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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Welcome to the world of toy models. The reason Willis isn’t getting the results he expected is because there are many different toys that all do the same thing. Not only do you have to use the same toys as the other guys you have use the same revision number toy and you have to have all the input parameters identical. It gets worse. In iterative calculations using floating point arithmetic you must also be using an FPU (Floating Point Unit) that rounds in exactly the same way. So you might get a different result between say an FPU in an IBM PowerPC FPU and an Intel FPU.
Count yourself lucky if you got an answer to a complex highly iterative mathmetical calculation that differed by only 20% from the answer someone else got when you took no pains at all to duplicate the environment and parameters. I’m surprised it was that close.
I want to see also surface temperatures generated by such tool. Then we can compare it with some real observations, like winter HadCRUT data in Arctic (70-90N).
http://climexp.knmi.nl/data/tsicrutem3_hadsst2_0-360E_70-90N_n_suseason.png
I am eagerly waiting to see the “greenhouse model” surface T in 1940s, compared with reality. Or the warming in 1910-1940. Or the stationary temperature trend between 1950-2000. Can’t wait.
I liked this bit
by
Charlie A says:
August 18, 2011 at 6:44 pm
a simple climate model (MAGICC)
Wow really? they used MAGICC?
now thats more likely the truth:-)
to approximately reproduce ( is that a sort of, maybe? kind of ? )results from the AOGCM multi-model dataset at PCMDI.”
3.7 W m-2 is a global average. What is Modtran calculating?
Per IPCC TAR global average vs a single vertical profile can cause errors on the order of 5-10%:
“Several previous studies of radiative forcing due to wellmixed
greenhouse gases have been performed using single,
mostly global mean, vertical profiles. Myhre and Stordal (1997)
investigated the effects of spatial and temporal averaging on the
globally and annually averaged radiative forcing due to the wellmixed
greenhouse gases. The use of a single global mean vertical
profile to represent the global domain, instead of the more
rigorous latitudinally varying profiles, can lead to errors of about
5 to 10%; errors arising due to the temporal averaging process are
much less (~1%).” p. 356 or 8/68 of http://www.grida.no/climate/ipcc_tar/wg1/pdf/TAR-06.pdf (1.4MB pdf)
The next page has some history on the value used by IPCC for the equivalent radiative forcing of doubling CO2. For something supposedly based on relatively straightforward physics, I’m surprised to see the value being changed by 15% between SAR and TAR, with a 3.5 to 4.1 W m-2 band for the estimates.
“6.3.1 Carbon Dioxide IPCC (1990) and the SAR used a radiative forcing of 4.37 Wm−2
for a doubling of CO2 calculated with a simplified expression.
Since then several studies,…. The newer estimates
of radiative forcing due to a doubling of CO2 are between 3.5 and
4.1 Wm−2 with the relevant species and various overlaps between
greenhouse gases included. The lower forcing in the cited newer
studies is due to an accounting of the stratospheric temperature
adjustment which was not properly taken into account in the
simplified expression used in IPCC (1990) and the SAR (Myhre
et al., 1998b). In Myhre et al. (1998b) and Jain et al. (2000), the
short-wave forcing due to CO2 is also included, an effect not
taken into account in the SAR. The short-wave effect results in a
negative forcing contribution for the surface-troposphere system
owing to the extra absorption due to CO2 in the stratosphere;
however, this effect is relatively small compared to the total
radiative forcing (< 5%).
The new best estimate based on the published results for the
radiative forcing due to a doubling of CO2 is 3.7 Wm−2, which is
a reduction of 15% compared to the SAR."
Willis,
First off, Modtran is a moderate resolution analysis and not the line by line result you assumed. That doesn’t mean it isn’t quite accurate because as you have noted, one pretty much sees a small linear change when you do something like double or half the amount of co2.
The number 3.7W/m^2 comes from looking down at the troposphere, around 12km rather than way high up in the low ionosphere at 70km. Apparently, the ipcc doesn’t realize that the atmosphere extends past the tropopause. Actually, I’m sure they do but as you noticed, the difference between the co2 value and double that decrease substantially as you go higher. Also, there are embarrassing questions that can arise once you find that the temperature rise to well above Earth’s surface temperature way up there.
You noticed also that the numbers differ with cloud cover versus clear sky. Water and ice are going to absorb and emit more like liquids and solids and not like water vapor. Absorption tends to be virtually independent of temperature while emissions of solids and liquids tend to be more like full blackbody spectrums – but at a lower T than the usual surface amounts. It’s a bit more complex than that as the size of the droplets are in the range of the wavelengths of absorption and emissions and there is also scattering that occurs and different clouds vary in top temperatures, altitudes, optical thickness, droplet sizes. Optically thick clouds are pretty much going to negate much of the effects of the molecular absorption below them so far as the spectrum goes. You will see that in the fact that the big absorption bands don’t go down to 0, but rather go down to a colder black body temperature curve – associated with the cloud top temperature.
Having played with a Hitran model made from line by line calculations, I’ve seen that the curves of h2o or co2 doublings or halvings are not truly linear and that they do vary from that as you go through multiple doublings or halvings. Eventually, your 3.7 W/m^2 tropopause absorption increase/decrease per doubling/halving drops down to half that value after 7 or 8 halvings. After all, the total effect of co2 is under 30 W/m^2 absorption under clear skies with typical h2o concentrations and it’s possible to do an practically an infinite number of halvings. This is do to the atmosphere becoming more transparent and optical absorption path lengths increasing as the concentration decreases.
As far as Hansen goes, he’s published BS in the past, things like assuming Stefan’s law applies to the Earth’s atmosphere and the effective altitude of radiating energy. Sorry, don’t recall the source – some paper in the 90s or late 80s. Concerning his modeling, I recall seeing a paper with Lacis and others where they came up with a pure assumption that water vapor increased with temperature yet cloud formation decreased. BTW, I think they used a detailed 1-D model with Modtran or maybe even Hitran for that one. They also mentioned that another equally valid assumption did not create a decrease in cloud cover with increasing temperature but they Chose the first – and that became gospel.
Since clouds have an immediate effect upon ground temperatures and with less clouds in the sky, the temperature tends to rise due to the increased incoming solar radiation, one can ignore the obvious causality and jump to the foolish conclusion that warmer temperatures and more h2o vapor cause less cloudiness – like the assumption that ENSO causes sunspot cycles.
I think you’ll find that the Modtran calculator is probably quite accurate for the circumstances that the calculations are run. The ipcc is probably using the tropopause looking down or worse, using some empirical formula dating back to the 1960s (Budyko). I think that Hansen has been smoking those funny mushrooms instead of eating them.
CO2 in troposphere is net absorber, in stratosphere CO2 is net emitter.That’s the reason, why
stratosphere is cooling.In stratosphere there is not very much radiation left between 13.4 microns and 16 microns so CO2 molecules cannot absorb very much radiation but there is enough kinetic energy to excite CO2 molecules.There should be stratospheric adjustment, if you are calculating ground temperatures at 70 km height.
George Smith mentions 40 W/m2 going space which Trenberth put in his (incorrect but much reported) heat balance papers. Over at Climate etc you will see a number of mentions of 66 W/m2 and it appears from a slide in a presentation to KNMI by( the late) Dr Noor Van Andel that Trenberth acknowledged that he knows it is 66 W/m2 (Is it scientific fraud to not correct or withdraw his papers?). Then putting in the proper heat transfer by convection and phase change (evaporation at liquid surfaces) which removes heat from the surface there is no need to consider radiant absoption by so called greenhouse gases. It is generally accepted the difference between the adiabatic lapse rate (9.8K/1000m) and the “environmental” lapse rate 6.5K/1000m is due to heat from water vapor. On top of this there is the convective heat transfer to oxygen and nitrogen at all surfaces. These more or less non IR radiating gases exchange heat do to mixing. CO2 will not absorb any radiation from its surrounds if it is the same temperature as the surrounds but at the top of the atmospher it will radiate to space
Modtran is only a model which does not consider other forms of heat transfer.
We are really relying on Hansen and Myhre and Manabe and Ramaswamy running these Modtran/Hitran LBL radiative transfer models properly. [Let alone the fact that we are not sure the models are truly representative of how radiation moves through the atmosphere. Let alone the fact that the first 3.7 Watt/m2 produces a different “temperature” response than the next 3.7 Watts/m2 and so on].
I have never seen it all explained properly anywhere – not even half.
Willis,
I played with MODTRAN about 2 years ago and I discovered a curious thing about it.
For example: if you fix the ground temperature offset at 0 and switch the “hold water vapor” option from “pressure” to “Rel. Hum.” the outgoing radiation for a predetermined setup doesn’t change.
When you set a positive value for the ground temperature offset, switching the “hold water vapor” option from “pressure” to “Rel. Hum.” you get a reduction of the outgoing radiation at the TOA, while setting a negative value for the temperature offset, you get an increase of the the outgoing radiation at the TOA instead.
Since the simulation ground temperature is 299.7K that is 26.5°C, which strange phenomena should happen to WV for that temperature?
I also never been able to establish which is the angle of the field of view of the simulated spectrometer at the TOA. From my point of view, this should be an important parameter because the outgoing emissions from the GHGs should exit the TOA with different angles than the black body radiation coming directly from the ground, and if the simulation has been made for a narrow angle around the nadir view, it could exclude a lot of that outgoing GHGs scattered radiation.
To understand what I mean you could read this pdf from CNR:
http://www.atmos-chem-phys-discuss.net/6/4061/2006/acpd-6-4061-2006-print.pdf
See figure 3 at page 4076, and note in the upper graph the radiation which flows tangential to the atmosphere at about 34km. Note also that its spectrum is the inverse of the radiation at the nadir and that’s obvious for me because this is the part of the radiation spread by the CO2. The more CO2, the more is higher that peak at abt 650cm-1 in that graph. The more CO2, the more energy exits the atmosphere not from the nadir (in that case it exits tangent to the atmosphere)
For this I believe that simulators such as MODTRAN should be used knowing the field of view they are simulating, otherwise while they are very good tools to estimate the effective temperature at ground measuring the outgoing radiation at TOA, they could be meaningless for estimating the effective outgoing radiation a the TOA.
I have read every comment so far. You guys are precious. Reminds me of the men folk sitting around the Dinner table talking tractor language.
“Hey Jeb, how ’bout that new fangled Harvester 735-hp30? Needs the new JD 4589-7blade to really work.”
“Jethrow you crazy. The JD 4589-7blade won’t work. You can only use the International YUT-8blade on the Harvester PTO”.
Please continue.
RE: Main Article
“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.”
I have looked at this data over a wide range of CO2 levels, from zero to over 100,000 as a matter of curiosity. The linear log region runs from about 2 PPM CO2 to 792 PPM after that a gradual increase begins, which by 143,360 PPM CO2 yields temperatures about 4 deg K warmer than those predicted by the linear slope theory. As I can think of several reasons why the log relationship might fail at high concentrations of CO2, I cannot say that this is a ModTran quirk.
tallbloke says:
August 19, 2011 at 1:35 am
Roy Clark says:
August 18, 2011 at 9:34 pm
[,,,,]
Very interesting comment Roy. Willis will need to keep this thread focussed (good luck Willis), but your thesis deserves a thread of it’s own IMO.
====================
Exactly what I was thinking when I read Roy’s post.
Continuing Education units given to “climatologists” who read it.
*
Version is important, but scattering IS a photon absorption event, at the quantum level. GK
Cementafriend at 5.42am:
Really interesting point. Has it been discussed in the literature? There is also – as Kiehl & Trenberth (1997) made clear – large uncertainty in the figure they adopt for the wattage of ‘thermals’ (presumably heat transmitted to the air by conduction from the earth’s surface).
I don’t think Trenberth’s failure to update is fraudulent, although it may be poor science.
Typo corner: “These more or less non IR radiating gases exchange heat do to mixing.” I think ‘due’ is needed in place of ‘do’.
wow … model based science seems to be full of contradictions … oh wait … I seem to remember alot of science being done before computer models ever existed … maybe more obseravation and less models would be a more worthy exercise … and no I’m not accusing W. of too much reliance on models …
The online version is definitely one of the older ones. The more up to date versions are described at http://www.kirtland.af.mil/library/factsheets/factsheet.asp?id=7915, and handling the multiple scattering properly is one of the major upgrades.
That older version has known under and over estimates in various respects.
Hi Willis
As I have said before, you cannot “calculate” that which has never been tested. All these “fill in” programs are pure fraud so as to make you think that there are methods, that gave rise to measurements that gave rise to results…. But if you look for them (those methods), you find there are none. All you end up with (always) is the IPCC report.
I believe the original “test results” or values in W/m2 came from the observed global warming (originally 1750 was chosen as the start off date ) versus the increase of GHG’s seen in the atmosphere (since the start off date) where a proportionate allocation for the increase in each GHG was made depending on its increase. To a lesser agree I think they also compared the line by line analysis of each GHG to give a bit more or a bit less weight on the strength of a GHG but only in the areas of the spectrum where earth emits.
Which is of course why everything went wrong.
They did not even understand the “absorption” process correctly. When I made queries I found changes being made in the definition in wikipedia . Quite unbelievable. They also assumed there was no cooling effect by GHG’s.
http://www.letterdash.com/HenryP/the-greenhouse-effect-and-the-principle-of-re-radiation-11-Aug-2011
They had the horse completely behind the carriage. It is the worst mistake any scientist can make. You have assumed what the cause is of a problem before you actually determined it as the cause.
I believe that at some later stage they changed the 1750 date (to 1850?) which could help explain the differences you are getting now…. Obviously nobody is willing to admit to making any error, they had all tested it….
Didn’t they?
I want to thank you Willis for all you have done and said, it helped me a lot. I know I have come at the end of my own investigations. There is nothing more for me to figure out. I know now what is causing the extra warming besides the normal natural warming…. . And it is nothing to do with the CO2.
If you make a print of my tables here,
http://www.letterdash.com/HenryP/henrys-pool-table-on-global-warming
and really take some time to really study them you can easily figure it out for yourself
1) first the so-called ” global warming” is not global at all.
In the SH there is almost no warming. Clearly, you can see a big difference in the results between NH and SH?
But now, how can that be? We know from real science and experiments that the CO2 is distributed everywhere exactly the same. So, if the CO2 were to be blamed, should not the warming be the same everywhere in the world?
So, we conclude it never was the increase in GHG’s that caused any warming.
2) If you look in Argentina (where there was considerable de-forestation) you find severe cooling. If you look at Norway (where there is much increased forestry) you find warming.
3) the fact that SH has little landmass and that the NH has a lot of landmass is an another indicator that should give a clue.
4) we also know that there have been reports here on WUWT but also from the Helsinki university that there has been increased vegetation in the past decades, especially in the NH…..
…..wow. Did you all figure it out?
The warming is caused by us because we wanted more trees and a bigger garden…
Now what are we going to do about the so-called “global warming” problem?
Let us call it something else shall we?
I don’t have time to read all the refs on this. I’m guessing….
1D model? Any attempt to integrate different (re)-emission angles? That is, what is the mean free path length (obviously, a function of concentrations)? And the point made above that re-emission can be at different (longer) wavelengths is probably not considered.
Again guessing, it seems MODTRAN is based on a tool that might have been used to determine whether a high-altitude object could be imaged in IR from the ground. Once a photon is knocked off-course, it is lost. Using that logic, is re-emmission implicitly not allowed in MODTRAN? Is that approach accurate for atmospheric energy balance calculations? Doesn’t sound right to me.
With so many guesses, I must be wrong about a lot of this. Nevertheless, I’d like to echo the sentiment above. Toy models, don’t waste too much time on them.
Just for reference, my primary interest with Modtran was to get an indication of the *raw* CO2 concentration effect on transmission through the atmosphere. I am also assuming that this is under the condition of a fixed heat flow for any given concentration of CO2 as the greenhouse effect is based on a fixed amount of heat from the sun.
I see Willis is measuring the differential heat flow as the CO2 concentration is varied with fixed temperatures. The settings that show reduced sensitivity to CO2 relative to clear tropical air seem to indicate that CO2 is a lesser part the overall absorption of ground radiation in those cases. In other words, I suspect more of the CO2 absorption is being masked by other effects. This is why I have avoided these settings.
I have experimented with the sensor altitude which does seem to get problematic with settings below .05 km. If you reverse the direction of the sensor you get a calculation of the ‘back-radiation.’ All my measurements referenced here (above) were taken at the standard 70 km setting. That is in the mesosphere, nominally 50 km to 80 km. I understand this is that region of the atmosphere where the outward bound, 15-micron CO2 emission photons can finally escape into outer space.
steven mosher says:
August 19, 2011 at 12:03 am
Thanks, Mosh. While Google is indeed my friend, and told me lots of interesting things about the MODTRAN code (developed for the AIr Force, works well compared to other calculations), Google was unable to answer my question—why is the reported increase in absorption (instantaneous forcing) given by MODTRAN for CO2 doubling only about half of the Hansen/IPCC figures for instantaneous forcing?
Google wasn’t friendly enough for that …
w.
RE: Willis Eschenbach: (August 19, 2011 at 10:06 am)
“… my question—why is the reported increase in absorption (instantaneous forcing) given by MODTRAN for CO2 doubling only about half of the Hansen/IPCC figures for instantaneous forcing?”
I am afraid that might be a case of the devil being in the details. You will note that there are two options for dealing with a water vapor. Also ModTran is intended for use with real atmospheres. Hansen may be modeling an aggregate atmosphere. One way to increase the sensitivity to CO2 is make an assumption that reduces width of the open transmission zone. If Hansen provides emission plots similar to those returned by ModTran, it might be possible to make a detailed comparison between the two.
“”””” Brian W says:
August 18, 2011 at 11:53 pm
Willis Eschenbach
You sure are a slippery fellow, but since you ask . The current solar constant is stated as 1366w/m2 correct? My Passive Solar Energy book circa 1979 gives the solar constant as 429.2 btu’s/sq. ft./hr. This is equal to 1353.95w/m2, for a difference of 12w/m2 (rounded). “””””
The 1366 number is the one, I have used until quite recently; based on my eyeballing of almost three complete solar cycles of obsered data, unfortunately from several different satellites.
But I believe if you research the WUWT archives, you will find that quite recently; maybe the last few months even, NASA in fact issued a new preferred number; that is more like 1362 W/m^2, so that is the number I use now. When I learned about this stuff in school, the value in common use was 1353 W/m^2.
Where people get these 192 or 234 or other solar constant numbers form, I can’t imagine. When my wife turns on a stove hotplate so that it glows red, for the 3 1/2 minutes it takes to poach my egg, starting from cold water (plus egg); it is little comfort to me, that the average Temperature of that hot plate , is about 20-25 deg C. I still burn myself, if I touch it while it is poaching my egg.
Not surprisingly, the earth too reponds differently to the actual real incoming solar insolation, compared to what happens with just the annual average insolation. That’s why climate is the integral of the non-linear weather, and not the average of a presumed linear weather.
Roger knights:
The leaving out of forms of “to be” might just be some general semantics / e-prime mischief. I am seeing it happening quite often lately, even in some books.
Frank says:
August 19, 2011 at 12:05 am
Then what is the squiggly red line in the top right? AFAIK, it shows net absorption at every frequency … isn’t that an absorption spectrum? Yes, there is both absorption and emission at every level, but what we are looking for is the net absorption, which MODTRAN gives.
I understand all of that … but I don’t see that it makes a difference, and the cloud calculations are immaterial for what I am looking at, clear-sky conditions.
The IPCC usually talks about the top-of-atmosphere (TOA) forcing. They describe the TOA as:
In other words, say up 70 km or so, looking downwards. But they are often inconsistent in their usages. I do find the following:
which as you say they also use. That seems to me like the dumbest definition on the planet. To start with, the location of the tropopause varies around the planet. Second, they don’t give us a definition of the tropopause. 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. However, picking a quantity that cannot be physically measured as your main gauge of change seems … well, I’ll just call it “suspicious” and leave it at that.
In the IPCC glossary, the tropopause is defined as:
That is a useless definition from a useless pack of wankers. The problem is that often there is no clear defined “boundary” between the troposphere and the stratosphere, so real scientists use another definition. They use a definition that involves the location of a specific temperature change. The WMO, for example, uses the following definition:
Nice and clear, can be measured quite accurately … whereas the IPCC “definition” is just mushy new-age junk.
You’d think that there’d be a clear boundary between troposphere and stratosphere, and in the tropics there often is. In the Arctic Summer, on the other hand, the “boundary” is often kilometres deep, a region where there is no vertical change in temperature. The MODTRAN shows no temperature change from 10 to 22 km altitude … so which one is the “tropopause”, 10 km or 22 km or somewhere between? The WMO definition tells us exactly … the IPCC definition tells us nothing.
The answer seems to be, in IPCC science the height of the tropopause is whatever you want it to be. In the previously cited Hansen paper, they show two different zonal estimates of the height of the tropopause, which they used in two different types of calculations (p. 5 lower right) … why not just one standard tropopause height? How can they use two different tropopause heights for two different calculations and still keep a straight face?
Ah, this is climate science, so one hesitates to speculate … however, let me redo my previous figures using what those clowns specify as the tropopause height. From Hansen’s figure, this would be about 100 hPa in the tropics, 200 hPa in the sub arctic, and 150 hPa in the mid-latitudes. Using those figures, I get from MODTRAN:
Tropical, CO2 doubling at 100 hPa = 4.5°C
Summer midlatitude, 150 hPa = 3.8°C
Winter midlatitude, 150 hPa = 2.5°C
Summer subarctic, 200 hPa = 3.0°C
Winter subarctic, 200 hPa = 1.8°C
So shifting to looking downwards from the tropopause gives us different answers … but the different answers don’t help a bit. The average of the MODTRAN numbers still isn’t anywhere near the 4.5 value of Hansen, or the 4.1 value from the IPCC.
I did find an article by Peter Dietz called “Estimation of the Radiative Forcing
for CO2 Doubling” on the late great John Daly’s old web site (ah, you are sorely missed, John). The article is here. He finds a much reduced forcing from the doubling of CO2. I would welcome comments on his analysis, I can follow his explanation but I can’t gauge the quality of his objections and claims.
Thanks for the citation, Frank. Indeed, that’s the recurring problem I have, either paywalled or kinda circular references. In this case, all Myhre does is propose a new constant for the amount of CO2 due to a doubling, 3.71 W/m2 per doubling instead of the old figure of 4.6 W/m2 per doubling. He doesn’t say either where he got the old constant, or whether they calculated the new one and if so how … science as done before the world woke up and asked the climate scientists to show their work.
w.
Just when I thought I was finished there is something to figure out again.
Perhaps the increased vegetation that caused the extra warming was in part also due to the increase in CO2. The circle is complete.