Since I’m tired/bored of the climate “debate” I thought I might write a quick post about something that’s related to climate change, but probably not particularly controversial. I came across a paper recently by Shields et al. (2014) called Spectrum-driven Planetary Deglaciation Due to Increases in Stellar Luminosity.
Essentially, they used a GCM to try and understand how planets around different types of stars might move into – and out of – snowball states. Stars are typically divided into different spectral types, the spectral sequence being O B A F G K M, with O stars being really hot and luminous, and M stars being cool and relatively dim.
As an aside, the original spectral classification ran from A-Z and was determined by the strength of a hydrogen spectral line in the visible. However, this particular spectral line is only present if the gas is hot enough for enough hydrogen atoms to be excited into the second energy level. If most are in the ground state, then the dominant spectral line is actually in the UV, and so wasn’t detected by early instruments. Additionally, if the gas is so hot that the hydrogen is fully – or almost fully – ionised, then this spectral line isn’t present either. Therefore the original classification (A-Z) went from stars with surface temperatures around 10000K (A stars) to stars that were both hotter (weaker spectral lines because hydrogen was becoming ionised) and cooler (weaker spectral lines because not enough hydrogen was in the n=2 state). When they realised this, they re-arranged it as a temperature sequence and we get the OBAFGKM series.
Anyway, back to the paper. They considered planets around M-stars (cooler than the Sun), G-stars (like the Sun), and F-stars (hotter than the Sun) and either started with an insolation similar to what we have today and reduced it to see when the planet would move into a snowball phase, or started from a snowball phase and increased the insolation. They used CO2 concentrations similar to today on the Earth, and CO2 similar to what we’d expect as we moved out of a snowball phase. The basic result is shown below. The hysteresis comes from the difference between what happens if you start in a warm phase and reduce the insolation, or start in a cool (snowball) phase and increase the insolation.
Figure 1 from Shields et al. (2014)
What they find is that the transition out of, or into, snowball phases is smoother for M-stars (cool) than for F- and G-stars (hotter). The idea, if I understood it properly, is that M-stars emit most of their energy in the infrared, which is absorbed more by ice than is shorter wavelength (visible and UV) radiation. Therefore, hotter stars require a bigger input of energy before the ice starts melting and when it starts, the transition tends to be faster than around M-stars.
As you can see from the figure above, for modern CO2 concentrations a snowball planet around a Sun-like star would require an insolation greater (more than 100%) than our insolation today. We moved out of our snowball phase because volcanic outgassing increased CO2 concentrations to levels much higher than today. They also considered this, and showed that M-stars would more easily move out of their snowball phase if CO2 increased, than F- and G-stars. The basic conclusion of the paper is that
Planets near the outer edge of the habitable zones of M-dwarf stars will become more hospitable for surface life earlier in their host stars’ evolutionary paths than their ice-covered counterparts orbiting brighter stars, although this may take a longer absolute time, as an M dwarf brightens more slowly than a G dwarf.
which is interesting, although we have yet to find another planet that we really think might be habitable. Having said that, planets around M-stars are our best bet at the moment.
This paper also reminds me of something else that I think is related. I recently saw a paper that was arguing that the oceans are poor emitters of infrared, unlike ice. This suggests that the reduction of Arctic sea ice can further enhance warming because the ocean surface will emit less infrared than would be emitted were it still covered in ice. If anyone remembers which paper this was, maybe they can point it out. Anyway, enough from me.
...and Then There's Physics 
They considered M-stars, G-stars and F-stars, not K-stars (to correct what confused me in your text). Interesting results though! The hysteresis loops really clarify the process.
Blast, knew I’d make some kind of silly mistake. Thanks.
ATTP
I think it was Feldman et al. (2014) Far-infrared surface emissivity and climate
http://www.pnas.org/content/early/2014/10/29/1413640111
That’s the one. Thanks.
I think talking about Alcubierre Drives would be more entertaining.
http://en.wikipedia.org/wiki/Alcubierre_drive
Maybe a discussion about the movie Interstellar?
Years ago I learned a mnemonic for the main sequence of stars:
Oh be a fine girl, kiss me
M2,
One can, of course, replace “girl” with “guy” so that anyone can use it. Alternatively you can use Only Boring Astronomers Find Gratitude Knowing Mnemonics.
I found the Feldman et al. paper quite interesting. The first thing that came to mind after reading it was that some hard data on emissivity should probably be acquired; the emissivity used for water and ice in the paper are calculated values, not measured ones.
A well-calibrated airborne mid- to far-IR spectrometer flown over ice, snow and sea surfaces of known temperature seems like a relatively modest experiment that could readily fill this apparent gap in Earth and atmospheric science knowledge.
There are libraries of emissivity data and the difference btw sea water and snow is not so big, about 0.01 but that does not include sea water and ice practically overlay each other except below 1000 cm-1 where water has a much higher emissivity ) about 0.5.
http://www.icess.ucsb.edu/modis/EMIS/html/water.html for example
Eli,
The Feldman paper talks about wavelengths longer than 15 microns, which your data doesn’t seem to show.
“This suggests that the reduction of Arctic sea ice can further enhance warming because the ocean surface will emit less infrared than would be emitted were it still covered in ice.”
True but only in the unlikely case the surface of the ice and the surface of the sea are the same temperature (which will be so for thin sea ice). Because of the 4th power relationship of temperature to energy, thicker ice at -40 C will be radiating much less energy per square meter than water at 0 C, despite having a slightly higher emissivity.
Some rambling thoughts:
The net effect is that with ice gone, actual power emitted will necessarily increase simply because you have a vast warmer area exposed to the night sky. I calculate about 1.9 times more power to be emitted at 0 C than -40 C, solely due to temperature, but the paper suggests a 0.1 to 0.2 reduction in emissivity and that will reduce the power transmitted by the warmer sea.
A small other factor exists, and that is the portion of the energy captured by CO2. Wien’s displacement law is going to put the bulk of ice at -40 at long wavelengths below CO2’s capture wavelengths. Essentially all energy transmitted by ice will go directly to space which may be why a large area of ice is inherently stable (stays cold, stays ice), but the warmer sea puts some of its radiation in reach of carbon dioxide to capture and thus stays warm. This is a positive feedback mechanism suggesting a bi-stable system. Since it takes energy (and time) to go from ice to water or v/v, a plot would demonstrate hysteresis.
In the past few days I have been thinking about a Fluke VT04 thermal imaging thermometer and why it cannot “see” the emissions of carbon dioxide, making CO2 visible in the air and thus blocking view of anything more than a few meters in front of the imager.
Turns out that thermal imagers work in the 8 to 15 micron band, CO2 captures (and emits) strongly in the 4 to 5 micron band (more or less). The implication is that a rather significant portion of Earth-sourced infrared has an optical “window” and can go straight to space if no clouds are in the way. The actual portion of a particular thermal spectrum that is captured, or goes through the window, therefore depends on the temperature of the emitter. I am reminded somewhat of a tunnel diode that has a zone of negative resistance, increasing forward bias unexpected reduces forward current over a small range of forward bias. So too is the interplay between Wien’s displacement law and carbon dioxide going to create an unstable (or bi-stable) zone of temperature, with water/ice creating lag hence oscillation and hysteresis.
The reference of Feldman et al for the emissivity of water seems to be this 1973 paper of Hale and Querry
A net search revealed also the post of SoD on Emissivity of the Ocean, which helps perhaps in connecting the information of the Hale nad Querry paper to the emissivity.
ATTP: Perhaps your next post could address what leading astrologers say about climate change.
Which begs the question of identifying a leading astrologer. But it is intriguing.
http://www.modernvedicastrology.com/AstrologyOfClimateChange
Astute readers will notice that the entire first paragraph is repeated.
It’s embarrassing. Can you imagine a student walking in while a professor is reading: “A similar index of zodiac signs can be used whereby the fire signs Aries, Leo, and Sagittarius are all warming influences, while Capricorn, Aquarius and Gemini are cooling influences due to their association with Saturn and Mercury.”
After a spectacular display of mumbo-jumbo, charts and graphs, the conclusion:
“My analysis of these ingress charts does not come anywhere near to the requirements of such a predictive model.”
Well, there you go. This author is not willing to go out on a limb and predict anything. Good for him. Nobody can say he was wrong.
“Even in its current marginalized status, however, it is possible to regard studies like this one as evidence of how astrology can be a useful, complementary knowledge practice that can inform scientific endeavors.”
NOW we can say he is wrong!
Funny that you should ask
http://landscheidt.wordpress.com/
http://landscheidt.wordpress.com/
The weasel can fill you in
Missed that about longer than 15 microns. That’s in a region known occasionally as the vacuum IR, because there are no simple windows and detectors are no picnics.
The (distant) future necessity of responding to changes in solar liuminiosity suggests taking the Precautionary Principle to its evolutuionary limit– it’s never too early to get the observational ball rolling on studies of distant planetary systems that might be saved from stellar spectral changes by manipulating their radiative equilibrium.
Since albedo is energetically a lot easier to manipulate than stellar luminosity, planets with hydrospheres ( or other extensive surface liquids) , could adapt by evolutionary responses of marine flora and fauna, or alien species of exogeoengineering.