Guest Post by Willis Eschenbach
I’ve been messing about with the “Modtran” online calculator for atmospheric absorption. It’s called “Modtran” because it is a MODerate resolution program to calculate atmospheric infrared absorption written in ForTRAN, which calculates the result for each 1 cm-1 wide band of the wavenumber across the spectrum. Not quite a “line-by-line” calculation, but close. Here’s a sample of the input page:
Figure 1. User input page for the Modtran online calculation for infrared absorption. Left side is user input. Upper right graph shows absorption as a function of frequency. The lower right graph shows the GHG concentrations, pressure, and temperature, as a function of altitude. See here for an overview of the model. Click to enlarge
This shows the situation during the subarctic summer, with no clouds or rain.
Along the way, I ran into a curious mystery, one for which I have no answer.
Here’s the peculiarity I found. I decided to see what Modtran had to say about the “instantaneous forcing”. This is the forcing immediately after a change in e.g. CO2 or other greenhouse gas. In Table 1 of “Efficacy of Climate Forcings” , James Hansen et al. say that the instantaneous forcing from a doubling of CO2 is 4.52 W/m2.
So I tested that claim with Modtran using a variety of different locations, with different combinations of clear skies, cloud, and rain. I started by testing every few hundred PPMV increase, to see if the results were linear with the log (to the base 2) of the change in CO2. Finding that they were perfectly linear, I then tested each situation using 375 ppmv, doubled CO2 (750 ppmv) and two doublings of CO2 (1500 ppmv). I noted the absorption at each level, and compared that to the logarithm (base 2) of CO2. That let me calculate the forcing, which is typically given as the change in forcing for a doubling of CO2. Using Modtran, I get the following results:
Figure 2. Instantaneous forcing calculated by Modtran for different scenarios.
Now, this has the expected form, in that the forcing is highest at the equator and is lowest at the poles. The addition of either rain or clouds reduces the forcing, again as we’d expect, except during subarctic winter when some kinds of clouds increase the forcing slightly.
So the mystery is, according to Modtran, the absolute maximum instantaneous forcing from a doubling of CO2 is 3.2 W/m2 in the clear-sky tropics. I can’t find any combination of locations and weather that gives a larger value for the instantaneous forcing than that. And the minimum value I can find is subarctic winter plus cirrus, at 1.57 W/m2. I can’t find any combination giving less than that, although there may be one.
As a result, according to Modtran the planetary average instantaneous forcing from CO2 doubling cannot be any more than 3.2 W/m2, and is likely on the order of 2.4 W/m2 or so … but according to Hansen et al., the real answer is nearly double that, 4.5 W/m2.
So the mystery is, why is the accepted value for instantaneous forcing nearly twice what Modtran says?
Note that the answer to the mystery is not “feedbacks”, because we’re looking at instantaneous forcing, before any response by the system or any possible feedbacks.
All suggestions welcome, except those that are anatomically improbable …
w.
DATA: Excel spreadsheet here. You don’t need it, though. For any situation, simply use Modtran successively for two CO2 values where one CO2 value is double the other, and note the difference in the calculated upwelling radiation. This is the instantaneous climate sensitivity for that situation.
THE USUAL: If you disagree with me or someone else, in your comment please quote the exact words that you disagree with. This lets everyone know your exact subject of disagreement.
NOTE: I see as I finish this that they have an upgraded user interface to Modtran here … the results are the same. I prefer the older version, the graphics are more informative, but that’s just me.
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Phil. says:
April 15, 2014 at 11:53 am
So? In the head post, I quoted a value of 4.52 as Hansen’s claimed sensitivity. Are you seriously claiming Hansen used that value in 1988? If so, please post the citation.
And if you can’t find a citation to that value, will you admit you were wrong? I don’t get it, Phil. What’s your point here? You didn’t read the citation, you got caught out. Hey, it happens, no big deal, it’s happened to me more than once. More than twice, for that matter …
But now, rather than admit you didn’t read the citation, you’re backpedalling and doing lots of handwaving … are you aware that you are committing scientific suicide? There’s nothing that destroys a person’s scientific credibility faster than being unwilling to admit error.
w.
“””””…..Phil. says:
April 15, 2014 at 9:42 am
george e. smith says:
April 13, 2014 at 11:54 am
Also the notion that somehow the increase in CO2 somehow just “nudges out the edges of the absorption “band” and that results in the “logarithmic response to the CO2 increase……”””””
Well I already mentioned BOTH Temperature, and Density broadening, as manifestations of Temperature and altitude changes, so yes the GHG molecule is certainly aware of its atmospheric gas surroundings. But it remains unaware of another GHG molecule in its vicinity. I can see a linear increase in LWIR absorption due to a small increase in the number of GH molecules doing the absorbing; but I see no credible mechanism for slowing that rate down below linear to logarithmic, for example.
I might agree the relation could be non-linear; I can see no reasonable justification for calling it logarithmic, which is a precisely defined mathematical function.
One molecule to two molecules per volume; equal to one million to two million molecules per volume is what means logarithmic.
So we have at most a 25% of one doubling record of credible CO2 concentration.; not even one order of magnitude change.
Anybody ever do a controlled lab experiment over just doubling of CO2 or better yet, one decade increase ??
george e. smith says:
April 15, 2014 at 1:35 pm
“””””…..Phil. says:
April 15, 2014 at 9:42 am
george e. smith says:
April 13, 2014 at 11:54 am
Also the notion that somehow the increase in CO2 somehow just “nudges out the edges of the absorption “band” and that results in the “logarithmic response to the CO2 increase……”””””
Well I already mentioned BOTH Temperature, and Density broadening, as manifestations of Temperature and altitude changes, so yes the GHG molecule is certainly aware of its atmospheric gas surroundings. But it remains unaware of another GHG molecule in its vicinity. I can see a linear increase in LWIR absorption due to a small increase in the number of GH molecules doing the absorbing; but I see no credible mechanism for slowing that rate down below linear to logarithmic, for example.
I might agree the relation could be non-linear; I can see no reasonable justification for calling it logarithmic, which is a precisely defined mathematical function.
It’s called the curve of growth George, as you go from a weak absorption via a moderate absorption to a strong absorption the line shape changes and so you go from linear through logarithmic to square root. CO2 at the current level in the atmosphere are in the approximate logarithmic regime whereas methane is in the square root regime.
There’s an analysis in:
http://astrowww.phys.uvic.ca/~tatum/stellatm/atm11.pdf
You can find other versions by googling ‘curve of growth’.
Willis Eschenbach says:
April 15, 2014 at 12:08 pm
Phil. says:
April 15, 2014 at 11:53 am
Was it from “the 80s”?
Why no, it’s from 2005 … read the dang citations, Phil. I go to a lot of work to include them, and it will prevent you from looking foolish.
Nevertheless Willis, Hansen was using a value in excess of 4.0 in his 1988 paper which dated from ~1979 hence my comment, as to when it changed that’s another matter (probably 2007 AR4). It was regarded as a high value even then as I recall.
So? In the head post, I quoted a value of 4.52 as Hansen’s claimed sensitivity. Are you seriously claiming Hansen used that value in 1988? If so, please post the citation.
I’m saying that he was using a value in excess of 4.0 in his 1988 paper:
Hansen et al., J. Geophysical Research, vol. 93, pp 9431, 1988.
I got very similiatr results using tools from the http://www.spectralcalc.com website, from Gats, Inc. Some are available at no charge. A full set requires an available subscription ($45 for a month, $95 for 3). It takes a lot longer to run than MODTRAN, but should be more accurate. One has to breakdown into runs a number of wavelength bands and each one can take up to a few minutes.
See my paper http://climateclash.com/does-the-tropopause-limit-carbon-dioxide-heat-trapping/
Summary of results below
“1. Summary of results
We found the reduction of heat radiated to space caused by two times CO2 from the following sources (in Wm-2): the surface with clear skies at 3.38, low clouds at 2.71, medium clouds at 1.03 and high clouds at -0.30. The combined weighted value is 2.53 Wm-2.”
“The value of 2.53 Wm-2 is considerably less than the presently accepted value of 3.71 Wm-2. This latter higher value is consistent with the widely cited paper by Myhre et al (1998) that provides an empirical equation to fit their estimates of CO2 forcing as 5.35 ln(C / C0). It is interesting that the ratio of all-sky/clear-sky forcing that we get of 2.53 / 3.38 or 0.749 compares closely to the Myhre et al value of 0.734, so this cannot explain the differences.”
After doing my paper, I read that more CO2 causes stratospheric cooling which some how causes the forcing to increase which requires a correction. I estimate this at about 15%. so I end up with 2.9 W/m2, still musc less 3.7. I think the 3.7 W/m2 accepted number is too large.
Some people claim the equilvalent thing of the corrction is to run the obsevation point at the top of the tropsphere instead of at 70 to 100 km at the TOA. However this misses out on the CO2 emissions around 15 microns where the absorptions are so strong that the final emissions level extend above the troposphere where the temperatures can actually rise with altitude, thus provide, more not less, heat to space with mode CO2. Figure 3 in my paper shows this and Figure 9 shows for clears skies measuring outgoing radiation reduction for 2x CO2 at 15 km around the top of the troposphere is about 50% higher than seen at 70 km. This is too much of a correction it seems. (BTW, how does a person paste a bimap here).
I would like to compare with MODTRAN. What is the cost?
Conclusions (from my paper)
“The results here using modern tools indicate substantially less (about 32%) radiation forcing heat unbalance caused by increased CO2 content then the presently accepted values such as in cited in Myhre et al. This brings into question estimates often cited as being the “settled” values from many years ago and whether they should be redone by others with new tools and techniques. Of particular significance is the fact that the estimates from the radiance tools used here match closely with satellite data for both clear and cloudy sky conditions. We were disappointed in the excellent paper by Kiehl and Trenberth (1997), that we used for part of our work, that the authors, after estimating outward radiation that matched satellite data quite well for existing CO2 content, did not repeat it for double CO2 as we did here. They did attempt to assign the relative importance of existing greenhouse gases, but this is of little value in answering the central question of climate sensitivity.”
Additional break down of results are below.
A2. CO2 forcing at the “Top of the Atmosphere” using the Radiance Tool
For each case of clear and cloudy skies, and for each bandwidth where CO2 is active, the outgoing radiation at 100 km from 1x and 2x CO2 were determined, and from that the increase. Each run took about 2 to 3 minutes. The results are shown below in the four tables. Note the significant reduction for the cases from the cloud tops. And at 10 km, the heat loss increases slightly with 2x CO2 because the altitude’s increase with temperature at the higher attitudes.
Table A1 – From the surface at 288 K with clear skies above; weighting = 42%
—————-Wavelength – Microns —————–
Condition 12 – 13.5 13.5 – 15 15 – 16.5 16.5 – 18 18 – 19 Total – Wm-2
CO2 at 330 ppm 30.20 13.28 11.31 15.83 9.92 80.55
CO2 at 660 ppm 29.15 12.34 10.82 15.08 9.88 77.28
Decrease 1.05 0.94 0.49 0.75 0.04 3.27
Note: Add 0.11 decrease from the 4 to 5 micron range
Table A2 – From cloud tops at 2 km at 275 K with clear skies above; weighting = 40%
Wavelength – Microns
Condition 12 – 13.5 13.5 – 15 15 – 16.5 16.5 – 18 18 – 19 Total – Wm-2
CO2 at 330 ppm 26.18 13.10 11.25 15.39 9.64 75.56
CO2 at 660 ppm 25.49 12.29 10.80 14.74 9.60 72.91
Decrease 0.69 0.81 0.45 0.65 0.04 2.65
Note: Add 0.06 decrease from the 4 to 5 micron range
Table A3 – From cloud tops at 6 km at 249 K with clear skies above; weighting = 6% Wavelength – Microns
Condition 12 – 13.5 13.5 – 15 15 – 16.5 16.5 – 18 18 – 19 Total – Wm-2
CO2 at 330 ppm 17.70 12.13 10.79 12.62 7.79 61.03
CO2 at 660 ppm 17.49 11.80 10.58 12.35 7.78 60.00
Decrease 0.21 0.33 0.21 0.27 0.01 1.03
Table A4 – From cloud tops at 10 km at 223 K with clear skies above; weighting = 12%
Wavelength – Microns
Condition 12 – 13.5 13.5 – 15 15 – 16.5 16.5 – 18 18 – 19 Total – Wm-2
CO2 at 330 ppm 10.58 10.40 9.69 8.89 5.44 45.00
CO2 at 660 ppm 10.57 10.57 9.85 8.87 5.44 45.30
Decrease 0.01 -0.17 -0.16 0.02 0.00 -0.30
Using the weighting described above, we get for the combined forcing for 2x CO2:
(A1) F = 0.42 x (3.27 + 0.11) + 0.40 x (2.65 + 0.06) + 0.06 x 1.03 + 0.12 x (-0.30) = 2.53 Wm-2
A3. Comparing the radiance estimates of total outgoing radiation with satellite data
The preceding work centered on the 12 to 18 micron range because this is the major band where CO2 plays a role. However we also used the radiance tool over the full range that virtually covers the complete longwave spectrum associated with the global average temperature. The results are shown in Table A5. The total leaving the top of the atmosphere under clear skies is estimated at 265.9 Wm-2, close to the satellite data of 265 Wm-2 as reported by Kiehl and Trenberth (1997).
Table A5 – Radiation leaving the surface and the atmosphere by wavelength (clear skies)
Wavelength – Microns
4 – 8 8 – 12 12 – 18 18 – 100 Total – Wm-2
GHGs active All O2, O3 CO2, H2O H2O ––
From Surface (Wm-2) 46.83 99.10 110.60 132.49 389.1
Leaving Atmosphere (Wm-2) 15.61 88.85 70.63 90.81 265.9
Percent Leaving Atmosphere 33.3 89.7 63.9 68.5 68.3
When this was repeated for the three cloudy cases, the totals dropped from 265.9 to 240.2, 188.2 and 135.2 Wm-2. The combined total, using the weighting above, drops to 235.4 Wm-2, compared to 235 from Kiehl and Trenberth.
The agreement of the radiance tool with satellite data regarding outgoing radiation provides confidence in using it to estimate how it will change with increased CO2 concentrations.
Note: Pasting tables from my Word document did not work good even though I manually adjusted them in my view of the comments before submitting them.
Hmmm, guys I thought that space was freezing cold and a vacuum. Maybe my physics teacher was wrong.
bushbunny says:
April 20, 2014 at 8:22 pm
Space has no temperature because it has no particles.
Temperature is a measure of the kinetic energy stored in matter.
Testing pasting Table in Courier Font
Table A1 – From the surface at 288 K with clear skies above; weighting = 42%
Wavelength – Microns
Condition 12 – 13.5 13.5 – 15 15 – 16.5 16.5 – 18 18 – 19 Total – Wm-2
CO2 at 330 ppm 30.20 13.28 11.31 15.83 9.92 80.55
CO2 at 660 ppm 29.15 12.34 10.82 15.08 9.88 77.28
Decrease 1.05 0.94 0.49 0.75 0.04 3.27
Note: Add 0.11 decrease from the 4 to 5 micron range
[The mods recommend using the [pre] and [/pre] (with angled html-brackets instead of square brackets) to generate tables from text using a fixed-width non-proportional font. Mod]