A Modtran Mystery

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:

modtran ir in the atmosphereFigure 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:

increase in forcing for CO2 doubling ModtranFigure 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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Jim s

Well, and I might be wrong, but the theory of CAGW does not rely on CO2 alone. The theory states that increasing CO2 leads to increasing H20 and the increased H20 creates hot spots in the tropics and it’s these hot spots (via more H2O) that do the warming. CO2 by itself can’t. I’ll only add (the good news) that no hot spot has ever been detected and no increase in H2O has been observed.

Dave Hardesty

Perhaps Hansen and company used LOWTRAN, back in the day it was used for quick rough calculations in the Electro-Optical world since even MODTRAN took a lot of computing resources and time (early 80’s). When we wanted/needed very precise results back then we used HITRAN, but the calculations were so expensive in time and computing resources that we kept the transmission results as tables for later use for as long as possible. From what I can recall the results from using LOWTRAN vs HITRAN could be enough to account for the delta you’ve found.

Rick

Emission happens typically 1 ns after absorption.

If I understand what you’re saying…
You ‘checked the reference’ on something ‘everybody knows’, and couldn’t replicate it.
“Check your assumptions.”

R. Shearer

Interesting discussion around this going on at JC’s site.
Spartacusisfree | April 12, 2014 at 12:11 pm |
Reply to RobertinAz:
MODTRAN is very good at simulating the planet IR balance. This is because it was derived from the correct physics; 160 W/m^2 mean surface thermalisation. Because it’s proprietary, it can’t be ‘altered’. The IPCC climate model heat transfer is a scam, based on assuming the surface IR is at the 396 W/m^2 black body level, plus the convection and evapo-transpiration.
They then put in fake cooling from the top by incorrectly claiming you can apply Kirchhoff’s Law of Radiation to the semi-transparent atmosphere. When the 40% residual extra energy has produced imaginary extra water evaporation and ‘positive feedback’, they offset it in hind casting by exaggerated low level cloud albedo.
The planet has ~0.97 IR emissivity, used in MODTRAN.
Curious George | April 12, 2014 at 2:38 pm |
Spartacus – you seem to be familiar with MODTRAN. Has it been used in climate models? Does it handle clouds? Does it correctly predict daily surface temperature variations – a) in Sahara, b) in Kansas, c) in the Amazonia?

Willis;
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.
>>>>>>>>>>>>>>>>>>>>>>>>>
I can’t get the link to load, but my understanding has always been that CO2 doubling = 3.7 w/m2 was the generally accepted value. Is my memory faulty or is there some difference between the two references?
[Loads fine for me, it’s the link in the “References” at the bottom of the page I linked to in the head post. -w]

michel

Yes, this is very odd indeed. I look forward to an explanation from Nick Stokes!

Willis,
Isn’t it that the 4.5 W/m2 from Hansen is for CO2 itself in the atmosphere, but that is not taking into account the overlapping bands with water vapour?

Generic Geologist

I would not rule out the possibility that the issue that you uncovered is known, but ignored by climate modelers. It would be just one more “parameter’ that needs to be “adjusted” to give them the answer that they want. Very similar to the residence time of CO2 in the atmosphere. When no one was concerned about it and it was a purely academic exercise the residence time was around 10-12 years. Once it became a “parameter” it was “adjusted” up to 100 years to fit the IPCC models.

If the atmosphere were 10 meters deep. I might consider modtran predictions meaningfull. Modtran is just another simulation. No one it seems is intelligent enough to define, predict or measure molar absorptivity for gasses.
It is clear that greenhouse gases do slow radiative cooling rate. H20 is usually over 10,000 parts per million n the tropics. Day night termperature ranges increase from the tropics to the poles. That change can be correlated with prevailing dewpoint. It cannot seen in a trace change in CO2.
The idea of radiative forcing seems a violation of the laws of themodynamics whenever heating is part of the discription.
Where are the experts?
NIST it seem cannot not tell us what ratios are for CO2 and H20, but 10.000 is a bit bigger than 400.
http://webbook.nist.gov/cgi/cbook.cgi?ID=C7732185&Units=SI&Type=IR-SPEC&Index=0#IR-SPEC
http://webbook.nist.gov/cgi/cbook.cgi?ID=C124389&Units=SI&Type=IR-SPEC&Index=0#IR-SPEC
Each graph must be anotated.
Notice: Concentration information is not available for this spectrum and, therefore, molar absorptivity values cannot be derived.

Something has changed in the online MODTRAN calculator. It produces somewhat different results than it used to. Ref. note #2, here:
http://www.burtonsys.com/climate/MODTRAN_etc.html

D. J. Hawkins

@Jim s says:
April 12, 2014 at 12:12 pm
Perhaps the word “instantaneous” has a different meaning in your neck of the woods. Please note we are not discussing water vapor feed backs or hot spots in this particular thread. Hansen’s claim of 4.5 W/m2 is the instantaneous value before the feedbacks kick in.

P.D. Caldwell

FYI ” . . . Table 1 of “Efficacy of Climate Forcings” , James Hansen et al . . .” loaded a moment ago.

Rud Istvan

The mystery is indeed deeper. Because the IPCC value for doubling from present is in fact about 3.7. Cited in many papers, including Trenberth and others.
My money is on Modtran.

DHR

The GISS zonal maps for instantaneous forcing for 2xCO2 and 1/2CO@ are the nearly precise inverse of each other. It’s not obvious to me why removing half of say 350 ppm should have the same effect, inverted, as adding another 350 ppm,

toms3d

Willis, I love your posts. I would like you to do modran for h20 at x y z dewpoints then take the residue out and feed it to modtran C02 and get .0001C or so feedback.
I know modtran does not work that way. What is the dew point for 1000 ppm of H20.
Somewhere below 0F.
Spread sheet showing h20 ppm vs dewpoint temp.
http://toms.homeip.net/global_warming/SpreadSheets/Goff-Gratch-vaporpressure.sxc

Greg Goodman

If it is linear, it should be the same thing but I think the doubling is usually taken from an assumed pre-industrial baseline of 280 ppmv.
I’ve also seen the usual figure for unamplified CO2 to be 3.7 W/m2/K.

Greg Goodman

This MODTRAN/HITRAN model is where I came in to all this climate mess.
Years ago a friend sent be a link to Dr David Archer’s site where he had course notes and an interface to do this sort of simulation on either MODTRAN or HITRAN (can’t recall which).
He was basically pointing out that cutting atmospheric CO2 in half would not make a bit of difference.
Oddly ,since that time he’s turned his coat and now seems to be a confirmed warmist.
Perhaps his V.C. had a word about where grant money comes from !

The main reason for that is in the influence of stratosphere. Radiative forcing is defined as a change in the flux just above troposphere after stratospheric temperatures have reached the new radiative energy balance, i.e., after the stratosphere has cooled. UChicago MODTRAN does not allow for cooling stratosphere. Results calculated at 17 km looking down are closer to the correct ones, but fully correct values require a model that makes the stratospheric corrections.

Kon Dealer

You don’t actually think Hansen is telling the truth about “instantaneous forcing” do you?

Coldlynx

Please continue with your Modtran mystery research. May i suggest that you check heat balance and heat transfer in Modtran. How the energy that is radiated towards space at a certain level reach that level from earth.
Clue: it can not be done by radiation

george e. smith

I have never been able to determine whether this MODTRAN calculation is for a one shot absorption by GHGs or whether it includes ALL of the multiplicity of absorptions and re-emissions, including the isotropic re-distribution that occurs at each and ever re-emission event.
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.
Consequently, I have no confidence in any such calculations.
I also know what the logarithm function is; so a CO2 doubling is 280 > 560 ppm CO2 and it also is 1 > 2 ppm CO2, or one molecule > two molecules of CO2 per liter of air.
The “observed” Temperature and CO2 data, track equally well, whether you take the log base 2 of the CO2 or log base 2 of the Temperature, or the log of neither.
Namely they don’t track at all; see Monckton’s last 17 years and 8 months for example, plus Mauna Loa CO2 over the same time frame.
I think the whole idea is rubbish (of CO2 induced warming).
Yes I do believe CO2 captures some LWIR radiation frequencies; so don’t go there. Roy Spencer, and Frank Wentz can explain the whole thing. It’s called the “oceanic effect”

daveburton says:
April 12, 2014 at 12:53 pm
Something has changed in the online MODTRAN calculator.
Indeed, in the current online version refered by Willis, you still can choose between water vapour influence as pressure or relative humidity, but the results are exactly the same…
In another version at the same university, you can’t even choose the water vapour effect anymore:
http://climatemodels.uchicago.edu/modtran/
WUWT?

Hansen estimate does not take into account of overlap between CO2 and WV?

gbaikie

I was curious where global warming was suppose to warm.
Your results results don’t seem to include the idea that arctic was suppose to get more warming
than anywhere else in the world.
Generally don’t think CO2 does much warming and few watts per square meter sort of goes along with what I assume.
As to your question, maybe Hansen simply applied it global vs doing regionally. And I would guess
doing this should distort the results. But I also think by doing it regionally one also distorts the results. So I find it interesting and interest topic to discuss. Likewise, I would interested in comparison between night and day, though the winter and summer sort does this.
It seems to be global warming is entirely about night time and winter increase in temperature, just any greenhouse effect on the Moon would be entirely about night time and polar warming. Or global warming is not going to increase daytime surface temperature on the Moon of around 120 C, but it could dramatically increase nighttime temperature on the Moon.
And on Earth, if one talking about time of when Earth had average temperature of 25 C, I would not expect much increased temperatures in tropics [maybe less cooling at night in tropics] but mostly expect the Temperate Zones to have a significant increase in average temperature. Or it would be tropical in sense one doesn’t get freezing temperatures at night- and therefore tropical plants could grow in these regions- you can grow orange trees in Oregon or even Canada.

Willis Eschenbach

Ferdinand Engelbeen says:
April 12, 2014 at 12:29 pm

Willis,
Isn’t it that the 4.5 W/m2 from Hansen is for CO2 itself in the atmosphere, but that is not taking into account the overlapping bands with water vapour?

In both cases (mine and Hansens) it’s from taking the current situation and instantaneously doubling the CO2, including all overlaps in both cases.
w.

Ralph Kramden

FORTRAN? Now that brings back some memories. I didn’t know anyone used FORTRAN anymore. I wonder if they store the source code on punch cards? Just kidding, I loved FORTRAN.

Pamela Gray

It’s cuz de heat is hidin under de clams in de oceans, doncha know. And dats a tragedy!

Willis Eschenbach

tom watson says:
April 12, 2014 at 12:52 pm

If the atmosphere were 10 meters deep. I might consider modtran predictions meaningfull. Modtran is just another simulation. No one it seems is intelligent enough to define, predict or measure molar absorptivity for gasses.

Since you haven’t provided the slightest scrap of evidence for your claim that Modtran has significant errors, it seems that you are not intelligent enough to understand that on a scientific website, claims are meaningless without facts, logic, math, or observations to back them up.
Assuming that scientists might be wrong is a good thing. Assuming that they are idiots is always a mistake. Scientists have problems, to be sure … but lack of intelligence is not generally among them.
In fact, if you had taken the time to look at the manual and run the model and inspect the results, as most intelligent folks would do before commenting, or even read the caption to Figure 1, you’d have noticed that Modtran explicitly calculates the concentration of the variables at 33 of altitude levels, and uses that in the final calculation.
w.

tgasloli

The absorption curve should not be linear, check what it does with concentrations of 50, 100, and 200 ppmv.

Willis Eschenbach

daveburton says:
April 12, 2014 at 12:53 pm

Something has changed in the online MODTRAN calculator. It produces somewhat different results than it used to. Ref. note #2, here:
http://www.burtonsys.com/climate/MODTRAN_etc.html

Thanks, Dave. According to your data at the link, the 2xCO2 forcing is 3.2 W/m2 … which is identical to my results in Figure 1. So I’m not sure what you mean. I calculated the CO2 forcing from your data as the I_out for 285 ppmv minus the I_out for 570 W/m2.
w.

Willis Eschenbach

DHR says:
April 12, 2014 at 1:05 pm

The GISS zonal maps for instantaneous forcing for 2xCO2 and 1/2CO@ are the nearly precise inverse of each other. It’s not obvious to me why removing half of say 350 ppm should have the same effect, inverted, as adding another 350 ppm,

Good question. It’s because the forcing is logarithmic (base 2). A doubling or a halving have inverse effects.
log2(8) = 3
log2(4) = 2
log2(2) = 1
So for example, dividing 4 in half or doubling it each change the log2 by 1 unit …
w.

Why do we have this discussion? It’s not CO2 and never has been. Wake up! It is the Sun.
Remember, in 1970, it was the Solar constant. Now with Soho, we find the EUV [10.7 cm flux] varies wildly. The Flux is used to determine the amount of atmospheric drag on satellites. The Flux puffs us the upper atmosphere creating a “insulation blanket”. The CO3 [ozone] reflects [absorbs] the infrared from both the Sun and Earth. The increase in “insulation” prevents heat from leaving the North and South pole. The decrease in the Flux allows heat to escape.
Watch the Antarctic set awesome new record ice extents due to the Flux being down [less than 140 during a Solar peak is a scary amount on low side].

Roy Spencer

Willis, try doubling CO2 from pre-industrial and see what you get.

jim2

@ 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.

Willis Eschenbach

Coldlynx says:
April 12, 2014 at 1:53 pm

Please continue with your Modtran mystery research. May i suggest that you check heat balance and heat transfer in Modtran. How the energy that is radiated towards space at a certain level reach that level from earth.

You raise an interesting issue, Coldlynx. Modtran is a radiation model and doesn’t deal with heat balance and transfer other than indirectly. By that, I mean that you can adjust surface temperature, and the model recalculates atmospheric temperature (at 33 levels) assuming that the lapse rate is unchanged.
In other words, it cannot do what you propose because it is not included in the model. Note that this is not a shortcoming of the model. Every model only deals with certain things, you can’t escape it. It just means that you’ve picked the wrong model for what you want to investigate.
However, none of that matters to this study because I’m dealing with instantaneous forcing, before any atmospheric or surface temperature response.

Clue: it can not be done by radiation

Clue. If you have something to say, say it. Leaving clues doesn’t work.
Regards,
w.

GregB

What Roy Spencer says – 285 and 570 rather than 375 and 750. Probably a log relationship (or two) rather than linear.

Willis Eschenbach

Roy Spencer says:
April 12, 2014 at 2:59 pm

Willis, try doubling CO2 from pre-industrial and see what you get.

Interesting question, Dr. Roy. It turns out I had tested that before writing this post, and it’s the same, e.g. tropics clear is 3.2 W/m2 per doubling of CO2.
Following on from that, I greatly like this part of science on the web, which is that I get all this insightful feedback and interesting questions and suggestions. Since the question was interesting, I looked further at the bottom end of the CO2 concentrations and found the following results (again, tropics clear):
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.

GregB

OK – When all else fails then either Hansen or Modtran is wrong. I know who I’m betting on.

Willis Eschenbach

Ralph Kramden says:
April 12, 2014 at 2:45 pm

FORTRAN? Now that brings back some memories. I didn’t know anyone used FORTRAN anymore. I wonder if they store the source code on punch cards? Just kidding, I loved FORTRAN.

Ah, yes, the famous Hollerith punch cards. The best part was after punching all 173 cards for your whiz-bang program, you turn them in to the resident Cerebus guarding the holy computer … and get them back three days later saying you made a mistake on card 11. A mistake which will require you to repunch perhaps a third of the cards …
But yes, of the three computer languages I learned during the 1960s (ALGOL, COBOL, and FORTRAN), only one survives, like some dinosaur who never got the news about the asteroid … I fear that since learning R, I have no interest in any of the others. Yeah, I still write in Basic and Pascal and Mathematica, but R is da bomb …
w.

Stargazer

Boy, does this bring back memories. I wrote a program at GSFC during 1972-1982 called the Synthetic Spectrum Program (SSP) (re: Rudy Hanel, Virgil Kunde, et al.) with parameters to describe the various atmospheres we wanted the simulate in the IR for remote sensing analyses: Earth, Mars, Jupiter and Saturn. It was written in FORTRAN. I remember a copy was sent to NCAR in the early 80’s. I verified that the program (substantively unchanged) was still in use in the mid-90’s. I wonder how much of that program is the basis for later models? The SSP did a very good job in a clear atmosphere. Clouds & aerosols were (and I think still are) a confounding problem that we were not able to solve then.

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.

Willis Eschenbach says:
April 12, 2014 at 3:34 pm
I’m a Forth guy. But I play with bits. And controlling things. In real time.

Richard G

Willis Eschenbach says: “Modtran is a radiation model and doesn’t deal with heat balance and transfer other than indirectly.”
Thanks for answering my Q before I could ask. And also thanks for your thoughtful inquiries. So Modtran could also mean MODEL Fortran?
Another case of “It’s Models All The Way Down.”
Has anybody actually, like, MEASURED this stuff? My default suspicion says : No, not really possible. But we sure can guess good.
P.S. I’m not a computer geek, just somebody who understands how really difficult it is to actually collect good data in the real world.

Berényi Péter

Wikipedia says:

Forcing due to atmospheric gas
For a greenhouse gas, such as carbon dioxide, radiative transfer codes that examine each spectral line for atmospheric conditions can be used to calculate the change ΔF as a function of changing concentration. These calculations can often be simplified into an algebraic formulation that is specific to that gas.
For instance, the simplified first-order approximation expression for carbon dioxide is:
ΔF = 5.35 × ln C/C₀ W/m²
where C is the CO₂ concentration in parts per million by volume and C₀ is the reference concentration.

If C/C₀ = 2, that is, for a doubling of atmospheric CO₂ concentration this formula gives 3.7 W/m². However, the term “radiative forcing” in this case is probably not equivalent to the “instantaneous radiative forcing” used by MODTRAN. The wiki value may be related to the IPCC usage.

The radiative forcing of the surface-troposphere system due to the perturbation in or the introduction of an agent (say, a change in greenhouse gas concentrations) is the change in net (down minus up) irradiance (solar plus long-wave; in W/m²) 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.

Sure it is a rather contorted definition, because
1. the “tropopause” is not a well defined surface (see tropopause folds)
2. allowing one side to adjust while holding the other side fixed excludes empirical testing.
Instantaneous radiative forcing“, although it can’t be tested either, is a bit better, because

Radiative forcing is called instantaneous if no change in stratospheric temperature is accounted for.

This latter usage at least treats the entire atmosphere uniformly. Which is preferable, since heat capacity of the stratosphere is negligible, so the surface along which “forcing” is defined can be moved upward at leisure. Forcing at ToA (Top of Atmosphere) is the same as at the ill defined tropopause.
Now, the stratosphere is supposed to cool down with increasing GHG concentration. If this cooling is taken into account while the troposphere below is “held fixed”, it should increase radiative loss through the tropopause, because there is a larger temperature difference. Therefore the 3.7 W/m² given by the IPCC is an upper bound to instantaneous radiative forcing, which is consistent with your thought experiment using MODTRAN, but excludes higher values.
The NASA GISS ModelE Climate Simulations page you were referring to uses a somewhat more consistent termonilogy.

– “Fi”, the instantaneous forcing, is the radiative flux change at the tropopause after the forcing agent is introduced.
– “Fa”, the adjusted forcing, is 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.

That is, they call “adjusted forcing” what is referred to as “forcing” by the IPCC. Now, their values are based on the output of Model E
Fi = 4.52 W/m²
Fa = 4.12 W/m²
Note the Fa > Fi relation does not hold for Model E, which is truly amazing. But hey, all models are wrong, but some are useful. And in this case the higher the values are the more fit for purpose they’ll be, provided the “purpose” is to generate scare.
Otherwise all such calculation, including MODTRAN is based on assumptions about the “average” atmospheric temperature/moisture profile in different regions and/or under different meteorological conditions, which may or may not be adequate.
I reckon even the IPCC adjusted forcing estimate of 3.7 W/m² is too large (derived for the US standard atmosphere or some such artificial constuct). Based on your fiddling with MODTRAN it should be below 3 W/m² (but probably above 2.4 W/m²).
Relation between reality and theory is always difficult. For instance we understand clearly why the stratosphere should cool down with increasing GHG concentrations. And indeed, according to RSS, during the past 35 years temperature of the lower stratosphere has decreased at an average rate of -0.28 K/decade. The only trouble is that almost all the decline happened close to the beginning of observations, during the last 2 decades this rate is only -0.03 K/decade, almost an order of magnitude smaller.

Willis;
[Loads fine for me, it’s the link in the “References” at the bottom of the page I linked to in the head post. -w]
>>>>>>>>>>>>>>
Nope, can’t load it. Even googled it, comes up with the link, can’t load it. Tried multiple browsers. I going to go all conspiracy and wonder if Canadian IP addresses are being blocked to prevent Steve McIntyre from looking at their data.
Not a big deal, but the 3.7 versus 4.x things is the real mystery to me. I don’t think they explicitly state it in AR4, I think you have to go back to AR3 or Ar2 to find the number, but 3.7 is what I’ve always seen quoted before.

Nullius in Verba

I’m not sure if this has any relevance, but I notice Hansen defined fi to be the forcing at the tropopause, rather than TOA. MODTRAN in the screenshot appears to be set at 70 km altitude. Is it possibly being affected by absorption/overlap in the stratosphere?

jorgekafkazar

Ralph Kramden says: “FORTRAN? Now that brings back some memories. I didn’t know anyone used FORTRAN anymore…”
I interviewed for a job about 15 years ago that involved patching and updating an extremely complex program that was still in FORTRAN.

bones

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.

charles nelson

Water vapour.