Guest Post by Willis Eschenbach
There’s an online calculator called MODTRAN that calculates the absorption of longwave (“greenhouse”) radiation for various greenhouse gases (“GHGs”), and shows their resulting effect. It does this on a “line-by-line” basis, meaning it examines each interval of the longwave spectrum for each greenhouse gas at each altitude, and calculates the resulting absorption by each species given the concentration and the partial pressure of that species. Figure 1 shows the calculation results for the default values of CO2, ozone, and methane.
Figure 1. MODTRAN results. The jagged red line at the top right shows what is not absorbed by the atmosphere. Colored lines in the background are theoretical “no-absorption” curves for various temperatures. The big “bite” out of the middle section of the jagged red line is mainly water vapor absorption, although it overlaps with the CO2 absorption bands in parts of it. The graph at the lower right shows the pressure, temperature, and the concentration of H20, Ozone, CO2, and CH4 at various elevations. The number “Iout” is the total energy that is not absorbed, so as absorption increases, that number will decrease.
That all seems straightforward, it looks the same as in heaps of textbooks … so where’s the MODTRAN oddity?
The oddity arose as a result of my wanting to know more about the doubling of CO2, and the 3.7 watts per square metre of increased absorption that IPCC claims the aforesaid doubling of CO2 is supposed to cause. To find out what MODTRAN says, I put in 750 ppm of CO2 in the top cell, and I had MODTRAN recalculate the Iout. To my surprise, I found that it was 284.672 … which when subtracted from the starting Iout shown above of 287.844 gives us only 3.2 watts per square metre increased absorption (forcing change) for a doubling of CO2.
I had left the “No Clouds or Rain” choice selected, thinking that the biggest change in CO2 would be in clear-sky conditions. So I figured “well, perhaps clouds or rain increase the absorption when CO2 doubles” … but investigating various cloud results showed that was not the case, they all gave smaller absorption changes. My original intuition was correct, clear-sky conditions give the biggest change in absorption for a doubling of CO2.
So I thought, “well, perhaps I’m looking at the wrong region of the Earth”. The other latitude bands available in MODTRAN are Midlatitude Summer and Winter, and Subarctic Summer and Winter. I took nominal CO2 values to represent the CO2 concentration in 1850 (285 ppmv), default (375 ppmv), doubling of 1850 value (570 ppmv) and doubling of the present value (750 ppmv). I figured that would give me two doublings, and let me see if the increases were linear with the logarithm of the number of doublings. I used MODTRAN to calculate the absorption change in each latitude band. Figure 2 shows those results, with the X axis being the number of doublings, and the Y-axis showing the increase in longwave absorption.
Figure 2. MODTRAN and IPCC values for the increase in forcing due to increasing CO2. The forcing change in each region per doubling of CO2 in watts per square metre is shown after the name in the legend, followed by “T=” and the surface temperature.
First thing I noticed is that the lines are all straight. So MODTRAN does indeed show a linear relationship between logarithm of the CO2 increase and the calculated increase in absorption. So no surprise there.
What was a surprise is that none of the other latitude bands had larger changes in absorption than the tropics. I’d thought that since the IPCC says the global average change from doubling CO2 is 3.7 W/m2, that because the tropics were at 3.2 W/m2, somewhere else the absorption must be above 3.7 W/m2 to make the average correct. But that’s not the case. They’re all smaller.
I also thought that the difference in absorption might be due to the different surface temperatures … but Midlatitude Winter and Subarctic Summer have about the same calculated absorption, yet their surface temperatures are about 15 degrees apart.
Note that what I have shown, the change in absorption, is also called the “instantaneous” forcing, abbreviated Fi. There are various other forcings one can measure. Hansen discusses them here (PDF), and gives a value of 4.52 W/m2 for the instantaneous forcing from a doubling of CO2 according to his climate model (Table 1, p. 7). Presumably his model does a line-by-line calculation similar to MODTRAN to figure out the absorption changes.
The IPCC, on the other hand, says:
The simple formulae for RF [radiative forcing] of the LLGHG [long-lived greenhouse gases] quoted in Ramaswamy et al. (2001) are still valid. These formulae are based on global RF calculations where clouds, stratospheric adjustment and solar absorption are included, and give an RF of +3.7 W m–2 for a doubling in the CO2 mixing ratio.
SOURCE: IPCC AR4 WG1 (PDF) page 140
So it appears the IPCC result is not based on a line by line calculation …
And that’s the MODTRAN oddity. Here’s the question:
1. Why does the MODTRAN calculated line-by-line change in absorption range from a low of 1.7 W/m2 to a high of 3.2 W/m2, while Hansen is saying the answer is really 4.5 W/m2 and the IPCC uses 3.7 W/m2?
Since according to MODTRAN (and logic) clouds reduce the effect of a doubling of CO2, and the IPCC (and presumably Hansen) are using all-sky conditions, that makes the IPCC/Hansen figures even farther from the MODTRAN figures.
Please note that (per Hansen) the instantaneous forcing Fi is greater than the adjusted forcing Fa by about 0.4 W/m2. The IPCC is saying that the 3.7 W/m2 is the adjusted forcing Fa, the forcing after the stratosphere adjusts to the change. So their value for instantaneous forcing would be larger, removing the stratospheric adjustment would put it at about 4.1 W/m2. So the IPCC is closer to Hansen’s value for the instantaneous forcing … but it means they’re further from the MODTRAN calculations.
I don’t know what I’m missing here, and I don’t understand these results, so any assistance gladly accepted.
w.
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John Marshall says:
August 19, 2011 at 2:04 am
I get it from the ice core data. The man that collected the data you refer to, Beck admits that it is not usable for “background” CO2 levels. See my discussion of the issue here, in particular Figure 5.
w.
Fouse says:
August 19, 2011 at 5:37 am
Not sure what you mean here. At any level, CO2 both absorbs and emits radiation. If it consistently absorbed more than it emits, it would constantly warm, and it’s not doing that … so I’m not clear what you mean by “net absorber”.
w/
Pamela Gray says:
August 19, 2011 at 7:23 am
Oooh, I love it when good-looking women talk farming like that, makes my pulse race and my knees weak … please continue.
w.
steven mosher says:
August 19, 2011 at 12:03 am
GIYF
Possible meanings:
Given It’s Your Fault
Got It Yet Fool? (that’s the nice version)
Gallium Indium Yttrium Fluoride
Grampa Is Your Father (more common in Appalachia)
Goodness! It’s… Yes! Friday!!!!
Happy Friday.
Wills:
“Fouse says:
August 19, 2011 at 5:37 am
CO2 in troposphere is net absorber, in stratosphere CO2 is net emitter.
Not sure what you mean here. At any level, CO2 both absorbs and emits radiation. If it consistently absorbed more than it emits, it would constantly warm, and it’s not doing that … so I’m not clear what you mean by “net absorber”.”
Could he refer to the fact that the CO2 has a non-polarized molecule so that at rest when it is mixed with other GHGs such as WV is most probable it get photons and shares the energy with the surroundings molecules, then vice-versa?
In fact it needs three contemporaneous collisions to bend when it is at rest, while just two collisions are enough to share the “trapped” energy when it is already excited by an LW IR photon.
In fact at troposphere levels MODTRAN shows no emission in the middle of the 650cm-1 pit, the emission peak there rises at altitude levels where CO2 substantially remain the only GHG.
Has everyone (but me) seen this interesting blog? (Don’t walk away before reading the feedback and responses)
http://theendofthemystery.blogspot.com/2010/11/venus-no-greenhouse-effect.html
RE: Massimo PORZIO: (August 19, 2011 at 1:19 pm)
“CO2 in troposphere is net absorber, in stratosphere CO2 is net emitter.”
I believe what is being claimed is the concentration of CO2 in the stratosphere is so thin that it can emit radiation directly to outer space. I used to think that as well, but I have since found out that this only happens in the mesosphere, 50 to 85 km up.
Wikipedia: “Mesopause”
“The mesopause is the temperature minimum at the boundary between the mesosphere and the thermosphere atmospheric regions. Due to the lack of solar heating and very strong radiative cooling from carbon dioxide, the mesopause is the coldest place on Earth with temperatures as low as -100°C …”
“”””” Massimo PORZIO says:
August 19, 2011 at 1:19 pm
Wills:
“Fouse says:
August 19, 2011 at 5:37 am
CO2 in troposphere is net absorber, in stratosphere CO2 is net emitter.
Not sure what you mean here. At any level, CO2 both absorbs and emits radiation. If it consistently absorbed more than it emits, it would constantly warm, and it’s not doing that … so I’m not clear what you mean by “net absorber”.”
Could he refer to the fact that the CO2 has a non-polarized molecule so that at rest when it is mixed with other GHGs such as WV is most probable it get photons and shares the energy with the surroundings molecules, then vice-versa?
In fact it needs three contemporaneous collisions to bend when it is at rest, while just two collisions are enough to share the “trapped” energy when it is already excited by an LW IR photon. “””””
So if the CO2 molecule having a zero electric dipole moment, can be excited into the bending mode oscillation, by absorbing a 15 micron wavelength photon; which is about 85 meV; how much energy must be imparted to the resting CO2 molecule, in a collision with say an N2 molecule, that being the most likely collision candidate, for thermally exciting a resting CO2 molecule into re-emitting a 15 micron photon. At the lower altitudes, where we are assured lies the CO2 that is doing all of the absorbing, the mean time between collisions is much shorter, than the lifetime of the excited state, so that spontaneous re-emission is a rare occurrence, except in the stratosphere, where the mean collision interval gets to be longer than the radiative lifetime.
So what is the mean kinetic energy of a N2 molecule at an atmospheric Temperature of 288 K which is the current claimed value for the mean global Temperature. I’m sure some of you PhD Physicists out there, can work out that simple statistical mechanics problem, and tell us how likely it is for a CO2 molecule to gain enough energy thermally from a collision, to emit a 15 micron photon.
And if a CO2 molecule is thusly excited; what is the probability of it radiating, before it gets hit again by another N2 molecules, and perhaps robbed of iots extra energy ?
Fouse 5.37 am CO2 in troposphere is net absorber, in stratosphere CO2 is net emitter.
At 300 ppm the absorbance of the CO2 column is around 2000 abs, where 1 abs absorbs 90%, 2 abs absorbs 99% and so on. The abosrbance is so strong that it is safe to say, at all levels the 13.6-16 micron radiation is determined entirely by the ambient temperature at that level. While the temperature is decreasing with altitude (troposphere) the net 13.6-16 micron energy will be decreasing with increasing altitude. When the temperature is increasing with altitude the energy will be increasing with altitiude. I suspect that is what Fouse is referring to.
HOWEVER the Nimbus data from space shows a black body emission temperature to space at the CO2 line of 220K. The only place in the atmosphere that is so cold is the tropopause and that means this emission has to be coming from the tropopause. That in turn means there cannot be significant CO2 above the tropopause because if there were it would be absorbing the emission from the tropopause and in turn emiting to space at its black body temperature. Since the stratosphere is warmer than 220K the black body emission temperature would be higher than 220K.
The Nimbus data implies that the top of the CO2 column has to at the tropopause (or the lower stratospjhere which is at about the same temperature). That means the stratosphere is NOT well mixed with respect to CO2. In which case, Fouse’s point is moot.
I think the whole problem with any models is they concentrate on radiation. Surely every part of the atmosphere radiates ? Surely every part of the atmosphere heats up via contact with warm surfaces and convection carries this warm air upwards in a random fashion ? So to my way of thinking the radiation measurements aren’t coming solely from GHGs but the whole of the atmosphere – or am I wrong and do N2 and O2 have special properties that make them exempt from physics.
I simply do not believe the models are anywhere near right and the basic assumptions are too simplified We obviously do not know as much as the modellers seem to think or else their predictions might be even somewhere near observations.
I think absorbtion by a small proportion of the atmosphere serves to slow down the cooling after the sun sets – I doubt it will increase temperatures much if at all.
The sun on the other hand is obviously the main source of energy on earth and there are inconsistencies in what I read about the sun – several credible sources quote different values for the sun’s temperature with a variation of ~10%.
Every GHG document I have read seems to say the incoming insolation is short wave and the atmosphere is transparent to it but ~ 44 % is infrared and ~6% UV – so a significant component of insolation appears to be capable of absorbtion by the atmosphere.
Spector at 3:23.
Interetsing quote you give from Wikipedia however it is one I have considerable problem with. If CO2 is emitting strongly it is also absorbing strongly (emissivity equals absorptivity) and that means that the black body emission temperature as seen from space should be the temperature of the mesopause ie: 175K. But it is not, it is 220K – the temperature of the tropopause hence there is a slight problem.
Note also, any strongly emitting layer of gas will have an emissivity of 1 so the difference cannot be due to low emissivity. This is becuase if a gas layer emits strongly it also absorbs strongly and that in turn means that at the absorption wavelength it will look like a black body (something that absorbs all energy at that wavelength).
Oh, yeah, forgot to mention. The IPCC agrees with the Hansen estimate of about half a degree (Hansen, 0.4°) for the difference between Fi (instantaneous forcing as discussed here) and Fa (forcing after stratospheric adjustment). They say (page 11, bottom right)
This means that Hansen gives global all-sky Fi (at the tropopause) as 4.5W/m2 per doubling of CO2, and the IPCC estimates it at 4.2.
MODTRAN gives from 4.5 (tropics) to 1.8 (subarctic winter) as values for the clear-sky conditions. Assuming ((I can’t find specifics) that “subarctic” means 65°-45° N/S, that “Midlatitudes” means 45°-25°, and that “tropics” is the rest, the area-weighted average of the MODTRAN results is 3.5. This is already well below that of Hansen/IPCC. But it gets worse
Clouds reduce the effect of doubling CO2 in all regions. This is because some percentage of the total DLR is due to the clouds. In that situation, changing CO2 doesn’t matter as much, the DLR stays high due to the clouds whether the CO2 is present or not.
Add to that the fact that the world averages around 70% cloudy. That means the real effect of doubling CO2 will be much less than the clear-sky conditions. Merely adding cumulus drops the MODTRAN result from 3.5 to 2.8. That’s 0.7 W/m2 from just cumulus.
So I’m simply not feeling the love here. We have been assured that the 3.7°C per doubling sits on solid science. But so far, I’m not finding that science. And what science I do have access to, MODTRAN, gives me a much lower number than the Hansen/IPCC numbers. With clouds, and the half a watt adjustment from Fi to Fa, we’re down to an adjusted forcing Fa of 2.3 W/m2, compared to IPCC’s canonical figure for Fa (3.7 W/m2) and Hansen’s number (Fa = 4.1 W/m2).
So no matter how I slice it we’re still a long ways apart.
w.
As I mentioned yesterday, it is OK, but the elevation should be set to the tropopause not 70 km for the more traditional tropospheric forcing. The stratosphere cancels some forcing.
RE: michael hammer: (August 19, 2011 at 4:07 pm)
“…If CO2 is emitting strongly it is also absorbing strongly (emissivity equals absorptivity)…”
That is true, but at that high altitude, the CO2 molecules are so few and far apart that any photons that they emit may have almost a 50 percent chance of getting scot free into outer space without being absorbed another CO2 molecule. At -100°C, the energy of escaping CO2 photons must be balanced by that of the absorbed solar photons in the same time period. These photons come from a very thin slice on the far IR tail of the solar spectrum.
Setting the altitude to 16 km (tropopause) you get 4.5 W/m2 in MODTRAN. Solved.
Willis Eschenbach says:
August 18, 2011 at 11:17 pm
Does anyone have any actual information on this question?
============================================================
lol, Willis, I don’t. And, I’d usually pass on commenting that I don’t know something and then babble meaningless words. But, it seems in vogue to simply comment about a tangential issue or two on this thread. I think mostly because no one else knows, either. But, I didn’t want to miss out just in case this caused some type of euphoria or something. Even though, I’m wasting your time by you reading this tripe, there is a bright spot! I’m not sending you to another web site, pdf, or model that won’t tell you the answer either, as seems to be another “in vogue” thing to do. 🙂
But, knowing you Willis, you’ll keep at it until you find a reasonable explanation. I’d help, but I’ve other adventures of my own. Do share when you do find a reasonable explanation.
James
PS……. To any of those wondering……. no, no buzz, no euphoria….. not even pink clovers and green sky. 🙁
I think you want Figure 4 in the following paper, which compares a number of AR4 AOGCMs to line-by-line calculations for the top of the model, 200 mb (which is an approximation for the tropopause/TOA), and the surface: http://www.cgd.ucar.edu/cms/wcollins/papers/rtmip.pdf
The paper uses clear-sky assumptions, and does not include the stratospheric forcing adjustment, both of which would presumably reduce the total forcing at the TOA-approximation. A related paper which does look at cloud effects is http://cfmip.metoffice.com/iq.pdf – while it is actually most interested in including the tropospheric response to forcing, it does note on page 6 that all-sky forcing would be 4 to 14% smaller than clear-sky alone even for instantaneous measurements.
“It seems like they picked the hardest, most un-measurable quantity they can pick as their standard, so they can say anything they want about it and no-one can deny it because you can’t measure it … but that might just be my paranoia. ”
Yes. It is just your paranoia. They pick TOA because it is _physically relevant_: eg, it is the altitude at which forcing is most likely to be linearly related to surface temperatures. Yes, it makes life more complicated sometimes – the paper I’ve linked to uses 200 mb rather than the real tropopause because not all models produce tropopause-relevant calculations. Yes, the tropopause changes height between the tropics and the poles. Heck, the tropopause changes height due to the addition of GHGs. That doesn’t make the people who work with TOA forcing “wankers” or “clowns” just because they didn’t explain things clearly enough for you.
michael hammer says:
The Nimbus data implies that the top of the CO2 column has to [be] at the tropopause
Not really. Near the tropopause, the continuous CO2 spectra begins to look more like individual lines (due to changes in temperature and pressure). As a result, the wings become more transparent with increasing height. Since the resolution width of the Nimbus spectrometer is fairly broad, the fine structure is obscured (averaged out) and what is seen is mostly the energy released at the bottom of the tropopause. (The bottom is about -55°C, the top is about -70°C.) In addition, the energy emitted in the still opaque spikes are absorbed by the CO2 higher in the stratosphere.
The exception to this is the central peak which remains very strong (and broad) up to the stratopause. In fact, the disintegration of this central peak may be what “defines” the stratopause, since above this point, the atmosphere becomes transparent to CO2 emissions.
Above the stratopause, the atmosphere cools until there is no longer enough emission from the remaining CO2 molecules .. at the mesopause. Above that, the atmosphere warms to over 1,000C.
CO2 Absorption in the Stratosphere
At the tropopause level, I believe the CO2 band at 15 microns is still saturated, but the width of the saturated region is not as wide as at the surface. Even so, I would most of the typical CO2 emission spectrum is likely to be blocked.
I found a website that provides a graph showing the purported absorption of long-wave radiation by the seventh 3-km layer of the Earth’s atmosphere, from altitude 18 km to 21 km, just above the tropopause.
http://homeclimateanalysis.blogspot.com/2010/09/earths-tropopause.html
In the stratosphere, temperatures rise with increasing altitude until they reach a maximum at the stratopause (46-54 km). From that point up, a progressive cooling sets in. This may, loosely speaking, represent the altitude at which outward-bound emission photons from CO2 molecules begin escaping to outer space.
RE: ModTran: I note that the sensor altitude may be set as high as 100 km, 101 does not work.
Forcing
If ‘traditional forcing’ is measured at the tropopause level as Jim D says, then I assume this term was intended to designate the energy flow driving the troposphere as a function of temperature. As the troposphere is becoming thinner at higher latitudes, this may reduce some of the discrepancies between ModTran and Hansen’s results. At an earlier time, this forcing might have been given a name like ‘tropomotivation.’
Willis, spectra tools, like MODTRAN, assume a “pencil of radiation” (basically, a narrow beam) while climate models must integrate that over a horizon-to-horizon semi-sphere. I have not been able to derive the necessary equations, but several sources suggest that this effectively doubles the thickness of the gas column used in a 1D analysis.
Clemenzi at 10:57
Robert, I agree that at the line edges the absorbance is lower but I do not this this invalidates in any whay what I am getting at. Consider, at sea level 300 ppm the total absorbance of CO2 is about 2000 abs (Heinz Hug). If we assume the atmosphere is well mixed (which I question) then the amount of CO2 above any given altitude is simply given by the pressure at that altitude. So the total CO2 absorbance above 0.1 bqar (100 mBar) is simply 200 abs and so on.
Now 1 abs absorbs 90% of the incident light and thus has an absorptivity/emissivity of 0.9. For 2 abs the figure is 99% which is a reasonable approximation of a black body. Thus as a rough approximation we can say that only the last 2 abs of the atmospheric column can radiate to space. From paragraph 1 this means, for a well mixed atmopshere, the pressure at which that radiation will occur (at the line centre of course, the absorbance at the line edges will be significantly lower as you point out correctly) is at about 1 millibar. Now 1 millibar occurs at an altitude of about 50 km which corresponds to the stratopause. If the atmosphere was well mixed with respect to CO2 we should see an equivalent black body temperature at the line centre corresponding to the stratopause. This is about 270K or only about -3C. Clearly this is not observed.
Further, if we go back to the Wikipedia comment that significant CO2 emission is occuring from the mesopause, this is at an altitude of about 80km where the pressure is about 0.01 millibar. The absorbance of the CO2 column above that altitude would be about 0.02 abs at the line centre giving it an emissivity of around 0.02 at the line center reducing as one moves out to the line edges. This is not high enough to significantly affect the observed emission intensity.
I suspect the stratosphere is indeed very stratified and that the CO2 being so much heavier than N2 and O2, pools in the lower stratosphere where the temperature is very close to that of the tropopause.
Also, I think the CO2 line at around 14.5 microns is a single extremely pressure broadened line not a forest of close spaced lines (although admittedly I cannot swear to that).
RE: michael hammer: (August 20, 2011 at 12:29 am)
Also, I think the CO2 line at around 14.5 microns is a single extremely pressure broadened line not a forest of close spaced lines (although admittedly I cannot swear to that).
All you have to do to see this is check out the Savi-Weber HITRAN online utility that provides raw spectrum plots:
http://savi.weber.edu/hi_plot/
Select ‘CO2(Carbon Dioxide)’ [Next] select ‘hitran’ [select frequency] select plot by wavelength and enter minimum (14.5) , maximum (15.5) and hit [plot] for a more detailed view of the center region, enter minimum (14.9) , maximum (15.0) and hit [plot] . These lines represent possible quantum states of the molecule including rotation while it is also vibrating.
For those needing Web Acronym disambiguation:
http://www.gaarde.org/acronyms/
and
http://www.netlingo.com/acronyms.php
Or just read them for fun!
RE: Robert Clemenzi: (August 19, 2011 at 11:06 pm)
“Willis, spectra tools, like MODTRAN, assume a “pencil of radiation” (basically, a narrow beam) while climate models must integrate that over a horizon-to-horizon semi-sphere. I have not been able to derive the necessary equations, but several sources suggest that this effectively doubles the thickness of the gas column used in a 1D analysis.”
It sounds like you are saying that MODTRAN is assuming a narrow beam emitter (or a narrow beam receptor or both) as opposed to hemispherical emitter. ( I have observed that placing the sensor below about 0.05 km results in declining levels.) With the assumption of a uniform atmosphere and distribution of surface radiation, I assume that one could perform an integration of the total energy received over all paths as a function of the total direct path attenuation. If such a correction is not being made, then MODTRAN would not be producing accurate results. I can only imagine this being the case only if the system being tested by the Air Force did not ‘need to know’ the difference.
RE: Jim D: (August 19, 2011 at 8:12 pm)
“Setting the altitude to 16 km (tropopause) you get 4.5 W/m2 in MODTRAN. Solved.”
……
“2.2 Concept of Radiative Forcing…Ramaswamy et al. (2001) define it as ‘the change in net (down minus up) irradiance (solar plus longwave; in W m–2) at the tropopause after allowing for stratospheric temperatures to readjust to radiative equilibrium, but with surface and tropospheric temperatures and state held fixed at the unperturbed values’.
–‘Changes in Atmospheric Constituents and in Radiative Forcing,’ Forster and Ramaswamy, PP 133