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
I agree with Ian Schumacher when he say’s (within context) “a paradox means that one of the things we think we know is wrong”. And Ian is correct! all things being equal, there should not be a so-called paradox. Ian please do a follow up on this.
Willis,
Unfortunately to understand most of the past we have little choice to but to use models – guided of course by the very little empirical evidence we have. It’s either that or just throw our hands up and say “we will never know”, which very well might be true.
Milankovich cycles, are correlation, not cause and effect. The correlation in some areas of Earth’s past are so good that we must assume a cause is there somewhere, but from my reading it isn’t nearly as clear-cut as you imply. The contribution of orbital forcing to ‘variance’ in season changes, for example, is minor. As minor as a little more or a little less CO2 some might claim (in which case we should probably be in a cold phase right now), or a large volcanic eruption. Also “the ‘traditional’ Milankovitch explanation struggles to explain the dominance of the 100,000-year cycle over the last 8 cycles.” – quoted from Wikipedia (with apologies).
If you believe I’m wrong and there is certainty, then when will the next cold phase of the ice-age start? I’d greatly appreciate knowing since it seems rather important (if within mine or my children’s children’s lifetimes). Strangely I can’t seem to find any answer to this on the internet, but perhaps my searching skills are not what they should be.
Ian
p.s. Doing more research. Apparently we also really have no idea where the water for the oceans came from. So, in fact, I beginning to question if we even really know if early Earth was entirely covered in ocean. I suspect now it is a strong hunch only.
I’m willing to admit that perhaps it is only me that knows almost nothing, in which case I do welcome being ‘kindly’ informed of how the world really works outside of Wikipedia.
Ian Schumacher says:
October 21, 2012 at 9:13 pm
Thanks, Ian. I fear you are presenting what is known as a “false dichotomy”. The false dichotomy is that we have only two choices when it comes to understanding most of the past—use faulty computer models, or throw up our hands and give up.
I fear that your point of view would have been incomprehensible to most scientists in history, for a simple reason—they didn’t have either computers or computer models. And according to you, to understand most of the past, it is a requirement to have computer models, because if we don’t have computer models (again according to your dichotomy) we might as well just quit. Throw up our hands. Walk away.
Almost makes me tear up and cry, thinking of all of those poor doomed pre-computer scientists futilely trying to understand the past, all the while not knowing that without a computer, they were on a totally hopeless quest, because you simply can’t understand the past without a computer …
I gotta admit, sometimes I fear for the new generation of scientists. Seems like they think that nothing is possible without email and google and smartphones and computers and the like.
So let me make it clear. Often, computers are not better than nothing. Sometimes they are much worse than nothing. And the results from said computers are not evidence of anything. Yes, we should use them. But no, far too often their results cannot be trusted.
The part that mystifies me is why people don’t ask for the bona fides of any given computer program. Instead, they blindly take any random computer results and assume that they have meaning, that they are valuable, that they are better than flipping a coin … whereas in fact, it is quite possible that such results are meaningless, valueless, that they lead you down the wrong path, and that you’d be much better off flipping a coin.
w.
Willis Eschenbach says:
October 22, 2012 at 9:32 am
[blockquote] Thanks, Ian. I fear you are presenting what is known as a “false dichotomy”. The false dichotomy is that we have only two choices when it comes to understanding most of the past—use faulty computer models, or throw up our hands and give up.
I fear that your point of view would have been incomprehensible to most scientists in history, for a simple reason—they didn’t have either computers or computer models. And according to you, to understand most of the past, it is a requirement to have computer models, because if we don’t have computer models (again according to your dichotomy) we might as well just quit. Throw up our hands. Walk away.
Almost makes me tear up and cry, thinking of all of those poor doomed pre-computer scientists futilely trying to understand the past, all the while not knowing that without a computer, they were on a totally hopeless quest, because you simply can’t understand the past without a computer …
I gotta admit, sometimes I fear for the new generation of scientists. Seems like they think that nothing is possible without email and google and smartphones and computers and the like.
So let me make it clear. Often, computers are not better than nothing. Sometimes they are much worse than nothing. And the results from said computers are not evidence of anything. Yes, we should use them. But no, far too often their results cannot be trusted.
The part that mystifies me is why people don’t ask for the bona fides of any given computer program. Instead, they blindly take any random computer results and assume that they have meaning, that they are valuable, that they are better than flipping a coin … whereas in fact, it is quite possible that such results are meaningless, valueless, that they lead you down the wrong path, and that you’d be much better off flipping a coin.
[/blockquote]
Superb summary Willis!
Ian, regarding Milankovich, take a look here for some recent thought on the subject.
w.
Willis Eschenbach,
I’m afraid you are being very narrow minded about what comprises a ‘model’. Kepler’s laws are a model, Newton’s laws are a model. Rutherford’s atomic model, is a model. All ‘wrong’ strictly speaking, but very useful approximations non-the-less. I definitely did not mean ‘computer model’ only. Although, just because it runs on a computer that doesn’t make it automatically wrong either. You’ve been blinded by the failure of climate science to think that all computer models are useless (I guess someone needs to tell the circuit designers they need to do it all by hand from now on). Computer models are tremendously useful and should not be shunned en-masse just because of a failure in an area of chaotic dynamics, in which we probably should expect them to fail.
Last night when I went to bed I thought … hmmm, Willis will probably focus on some small aspect of my comment, criticize that and ignore the rest. Looks like my ‘model’ is fairly accurate so far 😉
I respect your knowledge Willis, but you could really benefit from learning phrases like:
– you make a good point.
– I stand corrected.
– I don’t know.
Perhaps these never apply to you, in which case you should definitely use your omniscience in giving us specifics. Like when the next ice-age will occur – and so on.
Willis,
Unlike certain others who’s name may occasionally be mentioned at WUWT, I’m happy to acknowledge when I’ve got a sign wrong in one of my parameters. Diurnal range decreases with latitude, not increases as I had it in my rough calculations.
Rotation speed is a first order effect on a cold dry mistress of a moon, a second order effect on a warm soggy earth if you get your sums wrong, and a third order effect here.
R
Ian Schumacher says:
October 22, 2012 at 10:15 am
Thank, Ian. Yes, you are right. I am speaking about a specific type of model, the computer-based iterative climate model that was used to produce the results described in the study under discussion. I’m sorry, I thought that would have been clear from the context.
Again, you are right, I am discussing the specific type of model used in the paper.
Your accusation that I think that “all computer models are useless”, however, is completely untrue. I have been writing computer programs for fifty years now, I’ve written a host of models of physical and financial systems. I know their pluses and their minuses as a result of spending far too many hourssitting up late at night and debugging them. I am or have been fluent in a variety of computer languages—Basic, Pascal, C, LISP, Fortran. Mostly these days I write in R, Visual Basic, Mathematica programming languages, and Pascal. I have created and run models on the STELLA platform. I both write and use a host of computer models for a variety of tasks in my scientific research. Clearly, I don’t think “all computer models are useless”.
My objection is to the untested, unverified, unvalidated Tinkertoy™ global climate models. Truly, I don’t care if the model in this study clusters model storms at the model Equator when the model Earth rotates at twice the Earth’s speed. The next model could easily say the opposite. Look at the model predictions of the areas of rainfall changes with warming … some say increased rain in the same area where other models say increased droughts.
So until their whiz-bang model can be shown to be valid for novel situations (not merely replicating data it was trained on), I treat it like I treat the stories of Tibetan monks levitating … interesting, but not meaningful. Anecdotal, not scientific.
w.
Willis,
I’m completely with you on the uselessness of Tinkertoy climate models. I did object to your dismissing the computer model used in this case, only to turn around as say “how it would really be”. That came across as a bit arrogant and I apologize if I interpreted that incorrectly.
Also I wanted to emphasis how little we know. I used Ice-ages as an example, (of which we do know something, just no details about the actual mechanism). I could have used a safer example of which there are plenty.
Also, regardless, there is a paradox. I may have missed your explanation for the paradox, but even given your considerable knowledge and intelligence, I would still have to say ‘maybe’. Until it’s backed up by some good math (which may or may not be put into a computer model), some predictions, and the discovery of previously unknown empirical evidence to back it up – it’s all just conjecture and we shouldn’t be too keen on shooting down other theories so quickly. Let’s just say ‘maybe’. There is no harm in it, and it might actually be right.
Best to you.
Ian