FireBones said:
Thanks for taking the time to write this, but I really think you are missing my point regarding the nuances of the S-B law. I'm going to try to make that more clear in my replies. I apologize if some of them sound bitter...this medium is not a good one sometimes ;)
No problem at all. I don't mix up robust disagreement with aggression or bitterness. Furthermore, I don't expect you just to fall over and accept my explanations. I anticipate that we'll soon conclude this discussion without reaching agreement, and that's fine by me, as long as we have both been able to explain our particular view.
Then, perchance, if you still find any of this worth pursuing yourself, keep on double checking it for yourself, from a range of sources. I would personally recommend looking at what is said in a range of textbooks that deal with basics of atmospheric and planetary thermodynamics. Comparisons of different planets are a good way to look at the various gross factors that impact surface temperatures. I use the Moon and Earth comparison quite a lot to explain the differences in albedo, thermal absorption of an atmosphere, surface heat capacity, lateral heat transfer, and so on. But that's entirely up to you; this has been a good exchange in any case.
FireBones said:
This is what I'm disputing...Most of the warming due to our atmosphere has nothing to do with the greenhouse effect.
Then we do have a genuine point of real difference here, and it may be worth sorting it out, or at least clarifying how we get such different conclusions.
I have some questions about your account, which may help clarify where we stand. I've kept them pretty straightforward and hopefully friendly and collegial. I believe you are mistaken, but I'll be happy to have your answers or clarifications of what you are proposing. Similarly, I have tried to answer your questions.
If you can give references for your claims, this will clarify your claims much better. It is the usual expectation in this forum is that we back up claims with reference to peer reviewed scientific references or a suitable equivalent. I would consider that any conventional textbook used in mainstream universities should be okay. The Lunar handbook, we've both used, for example, is fine.
The idea here, as set out in our guidelines, is to learn about the practice of modern physics, as used and published by working physicists. That is what I have been using.
The "lowering radiating effectiveness" I refer to is not the one you are referring to. The lowering in the effectiveness of Earth's radiation I refer to would occur even if none of the atmospheric gases absorbed IR energy. This proves that the lowering of radiating effectiveness I refer to is not equivalent to backradiation.
Have you got a reference for this effect?
Suppose that the entire Earth surface was all the same temperature, of 16
oC, which you described previously as a "blackbody temperature of the green-house affected Earth". That is 289K, and by the Stefan-Boltzmann law, a blackbody at 289K radiates just over 395 W/m
2. Now this is indeed pretty close to what has been conventionally given as the amount of energy being radiated upwards from the surface. The modern value is usually given as 390 W/m
2, from Trenberth et al (2009), corresponding to blackbody of about 15
oC. In either case, this is significantly more than the total energy available from the Sun, which is at most 342 W/m
2.
Note that we have both already agreed that any variation of temperatures above and below a mean of 16
oC makes the Earth a more effective radiator, and thus
increases the energy being radiated to be above 395 W/m
2.
Question 1. Do you disagree that the energy radiated up from the surface is significantly more than the energy radiated down from the Sun? Or if you agree with this, then where does the surface get the additional energy required?
That's not true. If our atmosphere were transparent to radiation (going both ways) it would not be frozen over. The type of claim you are making mixes two different models: it half-transforms the molecules in the atmosphere (taking out the absorption aspect while leaving the reflection aspect) and uses that number. It is much more reasonable to either talk about:
A. "What the temperature would be if the Earth had no atmosphere"
B. "What the temperature would be if the Earth had an atmosphere, but the atmosphere lacked gases that interfered with radiation."
I'll take those as questions for my analysis. There is almost no reflection from the clear sky atmosphere. There is significant reflection from cloud. Of course, more reflection has a cooling effect. I presume we are agreed on all of this? Here then are my answers.
(B) is fairly easy to answer, if we just assume there's no interference with thermal radiation and leave the albedo unchanged. I did the calculation in the last post, and the result is a mean surface temperature of -18
oC, or less. As we have both noted, any [strike]sharing[/strike] variations in temperatures around the globe would give a more effective radiator, and hence
even lower mean temperatures to shed the same incoming solar energy. So by any account, this will freeze the planet very thoroughly.
(A) is more subtle, but in the end the same. If we assume no atmosphere, then we assume no cloud. So as well as having no greenhouse effect, we also have no reflection from the cloud. Now Earth is mostly ocean, and ocean water has a very low albedo, of around 0.06. (Ref: http://nsidc.org/seaice/processes/albedo.html albedo page) The solar input of 341.5 W/m
2, and albedo of 0.06, the total absorbed energy is 321 W/m
2, and that has a blackbody temperature of about 1
oC, all of which flows unimpeded into space. As before, the mean temperature must be below the blackbody temperature, and so there will be a lot of frozen ocean; much more than at present with mean temperatures about 15 degrees higher. But ice has a very high albedo, of around 0.5 to 0.7. So this means the Earth's albedo will actually end up higher than the current albedo, and then exactly as in the case (A) above, you end up with effective blackbody temperatures a long way below freezing, and a mean surface temperature
less than -18
oC as before.
As before, removing any horizontal mixing effect of the atmosphere only drives mean temperatures lower still, to shed the absorbed energy. The -18 is a strict upper bound.
So my answer to (A) and (B) is that without atmospheric interactions with thermal radiation, the temperature of the Earth's surface would have an average temperature of something less than -18
oC, and it would freeze solid. If you can explain your method in similarly quantified terms, it will help to see where the differences lie.
Question 2. What calculations or physical theory would you apply to estimate the effects in either case (A) or (B) above?
As a reference for my conclusions, the consequence of atmospheric interaction with thermal radiation I am using was first identified by John Tyndall, in the mid nineteenth century. See: "Contributions to Molecular Physics in the Domain of Radiant Heat" (Tyndall, 1872) (
17 Mbyte djvu file, 446 pages). Pages 421-424 contain a public lecture from 1863, in which he describes the freezing consequences that would occur without the capacity of the atmosphere to interact with thermal radiation. This remains basic in modern thermodynamics, and a part of any course in atmospheric physics.
Actually, the warming due to moderation is four times the warming due to the radiation-interfering effects of the atmosphere.
Question 3. I know what the word "moderation" means, but not as a technical term in thermodynamics for any specific effect. How do you obtain that factor of 4? Do you have a reference for this effect?
I think I have made a reasonable guess at this further on... but having in your own words would be better.
Actually, that value I gave is wrong...should be more like 220K or 225K. A good reference for this [and the same place I found the information on sub-surface temperatures of the moon] is "Lunar Sourcebook: A user guide to the Moon" (available via google books).
Ok, that's fine. It's more in line with what I would expect; especially given the even lower values at the landing sites for Apollo 15 and 17. But I could not find a one value for the calculated mean temperature over the whole surface in that reference.
My number is not incorrect if one is asking about the "effect of the atmosphere on Earth's temperature." Those sources that site "-18" or "-19" mix and match their numbers. They say they are calculating the blackbody temperature of the Earth without its atmosphere, but then they calculate the albedo of the Earth as though it had an atmosphere!
You described the number as (quote) "The blackbody temperature of the Earth". That is a well understood technical number; it is a radiating temperature for the whole planet, as measured from space, right now. This temperature for Earth is 255K, or -18
oC, and it is about 33 degrees cooler than the radiating temperatures at the surface, below our atmosphere. I gave references for it previously. It is a measurable quantity for our planet.
Of course, you could also try to calculate the temperature that would result if the whole atmosphere was stripped from the Earth somehow, and considering that the albedo would change. This is not the same thing, but I have shown a calculation above. It would freeze much of the ocean, since the radiating temperature would now be the same as the surface temperature, and this would in turn drive the albedo to very high values, dropping the mean surface temperature to well below the current planetary blackbody temperature of -18
oC.
You can breakdown the effect of the Earth's atmosphere (which is about 73 degrees C total) into three units:
1. Heating effects due to radiative interference -> 33 degrees
2. Cooling effects due to radiative interference -> -22.5 degrees
3. The general warming that exists due to moderation of temperature with no reference to radiation. -> ~50.5 degrees
References or methods of calculation would help here as well. However, I can work back from your numbers to figure out how they are obtained. Let me know if I have understood or not.
Point (1) I can understand. It is the difference between temperatures measured by the radiation going into the space, and temperatures at the surface below the atmosphere; taking temperatures which would give the appropriate amount of energy if uniform over the surface. It is, in fact, a quantification of the atmospheric greenhouse effect.
Point (2) is, I think, a measure of the effects of plantary albedo. Is that right? But remember, the atmosphere is not the only source of albedo! The bare surface albedo is greater than 0.06 (the low value for open ocean). By figures from Trenberth et al (2009), cited in msg #2, overall surface albedo is 23/184 or 0.125; similar to the Moon. Using 341.5 W/m
2 as the solar input, we get the following table:
\begin{array}{l|l|l|l}<br />
\text{Albedo} & \text{Energy flux} & \text{blackbody temperature (C)} \\<br />
\hline<br />
0 & 341.5 & 5.4 & \text{(Completely black planet)}\\<br />
0.06 & 321 & 1 & \text{(Planet all open ocean)} \\<br />
0.125 & 299 & -3.7 & \text{(Estimated albedo for Earth's surface only)} \\<br />
0.3 & 239 & -18 & \text{(Actual albedo for Earth)}<br />
\end{array}
So the cooling effect we can attribute to planetary albedo in total is about 23.5 degrees... similar to what you have given. The cooling effect of
atmospheric albedo, on the other hand, is a difference with bare surface albedo, and corresponds to about 14 or 15 degrees. Note also that this is still not the same as just removing the atmosphere, because the consequent freezing of the ocean would raise the surface albedo considerably, to be in the end higher than what we have at present.
Your point (3), is, I think, the consequence of horizontal heat transport and thermal inertia to help equalize temperatures around the globe. Without these effects, each point on the surface would simply be a blackbody temperature for the solar input incident on that particular point.
But here again, this is not only an atmospheric effect. The atmosphere has a role, but not as much as the ocean. The heat transport of ocean currents is larger than atmospheric transports. Even under sea ice the ocean continues to move heat around the surface. Also, the Earth has a much shorter day than the Moon, and water has a very high capacity to absorb heat. This is a stark contrast to the Moon with a month long "day", and a regolith surface.
Your number of -50.5 is very similar to the difference between backbody temperature of the Moon (270K) and mean surface temperature of the Moon (220K). This is completely useless for the Earth, even without an atmosphere.
My beef is that people refer to the first in isolation to the second...comparing Earth to a contrived version where only the warming radiative effects of its atmosphere are considered without reference to the cooling effects of its atmosphere and clouds (clouds that would not exist without the presence of an atmosphere...and in fact would not exist in a different atmosphere). My second beef is that the warming that is due to moderation (which makes the Earth a less efficient S-B radiator) is ignored completely, even though it dwarfs the combined radiative effect.
Given your numbers, I suspect that by "moderation" you mean the effects of thermal inertia and horizontal heat transport to help equalize temperatures around the globe.
Consider this. The heat capacity of water is 4186 J/K/kg. One meter depth of water has 1000 kg per m
2. At a temperature of, say, 25
oC, or 298K, water radiates approaching 450 W/m
2; cooler temperatures will be less, of course. But radiating all night (12 hours), one meter depth of warm water will shed almost 20 MJ of energy. That's enough to drop temperatures nearly 5 degrees. This still neglects all the effects of ocean currents to share temperatures around. Actual diurnal temperature ranges for the ocean are less than this, and certainly less than the 260 degrees of diurnal temperature variation on the Moon! Without an atmosphere, the mixing depth of the surface ocean layers is quite small, around a meter or so. This is what we see now in still air. Without the backradiation, the ocean will radiate quite efficiently, but the very high heat capacity still strongly damps any variation from day to night. Having about 5 degrees in the diurnal temperature range for the ocean is a reasonable upper bound.
Although it is certainly possible to look at temperature effects of thermal inertia, albedo, and horizontal heat transport, none of them are exclusive to the atmosphere only, and none of them invalidate the conventional calculation of the contribution of our atmosphere's greenhouse effect.
Finally, you really need to take into account that backradiation is a directly measured quantity. The earliest direct measurements were in 1954, and they confirm that as far as influx of energy to the surface, which is required to balance the large amount heat being radiated, atmospheric backradiation is the largest energy input to the surface, even larger than what is absorbed from the Sun. This can only happen because the atmosphere is able to interact with thermal radiation. Reference:
Cheers -- sylas
I hope it may be of some help. This gets a bit long; but I've found it interesting and worth recording.