Albedo, atmosphere, and predicted temperature of Venus

[Battlemage!]

The reason I am making this thread is because I have a question regarding predicted temperatures of planets based on their area, distance from the sun, and albedo. Going by the planetary equilibrium temperature,

T⁴ = [L(1-a)]/(16σπD²),​

I have seen numerous websites state that Venus would actually be colder than Earth if it had no atmosphere, despite it being closer to the sun. The main factor for this is its albedo (L is constant, and a smaller D to the sun would actually make Venus warmer by this equation, so albedo must be the deciding factor that makes Venus colder without an atmosphere).

One such website: https://www.acs.org/content/acs/en/climatescience/energybalance/planetarytemperatures.html
(these numbers show up in many articles on this topic)However, I have also read that a part of why Venus' albedo has its value is because of its atmosphere. This paper speaks about that:

http://journals.ametsoc.org/doi/abs/10.1175/2011JCLI3946.1

The vast majority of the observed global average planetary albedo (88%) is due to atmospheric reflection. Surface reflection makes a relatively small contribution to planetary albedo [...]

So, it appears that atmosphere has an affect on albedo. If that is the case, why are people who calculate what the temperature of planets would be without an atmosphere using the actual albedo of those planets? I've done the calculation myself with a chosen albedo of .12 (that of Mercury and the Moon) to hold it constant, and as expected Venus is hotter. So if albedo depends on atmosphere, why is everyone who does this calculation for temperature without an atmosphere just using the known albedos? Shouldn't they be taking the dependence of albedo on atmosphere into account if they are calculating what a planet with no atmosphere would be like?Am I totally wrong here? Thanks.

 

[Bandersnatch]

That article tries to make a point, that everything else being equal, if there was no atmospheric greenhouse effect (not no atmosphere as such), the temperature would be as stated.
In other words, they start with observables (albedo, distance, solar luminosity), and apply a 'simple black body model', and get those results. Since there's also measurements of actual surface temperatures being different, it's an indication that the model is incomplete.

 

[Battlemage!]

That article tries to make a point, that everything else being equal, if there was no atmospheric greenhouse effect (not no atmosphere as such), the temperature would be as stated.
In other words, they start with observables (albedo, distance, solar luminosity), and apply a 'simple black body model', and get those results. Since there's also measurements of actual surface temperatures being different, it's an indication that the model is incomplete.

EDIT- Oh I see. Yes, the article is talking about no greenhouse effect, rather than no atmosphere. Disregard all this. The reason I brought this up is because I saw other articles the other day discussing the notion of there not being an atmosphere. I just quickly googled that article to do this post while at work. But even so, if there is an atmosphere there has to be a greenhouse effect of some sort, doesn't there?

Anyway, here is a thread from here that discusses the topic:
https://www.physicsforums.com/threads/Earth's-surface-temp-without-atmosphere-vs-moons.172646/
In it the same thing I'm talking about happens: people argue that the Earth's temperature, without an atmosphere, would depend on its currently known albedo. But its current albedo would be different if not for the atmosphere, wouldn't it?Disregard this:

Yes, I know. That is tangential to my problem though. What I am concerned about is that the used the planet's actual albedo to calculate what it's temperature would be if it had no atmosphere. I will show below that they used the actual albedo of 0.75 by redoing the calculation and getting a very similar result:(units omitted for brevity)
Take the luminosity of the sun: 3.8x10²⁶
The albedo of Venus: 0.75
Distance of Venus to the sun: 108x10⁹
σ ≈ 5.67x10^-8

Plug that into the equation
T⁴ = [L(1-a)]/(16σπD²) = [3.8x10²⁶ (1 - 0.75)]/(16σπ[108x10⁹]²

and take the fourth root and I get: 231.2 K, which is very close to the value of 232 K that that article has.BUT!


Notice what I used for the albedo in that equation. I have bolded it. That equation assumes no atmosphere, just like the article says. The predicted temperature is just based on that equation. But it DOES use the actual Venus albedo. If the albedo of Venus depends on its atmosphere, and we're assuming there is NO atmosphere in the equation, how can we use the actual albedo of Venus?

That bold gets to the heart of my issue here. The predicted value assumes no atmosphere, but using the albedo assumes an atmosphere. It's contradictory to me. Shouldn't they instead use an estimation of what the planet's albedo would be if it had no atmosphere, rather than the actual Venus albedo?

 

[Bandersnatch]

But even so, if there is an atmosphere there has to be a greenhouse effect of some sort, doesn't there?

That's the whole point of these type of arguments that you're talking about, though - they attempt to ascertain the magnitude of the greenhouse effect by first assuming there isn't one (but keeping everything else as is, including albedo), and then comparing the result to actual measurements.

But its current albedo would be different if not for the atmosphere, wouldn't it?

Of course. But again, the people throwing the numbers for Earth temperature 'without atmosphere' are really talking about there being no greenhouse effect* - not about the case where you strip Earth of atmosphere (or paint it black, or cover it with ice, etc.)

*providing they know what they're talking about.

 

[Battlemage!]

That's the whole point of these type of arguments that you're talking about, though - they attempt to ascertain the magnitude of the greenhouse effect by first assuming there isn't one (but keeping everything else as is, including albedo), and then comparing the result to actual measurements.Of course. But again, the people throwing the numbers for Earth temperature 'without atmosphere' are really talking about there being no greenhouse effect* - not about the case where you strip Earth of atmosphere (or paint it black, or cover it with ice, etc.)

*providing they know what they're talking about.

Well, if I wanted to calculate these results with what the albedo would be without the atmosphere, what kind of suggestions do you have for a constant albedo for all the rocky planets? Or is there a resource you know about that would give albedo estimates for planets without atmospheres based on the composition of their surface?

Essentially what I'm after is a more accurate representation of what the temperatures of the planets would be if they didn't have atmospheres. I know these sources want to emphasize the importance of the greenhouse effect, which is fine. But I'm curious about just their temperatures without an atmosphere. If such a resource listing albedo estimates doesn't exist, I assume I'd have to find some relation between surface composition and albedo. Interestingly, the moon and Mercury have the same bond albedo. Would it therefore be a good estimate to use that albedo for rocky planets, do you think?

 

[Bandersnatch]

If I had to, I think I'd use Lunar albedo for barren Earth, since the two have nearly the same surface (crust, in case of Earth) composition. I don't know enough about Venerean composition to suggest anything similar (but again, if I had to - likely similar composition to Earth, so use Lunar).

The issue here is in what does this actually tell you about the supposedly 'real' albedo without an atmosphere?
To use Lunar (or Martian, or Mercurian) albedo, you need to assume that the surface had exactly the same chemical history as those substitutes, which is patently not true. Having in its history an atmosphere with oxygen, or water, or having a magnetic field, or being more or less differentiated (so, mass differences), will all affect surface chemistry, potentially changing albedo for bodies with otherwise identical composition.
Simply assuming that e.g. Earth never had an atmosphere is unphysical (if all the other conditions are the same - why would it not outgass? why would it be lost?).

The point being, these will be just fantasy scenarios, not 'real albedos'. There's too many arbitrary assumptions one needs to make.
At best, you will be able to say something like 'a body with albedo of X at distance Y would have Z equilibrium temperature'. So, for example, the Moon at Venerean orbit would have this or that temperature.

 

[Battlemage!]

Thanks. Good points. I suppose there is no real way to do anything other than your last suggestion. I guess the best I could do is learn about the various compositions and just look at it based on that.

 

[Ken G]

Notice what I used for the albedo in that equation. I have bolded it. That equation assumes no atmosphere, just like the article says. The predicted temperature is just based on that equation. But it DOES use the actual Venus albedo. If the albedo of Venus depends on its atmosphere, and we're assuming there is NO atmosphere in the equation, how can we use the actual albedo of Venus?

Yes, you are completely right, the comparison being made there is being described in a totally wrong way. The number 231 K has no bearing whatever on the T of Venus without an atmosphere, what it actually tells you is the T at the top of Venus' cloud layer. So no one should ever say that without an atmosphere, Venus would be colder than Earth, as that is just silly. But what they can say is that because of Venus' atmosphere, it is colder at the top of its cloud layer than the Earth is at its surface (and at the top of Earth's cloud layers also). That's still not particularly interesting though-- what is actually interesting is the contrast between the T at the top of Venus' cloud layer (231 K) and the T at Venus' surface (735 K). Obviously that comparison has nothing to do with Venus not having an atmosphere, because it is all about Venus' atmosphere. So the bottom line is, you are right, the verbiage in that article is describing the comparison it is making in wrong terms, the right comparison is the T at the top and bottom of Venus' atmosphere.

Here's what they should say: because of Venus' atmospheric albedo, it is colder at the top of Venus' atmosphere than is the surface of the Earth, but because of the greenhouse effect, Venus' surface is way hotter than the surface of the Earth.