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
Just some bickering…
“The Stefan-Boltzman law states that, at equilibrium, the outgoing radiation from a black-body equals incoming radiation….”
Ian, the Stefan-Boltzman law doesn’t say anything about incoming radiation. It simply states that the emitted radiation is proportional to the fourth power of absolute temperature – as in your equation.
Kasuha (October 16, 2012 at 10:34 pm)
“The problem I see on this logic is, earth temperatures are not like 1 2 4 2 1 but more like 281 282 284 282 281 (in Kelvin) – the difference, even to the power of four, isn’t that big”
Kasuha, I don’t know where you live where the temperature never varies by more than a couple of degrees but the range of Earth surface temperatures is closer to 100 degrees. So using the average surface temperature to calculate the average emitted radiation is not valid – as pointed out in the article.
(However, I’m told that for the Earth distribution of temperatures, using the simple average gives a good approximation in spite of the wide temperature range)
The early earth would have had 3 major heat sources: the sun, decay of radioactive isotopes (which would have been even larger than now), and residual heat from its accretion. This last would have included a major component from the heat produced when Theia impacted the proto-earth to produce the current earth-moon system.
Another variable to add to the models
Related:
http://discovermagazine.com/1993/nov/thefastyoungeart316
“The Fast Young Earth
by Tim Folger
From the November 1993 issue”
“There is no direct evidence to show that carbon dioxide levels were ever a thousand times higher. Jenkins thinks he has a better way out of the paradox. He and two colleagues at the University of Michigan, Hal Marshall and William Kuhn, propose that Earth’s rapid rotation rate and the absence of large landmasses 4 billion years ago were the keys to the planet’s warmth.
In their model, Jenkins and his colleagues used a 14-hour day and also assumed that Earth had no land. That is not a bad approximation, says Jenkins: most landmasses formed less than 3.5 billion years ago. Before then, Earth’s surface was probably one vast ocean dotted with volcanic islands.
This landlessness itself would have made the planet warmer; water reflects less sunlight than land and absorbs more, which means it has more energy to radiate to the air as heat. 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.”
Lesser cloud cover meant less shading from clouds and thus higher surface temperatures relative to the amount of incoming solar radiation than would otherwise be the case.
“Even without a massive greenhouse effect, their model suggests, and even in the face of a faint young sun, the fast young Earth would have been warm enough to keep its ocean from freezing. In fact, it would have been about 10 degrees warmer than it is today.”
As noted in a comment within http://wattsupwiththat.com/2012/05/01/weather-channel-founder-john-colemans-special-video-report-on-svenmarks-theory-of-cosmic-ray-induced-climate-change/
““One of the early attempts at solving the problems has been basically to adjust the greenhouse effect and you can do most prominently by just adding more carbon dioxide to the atmosphere.” “We’re not happy about it because we have deposits from the ocean at that time, and these deposits contain iron oxide minerals and we know from the observation of how they form today that this kinds of minerals cannot form if there’s a very high amount of CO2 or carbon dioxide in the atmosphere and the greenhouse solution to the faint sun paradox required about 30% CO2 in the atmosphere, but what we could see is that its very much lower.”
“The analyses of the CO2-content in the atmosphere, which can be deduced from the age-old Isua rock, show that the atmosphere at the time contained a maximum of one part per thousand of this greenhouse gas. This was three to four times more than the atmosphere’s CO2-content today. However, not anywhere in the range of the of the 30 percent share in early Earth history, which has hitherto been the theoretical calculation.”
“There is a lot of geological evidence to suggest that the continents on earth have grown over time, so there were very little or no continents 4 billion years. Of course there’s about one-third of the planet is covered by continents today. And continents are much lighter in colour than ocean and therefore, if you had less continent, you would have a darker earth and it would’ve absorbed more heat from the sun if it’s darker. So that’s one part of it. The other thing is that in order for the sun to be able to efficiently heat the surface, it needs to be able to penetrate the clouds and today a lot of the sunlight is reflected by the clouds; but again clouds are different today than they were on the early earth because at that time, we didn’t have the type of organisms that produce chemicals, an active part in cloud formation today.”
http://www.sciencedaily.com/releases/2010/03/100331141415.htm
http://www.nature.com/nature/podcast/v464/n7289/nature-2010-04-01.html
Although talking about variation on far lesser timescales is a less extreme situation, cloud cover continues to matter in recent climate. For instance, the global cooling scare ended when solar activity rose after cycle 20 (1964-1976). The two cycles from 1976 to 1996 had a stronger solar magnetic field with more GCR deflection leading to 3% less average cosmic ray flux (oulu.fi), fewer shading clouds, and the global warming scare. Then, in the late 1990s, Earth’s albedo trend and the trend in cloud cover changed, and, in no coincidence, after the 1998 El Nino, relative temperatures from then on have been flat to cooling ( http://www.woodfortrees.org/plot/rss-land/from:1998/to:2013/plot/rss/from:1998/to:2013/trend ).
I agree with Mike McMillan. The atmosphere of the ancient earth was supposed to be much thicker and denser. That was enough to raise the temperature higher than today, even with a fainter sun.
Kasuha says:
October 16, 2012 at 10:34 pm
“The problem I see on this logic is, earth temperatures are not like 1 2 4 2 1 but more like 281 282 284 282 281 (in Kelvin) – the difference, even to the power of four, isn’t that big.”
Really? Night in your place is only 3 K colder than day?
Wouldn’t the simpler explanation be that they miscalculated the brightness of the sun?
Considering that the calculations were done in a whole other century at a time where they for the longest time actually thought the calculated distance to the Andromeda galaxy were right, but were wrong due brightness issues. :p
Didn’t God do this in 7 days ?
Is it not also a factor that the dark side loses heat at a rate that is not linear wrt time. Therefore, a variation in night length would have a possibly complex effect on the global heat balance. I’ve seen this quoted as a reason why it is hard to model heat variations on other planets irrespective of albedo ot atmospheric variation.
“But ignoring that, If I assume an average afternoon temperature of 20C (293K) and an average dawn temperature of 0C (273K), I get a difference of only 15% ((6414247921.0 / 5554571841.0) – 1 *100 )) in
radiation extremes for today’s earth. The faster rotating ancient earth would presumably have been less. Picking a number out of the air — 7%. I think that would give us 15%-7% = 8% warming. Not enough. We need about four times that to account for the hypothesized fainter young sun..”
Faster rotation can not increase daytime high, but can only reduce night time low temperature.
So you are added to average average, e.g 20 + 0 divide 2 equals 10 C .
But instead just adding to 0 C. So if range is 5 C to 18 C, the average is only 11 C, but it’s well above freezing, so ice easily melts.
How about if we had a longer day- and therefore longer nite. The day time wouldn’t get much warmer but the night would get significantly cooler.
If a longer day did add significantly to high daytime average- one has longer days at higher latitudes in their summer one can have day light longer than 16 hours, and one isn’t getting very warm conditions as result. You aren’t going to break world daytime temperature highs in these regions.
But more significant, I don’t think your current rotation is at all counted in the simply model where Earth suppose to a blackbody and greenhouse gases are suppose to add +33 C.
And seems rather obvious that that Moon couldn’t get to 100 K at nite, if it’s day wasn’t 28 days long- if had 12 hour nite, it simply would not have enough time to cool this much.
ferd berple,
You got it right mate, the atmosphere was like a thick soup, and totally different in composition to now, probably closer to Venus. We were more fortunate, being a little further from the sun and evolving with life. Lucky us.
“Models of stellar evolution predict 25% less” means this is a hypothetical paradox. What is real is the Jurassic fossile records of 11 meter Pterodactyal and current 5 meter Peruvian condor, along with half meter [twenty inch] Meganeura Dragonfly and current quarter meter Atlas moth wingspans. Of the four parameters for flight, thrust, lift, drag and gravity one must assume that lift as a function of wing area would be the limiting factor on wingspan. Therefore the Jurassic was at least double, or since wing area is a square, then four times the present atmospheric density. This solves the dinosaur hot-cold blooded issue as well. Most likely the atmosphere has undergone continious decay since origin. The Lunar polar ice caps are accreation from billions of years of full Moon passage in the solar wind eroded Earth atmosphere. The paradox is then, why do so many fall for every hypothesis.
“The faster spinning Earth allowed dragonflies with three foot wingspans to fly due to centrifugal force.”
AAhhhhhh yes!… that would also explain the dinosaurs long necks!
Interesting. By the same token would it not be the case that cloud cover causes a greater uneveness in temperature and therefore an additional lower averge temperture? Similarly ice caps?
After all the distribution of both is somewhat patchy?
If you are right here it would seem that something very significant is being missed.
Eco-geek
Venus’ days are 110 Earth days long. Think of how much energy accumulates on the surface and in the atmosphere when the Sun is up for 2240 straight hours. Strong winds then transfer that heat accumulation back to the darkside. One can calculate the numbers and get something close to what Venus temperatures are.
Now take an early Earth where it heats up less during the day but cools off less at night. The average temperature change between day and night is then only half of today or just 5C on land, less than 1C in water, less than 1C at the tropopause. Still leaves us short but more stable. Less freezing then in the mid-latitudes given warmer nights but cold enough enough at the poles that there is large, large sea ice areas and high overall Albedo. We still need something else.
“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.”
I call this the wet earth fallacy.
I believe most of the water on earth was accreted from space, AFTER it’s initial formation. Their hypothesis is based on a static volume of water on earth, which I think is clearly wrong.
http://earthsky.org/space/did-comets-bring-water-to-earth
It was the moon that caused the Earth to be warmer when the sun was fainter, It was much closer to earth than it is today and has been moving away for millions of years, a closer moon would make tides much higher, it would have a larger influence on the tectonic plates and cause more movement, there would be more energy in the system and volcanic activity would be higher, the atmosphere would be denser, and possibly earths gravity was weakened and electromagnetic activity would have been much higher including flipping the earths magnetic north and south poles more frequently, the speed of the earth would be a minor factor but it can be measured so it’s important, The rate at which the moon has been moving away and slowing down would be equal to the slowing down of earths rate of spin.
DDLeone says:
October 17, 2012 at 3:30 am
Wouldn’t the simpler explanation be that they miscalculated the brightness of the sun?
============
Not impossible, but the estimate is a modern one based on the current size and temp of the sun, the probable age of the solar system based on radiometric dating of the oldest rocks we can find, and observed trends in stellar evolution,
How about all the models are wrong. There is almost no raw data as to time – is the rock 100,000 years old or a billion, what there is relies on speculation and assumptions as there isn’t a time machine we can put a rock into and see it 1M years later, things like rates of erosion can change but that ruins the calculations.
I know why it is so hard to dissent from the consensus, but instead of trying to resolve two very conflicting dates with even more epicycles, can’t we just say we don’t know or one is wrong? Is that too ecentric? Or are we bound to keep going in perfect circles?
Robertvdl says:
October 17, 2012 at 3:35 am
Didn’t God do this in 7 days ?
==================
One day., two at most. … If you believe Genesis.
@Robertvdl:
Actually, He knocked it out in 6 days so He could catch the Game of the Week.
That a faster rotating earth -distributing heat more evenly- would sustain higher temperatures seems to make sense.
One other factor to consider. If the earth rotated faster and the moon orbited faster (and closer) around it, the tidal (and perhaps Coriolis) effects would have been greater. All that shifting stuff around would also have generated more heat.
For a more extreme example.
http://en.wikipedia.org/wiki/Volcanism_on_Io
Don K: “If I assume an average afternoon temperature of 20C (293K) and an average dawn temperature of 0C (273K), I get a difference of only 15% ((6414247921.0 / 5554571841.0) – 1 *100 )) in
radiation extremes for today’s earth. The faster rotating ancient earth would presumably have been less. Picking a number out of the air — 7%. I think that would give us 15%-7% = 8% warming. Not enough. We need about four times that to account for the hypothesized fainter young sun..”
Whatever the merits of Don K’s back-of-the-envelope estimate may be, they point up how shallow the main post was; the author shouldat least have given us calculations of that type. Having failed to do so, he has wasted our time.
1. Maybe the earth was closer to the sun in the past, the moon recedes from earth a few centrimetres a year, and tides were greater in the past when the moon was closer to earth.
2. Maybe there was more volcanism and geothermal activity, although I have heard this often with pictures of dinosaurs against a backdrop of volcanos, I’ve never seen any real evidence for it. Continental drift is ultimately driven by radioactivity in the earth’s crust and mantle, this may have been higher in the past, meaning more tectonic drift and more volcanos. I also read somewhere that Venus once had continental drift, but this shut down some time ago.
3. Maybe the sun wasnt that faint.
4. Maybe the earth has a fairly strong thermostat, responding to T changes by adjusting its thermostat.
5. Maybe the earth was frozen, I’m not sure the geologists are certain that it wasnt.
6. Rotating faster would likely have also meant more geothermal activity.
Ever noticed that South America, Africa, Australia are sitting upright with respect to the roation of the earth? I suspect this is because of centrifugal forces on continental land masses, places like New Zealand trend oblique to the earths axis due to local strong volcanic/tectonic factors, which over-ridge centrifugal forces. The boundary of plates might also be effected by the rotation of the earth, it would be surpising if they weren’t, after all, when a plate splits, why wouldnt it split along stress trends determined partly by the rotation of the earth?
Wouldn’t a faster spinning earth create much higher wind velocities?
If yes, would this increasing convection of heat from the surface to the upper atmosphere?