Guest post by Ira Glickstein
The Atmospheric “greenhouse effect” has been analogized to a blanket that insulates the Sun-warmed Earth and slows the rate of heat transmission, thus increasing mean temperatures above what they would be absent “greenhouse gases” (GHGs). Perhaps a better analogy would be an electric blanket that, in addition to its insulating properties, also emits thermal radiation both down and up. A real greenhouse primarily restricts heat escape by preventing convection while the “greenhouse effect” heats the Earth because GHGs absorb outgoing radiative energy and re-emit some of it back towards Earth.
Many thanks to Dave Springer and Jim Folkerts who, in comments to my previous posting Atmospheric Windows, provided links to emission graphs and a textbook “A First Course in Atmospheric Radiation” by Grant Petty, Sundog Publishing Company.
Description of graphic (from bottom to top):
Earth Surface: Warmed by shortwave (~1/2μ) radiation from the Sun, the surface emits upward radiation in the ~7μ, ~10μ, and ~15μ regions of the longwave band. This radiation approximates a smooth “blackbody” curve that peaks at the wavelength corresponding to the surface temperature.
Bottom of the Atmosphere: On its way out to Space, the radiation encounters the Atmosphere, in particular the GHGs, which absorb and re-emit radiation in the ~7μ and ~15μ regions in all directions. Most of the ~10μ radiation is allowed to pass through.
The lower violet/purple curve (adapted from figure 8.1 in Petty and based on measurements from the Tropical Pacific looking UP) indicates how the bottom of the Atmosphere re-emits selected portions back down towards the surface of the Earth. The dashed line represents a “blackbody” curve characteristic of 300ºK (equivalent to 27ºC or 80ºF). Note how the ~7μ and ~15μ regions approximate that curve, while much of the ~10μ region is not re-emitted downward.
“Greenhouse Gases”: The reason for the shape of the downwelling radiation curve is clear when we look at the absorption spectra for the most important GHGs: H2O, H2O, H2O, … H2O, and CO2. (I’ve included multiple H2O’s because water vapor, particularly in the tropical latitudes, is many times more prevalent than carbon dioxide.)
Note that H2O absorbs at up to 100% in the ~7μ region. H2O also absorbs strongly in the ~15μ region, particularly above 20μ, where it reaches 100%. CO2 absorbs at up to 100% in the ~15μ region.
Neither H2O nor CO2 absorb strongly in the ~10μ region.
Since gases tend to re-emit most strongly at the same wavelength region where they absorb, the ~7μ and ~15μ are well-represented, while the ~10μ region is weaker.
Top of the Atmosphere: The upper violet/purple curve (adapted from figure 6.6 in Petty and based on satellite measurements from the Tropical Pacific looking DOWN) indicates how the top of the Atmosphere passes certain portions of radiation from the surface of the Earth out to Space and re-emits selected portions up towards Space. The dashed line represents a “blackbody” curve characteristic of 300ºK. Note that much of the ~10μ region approximates a 295ºK curve while the ~7μ region approximates a cooler 260ºK curve. The ~15μ region is more complicated. Part of it, from about 17μ and up approximates a 260ºK or 270ºK curve, but the region from about 14μ to 17μ has had quite a big bite taken out of it. Note how this bite corresponds roughly with the CO2 absorption spectrum.
What Does This All Mean in Plain Language?
Well, if a piece of blueberry pie has gone missing, and little Johnny has blueberry juice dripping from his mouth and chin, and that is pretty good circumstantial evidence of who took it.
Clearly, the GHGs in the Atmosphere are responsible. H2O has taken its toll in the ~7μ and ~15μ regions, while CO2 has taken its bite in its special part of the ~15μ region. Radiation in the ~10μ region has taken a pretty-much free pass through the Atmosphere.
The top of the Atmosphere curve is mostly due to the lapse rate, where higher levels of the Atmosphere tend to be cooler. The ~10μ region is warmer because it is a view of the surface radiation of the Earth through an almost transparent window. The ~7μ and 15μ regions are cooler because they are radiated from closer to the top of the Atmosphere. The CO2 bite portion of the curve is still cooler because CO2 tends to be better represented at higher altitudes than H2O which is more prevalent towards the bottom.
That is a good explanation, as far as it goes. However, it seems there is something else going on. The ~7μ and ~15μ radiation emitted from the bottom of the Atmosphere is absorbed by the Earth, further warming it, and the Earth, approximating a “blackbody”, re-emits them at a variety of wavelengths, including ~10μ. This additional ~10μ radiation gets a nearly free pass through the Atmosphere and heads out towards Space, which explains why it is better represented in the top of the Atmosphere curve. In addition, some of the radiation due to collisions of energized H2O and CO2 molecules with each other and the N2 (nitrogen), O2 (oxygen) and trace gases, may produce radiation in the ~10μ region which similarly makes its way out to Space without being re-absorbed.
There is less ~15μ radiation emitted from the top of the Atmosphere than entered it from the bottom because some of the ~15μ radiation is transformed into ~10μ radiation during the process of absorption and re-emission by GHGs in the atmosphere and longwave radiation absorbed and re-emitted by the surface of the Earth.
Source Material
My graphic is adapted from two curves from Petty. For clearer presentation, I smoothed them and flipped them horizontally, so wavelength would increase from left to right, as in the diagrams in my previous topics in this series. (Physical Analogy and Atmospheric Windows.)
Here they are in their original form, where the inverse of wavelength (called “wavenumber”) increases from left to right.
Source for the upper section of my graphic.
Top of the Atmosphere from Satellite Over Tropical Pacific.
[Caption from Petty: Fig. 6.6: Example of an actual infrared emission spectrum observed by the Nimbus 4 satellite over a point in the tropical Pacific Ocean. Dashed curves represent blackbody radiances at the indicated temperatures in Kelvin. (IRIS data courtesy of the Goddard EOS Distributed Active Archive Center (DAAC) and instrument team leader Dr. Rudolf A. Hanel.)]
Source for the lower section of my graphic.
Bottom of the Atmosphere from Surface of Tropical Pacific (and, lower curve, from Alaska).
[Caption from Petty: Fig. 8.1 Two examples of measured atmospheric emission spectra as seen from ground level looking up. Planck function curves corresponding to the approximate surface temperature in each case are superimposed (dashed lines). (Data courtesy of Robert Knutson, Space Science and Engineering Center, University of Wisconsin-Madison.)]
The figures originally cited by Dave Springer and Tim Folkerts are based on measurements taken in the Arctic, where there is far less water vapor in the Atmosphere.
[Fig. 8.2 from Petty] (a) Top of the Atmosphere from 20km and (b) Bottom of the Atmosphere from surface in the Arctic. Note that this is similar to the Tropical Pacific, at temperatures that are about 30ºK to 40ºK cooler. The CO2 bite is more well-defined. Also, the bite in the 9.5μ to 10μ area is more apparent. That bite is due to O2 and O3 absorption spectra.
Concluding Comments
This and my previous two postings in this series Physical Analogy and Atmospheric Windows address ONLY the radiative exchange of energy. Other aspects that control the temperature range at the surface of the Earth are at least as important and they include convection (winds, storms, etc.) and precipitation (clouds, rain, snow, etc.) that transfer a great deal of energy from the surface to the higher levels of the Atmosphere.
For those who may have missed my previous posting, here is my Sunlight Energy In = Thermal Energy Out animated graphic that depicts the Atmospheric “greenhouse effect” process in a simlified form.
I plan to do a subsequent posting that looks into the violet and blue boxes in the above graphic and provides insight into the process the photons and molecules go through.
I am sure WUWT readers will find issues with my Emissions Spectra description and graphics. I encourage each of you to make comments, all of which I will read, and some to which I will respond, most likely learning a great deal from you in the process. However, please consider that the main point of this posting, like the previous ones in this series, is to give insight to those WUWT readers, who, like Einstein (and me :^) need a graphic visual before they understand and really accept any mathematical abstraction.
Oliver Ramsay says:
March 16, 2011 at 7:05 am
Phil. says:
“What is critical is that the dichroic directs the IR photons back towards the filament where they are absorbed thereby increasing the filament temperature.”
——————————
Then it does it again and gets even hotter, then again and again.
It does it at 100 degrees, at 500 degrees, at 1,000 degrees. What stops the process?
It’s a convergent series! A decreasing fraction is recycled as the temperature is increased.
“””””Tim Folkerts says:
March 15, 2011 at 7:22 pm
George,
Not that is really matters here, but you got your relativity wrong when you said “Remember that the energy of a real particle travelling at a velocity (v) has an energy of mv^2 /2 ; NOT mv^2 .” “””””
Not that it really matters; but I don’t recall saying anything about relativity. I was talking about a Volkswagen Beetle doing 60 mph (v). And off hand I don’t remember what (m) is for a VW beetle (at 60 mph), the energy is still (1/2) m.v^2 .
“”””” davidmhoffer says:
March 15, 2011 at 3:29 pm
George E Smith;
Remember that the energy of a real particle travelling at a velocity (v) has an energy of mv^2 /2 ; NOT mv^2 .>>>
George, its been a long time since I worked my way through E=MC^2. Here’s my recollection as it pertains to this discussion: “””””
David, I really wasn’t intending to be nit picky; and I’m sure you would get it correct when you need to use it.
Only reason, I mentioned that a real particle travelling at a velocity (v) has energy (1/2)m.v^2 as compared to your m.c^2 for the photon, was to make the point that the reason for mc^2 has nothing to do with the quite coincidental factoid that the photon (or EM wave) is travelling at a velocity (c).
It is certainly true that a high enough energy photon say 1.02 MeV, can be converted into the mass of an Electron, plus that of a Positron, in pair production for example; but they then won’t be travelling anywhere near (c) for example.
So I wasn’t really calling attention to a missing (1/2); that’s typeo stuff.
Phil. says:
“It’s a convergent series! A decreasing fraction is recycled as the temperature is increased.”
————————–
With every increase in the filament’s temperature, exponentially more energy is radiated.
Therefore, there is more to be absorbed by the filter and it gets hotter. (This happens even on my planet!)
The filter then radiates exponentially more at its new, higher temperature.
Now, there is more for the filament to absorb.
It may be a smaller fraction of the total energy radiated but it’s more energy than it was before.
Looking at it from another angle, the premise has been presented as applying at any and all temperatures, so it winds up sounding like this;
” A cold thing will heat a hot thing a finite number of times, but this effect can be observed starting at any temperature.”
It doesn’t work with conduction, either, which isn’t much different, except that the spatial separation of the two objects is much smaller. The things don’t literally touch one another, because electrons still don’t get along.
So let me see if I can understand this dichroic light bulb; now that Phil has succinctly explained how it works; follow me on this, in case I run out of sand to scratch in, and mess it all up.
We have this incandescent light bulb filament (aka planet earth), and the surface of the light bulb filament (aka planet earth) is being heated to incandescence (aka LWIR radiation emission) by the continuous input of energy from electricity (aka solar spectrum photons from the sun).
When the electricity (aka solar spectrum photons from the sun) shuts off, the surface of the filament (aka planet earth) gets cold; and when the electricity (aka solar spectrum photons from the sun) turns back on, the surface of the filament (aka planet earth) heats up to incandescence. Now due to the latest in terracomputing models, we can say, that if the filament (aka planet earth) doesn’t have any way of getting rid of the energy it receives; it will heat up to a Temperature of 800,000 Kelvins, in a billion years; due (according to said models) to the continuous input of energy from the electricity (aka solar spectrum photons from the sun).
Fortunately for us, the filament (aka planet earth) does have several mechanisms for getting rid of that excess energy, that is heating it towards 800,000 Kelvins. It can radiate thermal (black body like) continuum radiation to space; it can conduct heat to other materials contacting the filament (aka planet earth), such as the residual gas contained in the envelope of the lamp(aka the gas surrounding and in contact with the surface of planet earth), and thereby carry heat away by convection (to some cooler place).
As a result the residual gas in the envelope (aka the atmospheric gases around the surface of planet earth) also become heated by the filament (aka planet earth). These various processes do provide a means for the filament (aka planet earth) to rid itself of the excessive input energy from the electricity(aka solar spectrum photons from the sun), and as a result, the filament (aka planet earth) does not rise to 800,000 Kelvins; but stops at a mere 3000 Kelvins (aka 288 K, or +15 deg C or +59 deg F).
Now if we place an intervening dichroic layer (aka trace amounts of various and sundry green house gases, like CO2 (the King) and H2O (the servant) and Ozone) this dichroic layer (aka trace amounts of various and sundry green house gases, like CO2 (the King) and H2O (the servant) and Ozone) stops the exit of some of the previously escaping photon energy, and returns that energy back to the filament (aka planet earth) where it gets absorbed, thereby raising the temperature of the filament (aka planet earth).
As a direct consequence of this serendipitous extra heating from the back radiation due to the dichroic layer (aka trace amounts of various and sundry green house gases, like CO2 (the King) and H2O (the servant) and Ozone) , the original Temperature of the incandescent filament (aka planet earth) can be maintained indefinitely with LESS input of electrical energy from electricity (aka solar spectrum photons from the sun); so we can turn down the electricity (aka solar spectrum photons from the sun), and get EXACTLY the same filament (aka planet earth) Temperature as we had prior to the addition of the dichroic layer (blanket) (aka trace amounts of various and sundry green house gases, like CO2 (the King) and H2O (the servant) and Ozone) .
So despite this lower input of electricity to the filament (aka solar spectrum photons from the sun); we still have the exact same filament (aka planet earth) Temperature as we had before we added the dichroic layer (aka trace amounts of various and sundry green house gases, like CO2 (the King) and H2O (the servant) and Ozone) .
But of course, we don’t turn down the electricity (aka solar spectrum photons from the sun); THEY ARE NEEDED TO MAINTAIN THE INCREASED TEMPERATURE OF THE FILAMENT (aka planet earth).
Well I don’t know about you; but it is still quite clear, that you don’t get ANY increase in filament (aka planet earth) Temperature, unless you supply the energy necessary from the electricity (aka solar spectrum photons from the sun.)
Actually George we do turn down the voltage and maintain a higher temperature white light. The reduction in voltage is not the cause of the increase that is the presence and nature of the dichroic.
Oliver Ramsay says:
March 16, 2011 at 11:39 am
With every increase in the filament’s temperature, exponentially more energy is radiated.
Well T^4 not exponential.
Therefore, there is more to be absorbed by the filter and it gets hotter. (This happens even on my planet!)
The filter then radiates exponentially more at its new, higher temperature.
Now, there is more for the filament to absorb.
Apparently you don’t understand how a dichroic works, wavelengths below a threshold are transmitted, those above are reflected, there is no absorption/emission.
It may be a smaller fraction of the total energy radiated but it’s more energy than it was before.
No, it isn’t what you have forgotten is that as the temperature goes up the blackbody spectrum shifts to shorter wavelengths thereby a progressively smaller fraction is reflected.
Of course it is possible to set up a condition where the filament is operating near its maximum temperature and then adding a dichroic coating will cause the filament to melt.
George and Phil: Are you two really disagreeing? It seems like you are just emphasizing two sides of the same coin. Yes, it is necessary to have some sort of heat source and yes the dichroic coating (or the greenhouse gases) leave the temperature hotter than it would be in their absence. Now, can we all be friends? 😉
George,
Before I contemplate a reply to your last comment, I was hoping you could tell how much of that was sarcasm. You see, I agreed with most of what you said — right up until your conclusions. But along the way you were sounding more and more sarcastic (eg “king” CO2).
So either I agree with most of your science but am confused by your conclusions, or I missed the sarcasm and need to disagree with much more of what you said.
No, it isn’t what you have forgotten is that as the temperature goes up the blackbody spectrum shifts to shorter wavelengths thereby a progressively smaller fraction is reflected.
————————————
There’s still more emission at any wavelength at the hotter temperature than there was at the lower.
Are you saying that it’s only reflection that can achieve this heating and not absorption/emission and conduction?
>>
Tim Folkerts says:
March 16, 2011 at 10:15 am
I like most of what Jim said @ur momisugly March 16, 2011 at 3:00 am, except
“The total energy in the atmosphere is 519 W/m² ”
519 W/m^2 is the RATE at which energy is ENTERING the atmosphere. More specifically, 519 W is the average rate at which energy is entering an average column of air 1 m^2 on a side stretching from the ground to the top of the atmosphere. (It is also the rate at which energy is leaving that column — with any long-term imbalance leading to a long-term warming or cooling of the air).
<<
You are right; I was being sloppy with my terms. (As some have been in discussing the rest mass of a photon, I figure I’m in good company.) The correct phrase should have been: “The total energy flux in the atmosphere is 519 W/m2.” (The “per meter squared” unit implies a column.)
>>
The total energy in the atmosphere would millions of joules per 1 m^2 column
<<
Ahh yes, I disagree, but not enough to worry about it.
Jim
Tim Folkerts says on March 15, 2011 at 7:50 pm : “The molecules in the atmosphere are warm. All warm things emit EM radiation. It is pretty much that simple. Calculating the exact value or determining how much comes from CO2 vs H2O vapor vs H2O liquid (clouds) would not be trivial, but the principle of thermal radiation is undeniable.”
I know that Tim but incoming solar irradiation is 342 W/m² of which 107 W/m² is reflected back to space and cannot be counted again. That leaves 235 W/m² which are absorbed by the Earth System or ES i.e. surface and atmosphere. The same 235 W/m² is what is keeping the ES at an average temperature of 14 or say 15 °C. until, as the plan shows 235 W/m² leaves for space at the TOA. The plan shows averages (or 24/7 short & long wave radiation) so there is no need to take into account night and day. In other words a steady stream of 235 W/m² is circulating and keeping the ES steady at the same average temperature. Be that as you say by “Thermal Radiation” or as I would like to call it by “Atmospheric Insulation” In any case the plan shows 324 W/m² of radiation being emitted from GHGs towards the surface which amounts to 89 W/m² more than is being supplied to the ES by the Sun. That is why I ask: Where does that figure of 324 W/m² used for back-radiation come from?
davidmhoffer says:
March 15, 2011 at 8:11 pm
Sorry, I sometimes assume people know things that they don’t. Standard deviation IS the estimated uncertainty, this is basic metrology, it HAS to be estimated by definition. If the uncertainty was known, there wouldn’t be any need to statistically calculate the “estimated uncertainty” (usually at a 95% confidence interval), which is usually stated as the 1 sigma standard deviation.
That aside, I was not trying to offend anyone. I am simply totally frustrated with all of this nonsense that passes for “science” in the name of the CAGW agenda. Just for instance, this constant switching back and forth between “thermal energy” and thermal IR as if they were the same thing. And calling the downwelling long wave “backradiation” is ludicrous. This term is nothing but a combination of backscatter (the term for EM waves that have been REFLECTED by a gas) and radiation. If they told you up front that at least the first 78W of that DLW was actually from the solar absorption by the atmosphere, and then told you that the reason only 40W of surface absorption was able to make it through the “window” is because clouds REFLECT the majority of it straight back down toward the surface, they would probably also have to explain how EM waves are converted to current sheets at the reflection planes.
Whew. Talk about your run-on sentences. Sorry, if I keep ranting on like this I might blow a gasket.
Anyway, the average clear-sky solar radiance measured at the surface is ~231W. The datasets I have seen indicate that the clear-sky solar reflected is ~30W, and ~80W of atmospheric absorption (which includes water vapor), or a total clear-sky absorption of ~311W. The only thing missing in clear-sky measurements is clouds. Returning to the bane of these guys, Kirchoff, if clouds emit 30W, they have to have absorbed 30W. Try reconciling that with the global energy flow diagrams if you can. There is an explanation, but it’s late, and I don’t have time to get into it right now.
GREAT question, Oliver Ramsay, and I’ve got an excellent answer!
According to the Stefan-Boltzmann law, the radiation from a hot object increases according to the fourth power of the temperature. When expressed in Joules, it is 5.7 x T^4 (where T is temperature in Kelvins)
So, using your examples, at a tungsten filament temperature of 100ºC, which is 373 Kelvins, the radiation is proportional to 5.67 x 10^-8 x 373 x 373 x 373 x 373 = 3 Joules. When the filament radiates, it releases energy, which tends to cool it down, counteracting the input electrical power and the reflected IR radiation, which tends to warm it up. When the filament is at 100ºC, the electrical input power and reflected IR radiation pumps in much more power than is lost by radiation, so the filament continues to warm up.
At 500ºC, which is 773 Kelvins, the radiation is proportional to 5.67 x 10^-8 x 773 x 773 x 773 x 773 = 20,000 Joules. Notice how the radiation increases real fast with temperature? As a tungsten filament heats up, its resistance increases, so, at constant input voltage, the electrical current will decrease somewhat, reducing the input electrical power a bit. On the other hand, with a hotter filament, there will be more light and IR produced, so the reflected IR from the coating on the inside of the bulb will increase, tending to heat the filament more. When the filament radiates, it releases energy, which tends to cool it down, counteracting the input electrical power and the reflected IR radiation, which tends to warm it up. When the filament is at 500ºC, the electrical input power and reflected IR radiation pumps in much more power than is lost by radiation, so the filament continues to warm up.
Incandescent light bulbs are designed such that, at their rated voltage, a balance is reached at a filament temperature of about 3200ºC, which is around 3500 Kelvins. The radiation is proportional to 5.7 x 10^-8 x 3500 x 3500 x 3500 x 3500 = 9,000,000 Joules. WOW, radiation increases real fast with temperature! When the filament radiates, it releases energy, which tends to cool it down, counteracting the input electrical power and the reflected IR radiation, which tends to warm it up. When the filament is at around 3200ºC, the electrical input power and reflected IR radiation pump in about the same amount of power as is lost by radiation, so the filament temperature is stabilized at around 3200ºC (about 6000ºF).
Incandecent light bulbs are designed to operate that way because temperatures much higher than that will cause the filament to turn from solid to liquid. That is why a light bulb designed for 120 volts will “burn out” if you connect it to a 220 volt circuit.
Oliver Ramsay says:
March 16, 2011 at 3:41 pm
No, it isn’t what you have forgotten is that as the temperature goes up the blackbody spectrum shifts to shorter wavelengths thereby a progressively smaller fraction is reflected.
————————————
There’s still more emission at any wavelength at the hotter temperature than there was at the lower.
Are you saying that it’s only reflection that can achieve this heating and not absorption/emission and conduction?
No I was telling you how the dichroic works, which is the basis of this practical device.
UncertaintyRunAmok says:
March 16, 2011 at 5:49 pm
Returning to the bane of these guys, Kirchoff, if clouds emit 30W, they have to have absorbed 30W.
No they don’t you misunderstand Kirchoff’s Law.
Phil says:
“No I was telling you how the dichroic works, which is the basis of this practical device.”
————————–
You didn’t tell me “how the dichroic works”, you mentioned one fact about it, of which I was fully aware and referred to in previous comments. We can spend more time on that if you wish.
I assume that the word “No” in your reply is the answer to the question “Are you saying that it’s only reflection that can achieve this heating and not absorption/emission and conduction?”.
If that’s the case then whether it’s a reflector or radiator or conductor should not be the salient point.
The bulbs I’ve seen of this kind either transmit IR through the rear reflector in order to reduce heating of the illuminated area or they reflect IR from the front of the bulb in order to achieve an effect as it is then reflected from the back having undergone a shift. I’m not aware of any claim being made on their behalf that they will save energy.
Ira says
“GREAT question, Oliver Ramsay, and I’ve got an excellent answer!”
————————————
I’m sorry. I agree that it was a great question but I disagree that it was an excellent answer.
I was looking for more than just the statement that reflected IR is a power source.
Oliver Ramsay says:
March 16, 2011 at 11:26 pm
The bulbs I’ve seen of this kind either transmit IR through the rear reflector in order to reduce heating of the illuminated area or they reflect IR from the front of the bulb in order to achieve an effect as it is then reflected from the back having undergone a shift. I’m not aware of any claim being made on their behalf that they will save energy.
Perhaps you should have read the link that I gave earlier.
http://www.bulbs.com/blogs/light_source/post/2010/12/03/Cooler-Than-Ever-Halogen-IR-Bulbs.aspx
Or you could have found many others such as this one:
http://www.sylvania.com/ConsumerProducts/LightingForHome/Products/BulbType/Halogen/Infrared
Note the claims like this one:
“Reduced Energy Costs
Since halogen IR lamps produce more light with fewer watts than conventional halogen lamps, it is often possible to save energy by using a lower wattage IR lamp to replace a higher wattage lamp.”
I guess you missed that?
O H Dahlsveen asks “Where does that figure of 324 W/m² used for back-radiation come from?”
At one level, the answer is simply “IR spectroscopy can measure the EM energy and the result is about 324 W/m^2”
At another level, the answer is related to a brief side conversation I had with Jim:
>>The total energy in the atmosphere would millions of joules per 1 m^2 column
>Ahh yes, I disagree, but not enough to worry about it.
The specific heat capacity of air is very nearly 1000 J/kg*K. The atmosphere has a mass of about 5E18 kg. The earth has an area of about 5E14 m^2. So the mass above any m^2 is about 10,000 kg. This means that warming a 1 m^2 column of air by 1 K would take ~ 10,000,000 J. Since the air is well above 100 K, then warming it from o K would mean it contains a few Billion J of energy.
When looked at from that perspective, losing a few hundred J each second via radiation back to the earth doesn’t seem so amazing.
O H Dahlsveen says:
Just to expand on what Tim says, the point is that this number for the back-radiation is not in any way constrained by the original problem, at least if you assume you don’t know the total energy flows away from the surface. Once you do determine those flows (e.g., the amount radiated by the surface, the amount lost due to convection and evapo-transpiration), then you could determine it by balancing those energy transfers from the surface and the energy transfers to the surface (from the sun and from this back-radiation term).
How much back-radiation there is depends entirely on the details of the atmospheric composition and the variation of temperature with height in the atmosphere. Experimentally, it is determined by actually measuring it. Theoretically, it is determined by solving the problem of radiative / convective transfer in the atmosphere, given the measured IR absorption spectra of the constituents.
“”””” Tim Folkerts says:
March 16, 2011 at 1:55 pm
George,
Before I contemplate a reply to your last comment, I was hoping you could tell how much of that was sarcasm. You see, I agreed with most of what you said — right up until your conclusions. But along the way you were sounding more and more sarcastic (eg “king” CO2). “””””
Sorry Tim; that “King” CO2 certainly was an off-stage comment (stage left); an obtuse snark, at those who like to claim that CO2 is THE greenhouse gas and rules the roost, while H2O is NOT a greenhouse gas, and merely the hand maiden of CO2 to appear on demand, and warm the place up; which CO2 by itself is clealry incapable of doing; witness, how cold it gets at night in an arid desert, sans H2O, and with CO2 (presumably) firing on all cylinders.
I am personally of the opinioin, and believe I ultimately will be proven correct, that this planet, if it had not a molecule of CO2 in its atmosphere, would be about the same Temperature that it is now; it would simply have slightly less global average cloud cover; as in cloud area percentage, cloud optical density, cloud persistence time, and as Stephen Wilde would say some strategic shifting of where the clouds were.
Yes the loop gain is not infinite, so there would be some slight average Temperature drop; but nothing like the 24 deg C drop that the IPCC would claim with Climate Sensitivity set at 3 deg C per doubling, and eight halvings to get down under 2 ppm of CO2 from today’s 390. It is logarithmic isn’t it ??
Well we currently have a global temperature range of about 150 degrees C between extremes; a couple of degrees extra here and there will hardly be noticeable. Humans moved around with the climate; and never even realized that they were even going anywhere; it was all totally transparent; and will remain so.
“”””” Joel Shore says:
March 16, 2011 at 1:54 pm
George and Phil: Are you two really disagreeing? It seems like you are just emphasizing two sides of the same coin. Yes, it is necessary to have some sort of heat source and yes the dichroic coating (or the greenhouse gases) leave the temperature hotter than it would be in their absence. Now, can we all be friends? 😉 “””””
Joel, I believe that I am about on the same page as Phil; perhaps my emphasis is different.
My view is simply that the earth surface is NOT warmed by the “Return” (be it reflection, or absorption/re-emission, or re-conduction or re-convection etc) of LWIR radiant energy that originated at the surface in the first place; but it IS warmed by the additional input solar spectrum energy, that enters the system; during the delay time by which the GHG effect SLOWS THE EXIT of the surface emitted radiation.
I’m already on record, as agreeing, that the GHG effect is real, and that the earth is warmer as a result; the contrary view, is in my opinion a suicidal defense position.
Where I differ from the AGW catastrophists, is that I also believe that the GHG effect, is also somewhat irrelevent, since I believe the whole system is in stable feedback control as a consequence of the physical properties of H2O.
If water had a different freezing point, or boiling point, or vapor pressure curve, or specific heat , or latent heat; etc, then the range of Temperatures on earth would be different; BUT THEY AREN’T, so it isn’t.
Key evidence is that incoming solar spectrum energy goes “mostly” into the deep oceans during daylight, and hasn’t really showed up for work yet, when tomorrow’s sunrise occurs, and maybe won’t show up for weeeks or months.
Plus there is that little difference of opinion with that person who writes under the pseudonum of ‘Mike’ about whether water molecules in the atmosphere, reduce the amount of incoming solar spectrum energy that reaches the surface. That is irrefutable, incontrovertible, even axiomatic. I’ve also explained many times, that the portion of that incoming energy, that is captured in the atmospehre by H2O, and thereby DOES warm the atmosphere is itself split in half, before it can reach the earth as atmospheric emissions of LWIR radiation (or any re-conduction or other thermal energy transport process to the surface). The other half of the atmospheric H2O captured solar energy is eventually lost to space; so it never reaches the surface either as solar spectrum radiant energy, or any other form of energy, since the atmospheric emissions are isotropic.
And just for good measure; what I asserted was true for H2O molecules is also tue for some other green house gases; for example CO2 itself (the king) and also ozone. Both of those molecular species in the atmosphere also intercept some solar spectrum energy, before it gets a chance to reach the surface.
But Joel, I DO consider any difference with Phil to be a caution, that maybe more digging is required, before I cement my view of the reality; and I always thought that we all really were :-}
Oliver Ramsay says:
March 17, 2011 at 12:02 am
Ira says
“GREAT question, Oliver Ramsay, and I’ve got an excellent answer!”
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I’m sorry. I agree that it was a great question but I disagree that it was an excellent answer.
I was looking for more than just the statement that reflected IR is a power source.
And you got more, including the fact that resistance goes up with temperature and hence the heating effect goes down as temperature goes up (V^2/R).
You also had it explained to you again that T^4 isn’t exponential.
Your assertion that you knew what a dichroic is seems unlikely since you appeared to think that it absorbed radiation and heated up thus radiating more!
“Therefore, there is more to be absorbed by the filter and it gets hotter. (This happens even on my planet!)
The filter then radiates exponentially more at its new, higher temperature.
Now, there is more for the filament to absorb.
And an aside to the dichroic lamp coating issue; I am sure some of you folks are too young to know about “photographic film” and “color slides”, and “slide projectors”; they are the sort of vaccuum tubes (valves) of the family picture scene.
The Typical “slide Projector” had a 500 Watt (electrical) tungsten filament bulb that had a straight ribbon like filament or even a couple. The projector also contained a dichroic “cold mirror”, which was a high reflectance coat for visible wavelengths, but transmissive for non-visible near and IR wavelengths. The mirro was of course outside the lamp bulb and was concave spherical, and placed to the lamp filaments were optically at the center of curvature of the mirror. Well actually they are slightly off center.
When replacing a burnt out bulb (far too often), a very necessary lamp mirror alignment process was required before returning the projector to service.
The projector “projection lens” had to be extended so as to form a real image of the lamp filament on the projection screen.
With any luck, one would also see an image of the mirror reflection of that filament, of course inverted reverted swapped every which way, as happens with an object at the center of curvature of a sphere.
Once the lamp filament was in sharp focus on the screen, then one had to adjust the position of the mirro to get the image of the filament, also to be in sharp focus on the screen; and the last adjustment, was to turn the mirror slightly off axis, so that the filamen image was displaced sideways, from the filament, creating an extra or extra pair of light souces, that were evenly spaced from the actual filament(s); and NOT laid right on top of those filaments.
So the “heat” from the lam out the back passed right on through the mirror, to where the cooling fan extracted it, and the light from the back of the filament was added to that from the front, and sent to the optics, and the extra two filaments doubled the area of the illuminations source, which thus gave a wider angle source, so it created a more uniform illumination at the “slide plane” where the “color slide” would go to get projected on the screen.
So that is the exact opposite of what Phil described, and the projector manufacturer also warned the user to ensure that the filament reflection was NOT placed coincident with the actual filaments, to ensure that any heat that was reflected by the mirror, did not allow the filament temperature to rise; otherwise it would burn out even sooner. But it is till the electricity that heats the filament, and ultimately will burn it out.
Oliver Ramsay says on March 17, 2011 at 12:02 am: “I’m sorry. I agree that it was a great question but I disagree that it was an excellent answer.
I was looking for more than just the statement that reflected IR is a power source.”
I think we are looking for the same thing Oliver. I am looking because I am a firm believer in the fact that radiation is a transport system for energy which can no more increase the surface-temperature than a passenger train can increase the worlds population. – If it is a fact that back-radiation from GHGs is warming the surface then why is back radiation from the surface to GHGs not constantly warming say the clouds and the clouds further warming themselves up through “inter-cloud back-radiation”? Now there’s a new word but I like it as clouds must be able to do this, according to AGW and other science data as clouds are made up of individual water droplets and each droplet can therefore emit and absorb radiation from it’s surface.
There can be no end to radiation and back-radiation within a cloud as long as heat is increasing – and vice-versa. – It is called perpetual motion I believe.
However I do suspect the fact is that when water evaporates from the surface the resulting vapor is as warm as it ever is going to be unless it later mixes with warmer air rising from below.
O H Dahlsveen says:
Actually, it is called an infinite series. (Besides which, as I noted before, perpetual motion is only impossible if there is no energy source…which alas is not the case for the earth.) That the sum of an infinite series can lead to a finite result may have been a mystery in the days of Xeno’s Paradox but is not a mystery today: Consider the geometric sum 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + …, which, in the infinite limit, converges to the value 2.