE NOT causing the warmth near surface nor the mugginess; the clouds and their height are a consequence of those factors., not the cause of those things
Seems like someone is forgetting the surface and near surface temps were a lot hotter then also.
The most interesting rocks in greenstone belts are komatiites, cooled from ultramafic lava flows
Ultramafic magma (< 45% silica) requires near surface magma temperatures of more than 1600°C
250°C hotter than any recent flows
During Earth’s early history, radiogenic heating was greater and the mantle was as much as 300 °C hotter than it is now This allowed ultramafic magma to reach the surface
From a PP page @ur momisugly http://www.google.com/url?sa=t&rct=j&q=early%20earth%20lava%20flows&source=web&cd=24&cad=rja&ved=0CDMQFjADOBQ&url=http%3A%2F%2Fwww.hartnell.edu%2Ffaculty%2Frbarminski%2Fgeology%2520ppt%2Fchapter8%2520hadean%2520and%2520archean.ppt&ei=F6-AULDGDq2-2AWLt4HwBw&usg=AFQjCNE82W6PAQ8jw2zlcxfouJQNuJ8-RQ
“Why Early Earth Didn’t Freeze Over Still a Mystery”
Global warming gases cannot explain why Earth was not frozen billions of years a…
7users liked this commentThumbs UpThumbs Down1users disliked this comment
7 mths ago Remove
Why is this such a mystery?
I’ve discussed this subject for many years.
The reasons the Earth was at a relatively similar global temperature to today was not only the fact that oceans covered more area than they currently do, but the planet rotated on its axis at a much faster rate. This gave forth a ‘Super Coriolis’ effect yielding much faster jet stream winds and ocean currents. So not only were there more oceans, they transferred heat from equator to pole much quicker, due to the faster rate of speed ocean currents brought warm waters north.
http://news.yahoo.com/why-early-earth-didnt-freeze-over-still-mystery-201602915.html?bcmt_s=m#ugccmt-container
I’m glad someone finally presented a paper about this. As I mention in this comment from an article 7 months ago, I’ve been talking about this for years.
I put forward this hypothesis with some rough figures in comments to Willis’ post The moon is a cold mistress http://wattsupwiththat.com/2012/01/08/the-moon-is-a-cold-mistress/#comment-858665 .
I think that Willis counterargument above reduces the magnitude of this effect but does not remove it. There are large parts of the world with a much larger diurnal range than the sea off California.
I’d therefore say that this hypothesis is one of several factors which PARTLY resolves the faint sun paradox.
It seems to me the earth is always gaining mass from meteorites, dust & comets. This additional mass would both slow the rotation and increase the orbital radius over time.
rgbatduke
You are interesting.
Roy McGregor says:
October 19, 2012 at 10:11 am
I gotta admit, I grow weary of providing numbers for people that should provide them themselves.
Where I live the average diurnal air temperature range is about 10°C. This means that the change in radiation P1/P0 = 1 + 6 (∂T/T)^2 = 1 + 6 (5/288)^2 = 1.0018
This means that the temperature variation is increasing the radiation by about a tenth of a percent … now if the earth was rotating twice as fast, maybe that would be reduced to half a tenth of a percent …
So no, this is still a long ways from being a factor which resolves anything … the changes are way too small to make a meaningful difference.
Run the numbers, dear friends, before you make these kinds of claims …
w.
Regarding the projected changes in temperature from the doubling in rotation speed, it’s about a half a tenth of a percent. A swing of ± 5°C makes a change in average temperature of about 0.2°C … tiny.
Me, I divide factors into three levels—first order, second order, and third order.
Some factors can change a variable of interest by more than 10%. I call these first order factors, they can make a big change. You always have to include these factors.
Second order factors make a change from one to ten percent in the variable of interest. They are not large, but you can’t ignore second order factors in a more detailed calculation, particularly if there are a number of them.
Finally, there are the third order factors. These can only change the variable of interest by less than one measly percent. In general, these factors can be safely ignored in any but the most precise and accurate of analyses.
So when the “fast rotation” theory comes along, and it only changes the radiation by much less than a percent, I have to say it’s a third order factor at best.
w.
I found this about sun like young stars:
” Solar variability
We don’t have a direct record of the sun’s history, but astronomers can study other stars that are similar to our sun at an earlier age. These young sun-like stars appear to be more active, with possibly stronger winds and more ultraviolet light emission. Therefore, it’s likely that our sun was stripping planets of their atmospheres at a faster rate in the past.” (emphasis mine)
How sure are we that there is a paradox to solve with a young sun based on observations of young stars?
http://www.space.com/11187-earth-magnetic-field-solar-wind.html
Willis Eschenbach,
Yes, variability is too small to be a factor. You made your point. But perhaps you are a bit too quick to dismiss fast rotation as a factor for other reasons? Did you look at the article pointed to by Henry Clark?
http://discovermagazine.com/1993/nov/thefastyoungeart316
“The Fast Young Earth
by Tim Folger
From the November 1993 issue”
“What surprised Jenkins and his colleagues, though, was the dramatic effect of the rapid rotation rate. On their fast-spinning model Earth, most storms and clouds were confined to the equatorial and subtropical regions, and global cloud cover was 20 percent less than today’s.”
I know this isn’t ‘my’ variability cause-and-effect, it’s something completely different.
We have a lot of theories, but we know almost nothing about early Earth (we still have no idea how the moon came to exist even). What we do know is that we have a paradox. A paradox means that one of the things we think we know is wrong. That’s why paradoxes are awesome. Something in our understanding is wrong so we shouldn’t be too sure of ourselves about any of the things we currently take as ‘fact’ and we should keep an open mind.
For instance, it strikes me as very odd that we still do not know exactly why the Earth goes into and out of ice-ages. Earth A, warm and cozy. Earth B, frozen wasteland. Same Earth, same Sun, same ocean. What’s causes the difference between the two? We really have no idea.
It strikes me as odder still that people don’t even seem to care that we can’t explain this, yet feel perfectly comfortable putting forth this theory or that theory about why some utterly minor variation occurs. If we can’t solve that major puzzle then we really should admit to ourselves that we know almost nothing.
Ian Schumacher says:
October 21, 2012 at 7:20 pm
Thanks for the reply, Ian. I fear that I pay little attention to what various climate models have to say will happen under imaginary circumstances. In this case, the idea that the models could even indicate that “storms and clouds” would be confined to the Equatorial area seems unlikely, given that both storms and clouds are well below the modeled gridbox size, and are not modeled directly.
As far as I know, entry into and exit from the ice ages is explained, at least to a first order, by the Milankovich cycles … am I missing something?
All the best,
w.