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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From that known source of climate alarmism, Wikipedia:
In the earlier 1979 NAS report[12] (p. 7), the radiative forcing due to doubled CO2 is estimated to be 4 W/m2, as calculated (for example) in Ramanathan et al. (1979).[13] In 2001 the IPCC adopted the revised value of 3.7 W/m2, the difference attributed to a “stratospheric temperature adjustment”.[14]
So Hansen disagrees with the IPCC? Who should we believe now? IPCC? Hansen? Modtran?
The debate is so messed up we don’t even know which version of wrong to debunk!
Willis, I don’t have any answers for you but once the energy is absorbed, it is re-emitted and has a new opportunity to be absorbed again so I’m not sure that a single absorption calc covers the situation.
How did you manage to keep to under 173 punch cards? Seems like I always had either 22 cards or 280. But the worse effect was dropping the box. /sarcasm
But more seriously.
Each time I’ve used Modtran, it failed the “practical test” of real world conditions: Predicting long wave radiation back away from a surface into a “sky” condition of specific pressure, 2 meter air temperature, ultimate Tsky temperature, relative humidity, and clarity. The program lists conditions for different environments: Willis has them above in the header paragraph. But those “generic” Arctic or Kansas wheat field” conditions did not ever appear to answer the general long wave radiation question for a specific series of weather conditions, surface temperatures, and surface emissivities.
bones says:
April 12, 2014 at 4:49 pm
M Simon says:
April 12, 2014 at 3:49 pm
Willis,
You say “which calculates the result for each 1 cm-1 wide band of the wavenumber across the spectrum.”. I might believe 1um. Or 100nm. Or 10nm. (I know nothing of MODTRAN) But 1/1cm seems rather broad. At 1cm you are more into microwaves than light. Although really it is all light. But common nomenclature.
———————————————————–
A reciprocal centimeter bandwidth is just an increment of the spectrum over which the calculations were performed. It is equivalent to going through the absorption bands in a fairly detailed way. At 10 microns in the NIR, once reciprocal centimeter would correspond to a wavelength band of about 1 Angstrom; i.e. 10^-10 meters.
____________________________________________
Not quite. The term wavenumber is defined as the inverse of the wavelength in centimeters. Thus, a wavelength of 10 microns corresponds to 1000 wavenumbers, or 1000 cm^-1. A change of 1 cm^-1 at 10 microns is a change of 1 part in 1000, or .01 microns, 10 nm.
The reason that wavenumbers are used is not to make things complicated; it is rather that the energy of a photon of radiation is proportional to its frequency, and the frequency of electromagnetic radiation is the speed of light divided by the wavelength. Thus the wavenumber is directly proportional to the energy of a photon, and what is perhaps more important, absorption and emission lines and bands tend to have about the same widths in energy terms, thus in wavenumbers, no matter what the frequency is [when they are due to similar physical processes]. It is very reasonable for MODTRAN to use wavenumbers, and 1 cm^-1 is, in fact, a medium spectral resolution, both in radiation physics and instrumental terms.
Coldlynx says:
April 12, 2014 at 1:53 pm
—————————————
The problem is that instantaneous radiative forcing actually gives no true answer to the change in atmospheric temperature profiles due to changing radiative gas concentration.
What do radiative gases do? Warm low down cool high up.
This increases buoyancy imbalance and increases the speed of vertical tropospheric circulation. This non-radiative transport combined with evaporation is the primary energy transport mechanism away from the planet’s surface.
Increased radiative gases speed up the primary energy transport mechanism away from the planet’s surface.
It should also be noted that the role of radiative gases in radiative subsidence of air masses from altitude is critical in tropospheric convective circulation. No radiative gases, and this circulation will stall. The lapse rate is a product of strong vertical circulation across a pressure gradient. Without this circulation, the lapse rate would trend isothermal via gas conduction.
Assuming constant lapse rate or speed of vertical circulation for changing radiative gas concentration is a dead end. Hold these constant for increasing radiative gases and the flawed models of the climastrologists will always show low altitude warming.
Sir George Simpson warned against this type of radiation only garbage in 1938 –
“..but he would like to mention a few points which Mr. Callendar might wish to reconsider. In the first place he thought it was not sufficiently realised by non-meteorologists who came for the first time to help the Society in its study, that it was impossible to solve the problem of the temperature distribution in the atmosphere by working out the radiation. The atmosphere was not in a state of radiative equilibrium, and it also received heat by transfer from one part to another. In the second place, one had to remember that the temperature distribution in the atmosphere was determined almost entirely by the movement of the air up and down. This forced the atmosphere into a temperature distribution which was quite out of balance with the radiation. One could not, therefore, calculate the effect of changing any one factor in the atmosphere..”
Apparently the Church of Radiative Climatology didn’t get the memo 🙁
Richard G says:
April 12, 2014 at 4:09 pm
My goodness, didn’t I just say above that scientists are not short of intelligence? Of course it has been measured, hundreds and hundreds of times. RTFM, my friend … I linked to this information. See here for a test comparison of Modtran results with observations …
w.
Jeff Id says:
April 12, 2014 at 5:18 pm
Thanks, Jeff, always good to hear from you. The close correspondence between model results and observations makes me think that they deal with that in some fashion. Here’s the link from above if you missed it.
w.
PS—for those who don’t know of Jeff’s work, a trip to his website is almost always worthwhile.
But look at the two cases in that graphic heading: The IRIS satellite is for the Sahara – I assume they means its IR measurements while the satellite was above the Sahara desert at some surface temperature, altitude, relative humidity and pressure – and the MODTRAN results are for a 22 deg C ! simulated surface at 325 ppm CO2 (not seen since perhaps the early 1950’s) for a tropical environment.
So, is this not a case of the two results lining up fairly closely at several radiation bandwidths, but for two very, very different conditions?
At a minimum, the CO2 levels in the simulation need to be 390-400 to match the satellite era – and CO2 is even than average earthwide over the deserts!. And the actual surface temperature of the Sahara when the IRIS satellite was overhead needs to be matched with the MODTRAN simulation for that Sahara relative humidity and Tsky emissivity.
“”””””……jim2 says:
April 12, 2014 at 3:06 pm
@ur momisugly george e. smith says:
April 12, 2014 at 2:02 pm
…
And if they are assuming a log base 2 behavior, that means they believe Beer’s Law applies, and it doesn’t because Beer’s law presumes the absorbed photons stay dead, and are never re-emitted at any wavelength.
…
That isn’t an assumption of Beer’s law. If that were true, after a while the sample would transmit all light impinging upon it because all the molecules would have already absorbed photon. That isn’t how it happens – it is a dynamic equilibrium of absorption-emission…….””””””
Beers Law, is a law from chemistry about the absorption of some “specific wavelength” by some molecular species in a dilute solution of that species.
It asserts that a path through such a solution absorbs a fixed percentage of the incident radiation for each length increment of the path length, or alternatively as a function of the concentration of the absorbing species. So if a one cm path absorbs 10% of the INCIDENT RADIATION at that specific wavelength, the next cm of path will absorb 10% of the remaining radiation of that incident wavelength., or if you like doubling the species concentration in a fixed path length , will absorb 10% of the incident, plus 10% of 90% of the incident radiation.
It applies ONLY to the ABSORPTION of the incident radiation.
It does NOT apply to the TRANSMISSION of energy through the sample, because most if not all materials RE-RADIATE the absorbed energy as some other wavelength radiation.
I have color glass filters which will extinguish a specific wavelength by four orders of magnitude; yet they transmit over around 50% of the radiant energy but at a lower frequency radiation.
The LOGARITHMIC RESPONSE of Beer’s Law, is entirely dependent on the absorbed radiation NEVER being re-emitted;
A claim of logarithmic absorption of radiation with concentration of an absorbing species, IS an assertion that Beer’s law applies.
It virtually NEVER applies to energy transmission, because the radiant energy refuses to stay dead.
If radiant energy is absorbed,, and not re-radiated as some fluorescence, or in the case of gases, the molecule returning to the ground state, then the Temperature must increase, and the energy either conducted away as heat, or else the material will radiate a thermal radiation spectrum based on the higher Temperature.
GHG absorption in the atmosphere does NOT obey Beer’s law, so it isn’t logarithmic, with concentration or thickness.
Whether or not authors claim Beer’s law applies; the logarithmic (or exponential absorption):
…..t = t0. exp (-alpha .s) is totally a consequence of Beer’s law assumption. So what if an undetected thermal radiation appears mysteriously as a result. Ocean warming is what leads to increased ocean energy emission in the LWIR, long after the chap who measured alpha has gone home to sleep.
If I wanted to start a fight ……..
Never mind, Willis has a new post.
RACookPE1978 says:
April 12, 2014 at 6:09 pm
Sorry, RA, but you need to read a bit more carefully. The graph (see the red type) says that the surface temperature is 320K, which is 47°C, not 22°C. So that’s likely quite close to actual conditions.
Next, the IRIS data is from 1972. And the NOAA MLO CO2 data gives the 1972 CO2 concentration as 327.45 ppmv … they used 325. Again, right there with the actual conditions.
Finally, they’ve cut the relative humidity in half, likely a reasonable approximation for the dry desert air.
So in fact, they’re using something very near to the actual conditions, not “very, very different conditions” as you claim.
Regards,
w.
Willis Eschenbach says:
April 12, 2014 at 5:51 pm
———————————-
Actually Richard G raises a good point.
Measurement from satellite is not what is required here. The correct empirical approach is simple and far cheaper than launching remote sensing assets.
All that is required is a flight of aircraft flying in vertically separated formation, 500′ to 40000′ simultaneously through the same airspace. LWIR sensors scanning 360 degrees perpendicular to flight axis. Gas sensors analysing radiative gas concentration. Repeat on different days and sky conditions in the same airspace.
But such as simple empirical experiment would give the “wrong” answer. No average EEH or ERL. Atmosphere radiating in 3D from clumps. Atmospheric “IR “window” constantly changing. No hope of using averages.
I have checked measuring sky LWIR from the ground. The pattern of emission is constantly changing from even to clumped. Constantly changing altitudes of emission and the IR window always fluctuates. And that is just one location. Regional differences would make a joke of averages and the whole EEH game.
Willis,
I was under the assumption that cooling the stratosphere ( which yields ‘adjusted’ response, not instantaneous ) tended to reduce forcing. I have been running some runs using the CRM ( column radiation model ) which used to underlie the CCM and found that the ‘adjusted’ forcing is greater than the ‘instantaneous’ consistent with what you have found. I’m not sure you can calculate the ‘adjusted’ by using this tool because it doesn’t allow you to specify a given profile for one run, then the same profile with a stratospheric cooling for a 2x CO2 scenario.
Hansen probably didn’t use actual data, but a model and then an inserted constant to be consistent with the model. So 4.52 W/m2 might be based on what would be expected from greenhouse gas models, based on an inserted value or ‘constant’ picked out of thin air.
I found this sort of thing when I was directed to papers Hansen wrote on atmospheric equilibrium, to try and determine whether the sun’s high activity in the 20th century has reached equilibrium in the atmosphere, I found in his papers that a constant was inserted into the equations to give a result that the atmosphere was currently not in equilibrium, meaning ‘more warming is in the pipeline’ from greenhouse gases, and it was clearly stated that the constant was based on greenhouse gas modelling. So to try and determine what greenhouse gases are doing, insert constants to make sure the result is consistent with greenhouse gas modelling. Wella!.
The data can then be adjusted or ignored.
Willis
Use HITRAN line-by-line calculations. That’s how 3.7 W/m^2 was calculated. It’s more accurate than band models.
michel says: April 12, 2014 at 12:26 pm
“Yes, this is very odd indeed. I look forward to an explanation from Nick Stokes!”
For some reason, Willis seems to be calculating at TOA (70km). But Hansen is definite about where he is calculating, at the tropopause. He says in his 2005 paper:
“The simplest forcing, and the only pure forcing, is
the instantaneous forcing, Fi. Fi is the radiative flux change
at the tropopause after the forcing agent is introduced with
the climate held fixed. The reason to use the instantaneous
flux at the tropopause, rather than the flux at the top of the
atmosphere, is that, as shown by Hansen et al. [1981], it
provides a good approximation to Fa, the flux change at the
top of the atmosphere (and throughout the stratosphere)
after the stratosphere is allowed to adjust radiatively to the
presence of the forcing agent.”
So I calculated Modtran at 17km, tropics.
375 ppmv CO2 – 289.0 W/m2 upwelling
750 ppmv 284.5 W/m2.
Difference 4.5 W/m2.
Jim s says:
“April 12, 2014 at 12:12 pm
Well, and I might be wrong, but the theory of CAGW does not rely on CO2 alone. ”
Yes that’s right
– it also relies on copious amounts of deplorable bullshit and hokum models
“””””…..Dave Schaack says:
April 12, 2014 at 5:37 pm
bones says:
April 12, 2014 at 4:49 pm …..”””””
Well Max Planck simply asserted that electromagnetic radiation carries a quantity (h) of “action”, about 1E-34 Joule-seconds, for each cycle of the EM wave.
Well some people use hbar instead, but they are using the action for each radian of the EM wave, rather than each cycle.
Some particle physics types use a system of units where c = h (or hbar) =1
So to them E = m = f
Konrad says:
April 12, 2014 at 6:22 pm
Yeah, those dumb scientist chumps … no way they’d do something like say this …
w.
-Doubling, Forcing
10-20 ppmv, 3.42 W/m2
20-40 ppmv, 3.49 W/m2
40-80 ppmv, 3.45 W/m2
80-160 ppmv, 3.36 W/m2
160-320 ppmv, 3.20 W/m2
By the time we get to the doubling from 160 to 320 ppmv, the change in forcing has stabilized at 3.2 W/m2. This agrees with my results looking at the doubling from 275 ppmv (pre-industrial) to 550 ppmv, which gave 3.2 W/m2.
w.–
So each 3.4 /m/2 is suppose to add 1 C?
And why doesn’t start at ppb.
Though Earth has never had less than 160 ppm, and doubtful CO2 anywhere in universe will be below 10 ppm.
And if 320 ppm of CO2 adds 5 C, why does wiki give a range of:
By their percentage contribution to the greenhouse effect on Earth the four major gases are:
water vapor, 36–70%
carbon dioxide, 9–26%
9% of 33 is 2.97 C and 26% is 8.53 C
Another very interesting article from Willis. This is habit forming.
Also, george e smith is smarter than I am. He says:
I think the whole idea is rubbish (of CO2 induced warming).
I’m not quite there yet. But it is clear from real world observations that if CO2-induced warming exists, it is fantastically exaggerated. If it does exist, it is so small that it can be completely disregarded.
george e smith, you are correct, I was thinking of a dilute gas phase scenario, not a solution.
Nick Stokes says:
April 12, 2014 at 6:30 pm
Dang, Nick, you surprise me … well spotted. I often forget that when the IPCC says “Top Of Atmosphere”, they mean the top of the atmosphere … except when they mean “Middle Of Atmosphere”. I don’t think that’s all of the answer but I suspect it’s most of the answer.
However, that brings up more issues. FIrst, as you point out, Hansen says that the radiation at the tropospheric level is a good approximation, not of Fi (instantaneous forcing), but of Fa (forcing after the stratosphere changes temperature.
I fear I don’t understand that. IF the instantaneous forcing Fi at the tropopause is really the adjusted forcing Fa … then what is Fi itself? It has to be larger than Fa, by definition.
Next, you’ve got the plan but your calculations are incomplete. To complete them, you need to subtract the downwelling forcing at the tropopause, because Hansen is discussing net forcing (up minus down). Here are those figures for clear-sky tropics.
ppmv, Upwelling, Downwelling, Net
375, 289.037, 9.470, 279.567
750, 284.484, 10.516, 273.968
Curiously, this increases the calculated value of the change from what you found (4.5 W/m2) to no less that 5.6 W/m2. And this puts it into fairly good agreement with Hansen’s results, which show about 5.2 W/m2 in the tropics. But that’s for Fi … and he says that what I’ve just measured is a good approximation of Fa.
This is one reason that I find this whole approach crazy. The problem is that it’s not possible to measure something “at the tropopause” in any but the most general way. In addition, I fail to see the diagnostic value in measuring the radiation in the middle of the atmosphere. If you do that, then if the stratosphere warms slightly and the troposphere cools slightly, the “TOA” radiation changes with no change in the global energy balance. How does that not make it useless as a tool to diagnose changes in the overall energy state of the system?
Nor is the IPCC consistent in the use of TOA to mean tropopause. For example consider this quotation from the TAR:
Clearly, they are NOT using the TOA balance to mean the balance at the tropopause, but at the actual top of the atmosphere. And the same is definitely true about the Chapter in the AR4, the one entitled “Top Of Atmosphere Radiation“. There, TOA means “as measured by satellite”, just as you would imagine. CERES uses the same terminology, where TOA means the radiation actually entering or leaving the system. So I forget about the bizarre corner of the IPCC world where TOA means troposphere.
In any case, Nick, credit where credit is due—even though your calculations were incomplete, I do think you’ve solved the mystery. I know I’ve been on your case in the past, but in this instance, you da man. My congratulations.
Now all we have is the mystery of why an unmeasurable mid-atmosphere quantity, which is free to fluctuate without changing the global energy balance, was picked as being diagnostic of the global energy balance … and of course the mystery of why even to the IPCC, “top of atmosphere” sometimes means the tropopause but mostly means what the satellites measure …
Best regards to all, and my thanks to Nick for actually doing the calculations.
w.
Oh, yeah.
“Dr. Strangelove says:
April 12, 2014 at 6:25 pm
Willis
Use HITRAN line-by-line calculations. That’s how 3.7 W/m^2 was calculated. It’s more accurate than band models.”
#################
HITRAN is the database not the model.
MODTRAN is a band model. If you want to use an LBL check here
http://rtweb.aer.com/