Guest Post by Ira Glickstein
Solar “light” radiation in = Earth “heat” radiation to Space out! That’s old news to those of us who understand all energy is fungible (may be converted to different forms of energy) and energy/mass is conserved (cannot be created nor destroyed).
My Visualizing series [Physical Analogy, Atmospheric Windows, Emission Spectra, and Molecules/Photons] has garnered almost 2000 comments, mostly positive. I’ve learned a lot from WUWT readers who know more than I do. However, some commenters seem to have been taken in by scientific-sounding objections to the basic science behind the Atmospheric “Greenhouse Effect”. Their objections seemed to add more heat than light to the discussion. This posting is designed to get back to basics and perhaps transform our heated arguments into more enlightened understanding :^)
As I’ve mentioned before, during my long career as a system engineer I’ve worked with many talented mathematical analysts who always provided precise results, mostly correct, but some precisely wrong, usually due to mistaken assumptions. I got into the habit of doing a “back of the envelope” calculation of my own as a “sanity check” on their results. If their results matched within reasonable limits, I accepted them. If not, I investigated further. In those days my analysis was really done using a slide rule and scrap paper, but I now use spreadsheets.
The graphic above is based on an excellent spreadsheet from http://serc.carleton.edu/files/introgeo/models/mathematical/examples/XLPlanck.xls. It uses Planck’s Law to calculate the black body radiation spectrum from the Sun, as observed at the top of the Earth’s Atmosphere. It also may be used to calculate the radiation spectrum from the Earth System (Atmosphere and Surface, see below for explanation) at any assumed temperature. (I will refer to this spreadsheet as “Carleton” in this posting.)
I modified the Carleton spreadsheet to compute the mean Solar radiation per square meter absorbed by the Earth System, which turns out to be 240 Watts/m^2. I then used the spreadsheet to determine the effective mean temperature of the Earth System that would emit an equal amount of energy to Space, and that turned out to be 255 Kelvins (-18ºC which is 1ºF).
Since the mean temperature at the surface of the Earth is 288 Kelvins (+15ºC which is 59ºF), that leaves 33 Kelvins (33ºC which is 58ºF) to be accounted for. Guess how we acount for it?
The yellow curve (above left) shows that Solar radiation is in a tall, narrow “shortwave” range, from about 0.1μm (microns, or millionths of a meter) to about 4μm, which we call ultra-violet, visual, and near-infrared. The vertical axis is Intensity of the radiation, measured in Watts/m^2/μm, and the horizontal axis is Wavelength, measured in μm. If you divide the area under the yellow curve into vertical strips, and add up the total area, you get 240 Watts/m^2.
Since we humans sense the visual portion of this radiation as “light”, that is the name we give it, and that has led to the false assumption that it contains no “heat” (or “thermal”) energy.
The violet curve (above right) shows that, assuming a mean temperature of 255 K, Earth System radiation to Space is in a squat, wide “longwave” range, from about 5μm to beyond 40μm, which we call mid- and far-infrared. If you divide the area under the violet curve into vertical strips, and add up the total area, you get the same 240 Watts/m^2 as is under the yellow curve.
DETAILED EXPLANATION
The graph on the left shows the actual observed Solar radiation spectrum (in red) as measured at the top of the Atmosphere. It is superimposed on a black body model (in blue) showing very good correlation. Thus, while the Sun is not exactly a black body, it is OK to assume it is for this type of “sanity check” exercise.
If you calculate the area under the curve you get about 1366 Watts/m^2. That means that a square meter of perfect black body material, held perpendicular to the Sun, would absorb 1366 Watts.
However, the Earth is not a perfect black body, neither is it a flat surface perpendicular to the Sun! So, to plot the yellow curve at the top of this posting, I had to adjust that value accordingly. There are two adjustments:
- The Earth may be approximated as a sphere, with the Sun shining on only half of it at any given time. The adjustment factor for this correction is 0.25.
- The albedo (reflectiveness) of the Earth system, primarily clouds and light-colored areas on the Surface such as ice, causes some of the Solar radiation to be reflected back out to Space without contributing any energy to the Earth System. The adjustment factor for this correction is 0.7.
After applying these adjustments, the net Solar energy absorbed by the Earth System is 240 Watts/m^2.
The graph on the right shows the black body model for an Earth System at a mean temperature of 255 K, a temperature that results in the same 240 Watts/m^2 being emitted out to Space.
Of course, the Earth System is not a perfect black body, as shown by the graph in the upper panel of the illustration below, which plots actual observations from 20 km looking down. (Adapted from Grant Petty, A First Course in Atmospheric Radiation, Figure 8.2, http://www.sundogpublishing.com/AtmosRad/Excerpts/index.html.)
The actual measured radiation is the dark squiggly curve. Note that it jigs and jags up and down between the topmost dashed curve, which is the black body spectrum for a temperature of 270 K and a lower dashed curve which is the black body spectrum for 230 K. This data was taken over the Arctic, most likely during the daytime. The Petty book also has a graph looking down from over the Tropical Pacific which ranges from 300 K down to 210 K. Observations will vary by tens of degrees from day to night, summer to winter, and Tropical to Polar.
However, it is clear that my result, based on matching 240 Watts/m^2, is within a reasonable range of the true mean temperature of the Earth System as viewed from Space.
NOTE ABOUT THE ABOVE ILLUSTRATION
WUWT readers will notice some apparent inconsistencies in the graphs above. The top and bottom panels, from Petty, peak at 15μm to 20μm, while the purple, blue, and black curves in the middle panel, and the Earth System curves from the Carleton spreadsheet I used (see above) peak in the 9μm to 11μm range. Also, the Petty black body curves peak at a “Radiance” around 100 mW/m^2/sr cm^-1 while the black body curves from Carleton peak at an “Intensity” of around 14 W/m^2/μm. Furthermore, if you look closely at the Petty curves, the labels on the black body curves are mirror image! What is going on?
Well, I know some of the reasons, but not all. (I hope commenters who are more fluent in this than I am will confirm my explanations and provide more information about the differences between “Radiance” and “Intensity”.) I have Googled and Wikied the Internet and am still somewhat confused. Here is what I know:
- The horizontal axis in Petty’s plots are what he calls “Wavenumber”, increasing from left to right, which is the number of waves that fit into a cm (centimeter, one hundredth of a meter).
- This is proportional to the frequency of the radiation, and the frequency is the inverse of the wavelength. Thus, his plots are the mirror image of plots based on wavelength increasing from left to right.
- The spreadsheet I used, and my previous experience with visual, and near-, mid-, and far-IR as used in military systems, always uses wavelength increasing from left to right.
- So, when I constructed the above illustration, I reversed Petty’s curves, which explains why the labels on the black body curves are mirror image.
- Fortunately, Petty also included a wavelength legend, which I faithfully reproduced, in non-mirror image, at the top of each plot.
But, that still does not explain why the Petty black body curves peak at a longer wavelength than the Carleton spreadsheet and other graphics on the Internet. I tried to reproduce Petty’s blackbody curves by multiplying the Carleton values by the wavelength (μm) and that did not move the peak to the right enough. So, I multiplied by the wavelength again (μm^2) and, voila, the peaks agreed! (I hope some WUWT reader will explain why the Petty graphs have this perverse effect. advTHANKSance!)
ANSWERING THE OBJECTIONS TO BASIC ATMOSPHERIC “GREENHOUSE EFFECT” SCIENCE
First of all, let me be clear where I am coming from. I’m a Lukewarmer-Skeptic who accepts that H2O, CO2 and other so-called “greenhouse gases” in the Atmosphere do cause the mean temperature of the Earth Surface and Atmosphere to be higher than they would be if everything was the same (Solar radiation, Earth System Albedo, …) but the Atmosphere was pure nitrogen. The main scientific question for me, is how much does the increase in human-caused CO2 and human-caused albedo reduction increase the mean temperature above what it would be with natural cycles and processes? My answer is “not much”, because perhaps 0.1ºC to 0.2ºC of the supposed 0.8ºC increase since 1880 is due to human activities. The rest is due to natural cycles and processes over which we humans have no control. The main public policy question for me, is how much should we (society) do about it? Again, my answer is “not much”, because the effect is small and a limited increase in temperatures and CO2 may turn out to have a net benefit.
So, my motivation for this Visualizing series is not to add to the Alarmist “the sky is falling” panic, but rather to help my fellow Skeptics avoid the natural temptation to fall into an “equal and opposite” falsehood, which some of those on my side, who I call “Disbelievers”, do when they fail to acknowledge the basic facts of the role of H2O and CO2 and other gases in helping to keep temperatures in a livable range.
Objection #1: Visual and near-visual radiation is merely “light” which lacks the “quality” or “oomph” to impart warmth to objects upon which it happens to fall.
Answer #1: A NASA webpage targeted at children is sometimes cited because they say the near-IR beam from a TV remote control is not warm to the touch. Of course, that is not because it is near-visual radiation, but rather because it is very low power. All energy is fungible, and can be changed from one form to another. Thus, the 240 Watts/m^2 of visible and near-visible Solar energy that reaches and is absorbed by the Earth System, has the effect of warming the Earth System exactly as much as an equal number of Watts/m^2 of “thermal” mid- and far-IR radiation.
Objection #2: The Atmosphere, which is cooler than the Earth Surface, cannot warm the Earth Surface.
Answer #2: The Second law of Thermodynamics is often cited as the source of this falsehood. The correct interpretation is that the Second Law refers to net warming, which can only pass from the warmer to the cooler object. The back-radiation from the Atmosphere to the Earth Surface has been measured (see lower panel in the above illustration). All matter above absolute zero emits radiation and, once emitted, that radiation does not know if it is travelling from a warmer to a cooler surface or vice-versa. Once it arrives it will either be reflected or absorbed, according to its wavelength and the characteristics of the material it happens to impact.
Objection #3: The Atmospheric “Greenhouse Effect” is fictional. A glass greenhouse works mainly by preventing or reducing convection and the Atmosphere does not work that way at all.
Answer #3: I always try to put “scare quotes” around the word “greenhouse” unless referring to the glass variety because the term is misleading. Yes, a glass greenhouse works by restricting convection, and the fact that glass passes shortwave radiation and not longwave makes only a minor contribution. Thus, I agree it is unfortunate that the established term for the Atmospheric warming effect is a bit of a misnomer. However, we are stuck with it. But, enough of semantics. Notice that the Earth System mean temperature I had to use to provide 240 Watts/m^2 of radiation to Space to balance the input absorbed from by the Earth System from the Sun was 255 K. However, the actual mean temperature at the Surface is closer to 288 K. How to explain the extra 33 K (33ºC or 58ºF)? The only rational explanation is the back-radiation from the Atmosphere to the Surface.
All matter above absolute zero emits radiation and, once emitted, that radiation does not know if it is travelling from a warmer to a cooler surface or vice-versa. Once it arrives it will either be reflected or absorbed, according to its wavelength and the characteristics of the material it happens to impact.
But will be reflected by a body of a higher energy level.
http://www.vermonttiger.com/content/2008/07/nasa-free-energ.html
In fig. 3 a box states:
CO2 & H2O ~15µ absorption; re-emit 7µ, 10µ, 15µ.
But re-emission at a higher frequency (shorter wavelength) than the original absorption is not possible.
Notice that the Earth System mean temperature I had to use to provide 240 Watts/m^2 of radiation to Space to balance the input absorbed from by the Earth System from the Sun was 255 K. However, the actual mean temperature at the Surface is closer to 288 K. How to explain the extra 33 K (33ºC or 58ºF)? The only rational explanation is the back-radiation from the Atmosphere to the Surface.
255K is the mean earth radiative temperature at around 4,000 metres altitude and above. Escaping IR radiation is from a volume of the atmosphere, not a flat surface.
The mean surface temperature of 288K is simply the compression factor of gravity on the air. Air at the surface has the highest density and returns highest temperature. Think deserts, polar regions, equitorial regions. All very different suface temperatures but always the same adiabatic lapse rate, water vapour content allowing.
http://www.vermonttiger.com/content/2008/07/nasa-free-energ.html
………
Figure 3 has a box which states:
CO2 & H2O ~ 15µ absorption; re-emit 7µ, 10µ, 15µ.
a body cannot re-emit at a higher frequency (energy level) than it absorbs.
There is a bathtub which can hold energy. (the earth’s atmosphere/surface/oceans)
There is a energy tap flowing into it. (the sun)
There is a hole in the tub where energy flows out. (radiative emission into space)
Inflow = outflow, energy in = energy out.
The quantity of energy the black-box “bathtub” is able to hold (wants to hold) can go up and down and is indicated by the temperature. When the variables which alter the level stored in the tub are changed (knobs turned) there will be an imbalance between inflow and outflow until the new equalibrium is reached – a equilibrium at which a different level of energy is stored in the tub. We expect a change in the total level of energy stored to affect the temperature at the bottom of the tub.
I expect the IR interference to be one of those variables but I’m sure there are many others. The claim that 30 degrees celsius at the surface is all due to the greenhouse effect is rubbish.
3 scenarious.
A. Black body earth (-30 % albido).
B. Earth with atmosphere and no IR interference.
C. Earth with atmosphere and IR interference.
A is cooler than B is cooler than C.
C – B = greenhouse warming.
Davidmhoffer,
The ground and ocean warm the lower levels of the atmosphere in the polar winters.
Does anyone else wonder what the rate of heat transfer to the surface is from conduction through the crust from the mantle?
We can account for the 33C difference without any need for an imaginary greenhouse effect. I urge everyone at WUWT to read this brilliant paper by physicist Joe Postma ;
http://www.globalwarmingskeptics.info/forums/attachment.php?aid=327”
Agree it was a brilliant paper. But this Postma paper was posted on Ira’s previous thread and Ira and others criticised the paper or would not read it all.
http://wattsupwiththat.com/2011/03/29/visualizing-the-greenhouse-effect-molecules-and-photons/
Ira Glickstein, PhD says March 30, 2011 at 2:02 pm
This post by Ira has not really moving forward at all with Ira still posting this for example
“How to explain the extra 33 K (33ºC or 58ºF)? The only rational explanation is the back-radiation from the Atmosphere to the Surface.”
This is just total nonsense. (The only rational explanation). It is one explanation and not a very good one. Unfortunately Ira is just ignoring comments on previous thread so this series is not moving forward. He could summarise the main areas of contention without giving a viewpoint rather than posting again his beliefs that he knows many disagree with
Engineering covers a considerable range of displines such as chemical, civil, electrical, mechanical etc. Heat transfer, thermodynamics, fluid dynamics are basic subjects for some of these disciplines but are not taught in all the disciplines. It is not surprising that some engineers do not understand the fundamental theory and experimental knowledge in these subjects. It is surprising, however, that qualified professional engineers who supposedly comply with a code of ethics which includes the requirement of competence should express opinions about a subject which they do not understand.
Ira, you have been sucked in by climate scientists who have no understanding of heat transfer, fluid dynamics and thermodynamics. You make no mention of heat transfer by convection and phase change (evaporation and condensation). One can only assume that you have no knowledge of this subject. For a quick overview I suggest that you look at Perry’s Chemical Engineering Handbook. Learn about Nusselt and Reynolds numbers. Also, take note of the definition of a black body -it has a surface, and all absorbs energy of all wavelengths. The atmosphere is not a surface and the trace gas CO2 only absorbs radiant energy in very narrow wavelengths ie it is not a black body. The basic Stefan Boltzman equation is not applicable to the atmosphere. Engineers have carried out a huge amount of research on radiation involving gases in heat exchangers.
Then read the following http://climategate.nl/wp-content/uploads/2011/02/CO2_and_climate_v7.pdf
Dishman says:
Ballistic trajectories are trajectories under the action of gravity. Note, he didn’t say they travel in straight lines.
However: the approximate speed of molecules in the atmosphere is about 1,700 km/h. The path isn’t very curved, in other words. And the mean free path of a molecule in air is about 65 nanometres. You’d be pretty amazing if you could measure the deviation from a straight line of a path segment with that length and curvature.
I’m reading the post by Joe Postma now. He appears to be saying my energy tub can only be filled to a maximum level and can’t hold more after that.
It already occurred to me that climate scientists didn’t really have any firm understanding of the mechanism of action of the greenhouse “theory”, hence this very subject has been at the front of my mind lately, hence my bathtub theorizing. I’m glad to see this particular issue is slowly but surely coming to a head.
If Joe is right they’ll just start saying that energy is being redistributed in a way to make the surface warmer.
Bryan,
I read the link you gave, and the guy got it partially wrong. He stated that a black body near a light bulb in equilibrium would not heat up if a reflector was then introduced to reflect back onto the black body some of the radiated heat. This is wrong. The black body would absorb the reflected radiation, and thus the equilibrium temperature would be increased. However, this is not related to the back radiation issue. The main remainder of yours and his points are correct, i.e., it is the effective average altitude of outgoing radiation and lapse rate that heats the surface, and backradiation is a consequence rather than cause of the heating. The reason is that buoyancy overcomes absorbed radiation heat transfer to prevent stagnant heating from the radiation.
John of Kent says:
Firstly, I do wish that people who think they know something would just be polite about it; this is not a peer-reviewed journal (thank goodness). Anthony is offering a wonderful service here. The way I look at it is: the entire article, including comments, is the publication. If an article contains fallacies, we will learn from the more knowledgeable commenters.
Having said that, you are not one of those more knowledgeable commenters. All radiators are absorbers. Contrary to your assertion, anything capable of emitting a certain wavelength at a certain temperature can absorb ditto. So yes, a photon radiated back towards the surface can indeed be absorbed by the surface. What this absorption will do, however, is raise the temperature slightly so that the surface now emits at a higher rate. Heat still travels on average from hot to cold. The temperature increase of the hotter surface, whilst happening only if the back radiation is happening, still comes about because of the impinging heat from the sun.
Think of it this way: focus a flame upon a single cubic inch of steel that happens to be part and parcel of a massive steel girder. The flame’s heat will flow into the steel all around and you will find it very hard to increase the temperature of the cubic inch by very much. Now focus your flame on a cubic inch embedded in another surrounding cubic inch, embedded in a very poor conductor. Your heat will heat the first cubic inch, which will heat the second. The poor conductor will prevent escape of much heat and the molecules of steel will bump upon each other. Molecules in your first cubic inch will bump (heat) those in the second, those in the second will bump those in the first. The entire two cubic inches will quickly increase in temperature. The outer cubic inch will never become hotter than the cubic inch being directly heated, and yet the directly heated part will rise in temperature. So there is such a thing as back flow of heat and it is by no means contrary to the 2nd law.
But having said that, the idea of back radiation as formulated by some warmists doesn’t hold much water. The most likely thing to happen to a CO2 molecule that has absorbed a photon and risen to a higher energy state is that it will collide with another molecule and transfer the energy into general heat of the whole gas. When that heats the gas enough, then the number of CO2 molecules undergoing the reverse phenomenon (getting knocked into a higher state by an impinging molecule – remember, these processes are always reversible) will rise enough to provide enough radiation that back radiation becomes significant. But there is a huge heat capacity to fill before that point is reached, since the CO2 is a trace gas heating a vastly huger bulk of N2, O2 etc. In the meantime, the heating of the gas starts convection, limiting the rise in lower air temperature to the adiabatic lapse rate. So once again, the back radiation has its effect auto-limited. Since all planets we see (Earth, Venus, Jupiter) are at close to maximum lapse rate, this is clearly a phenomenom that is quickly reached by almost any trace amounts of greenhouse gas in the atmosphere, and so the mechanism required for the AGW theory to work is already exhausted to within a few percent, and thus the phenomenon is basically harmless.
Ira,
I enjoyed your clear presentation of detail until I saw the kicker “How to explain the extra 33 K (33ºC or 58ºF)? The only rational explanation is the back-radiation from the Atmosphere to the Surface.”
There have been several good presentations of the correct reason. The presence of IR absorbing gases acts as a partial radiation insulator. However, the atmosphere is unbounded, so if there were even a small amount of local heating occurs due to absorbing IR, the warmer air would rises and then cool by adiabatic expansion. In fact, the atmosphere mixes and rises so strongly, that noticeable radiation warming does not occur. The absorbed radiation passes energy into the surrounding air, but the more energetic air molecules (from the velocity distribution) impacting the absorbing molecules cause radiation, and the average is so in balance that the air is considered to be in LTE. However, the fact of the partial radiation insulation (i.e., prevention of direct radiation to space) results in the radiation to space occurring at higher altitude (average about 5 km), and it is the adiabatic lapse rate combined with the equilibrium temperature at 5 km that results in the ground temperature. The back radiation and ground up radiation are a result of the increased temperature, not the cause!
I didn’t think he was right with the mirror example. If you shine a bright torch and a dim torch at a object it will get hotter than if you shone only the bright torch. If you shine the bright torch and reflect a mirror at the object it’s like adding another dimmer torch.
“Heat always passes from hot to cold, never the other way round, THERE ARE NO EXCEPTIONS!”
What about the sun corona? It’s a million degree and sun surface is cooler.
Perhaps you referring to solids. Such as warm air can not heat up a warmer surface via radiant energy.
Say, you had an object in space and it’s temperature was 100 K. This is a cold object, -173 C but compared to background temperature of Space 2.7 K it’s fairly warm. And it is certainly radiating energy into space. No part of earth is as cold as 100 K, if colder can not pass to warmer this means that with infrared telescope on Earth you could never detect such a cold object in space. It also means that your telescope mirrors would need to as cold or colder than any cool object you wanted to observe.
* Blackbody – As you have stated, the inbound radiation spectrum from the Sun can be approximated as black body (at it’s temperature) and from the surface (at it’s temperature). The implication being, a blackbody emits in a radiant distribution dependant on it’s temperature. But you incorrectly indicate that Atmosphere is also a black body and it is NOT.
“It also may be used to calculate the radiation spectrum from the Earth System (Atmosphere and Surface, see below for explanation) at any assumed temperature. ”
If CO2 absorbs at 15 micron, it also emits at 15 micron (not a blackbody distribution of all wavelengths based on atmospheric temperature). So where your chart says CO2 ‘Re-Emit 7, 10, 15 micron’ – that is not correct. Similarly for H2O. The purple, blue and black curves in your atmosphere graphic have no meaning.
The ‘looking down’ emission spectrum tells you where the energy was emitted if you look at the temperature curves. The atmospheric window wavelengths are like the surface temperature, cold from the antarctic, hot from the Sahara, with no emission from the intermediate atmosphere. The CO2 wavelengths always look like the tropopause temperatures no matter if they are measured over the desert or the poles, which tells us we are seeing emissions from high in the atmosphere, not re-emitted near the surface. And the H2O wavelengths seem to be in between, more like upper atmosphere and perhaps indicative of cloud tops or ice crystals.
But ‘looking down’ distribution doesn’t look like a one-temperature blackbody distribution. Using a one size fits all blackbody emission from the atmosphere at any one temperature is probably not a good assumption.
Radiant energy accounts for all of the outbound energy at the top of atmosphere, but only a fraction of the energy transfer at the surface. Understanding how the energy moves up through the atmosphere via non-radiative pathways is key in estimating potential GHG effects.
If we use values from Kiehl & Trenberth 1977, they show 60% of the surface energy transfer to the atmosphere is due to Thermals (convection) plus Evapo-transpiration (water evaporation and release as latent heat). Leaving no more than 40% as Radiant Energy transfer, with 24% of that 40% as direct loss to Atmospheric Window. Whatever the GHG affects may be, they are happening in the 16% of the total that is left. (And I read somewhere that Trenberth used 40 W / m-2, knowing that the actual ‘window’ value was more like 66 W/m-2. That would increase the ‘atmospheric window’ from 24% to about 39%, leaving only about 1% of the total for the net of all other radiant emissions).
How can that be, since we know the surface emits a blackbody distribution dependent on the surface temperature? One possible explanation is to look at what the energy ‘pathway’ might be. Sort of by definition, the radiant energy that is NOT in the atmospheric window wavelengths, is susceptible to being absorbed by one of the GHG, mostly CO2 and H2O. So the surface emits radiant energy, and the GHG susceptible wavelengths are absorbed fairly close to the surface. Next, we think that the absorbed photons are more likely to be ‘thermalized’ rather than re-emitted as photons (10,000 : 1 more likely thermalized). Thermalized means the GHG molecule collides with a non-GHG molecule in the air, converting the photon to kinetic energy, which can now be seen on a thermometer. Now all of the non-radiative pathways take over. In essence, the radiant emissions from the surface have ‘speeded up’ the energy transfer to get the energy into the other pathways. Hot air rises, clouds and thunderstorms happen when conditions are right, and generally energy moves up through the atmosphere at something like the wet or dry Lapse rate, as appropriate to conditions. When the energy gets high enough, the radiant pathways again become significant, and eventually take over, sending the energy out to space.
Of course the devil is in the details, but that description seems to fit with what others have said earlier. It is not all about just the radiant component.
“The only rational explanation is the back-radiation from the Atmosphere to the Surface.”
There’s an objection you haven’t addressed yet – that if extra heat tried to build up near the surface, convection would immediately carry it away again because warm air rises.
In an atmosphere without convection, it would indeed work as you suggest, and the Earth’s surface temperature would be about 60 C on average. When we stop convection artificially – with greenhouses and solar ponds – we do get much higher temperatures. But the mechanism doesn’t apply in a convective fluid, and the 60 C prediction (and other things like an exponential relationship of temperature with altitude) conflicting with observation falsify it.
The back-radiation explanation (or the “shells model” as I sometimes call it) was the original one developed by De Saussure, Fourier, etc. and was overturned in the 1960s by the work of Manabe, Moller, Strickler, and others. The actual explanation is that extra greenhouses gases raise the average altitude of emission to space, raising the altitude of the level that equilibrates to -20 C, and the warmth of the surface relative to this level is due primarily to the adiabatic lapse rate (adjusted for water vapour latent heat).
The surface temperature is the effective radiative temperature (-18 C) plus the average height of emission (5.5 km) times the (moist) adiabatic lapse rate (6 C/km).
T_surf = T_eff + z_emiss * MALR.
The CO2 greenhouse works by increasing z_emiss.
The tropical hotspot, incidentally, is supposed to be caused by also decreasing MALR, through water vapour feedback.
I’m very pleased to see a lot of people now picking up on the convection/lapse rate connection. Things have much improved over a few years ago.
Leonard Weinstein
……”The black body would absorb the reflected radiation, and thus the equilibrium temperature would be increased.”……
Yes I agree, he could have been clearer on that point.
This aspect causes a great deal of confusion and some intellectual mischief.
See if you would agree with this formulation.
The reflected radiation is the reflective insulation component.
If increased it will slow down the heat loss from the black body.
If the black body has an unchanged energy input its equilibrium temperature would be increased.
However if the energy input to the black body was cut off the temperature of the black body would drop despite the backradiation.
Ira, explaining the 33K temp difference between surface and top of atmosphere in terms of LWIR backradiation AKA greenhouse gas effect is misleading; as it is already entirely explained by the adiabatic lapse rate.
(see for instance William C. Gilbert here
http://bit.ly/fIhWPS
)
This leaves us with the question – if the lapse rate explains the temp difference, why does the purported greenhouse effect contribute nothing – to which my answer would be: As Absorption and re-emission of LWIR is an extremely fast process the re-radiation process can only delay heat transport via LWIR radiation to space by minutes at best – it’s a ping pong game of photons, but no heat is “trapped”, no matter how often Dessler et. al. use the term “heat-trapping gases” ( see here:
http://www.chron.com/disp/story.mpl/editorial/outlook/6900556.html
)
If this delay rises by a few percent due to increased CO2 levels then it is still only a short term delay.
And that is why we see no warming related to CO2 (if there were such warming, it would correlate to the Keeling curve, which it doesn’t).
And i see that others have mentioned Postma. A very good explanation of the lapse rate.
The 33K is the result of the warming by gravitational potential energy of the atmosphere below the -18°C isotherm determined by equality of radiation out to radiation in. It’s about 5.5 km. Because it would be the same for an atmosphere of the same average Cp but without GHGs, it is unconnected to greenhouse warming.
All that does is to provide extra heat in the lower atmosphere and it’s convected to the top where it can radiate away. In the absence of convection, we’d get another 44K warming so the convection/negative feedback is extremely efficient.
If you increase [CO2], [H2O] ust decrease in the upper atmosphere, as observed in 61 years’ radiosonde data. The mechanism is whatever is consistent with the 2nd Law’s requirement of maximum rate of entropy production.
Climate science’s confusion over greenhouse warming comes from the mistake made by Arthur Milne in 1922 when he solved a differential equation for IR absorption in the atmosphere using as boundary condition infinite thickness. The term it generated, extra ‘back-radiation’ is imaginary.
This is not to say there is no back-radiation: that is essential to match exactly the IR radiation from the atmosphere below that point in specific spectral ranges consistent with the local deviation from the lapse rate, e.g from clouds. So, the spectral curve will vary depending on whether there are clouds for example.
The problem is that most scientists haven’t a clue about practical conductive, convective, radiative heat transfer so are easy meat for the charlatans who have made a good career out of pretending there’s an effect of CO2. As an exercise they need to understand the UHI effect is caused by convective heat transfer. You get higher temperature because to get the required thermal equilibrium, you need more radiative flux from the Earth’s surface. Yet the sum of all the heat transfer components, equal to the short wave heating, remains the same once you have exhausted thermal storage effects.
Similarly, at night, you can freeze water by digging a hole in the desert to restrict convection even though air temperatures can be 20°C+.
Before anyone else contributes, they need to know some chemical engineering: http://rpaulsingh.com/teaching/LectureHandouts/Convection%20Heat%20Transfer_handout.pdf
davidmhoffer says:
May 8, 2011 at 3:19 am
“Why doesn’t it keep cooling off? After all, the atmosphere above the arctic is even colder than the arctic itself… Heck, at 25,000 feet its colder than that even at the equator! So… with 0 watts/m2 from the sun, the arctic nonetheless sticks right around -26 degrees. Hmmmmm…..wonder what keeps it from cooling off more….”
David, if the atmosphere above the arctic is colder than the arctic surface, do you want to imply here that this cold atmosphere is nevertheless capable of WARMING the surface? Are you sure you wanted to say that?
Ira:
As a sanity check you should do this calculation for the moon which receives exactly the same amount of solar radiation as the earth system and there’s no atmosphere or water to complicate the situation. Further, the average surface temperature of the moon was experimentally measured by two separate Apollo experiments where a borehole 3 meters deep was made and a probe with thermocouples at various depths was put into the boreholes. These experiments transmitted temperature data back for several years. The average temperature of the surface is that depth at which there is no daily, seasonal, or annual variation i.e. a constant year-round temperature. At two mid-latitude locations that temperature is -23C or -9F at all depths of 1 meter or more. The experiments were actually designed to measure the thermal conductivity of lunar regolith.
So it would appear on the face of it that your theoretical figure for the earth of 33C warmer than it would be for two approximate black bodies is somehow in disagreement with experimental reality by about 5C.
So before talking about the earth as an approximate black body, which we can’t measure because it ain’t one with a dynamic ocean/atmosphere wrapping it, you have to do a sanity check and see if your black body calculations agree with the measured temperature of the moon which actually is an approximate black body.
I can’t possibly take seriously any discussion which hinges on this commonly number that the earth is 33C warmer than it would be sans ocean and atmosphere when it appears to be 5C smaller than experimental observations. Near as I can tell from the facts that number should be 38C. Normally when two numbers like that differ by something near 10% I shrug it off because it’s still pretty close to agreement. But in this case 5C of disagreement five times greater than the commonly claimed 1C of anthropogenic warming to date.
This goes to the heart of the problem. Anthropogenic effects are so tiny as to easily buried in the noise of the real world and in the error margins of all these toy models of the real world.
This makes sense. Absent CO2 and water vapor, we would freeze. How much warming does each contribute? If CO2 did it all, and mankind producses about 3% of the CO2, then we are responsible for 3% of the 33C warming or about 1C. Thus AGW is real. Except for water vapor which may cause 90% of the 33C, in which case we cause 0.1C warming. Big deal. Given the daily and seasonal variations in temperature, I find it very hard to believe that 0.1C will have any measureable effect. Or be measureable at all.
“How to explain the extra 33 K (33ºC or 58ºF)? The only rational explanation is the back-radiation from the Atmosphere to the Surface.”
Are we suggesting that the earth’s surface is one black body and the atmosphere another? And thus the atmosphere radiates to the surface? However, the atmosphere and the surface are part of the same black body at TOA. Treating them separately below TOA may lead to nonsensical results.
A more reasonable explantion is that the missing 33 K is due to the weight of the atmosphere which compresses the gas nearer the surface, which we see as an increase in temperature.
We know this by comparing the atmospheres of Venus (CO2), Earth(N2O2) and Mars (CO2). All three planets show that temperature varies as the pressure of the atmosphere and the distance from the sun, independent of the composition of the atmosphere.
Venus is totally covered in clouds. If albedo has a 30% blocking effect on earth, then it should have a near 100% blocking effect on venus and the surface should be cold. But it is not.
If CO2 has a warming effect, the mars, which has a greater partial pressure of CO2 at the surface than does earth, should be warm, but it is not.
Climate science continues to build models. Why? Because the argument goes that their is only one earth, so we need models to tell us the effects of CO2 on climate.
This is a rubbish argument. Our two nearest neighbors have CO2 rich atmosphere. These are perfect models for us to judge if the GHG theory is correct, but climate science continues to ignore this more accurate alternative.
We hear about “run-away” greenhouse effect on Venus, without any explanation of how this is possible with 100% cloud cover if albedo and aerosols works as we think they do.
The facts are that the surface pressure of Venus is 90 times. Yes 90 times greater than on earth. This is why the surface temperature is high, even though according to climate theories about clouds and albedo, it should be low.
Why are the temperatures at the bottom of the oceans on earth not higher than the surface? After all this happens in the atmosphere, should it not happen in the oceans.
The reasons is compression. The oceans do not compress, so a cubic meter of surface water has the same number of molecules as a cubic meter of water from the deep oceans. However, the atmosphere does compress. So, a cubic meter of atmosphere at the surface has more molecules than a cubic meter of atmosphere higher up.
It is these molecules that carry the heat. If the energy of the molecules is unchanged, then the more you have per cubic meter, the greater the energy per cubic meter, which we will see as increased temperature.