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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RE: HenryP: (August 29, 2011 at 12:00 pm)
“You have to show me the cooling rate as well as any warming.”
Henry, with the MODTRAN tool sensor altitude set to 99 km, looking down and with your preferred abundance of CO2 and temperature offset (and, any other setting you wish to change), the ‘Model Output’ will show you how much power (Io W/m2) is leaving (or cooling) the Earth, at least over the wave number range of 100 to 1500 cycles per centimeter. BTW, the nominal 15-micron CO2 wavelength is at about 667 cycles per centimeter.
For lower altitudes, you normally have to subtract the energy coming back down (sensor looking up) from the energy coming up from below (sensor looking down–which should be larger) to obtain the net cooling energy that is getting out from that altitude. In my August 23 table, that is the last column on the right, showing the net cooling upward irradiance that is not being returned.
Note: I suspect that this program (MODTRAN) presumes an atmosphere with its heat content established by normal convective activity–that, even if clear conditions are specified. Otherwise, I cannot see how it could show more heat being radiated from the atmosphere than that leaving the Earth from the ground.
This tool does not show warming per se; it only shows how terrestrial radiant cooling is hindered or facilitated by the greenhouse gases in the atmosphere. Remember that this is a program created by man–it has limitations.
But Spector,
the SW being deflected and the LW being trapped in the manner as described by me in the quoted link, is a soup coming from the various components. Note that water vapor (0.5%) and oxygen-ozone (21%) also absorbs at 14-15 um. There is no way you can un-entangle the 0.04% of the CO2 out of this mess.
Do you understand the principle of re-radiation?
The re-radiation of earthshine or sunlight (in the areas where the molecules have absorption) happens at all levels.
then you say
it only shows how terrestrial radiant cooling is hindered or facilitated by the greenhouse gases in the atmosphere. Remember that this is a program created by man–it has limitations.
That would exactly exclude the warming that is hindered by the same substances by deflected light from the sun 0-5 um. In fact here, if you have read my footnote in the link that I referred you to , we can identify some of the absorptions from the CO2 as being quite unique. As far as the 4-5 um absorption of the CO2 is concerned, here we have water vapor also with absorption. So again, standing here in African sun, it will be difficult to determine out how much less IR (2 & 4-5um) is on my head because of the increase in CO2 above my head.
the conclusion is that we do not know what the net effect is of the increase in CO2 in the atmosphere as far as the cooling and warming is concerned.
http://www.letterdash.com/HenryP/the-greenhouse-effect-and-the-principle-of-re-radiation-11-Aug-2011
You understand what I am saying? You cannot do any “calculations” without taking into account the whole spectrum 0-20 um. Remember that the cooling by CO2 (at 0-5 um) by deflection of sunlight happens 12 hours a day while the entrapment of earthshine happens 24 hours per day.
Thus, I know that Modtran is a fraud. At best maybe a dinky toy. The problem with this toy is that many people think that the answers it gives are true….
RE: HenryP: (August 29, 2011 at 11:14 pm)
That would exactly exclude the warming that is hindered by the same substances by deflected light from the sun 0-5 um.
Yes, Henry that is all true. This program is at best a raw indication of a part of the issue. It does not show the effects of any solar or short wave terrestrial radiation (wave numbers greater than 1500 cycles per centimeter) or include controversial feedback effects. It only shows those IR radiation levels over the 100 to 1500 wave number band that Air Force (USAF) scientists expected to detect with their equipment while flying at various altitudes, weather, and locations. It does seem to indicate that water vapor is the primary cooling (and heat retention) agent of the lower atmosphere.
Henry@Spector
In that case you are also one of only a few people who actually do really understand the principle of re-radiation i.e.
62.5% back-radiated in the direction where the radiation came from (in a radius of 180 degrees)
37.5% radiated in the other 180 degrees
which explains what I see is happening around me and which is supported by my own observations.
Do you understand why that is so?
RE: HenryP: (August 30, 2011 at 11:28 am)
Henry@Spector
Henry, most of what you see is scattered optical radiation. For radiant heat transfer, the case is different.
Imagine that you are standing between two large non-reflecting walls. You point your IR irradiance meter at one and get a power reading of 300 watts per square meter. Then you point it at the other and also get 300 watts per square meter. We assume these walls are so large that virtually all the energy emitted by one is absorbed by the other. In this case, there is no net energy flow. It is like two people with a pointless agreement to pay each other $300 every month.
On the other hand, suppose you only get a reading of 200 watts per square meter emerging from the second wall. That would mean that it was accepting power at a rate of 100 watts per square meter from the first wall. In the MODTRAN case, with both ‘walls’ at the same altitude, there is no place for the heat energy to go from one but to the other ‘wall.’ That is why I say:
[W/m2 getting out] = [sensor looking down] – [sensor looking up]
You should be able to use this relationship to see just where MODTRAN thinks most of the radiant cooling is happening.
Radiative forcing is typically defined at the tropopause. Here’s an older IPCC definition:
” the change in net (down minus up) irradiance (solar plus long-wave; in Wm-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.[2] 2″
NET Irradiance going UP through the tropopause (~10 km) in the US standard atmosphere you get:
375 ppm = 269.569 – 30.546 = 239.023
750 ppm = 266.335 – 32.436 = 233.899
Change in NET UPGOING radiation is a loss of 5.1 W m-2, significantly higher than the IPCC global average of 3.7 W m-2.
I suspect that 3.7 W m-2 is a better representation, since cloudiness, surface temperatures etc change and I’m pretty sure that ModTran does not allow stratospheric relaxation, whilst the models used by the IPCC did do this.
RE: Matter: (September 12, 2011 at 8:44 am)
“Radiative forcing is typically defined at the tropopause.”
I believe that is correct, but it is interesting that this tends to maximize the impact of CO2 as an absorber because CO2 is radiative emissions to outer space occur primarily above the mid stratosphere.
I believe that MODTRAN is not a climate-modeling program per se, but a program developed by the U.S. Air Force to predict ambient infrared radiation levels that might be observed by aircraft flying in the atmosphere both looking down and also looking up. I believe the radiation seen looking up is only trapped terrestrial radiation at flight level. No solar radiation is included.
It’s results are limited to integrals calculated over the wavenumber range of 100 to 1500 cycles per centimeter (officially 100 to 1500 kayzers) which is equivalent to a wavelength range of 100 microns down to 6.67 microns. As noted above, this limitation does cause about an eight percent integration error, which might have been reduced by extending the integration limit up to 2500 kayzers. (4 microns)
I believe the IPPC values, as you say, are based on additional assumptions about the climate and MODTRAN only yields a raw effect. In tropical clear air, it seems to yield a raw slope of about 0.89 deg C per doubling with Io forced constant. I do not know how qualified this program is for atmospheres with abnormal CO2 concentrations.