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.
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That prior rant should read, of course, that Mr. Shore is NOT restrained at all. He seems to me to be the perfect example of a raving Ehrlich-style “progressive” idiot. But, thank God, such folk are losing this battle, and they know it. And that makes them very angry and prone to insults. Losing folks resort to insults, every time!
Robert Clemenzi says:
May 31, 2011 at 9:22 am
Phil, your spectracalc graphs are meaningless because they lack the
pressure, molar concentration, and path length
Graphs of a typical atmosphere show a very different picture. For one thing, the CO2 fine structure disappears because more than 95% (3-sigma) of the photons from 650 to 690 cm-1 are absorbed in the first 80 meters. Based on what I see, I feel safe assuming that the spectracalc CO2 path length was about 1 meter.
Your assumption is wrong, the pathlength was 10m. The fine structure is still clearly visible at 80m, and less than 95% of the photons between 650 and 690 cm-1 are absorbed in 80m.
It also appears that the water vapor concentration was about 500 ppm, where the actual value in the lower troposphere is about 10,000 ppm (yes, ten thousand ppm, aka 1% or 62% RH at 15C/59F).
No, the H2O concentration was 1% over the same path length of 10m.
Phil, thanks for the response. It appears that my program at 3 meters produces the same graphs as spectracalc at 10 meters. Most likely my error. That would also make the 95% absorbance around 250 meters (not 80m). Perhaps you could add plots for 250m and 1,000m.
Hmmmm.
“snip – multiple violations of policy – rephrase and resubmit – Anthony]”
Well, it is YOUR blog, but I fail to see any “multiple violations” (you did not elaborate, friend, and you really need to do so, to be fair!). And I don’t see why the word “piss” is any worse than your calling BULLSHIT on an article today.
I will repeat, hopefully without bullshit censorship, that Ira is being a biased “host” when he posts the following obvious baloney:
” Joel has been remarkably restrained in the face of IMHO unjustified personal attacks and postings by commenters who have not read his previous explanations and simply -thoughtlessly- repeat their Disbeliever mantra. I congratulate Joel for not hectoring us here on his (again IMHO) mistaken belief in the dangers of modest increases in mean temperatures and CO2 levels. He, along with others whose opinions are closer to mine, have taught me much on this Blog and I thank them, one and ALL.”
Mr. Shore is ANYTHING than a “restrained” person. He has insulted me many times here, just because I call his undocumented CRAP! And Ira-idealogue-PhD, you can repeat the “disbeliever” crap as much as you want, but it adds not one thing to the debate. It just shows that you have made your mind up, which is ALREADY TOTALLY UNSCIENTIFIC!
Simplifying the argument and considering CO2 alone in dry air, the first generation photons absorbed to extinction in a distance Lm of traverse of LWIR radiation are the ones ultimately responsible for any warming as they subsequently rattle around the atmosphere; the remainder shoot off to space, untouched, at the speed of light, as the transmittance of air for the remainder is 1.
A doubling of CO2 would not absorb any more (extra) first generation photons but the distance to the extinction point would reduce to Lm/2.
In an atmosphere well mixed by natural convection the subsequent mean retention time of these photons rattling around the atmosphere may be slightly increased (considering a Poisson distribution for a well mixed system this increase is probable). However as no additional heat or energy is absorbed (only that from the first generation photons) any temperature change would be very marginal.
The same argument applies to water vapour but with a larger absorption number for first generation photons (say about 200W/m^2 absorbed in a shorter extinction distance and about the same in the remainder shooting off to space; compared with about 80W/m^2 absorbed for CO2 etc).
I have carried out complex analyses in heat transfer equipment designs in the past involving series of thermal resistances and associated temperature drops – starting with changes of phase, boiling heat transfer to liquid metals, conduction through silicon carbide walls, convection and radiation from non-luminous gases and radiation from refractory walls all on a single spreadsheet. In all cases the subsequent energy audit balanced, predicted operating costs were reliable and correct (also capital costs) in the finished process plant. I didn’t whinge subsequently about any ‘lost heat’ from the balance as Trembarth does; what sort of analysis is he carrying out when he can’t even get a simple balance right.
Robert Stevenson says:
Again, your thinking on the issue is about where most scientists were in the mid-20th century. To see how and why they got beyond that, read here http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument/ and here http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument-part-ii/
The basic points, in a nutshell, is that one has to go beyond the first absorption and subsequent emission to consider the full problem of multiple absorptions and emissions and one has to consider the “wings” of the absorption band rather than it just being a binary problem of absorption or no absorption at a given wavelength.
As I understand it, Trenberth is complaining about the fact that, with the available satellites, we don’t currently have the capability to measure things down to the better than 1% level that would be necessary to see the fraction-of-a-W/m^2 changes in various quantities.
All in this thread: THANKS for continuing the discussion, on a high scientific level with (mostly) courteous disagreement. I have been reading every word but have not replied because you folks are doing fine and much of this is above my pay grade. I and others still tuned in are learning quite a bit. Please keep up the wonderful work.
Joel Shore says:
‘Robert Stevenson says:
Simplifying the argument and considering CO2 alone in dry air, the first generation photons absorbed to extinction in a distance Lm of traverse of LWIR radiation are the ones ultimately responsible for any warming as they subsequently rattle around the atmosphere; the remainder shoot off to space, untouched, at the speed of light, as the transmittance of air for the remainder is 1.
A doubling of CO2 would not absorb any more (extra) first generation photons but the distance to the extinction point would reduce to Lm/2.’
Again, your thinking on the issue is about where most scientists were in the mid-20th century. To see how and why they got beyond that, read here:
In 1900, shortly after Svante Arrhenius published his pathbreaking argument that our use of fossil fuels will eventually warm the planet, another scientist, Knut Ångström, asked an assistant, Herr J. Koch, to do a simple experiment. He sent infrared radiation through a tube filled with carbon dioxide, containing somewhat less gas in total then would be found in a column of air reaching to the top of the atmosphere. That’s not much, since the concentration in air is only a few hundred parts per million. Herr Koch did his experiments in a 30cm long tube, though 250cm would have been closer to the right length to use to represent the amount of CO2 in the atmosphere. Herr Koch reported that when he cut the amount of gas in the tube by one-third, the amount of radiation that got through scarcely changed. The American meteorological community was alerted to Ångström’s result in a commentary appearing in the June, 1901 issue of Monthly Weather Review, which used the result to caution “geologists” against adhering to Arrhenius’ wild ideas.
Still more persuasive to scientists of the day was the fact that water vapor, which is far more abundant in the air than carbon dioxide, also intercepts infrared radiation. In the infrared spectrum, the main bands where each gas blocked radiation overlapped one another. How could adding CO2 affect radiation in bands of the spectrum that H2O (not to mention CO2 itself) already made opaque? As these ideas spread, even scientists who had been enthusiastic about Arrhenius’s work decided it was in error. Work on the question stagnated. If there was ever an “establishment” view about the greenhouse effect, it was confidence that the CO2 emitted by humans could not affect anything so grand as the Earth’s climate.
I had heard of Knut Ångström, but hadn’t read of his experiments which match my spreadsheet analysis. The idea of a layered atmosphere as though it were a laminar boundary layer extension absorbing and re-emitting LWIR isn’t at all convincing but Knut Ångström’s work certainly is.