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One remarkable thing about the climate history of earth is that despite the fact that solar luminosity was fully 30% lower in the beginning, temperatures were actually quite close to today. Since then temperatures have stayed in a relatively narrow range, allowing life to develop. This lets one conclude that there are dampening mechanisms in the earths climate system.

But predictions for the next few 100 millions of years are unequivocal that the about 10% increase of solar illumination will massively increase temperatures on earth, leading to annihilation of at least all higher life (For details, see for instance here: Solar_evolution, When will Earth lose its oceans?)

Now, it stands to reason that at some point the climate dampening mechanisms will be overwhelmed by additional solar irradiation. But there is no indication that the next 10% will be it, if at all the last 500 million years seem to indicate a trend to cooler temperatures:

enter image description here

What are the assumptions that these models are based on to come to their dire predictions?

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    $\begingroup$ Note that the 30% lower luminosity you're referring to was 4.5 Gyrs ago, while the graph you're asking about only goes back 0.5 Gyrs ago, when solar luminosity was much closer to todays value. As far as 4.5 Gyrs back Earth must have had a different atmospheric composition with a much stronger greenhouse effect, otherwise no liquid water could have been flowing. $\endgroup$ – AtmosphericPrisonEscape Dec 27 '18 at 13:23
  • $\begingroup$ @AtmosphericPrisonEscape Yes, of course. In the context of the question, the purpose of the chart was to show that there is no obvious reason to assume that a "breakdown" point of the climatic temperature dampening mechanism is near. But even if you only go back 2.4 billion years ago, to the great oxygen catastrophe when the earth got its modern atmosphere, this still would be 15-20 percent less solar luminosity than today. $\endgroup$ – Menschmaschine Dec 27 '18 at 13:53
  • $\begingroup$ My point was: The composition, which gives atmospheric opacities of the past Earth's atmosphere is unknown, at most time periods. For the studies into the future, people usually assume the current composition, modified by some simplified geophysics. So there's already a huge mismatch in knowledge between the past and the present and how they are treated in the literature. $\endgroup$ – AtmosphericPrisonEscape Dec 27 '18 at 13:59
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In this regard you can think that the Earth system is like a house with heating but no Air conditioning. Therefore, it has a powerful mechanism to stay warm when the solar illumination is weak (greenhouse effect), but it has no such powerful mechanism to cool down if the solar illumination is too strong.

In hour analogy, let's say you have used your heating to keep your house nice and warm at 22°C over winter, when outside temperatures were much colder than that. As the temperature outside goes up in the spring, you turn down the power of your heating, so to keep the house at 22°C. Now, a ~10% increase in solar power output would be equivalent to the point were the outside temperature surpasses 22°C. Therefore, even with the heating off, your house temperature will start to rise over 22°C for first time, an you can't do anything about it.

The heating mechanism of Earth the greenhouse effect, specially the one due to ${CO}_2$. But most important, is the thermostat that have kept Earth's temperature in the range of liquid water. This thermostat is based on the fact that an increase of temperature leads to and increase of silicate weathering, that in turn leads to a drop in atmospheric ${CO}_2$ concentrations, and therefore to a drop in temperature. This negative feedback counteracts any warming due to increases in solar irradiation.

However, that trick will work only until the point when there is no more ${CO}_2$ in the atmosphere. Then, any increase in solar irradiation will have a direct effect on temperature, and other amplifying feedback will kick in. In particular the greenhouse effect of water vapor: The higher the temperature, the most water vapour in the atmosphere. And water vapor is a very effective greenhouse gas, therefore, that will lead to further increases in temperature.

The following figure gives an idea of the different radiative forcings as calculated by the IPCC AR5: enter image description here

However, those are relative to the year 1750. The total effect of green house gasses is about 155 W/m². That corresponds to a 45% of the total energy we receive from the Sun (340 W/m²). That would mean that if you take away all greenhouse gases you can counteract an increase of about 45% of solar power output. In other words, Earth can keep turning the heating down to keep the planet temperature stable as the Sun keeps increasing its power output. However, this calculation is very naive, because we can't remove all greenhouse gases (that would mean removing all the water too). The models you mention are more realistic in this sense and they suggest that the critical points is just a 10% of solar output increase, much closer than the 45% of my ultra-simplistic calculation above.

Said that, the references in that Wikipedia article doesn't seem to use models fully coupled with all the Earth's systems involved (carbon cycle, tectonics, methane, albedo feedback, etc.). Therefore, I would took that 10% value with a lot of caution. However, what is true is that at some point, if you increase solar power enough, the temperature controlling processes of our planet will be overwhelmed, and life on Earth's will face the bigger challenge ever for its subsistence.

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    $\begingroup$ There is nothing magic about this exact point in time. The source article: nature.com/articles/nature12827 found that the critical insolation is 375 W/m2, that happen to be 10% more than the current value. So the magic point in Earth's history is not now, but when insolation reach that critical value. Next week I'll go to my university and I'll be able to download the full paper to see more details, but for what they say in the abstract it seem the model is still quite simplistic and doesn't consider the silicate weathering feedback that would be key to delay that critical point. $\endgroup$ – Camilo Rada Dec 27 '18 at 17:32
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    $\begingroup$ @AtmosphericPrisonEscape That is true, but water vapor greenhouse effect is not an independent forcing, it just goes tied to temperature. Therefore, each forcing includes the water vapor increase and that is included in the radiative forcing. In other words, the forcing associated to a given increase in CO2, it the greenhouse effect produced by the CO2 plus the one produced by the increase of water vapor that follows. $\endgroup$ – Camilo Rada Dec 28 '18 at 6:42
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    $\begingroup$ Is that because forcing is quantifying a change $\partial E_{\rm rad} / \partial t$, while "goes tied to temperature" means that the classical greenhouse effect without forcing is a steady-state phenomenon, for which it is $\partial E_{\rm rad} / \partial t=0$ globally? $\endgroup$ – AtmosphericPrisonEscape Dec 28 '18 at 13:48
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    $\begingroup$ @Menschmaschine I edited the question to fix a big mistake in regard with the total radiative forcing of greenhouse gases. Have a look now at the paragraph below the figure. $\endgroup$ – Camilo Rada Dec 28 '18 at 21:32
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    $\begingroup$ @AtmosphericPrisonEscape No is not a rate or time derivative. The effect of water vapor is considered a feedback not a forcing, because it can not vary independently of temperature. $\endgroup$ – Camilo Rada Dec 28 '18 at 21:41
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Any star has a "goldilocks zone" https://en.wikipedia.org/wiki/Circumstellar_habitable_zone where the temperature is suitable for a planet to have Earthlike conditions. The extent of the zone - the edges where it's not too hot, not too cold, but just right - depends on the star's luminousity.

Now suppose that 4.5 billion years ago, the primeval Earth orbited somewhere close to the outer edge of the zone. (Which might be a factor in the "Snowball Earth"?) As the sun's luminousity increased, the zone moved outwards. If it continues to increase (as physics says it will), at some point the Earth's orbit will be inside the inner edge of the "just right" zone. Apparently this is calculated to be 10% over the current luminousity.

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