Atmospheric dust and albedo

[xeryon (OP)]

http://aurora2.pentarch.org/index.php/topic,5470.0.html

Ian came upon an interesting situation at the end of this fiction game he was playing/writing that likely should be addressed.

In a situation where a planetary bombardment causes extreme temperature decrease due to dust concentrations in the atmosphere the oceans subsequently froze and caused an increase in albedo.  The albedo increase caused the planetary surface temperature to plummet.  I am not sure what the original temperature was but the oceans freezing dropped the temperature from a reported -38.27oC down to -68.9oC.  Unless Ian responds with the original temperature information I have to make the assumption that the planetary temperature was likely a positive C amount to start with.  For arguments sake lets just say it was 0C (maybe it was a race of Abominable Snowmen?)

The following illogical sequence of events then occurred:  Planet is habitable at 0C, planetary bombardment occurs and a dust plume blots out the sun, surface temperature plummets as the concentrated dust in the atmosphere reflect the solar energy from reaching the planetary surface and starves the surface of the warming effects of it's host star.  Once the temperature decreases into the -30C range the oceans freeze.  The ice increases planetary albedo and the temperature drops an additional 30 points to -60C. 

If the dust was blocking the suns energy from reaching the planetary surface how exactly is the increase in surface albedo playing such a significant and immediate role in planetary surface temperature?  Should there not be a muting of the intensity of the effect based on the preexisting effects of the dust?

[Ghidorah]

Just as in Astronomy, dust is very effective at blocking many wavelengths of light (energy), but isn't so good at others (and the composition of the dust matters a lot as well).  So that means that a star total amount of energy output on a world goes down with most types of dust, but the energy that does make it to the surface still is there in some wavelengths.  Now add Ice and snow to the mix.  The cleaner the better but even fairly dirty Ice/snow is still less energy absorbent than plants, earth, and even water.  This means the planets multi-wavelength true albedo has just gone up again and you get a secondary chilling effect.  Kind of a nasty double whammy, eh?

[xeryon (OP)]

Sounds logical.  I was just taken aback, and so was the author, at the precipitous drop in temperature when this happened.  It just seemed to me that the end result was more intense than one would expect.

[Sematary]

Keep in mind when all water on Earth freezes you are bringing down the albedo for over 70% of the surface even excluding the Arctic Ocean which is normally frozen.

[IanD]

Thank you Xeryon for bringing this to a wider audience and thank you all for the explanation, I was indeed taken aback. The original surface temperature was +7.7^oC, with a base temperature of  19.92^oC. It was an ideal habitable world, amazing the difference a few lasers directed at the surface can do! 

Regards
Ian

[xeryon (OP)]

I still think from a logic perspective that increases in dust and increases in surface albedo are proportionally exclusive in their effects.  More dust equals less effect surface albedo has.  If the dust concentrations are not sufficient to greatly mute the effects of the increased albedo (due to dust only blocking some wavelengths of light) then maybe the strength of the effect from airborn dust needs to be reconsidered.

[Paul M]

If I have a dust shroud that causes x% of the incoming energy (light) to be reflected and this causes a drop in the surface temperature to the point where massive freezing of what used to be a good absorber so that now instead of 100% being absorbed y% is reflected back into space then the amount of light that used to be absorbed was:

Initial_energy = I0

accounting for reflection by atmospheric dust the amount entering the atmophere is:

New_energy_into_atmosphere = I0-I0*Rd where Rd is the amount reflected by the dust or Iatmos = I0*(1-Rd)

New_energy_into_surface = IAbs= Iatmos-Iatmos*Ri where Ri is the amount reflected by the ice
=I0*(1-Rd)-I0*(1-Rd)*Ri
=I0*(1-Rd-Ri+Rd*Ri)

so IAbs/I = 1-Rd-Ri+Rd*Ri  so for Rd = Ri = 0.5 IAbs/I0 = 1-0.5-0.5+0.5*0.5 = 0.25

For Rd = 0.5, Ri= 0.1 IAbs/I0 = 1-0.5-0.1+0.5*0.1 =0.405

To account for the dust reflecting energy back you have to do a sum of the bounces to infinity I'd think but I'm too lazy and it would just add in square terms anyway so I think it is a good approximation as with values of Ri or Rd < 1 the contribution of higher oder terms will be small.

It is a feedback effect and they happen in the real world.  It is, so far as I understand the situation, just such a feedback cycle that climate scientists are concerned about at the moment.  Admittedly with the result being a hotter planet rather than a colder one.

Also note in Aurora albedo is backwards...as you want a higher number.  As the temperature of the planet is Base*Albedo*Greenhouse_effect

I'm not sure if this supports or opposes the idea they are mutually exclusive but you can see they work together to make the situation bad for any planet in question.

[xeryon (OP)]

I do not have the capability of testing your equation but you clearly have more maths skills/background than I.  On the topic of albedo the number you want is neither a high nor a low number but the number which produces the desired effect in relation to the amount of solar energy reaching the body.  The number is just the abstract reflectivity of the planet compared to Earth (Earth = 1, correct?).  On a body which receives higher amounts of solar energy a higher albedo would generally be preferable to reduce surface temperature to bring the body closer to a habitable range.  For more distant bodies or ones orbiting stars with lower solar output lower albedo would allow more of the solar energy to be captured.

[Paul M]

My point is that in Aurora the temperature of the planet is determined by the formula: base temperature*albedo*greenhouse_effect.  So in Aurora a high albedo will produce a higher temperature.  In reality a high albedo means the object is highly reflective and hence should be a colder world.

In Aruroa Earth has an Albedo of 1, in reality it's albedo is 0.3.  Charcoal has an albedo of 0.04, fresh snow has an albedo of 0.9.  A number greater than 1 is impossible.

See Wikipedia for more information.

[xeryon (OP)]

Ok, so in real terms albedo is a scale of 0 to 1 with 0 being absolutely no light reflection and 1 being complete reflection.  Interesting to know.  Wiki will have to wait for another day.  It's an excellent resource for casual learners like me but one insanely deep time sink that I must resist the temptation to visit.

In terms of programming it seems logical to have your baseline start at 1 for simplicity but I wonder why the reversal of the scale?

[Paul M]

I don't know why, I can make guesses but they are shots in the dark in reality.  That is a question Steve has to answer.