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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Billions of years ago, the Earth was rotating up to twice the rate it is today
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I always wondered why there were only 12 hours on a clock.
Earth’s atmosphere was denser in the past. That’s how you support dragonflies with three foot wingspans, and that’s where the adiabatic lapse rate makes the surface warmer.
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.
Of course this rests on the premise that “this would have distributed temperatures on the Earth’s surface more evenly”
This assumption is not a given … a faster spinning earth can lead to greater latitudinal stratification, and less well distributed temperatures.
Well when you say it like that, it sounds rather simple.
The problem is, that the rotation rate of the earth; other parameters remaining the same, does not alter the duty cycle of solar heating one iota. Any spot on earth will receive the exact same total insolation in a single rotation, regardless of rotation rate..
Then you have to consider that 70% of the earth surface is ocean, and considerably more than 70% of the tropical earth surface is ocean, where the sun is incident more normally, through a thinner air path.
And the majority; 97-98% of that tropical sunlight hitting the ocean goes deep into the oceans where it is stored, so it cannot contribute to earth’s mean Temperature for a long time after it arrives, and that is rather unaffected by rotation rate,
It is true, that during the mid day hours (tropical) a given spot on earth’s equatorial region, will be under direct sun for a shorter period, with faster rotation, so the daytime surface heating would be less. That means as we well know, there would be less evaporation from the ocean and hence less cloud in the sky to increase earth albedo, so we would have a lower albedo, not a higher one.
The albedo contribution of polar ice is nowhere near the effect of tropical clouds.
Clouds are NOT a warming effect. They scatter sunlight to space so it never reaches the ocean, and in their evaporation, convection, condensation cycle they convey huge amounts of thermal energy into the upper atmosphere where it ultimately is lost to space as thermal radiation.
The simple fact that clouds and water in the atmosphere are a NEGATIVE feedback regulating mechanism, and not a POSITIVE feedback runaway mechanism, makes it entirely uinnecessary to search for answers to the so-called faint sun paradox; there is no paradox.
Water feedback regulates earth Temperatures whether insolation change is caused by solar cycles, or faint sun scenarios.
Now earth orbital changes, that shift the axis tilt and change the seasonal cycles, will result in shifts in energy flows around the earth depending on where large land masses, and water areas are located; but for a given set of orbital parameters, small changes in total insolation are masked by cloud feedback.
Earth’s seasonality is more a consequence of axis tilt, than it is of TSI. The earth is closer to the sun in Northern winters, than it is in northern summers, so clearly insolation is not the cause of northern winters, axis tilt is.
This is an important contribution to the dim sun paradox conundrum. An exact counter-balance between increasing insolation and temperature loss due to decellerating rotation would seem very fortuitous – almost like a religious anthropic argument (although of course this does not logically mean that it is wrong).
The daisyworld (Gaia) hypothesis of Lovelock and others is however, in my view, a very persuasive hypothesis, backed up by extensive and varied computer simulations. They have made a strong case that ecosystems of organisms under evolutionary pressure do robustly modify (regulate) their enviroment to suit their physiological requirements.
http://en.wikipedia.org/wiki/Daisyworld
So with the dim sun as with the CO2 question, the earth’s climate is as much about biology as it is about physics.
I should clarify one item above: “””””…..Any spot on earth will receive the exact same total insolation in a single rotation, regardless of rotation rate…….”””””
Obviously that isn’t true for one “daily rotation” , I should have made it clear that was one rotation around earth orbit; a year if you will. Since the earth sun distance changes daily, talking about one day events is not realistic.
But the daily heating / cooling duty cycle is the same regardless of rotation rate.
Thanks Mike, saved me saying it. But I’ll repeat it anyway
“Earth’s atmosphere was denser in the past. That’s how you support dragonflies with three foot wingspans, and that’s where the adiabatic lapse rate makes the surface warmer.”
IDEAL GAS LAWS, basic physics…..
greater pressure allows the atmosphere to hold more of the incoming heat.
A faster rotating Earth increases the temperature gradient between equator and poles. This is due to the fact that midlatitude eddies that are mostly responsible for the heat transport strongly depend on rotation rate; at faster rotation rates, these eddies become smaller in size and thus less efficient in transporting heat poleward. But the effect is not enough to resolve the paradox. Here is the current status of our knowledge about the paradox: http://www.leif.org/EOS/2011RG000375.pdf
Kasuha you have a point but the numbers would be more like 282-242 depending on humidty etc
Day and night temps vary by more then a couple K.
His example is obviously exaggerated to for illustration purposes.
The last paragraph does not mention water in vapourised state – clouds; and their contribution to albedo. This might at least reduce “the strong positive feedback” of water?
I saw a scientific documentary a few months ago, that explained that at one time millions of years ago our planet was a 100% ice planet. We are still an ice planet, but that phase ended due to volcanic activity. So there is some truth in this.
Now I’m no physicist but has the following observation got any relevance?
On a faster spinning earth, the side exposed to the sun (the daylight side) would not be exposed to the incoming radiation (source of the heat) for as long and would therefore not heat up as much as it currently does.
In 1998, Harvard University issued the following in their gazette. We are talking around 700 million years ago and they suspected it was then the sun was dimmer, and little CO2 in the atmosphere that sustained the planet being completely covered by ice. Volcanic activity increased the amount of CO2 emitted into the atmosphere that naturally warmed the Earth.
http://www.news.harvard.edu/gazette/1998/09.17/EarthWasComplet.html
I think I would credit Harvard University with publishing the truth, wouldn’t you?
Wouldn’t the young Earth have been in an orbit closer to the young Sun?
Somewhere in the back of my mind is teh recollection from orbital mechanics, that the Earth probably formed somewhere around where Venus can be found today (and of course Venus even closer in)
Andi
Non sequitur. ‘A fast spinning Earth distributes temperatures more evenly allowing for a significantly higher average temperature than a slow spinning Earth.’ – How does this relate to incoming radiation? The integral is the same irrespective of the time-scale. Not to say this idea is completely without merit, but it needs a lot more work before it gets any where near being a valid suggestion.
The faster spinning Earth allowed dragonflies with three foot wingspans to fly due to centrifugal force.
This argument doesn’t take account of the fact that the ocean doesn’t cool down fast at night. It is a vast store of energy why maintains night-time air temperatures near bodies of water. This is 75% of the planetary surface area.
“To me these solutions, while possible, ignore much the simpler explanation of a shorter Earth day.”
An interesting and fascinating idea, me thinks.
I have read that the moon orbit was much closer as well as being more volcanic activity on that early Earth. It was in effect a vigourously rotating petrie dish.
Mike McMillan has the correct answer, thicker atmosphere. Ian needs to drop the chalk and back slowly away from the blackboard. A simple empirical experiment can show the influence of a thicker atmosphere.
Take two identical containers largely transparent to SW visible and LWIR radiation. Within each chamber place an identically sized matt black target surface. Use a small hole to ensure one chamber maintains 1 bar pressure. Use a pump to increase the second chamber to above 1 bar and a water column regulator to ensure the chamber maintains a constant pressure during heating (1.2 bar – 2m column is sufficient). Within each chamber enclose a thermometer probe shielded from incoming and outgoing radiation. Equalise the starting temperature in each chamber then expose each to an identical amount of SW radiation. The chamber with the higher pressure heats faster and higher. No chalk or blackboards required.
Ian, when you have built and run this experiment you may look at designing one to explore the concept that condensing and non condensing radiative gasses in Earth’s atmosphere have a net cooling effect.
I had always assumed our planet was closer to the Sun (and therefore closer to the heat source) and had been steadily moving outwards – just like the moon – over the past 4.5 billion years.
“To me these solutions, while possible, ignore much the simpler explanation of a shorter Earth day.”
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Shorter Earth Day? Are you mad? We need longer! Earth Day is vital to promote understanding and appreciation of this fragile planet. It is an important day for self-righteous left-over hippies to get together and grok nature. It is an important day to celebrate of the birth of Vladimir Lenin. It is an important day for preach-ins and for brainwashing the children and getting their minds green.
Excuse me – I must go propitiate the Earth Spirits now by sacrificing a Denier…
Oh noes, the earth is slowing down we’re all going to freeze…must be all the (man-made) windmills – can’t just be the (natural) tidal friction.
/s 😉
Well … just maybe. One problem is that we don’t know what the Earth’s atmosphere 4.5B years ago looked like. Little or no Oxygen. We didn’t get that until most of the Iron was locked down in relatively insoluble forms billions of years later. Probably some Hydrogen. Nitrogen and water vapor probably. Carbon Dioxide?, Methane? So we don’t really know how it reacted to incoming and outgoing radiation.
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..
Of course, my estimate is just a cocktail napkin estimate by someone who doesn’t know what he’s doing (I think that qualifies me as a climate scientist, right? Where’s my grant?). But the numbers don’t seem to look very promising.