In several recent posts, we’ve been reviewing the provenance of the radiative forcing estimate of about 4 wm-2 and the logarithmic form for estimating climate response to increased CO2 levels. This has led on the one hand to several primary references, including Lacis et al 1981 and, on the other hand, to references to realclimate collaborator David Archer’s MODTRAN calculator.
I want to focus today on the structure of these calculations – or, at least, to do so to the extent possible given that the methodologies are poorly described. In our discussions, many readers have volunteered observations relating to formulas for simple absorbance of radiation by gas. However, what these observations fail to address is that the relevant calculation here requires a detailed specification of the atmosphere, which includes not just CO2 levels, but a temperature varying from surface to atmosphere exit, other radiative gases including water vapor, clouds, etc.
Given this atmospheric profile, the calculations yield downwelling (or upwelling) infrared radiation in wm-2. The Archer calculator provides Java results for a variety of conditions, permitting the calculation of upwelling and downwelling radiation at specified altitudes. (It would be nice to have this algorithm available in a Matlab or R function and probably it wouldn’t be too hard to convert.)
What catches my eye about these calculations is that atmospheric conditions are held rigid – as though it were a coincidence that the CO2 radiation-to-space maximum and tropopause are at the same elevation. My own intuition is that the atmospheric profile is itself affected by presence of CO2. In Lubo short note on the matter, he took a similar perspective, hypothesizing that additional CO2 would raise the tropopause – a change in atmospheric profile that doesn’t occur in the rigid calculations of Myhre et al and Archer, where the entire impact is concentrated on downwelling wm-2. The form of the problem strikes me as an interesting type of calculus of variations problem and it would be interesting to see what this type of mathematician could do with it.
On to a review of the sources.
Myhre et al 1998
I’m going to start my review with Myhre et al 1998 online here, as that is relatively recent and was relied upon by IPCC TAR. Unfortunately,they do not provide a detailed or even cursory description of their algorithm, saying only that radiative forcing is calculated as a “difference between irradiances”:
In this study, radiative forcing is calculated as the difference between irradiances in the pre-industrial and present day atmosphere due to changes in concentrations of WMGG as described in IPCC 1995. The full definition of radiative forcing includes stratospheric temperature adjustment (IPCC 1995). However radiative forcing prior to this adjustment is often used in the intercomparison of radiation schemes since it is less computationally expensive. We refer to these forcings as “adjusted” and “instantaneous” respectively.
They state that they only consider direct forcing (i.e. no feedbacks):
Only the direct forcing due to a change in well-mixed greenhouse gas (WMGG) concentration is considered here.
Whereas Lacis et al 1981, as shown below, appear to have used only one vertical atmospheric profile, Myhre et al say that more than one vertical profile must be studied. In this article, they use three vertical vertical profiles (SH, Tropic, NH):
Myhre and Stordhal 1997 and Freckleton et al 1998 have shown that for global radiative forcing calculations, it is not sufficient to use a single vertical profile. Freckleton et al 1998 have shown that three vertical profiles ( a tropical profile and northern and southern hemisphere extratropical profiles) can represent global calculations sufficiently. These profiles are used for all calculations in this study except for the adjusted BBM forcing calculations ….
They also compare results from line-by-line and more parameterized models:
Three radiative transfer schemes are used, a line-by-line (LBL) model [Edwards, 1992], a narrow-band model (NBM) [Shine 1991] and a broad-band model (BBM) [Myhre and Stordhal 1997] …
They report closely similar results for CO2 forcing from pre-industrial to the present for the LBL (1/76 wm-2), the Shine NBM model (1.79 wm-2) and the Myhre and Stordal 1997 BBM (1.80 wm-2). These values are consistent with the forcing values (1880-1985: 1.7 wm-2) discussed in Wigley 1987, which caused Wigley to reflect on the discrepancy between these results and GCM output).
The cursory description does not suggest any iteration in the process, so I take it that the atmospheric profile is held rigid through the addition of CO2.
Freckleton et al 1998
Freckleton et al is cited in Myhre et al 1998, and, to me, was a higher quality article, in the sense that it is actually a bit more than an abstract. They state that their results are based on the Shine NBM model (which is a parameterization of LBL models), asserting that the parameterization is an effective interpolation as follows:
We use the 10 cm-1 narrow-band radiative transfer scheme of Shine (1991) with the HITRAN 1992 (Rothman et al. 1992) spectral-band data, except where otherwise stated. In a number of publications (Freckleton et al. 1996; Christidis et al. 1997; Pinnock and Shine 1998) it has been shown that this scheme can reproduce both irradiances and forcings to within a few percent of line-by-line calculations for a wide range of gases.
While computer advances seem to make the need for NBM models increasingly unnecessary (especially in 1-D calculations), I don;t see the use of NBM radiation models as being problematic and, while I’ve not cross-checked the above claims, they don’t seem implausible to me.
Data for the three vertical profiles used in Muhre et al 1998 is available in print form in Freckleton et al 1998 (which I have transcribed from the pdf.) The plot below shows the temperature by altitude for the three profiles.
Freckleton also parameterizes clouds in the 3 profiles in terms of “high” (85 kPa), “medium” (50 kPa) and “low” (Tropic-10 kPa, Extratropic – 25 kPa). High cloud decreases quite noticeably from SH (31.8%) through the tropics (25.5%) to the NH ( 20.4%) – an interesting asymmetry, given the many statements about how uncertain cloud effects and feedbacks are. Mid-level clouds are higher in the extratropics (SH-23%, NH-26%) than in the tropics (13%), while low clouds are higher in the tropics (15%) and NH(14%) than in the SH.
Although both Myhre et al and Freckleton et al say that several vertical profiles must be considered, they don’t report actual results from these profiles.
Lacis et al 1981
Let’s go back and review the methodology of Lacis et al 1981 in light of the later methods. This early (1981) 1-D radiative-convective model was said to have been used in deriving the parameters and forms cited in Hansen et al 1988, which were cited in IPCC (1990). The parameters (though not the forms) were re-estimated in Myhre et al 1998, which was cited in IPCC TAR and IPCC TAR results were re-asserted without modification in AR4. So it still lives on a little bit. They said:
The 1-D model uses a time-marching procedure to compute the vertical atmospheric temperature profile from the net radiative and convective energy fluxes. The radiative flux is obtained by integrating the radiative transfer equation over all frequencies, using the temperature profile of the previous time step and an assumed atmospheric composition, The convective flux is the energy transport needed to prevent the temperature gradient from exceeding a preassigned limit (6.5 deg C/km) which parameterized effects of vertical mixing and large scale dynamics.
The radiative calculations were made with a method (Lacis et al 1979) which groups absorption coefficients by strength for efficiency. Pressure and temperature dependent absorption coefficients are from line-by-line calculations for H2), CO2, O3, N2) and CH4 (McClatchey et al 1973) including continuum H2) absorption (Roberts et al 1976). Transmission of thermal radiation by these gases is shown in Fig 1. Climatological cloud cover (50%) and aerosol properties (Toon and Pollack 1976) are used, with appropriate fractions of low (0.3), middle (0.1) and high (0.1) clouds. Wavelength dependence of cloud and aerosol properties is obtained from Mie scattering theory. Multiple scattering and overlap of gas absorption bands are included.
Model approximations and uncertainties are discussed by Hansen et al 1981. The models equilibrium sensitivity is ~3 deg C for doubled CO2. The model includes major feedback effects believed to operate in the climate system. The sensitivity is similar to the global mean sensitivity of 3-D climate models (NAS, 1979. It is widely believed that this equilibrium sensitivity is correct to within a factor of 2.
A detailed description of the radiative calculations will be given in a separate paper. …
Unfortunately, Lacis et al have here provided nothing more than an abstract of how their model works. I’ve been unable to locate the promised “detailed description of the radiative calculations” in any contemporary articles by Lacis, so perhaps this promise never materialized.
I was unable to locate any specification of the atmospheric parameters used in the Lacis et al calculation. I presume that they had to specifiy an atmospheric profile, as was done in Myhre et al? Did they use a U.S. mid-latitude atmosphere, a tropical atmosphere,…? Impossible to tell.
Thirdly, unlike Myhre et al, Lacis (Hansen) et al state that they use a type of iteration (“time-marching procedure”) to calculate the “vertical atmospheric temperature profile”. It would be very interesting to know how they performed this calculation. It sounds like an empirical solution to the calculus of variations problem and well worth seeing how they did it. It’s too bad that climate science documentation is so horrendous. Yes, I realize that this is from 1981, but 1981 papers in other disciplines can still be de-ciphered.
Archer Modtran
I think that it makes sense to view David Archer’s popular Modtran Java implementation in the same context as Myhre et al 1998.
Archer’s script appears to be structurally similar to the Myhre et al 1998 calculation in the sense that he uses an atmospheric profile (temperatures by altitude, gas composition, clouds etc) to calculate upwelling and downwelling radiation in wm-2. Archer provides for a wider range of profiles (tropical, mid-latitude summer and winter, subarctic summer and winter), each with a variety of cloud conditions and permits the calculation of both upwelling and downwelling radiation at different altitudes. It’s a very nice tool. Archer’s webpage says that his
This is an old model (1990’s), illustrative but not necessarily in strict quantitative agreement with current state of the art line-by-line models.
It would have been nice to know the major areas of difference and whether there are any material differences in the calculations. It seems to me that it wouldn’t be very hard to turn this calculator into an R- or Matlab function, which would definitely be handy as well.
I’ve experimented a bit with Archer’s program and will discuss these results on another occasion. In today’s context, the main issue that I wish to draw attention to is that Archer, like Myhre et al 1998, has a rigid atmospheric profile. Thus, the entire impact of additional CO2 goes to downwelling wm-2.
As someone who took some microeconomic courses and inhaled that approach to comparing different “equilibria” (or steady states), the rigid-atmospheric profile approach seems reminiscent of an economist doing supply-demand diagrams with completely inelastic demand and then reporting that price is very sensitive to changes in supply. I’ll discuss this analogy more on another occasion.
If CO2 levels are, in some way, connected to the atmospheric temperature profile, as seems to be the case, then the atmospheric profile should change with CO2 levels. I’m not sure that this should necessarily be termed a “feedback” if the atmospheric temperature profile (especially the tropopause location) is a type of calculus of variations problem. In this case, the new atmospheric temperature profile with additional CO2 should be calculated in the same step. As noted above, it would be interesting to examine the “time-marching procedure” of Lacis et al to see how they did it.
It also seems to me that one could derive some interesting mathematical properties of toy models that more precisely capture the mechanisms than the simple absorption models that preoccupy too many readers. The sort of toy model that I have in mind would specify an atmospheric analytically and likewise specify the radiation model analytically (in terms of simple functions) and then see what happened. If I remembered how to do calculus of variations, I’d try to do it.
Climate Audit 
76 Comments
If a change to CO2 produces a changed radiative profile which forces a changed equilibrium temperature profile that probably wouldn’t be called a feedback. But if that changed temperature profile produces a changed water vapor profile which produces a separate change to the radiative profile with a new change to the temperature profile, I would call that a feedback, and AFAIK so would most climate scientists.
As has been pointed out in other threads, IIRC, there are several different definitions of “tropopause”, including the point of zero radiative heating, the temperature minimum, and the kink in the lapse rate. These points are at different altitudes from each other, especially in the non-tropical tropopause. Thus a change to the temperature (and radiative) profile could include not only a height change but a change to the distances between the above points. (Or different changes for the tropical and polar tropopause.)
I don’t know if it’s better to define where the tropopause is based upon ozone / water vapor levels or where the lapse rate changes. Based upon what I’ve read, the more simple to describe (if not to determine) is the tropopause starts when the lapse rate drops to 2C/km in the troposphere and ends when the lapse rate hits -2C/km in the stratosphere. As far as I can determine. Nothing official….
Re: #2
My point wasn’t about which definition to use, but that with several different definitions you have to be careful about findings based on one definition being used in logic regarding another.
Also, the distance between these different points could be a driver for other atmospheric phenomena. That is, e.g., a small change to the distance between the zero heating point and the minimum temp point in the tropical troposphere could have a large effect on the behavior of the mid-latitude convective system. This could be true even if the change in distance was small relative to the change in height both experience.
Personally, I would define the tropopause as the region between whichever of the available points is lowest, and whichever is highest. Of course, that does sort of complicate the whole picture of layers like troposphere, stratosphere, etc. The question is whether the simple picture can even be used to create a predictive model.
I read in the Wikipedia, so it must be true, that in order for a CO2 molecule to absorb IR, it must be caught by the photon in the act of coliding with another atom. Does anybody know if this is correct? If it is, wouldn’t the effect be less not only for low pressure situations, but wouldn’t it also drop off as temperature drops and be less in the Arctic as a rule? I am trying to understand this from the root, and I guess what I wonder is, is there a profile of absorption for CO2 accross say, 10 meters of air, at various concentrations and various temps and pressures that are likely to be seen in the atmosphere? It seems like these would have to be the basis of any model of radiative forcing for the atmosphere as a whole, since apparently, nobody has formulated the effect strictly through calculations of Quantum Mechanics.
I’ll give you my understanding (since AFAIK the experts don’t answer such questions).
A CO2 molecule (or any other) doesn’t need to be in a collision in order to absorb/emit a photon at the exact wavelength of the quantum level change, ~14.7 microns for the relevant CO2 band. Collisions can produce a spread from a single line to a peak, greater for greater pressure (total density) and temperature. However, in addition to the 14.7 micron band, CO2 has a whole bunch of low-energy states that it can be in, and a photon that changes from one low-energy state to a combination of the high-energy state (0.0844eV=14.7 micron) and some other low-energy state can also be absorbed without a simultaneous collision. Under atmospheric conditions, the density of sub-lines due to this is sufficient that line-spreading from collisions smears the set of absorption lines into a single peak.
There is a good illustration of the narrowing of the band due to height (lower pressure and temp) on page 489 of Marshak and Davis, but I don’t know of any on-line.
Steve, should this discussion be taken off-line?
Steve: Yes. this is the sort of discussion that should go to the BB.
The calculator is calling a server-side cgi script – Where did you see any reference to Java?
Is the MODTRAN calculator based on radiation going straight up and straight down? That is the exception; not the rule. Most of the out going radiation is going off at some angle to space and not straight up,thus interacts with a longer column of atmosphere. Even the incoming radiation needs to account for the curvature of the earth’s surface. The size of the sky also changes with altitude. All of this can be calculated, but there are obvious temptations to simplify the equations in ways that might effect the outcome. If the algorithms are not available, how can anyone claim the calculations mean anything?
Steve: If you say it’s a cgi script, I’ll accept that. The calculations mean something but the devil is always in the details.
Reference #2 Sam U. The easiest way would be to define tropopause as the point of minimum temperature. That would be the minimum lapse rate and minimum H20 concentration would it not?
It is interesting that co2 is assumed to be so influential when water vapor would seem a more logical assumption to me (chicken or egg?).
This is only true if the transition causes a change in the dipole moment of the molecule. CO2 is asymmetric and some of the quantum level changes change the dipole. CO2 has other transitions that don’t change the dipole moment and to emit/absorb a photon there needs to be a “third” body.
N2, O2 are symmetric molecules and can only emit, absorb a photon in a three body process.
There are also rotational transitions that can emit/absorb a photon during a collisional process.
The probability of three body processes is much lower than process that only involve one molecule and one photon.
Re: #8
I’ve taken the discussion to the BB, as per Steve’s request.
Thanks and sorry. I am not trying to disprove the GCMs as my question may have implied, just understand them. I think it is relevant because you mentioned Lubos calculation, and his calculation depends on a tropopause that is defined as where CO2 has a 90% chance of escaping.I just can’t figure out how the altitude where that happens is calculated.
Steve,
I had similar ideas of simple models. I made an analytical model, but it turned out that the equations can’t be integrated analytically, so they are calculated numerically. I have already posted on this
http://www.climateaudit.org/?p=2031#comment-135765
In principle the radiation models are defined analytically. Currently the best model for a line shape is Voigth function which is avalytical. However, there are over 6000 lines for CO2 and over 60000 for H2O. That’s the problem. I used a Malkmus Statistical NBM.
Steve, let me explain how we used Modtran and you will get an idea
about why the atmospheric conditions are “held rigid.” The original observational
work for the transmission models were conducted by the DOD.( airforce) Basically, they wanted to
understand IR signatures and how they propagated so we could A.) shoot stuff down.
B. Avoid being shot down. C. watch warm bodies from space.
So if you were building a missile ( or its sensor) you would get a requirement that would
state, something like so. ( grossly over simplifying)
1. Detect a target of XYZ watt/m^2 at Z NM …. STANDARD US DAY.
Then you would use your certified version of the model
to present your results
to them, for standard day, tropical, winter etc etc..
The codes were built to provide a method for specifying the design of sensors and specifying the
IR signatures of vehicles. To do this “atmospheric standard” are constructed. It’s the same
with Aircraft design. You design to a variety of “standard atmospheres” ( desert, tropical, etc etc)
A nice history here that addresses Beers law and other things
http://spiedl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PSISDG002309000001000170000001&idtype=cvips&gifs=yes
7 captdallas
It’s a judgement call, I guess. However, I prefer the official definition that uses lapse rate, because that means the surface where vertical convection pretty much stops.
I think that is probably because the amount of water vapor at -50C and lower is pretty minimal (it’s frozen out).
13
Sorry, the “Sam’s IS…” sentence was not part of the quote. I should have gone in at the end of the subsequent paragraph — an would have if I had my wits about me.
Reference 13 Pat
As long as there is convection, the h20 can rise. To freeze out, H20 molecules would have to amass for gravity to overcome convective forces. So the altitude of minimum temperature would be were everything does truly pause. In the arctics were convective energy is lower, that altitude is lower. In the tropics it is higher. As I understand it, in the tropics water vapor is found at higher altitudes even with significantly lower temperatures
The official definition based on lapse rate is fine. However, at the Tropopause and above, CO2 heat emissions tend to radiate to space. Stan Soloman, I believe, researched CO2’s tendency to cool the Thermoshpere. I haven’t read his paper, just a news blurb, but CO2 and H2O interaction is an interesting subject.
Just my thoughts, back to lurking.
Re: #15
It’s not nearly that simple. Convection depends on a higher external lapse rate than the pseudo-adiabat, but in the upper troposphere the pseudo-adiabat is very close to the adiabat (~10K/Km) which means buoyancy is decreasing as the T-storm updraft rises. Even after the buoyancy changes sign, momentum can keep the air in the central column rising for a while.
After the air detrains, the mixture (of warm cloud and cold external air) will fall along the pseudo-adiabat until all the liquid is evaporated, and continue to fall along the adiabat until it matches the surrounding temperature. There is no automatic link to the altitude of minimum temperature except that at and above it the lapse rate is hyper stable, so overshoot will be limited.
Another important point, which I just recently learned, involves the zero heating point. Air above this point is actually being radiatively warmed, so it will tend to rise and carry any water vapor with it. This remains true whether the zero heating point is above or below the minimum temp point (AFAIK).
Gettelman et al found the typical clear air heating point to be around 15Km at several tropical sites, while the temp minimum was at 16-17Km, and most convective outflow was below it by 1-3 Km.
A. Gettelman, P. M. F. Forster, M. Fujiwara, Q. Fu, H. Vomel, L. K. Gohar, C. Johanson and M. Ammeraman, The Radiation Balance of the Tropical Tropopause Layer, Journal of Geophysical Research, 109, D07103, doi:10.1029/2003JD004190, 2004 PDF
The tropopause is the space between the troposphere and stratosphere, and is at about 5 miles at the poles and 11 miles at the equator. The exactness isn’t that important.
So it’s either where the lapse rate is next to nothing (heating/cooling less than 2C/km) which creates a barrier between tropo/strato, or it’s the region between the two where air doesn’t get colder than -50C and there is little or no moisture.
15 captdallas
I meant “freeze” literally. The water-vapor you talked about in #7 would have gone, turned into ice crystals/needles.
Which is why there’s not that much moisture in the air where the temp is under freezing and clouds don’t form.
ref 17 Pat,
I know it doesn’t seem to make sense. This link may help. Ice crystals can’t form without several molecules combining. The few molecules, the less chance of combining (freezing). If they don’t combine, it is still water vapor even at -50 degrees C. Admittedly there is not much water vapor, but above the Tropopause, there is a lot less of that not much. Anyway, it thought it was interesting,
Ref 20 AK Sorry I was overly simplistic and can’t type worth a flip. To get back on topic, the Tropopause is pretty neat. Somewhere around the Tropopause(TP), CO2 starts emitting more heat (IR) to space than back to Earth. Below the the TP, CO2 is excited by IR and releases IR primarily due to collisions with other molecules. Above the TP, possible above the stratosphere, CO2 absorbs energy through collision with other molecules and releases IR to space(mainly)cooling the Thermoshpere throught vibrational level drop and rotational means I don’t understand.
So I agree with Steve Mc. that single and even triple column models for CO2 irradiation don’t cut it. CO2’s warming potential decreases with altitude and interaction with other gases including water vapor. CO2 also has five vibrational states, I believe, at least in lasers. How many naturally occur, I don’t know. Solving the problem would require some serious partial differential equations IMO.
It is interesting though. Sorry, back to lurking.
Re: #21
Well above the tropopause. In fact emissions to space and to Earth are effectively equal at all heights, the important point is that it can emit more than it absorbs due to the very low density. However, the thermosphere is well above the stratosphere, in fact there’s a whole nother layer in-between: the mesosphere.
It’s true, however, that the behavior of these higher layers, and the regions separating them, need to be included in any understanding of the radiative effects of CO2 change.
In the link you posted, it says the following:
This is an oversimplification. In fact CO2 cools the atmosphere between the upper troposphere and the zero heating point (about 15 Km, per Gettelman et al), indeed even above it the effect of CO2 is to cool the atmosphere, although the heating effect of ozone (from absorbing UV) overbalances it.
Even in the lower troposphere, it’s water vapor as much as CO2 that serves to absorb thermal IR from the surface. And, AFAIK, conduction and evaporation/transpiration outdo them both.
26 captdallas
That makes sense, but I was under the impression that supercooled water-vapor nucleated on dust etc. and then the crystal slowly grew by the few water molecules around ‘condensing’ on it. Snowflakes. (I’m not an expert on this, though).
It’s more or less used in growing thin semiconductor films, known as Chemical Vapor Deposition or Molecular Beam Epitaxy.
Steve
do you really think you can fit the accumulated knowledge of a university department into your head in a matter of weeks? You are either self delusional or heading for a nervous breakdown or both.
Since the image I embedded was stripped out, I’ll provide a link:
Standardized Temperature Profile
Is Bugs a pseudonym for the pseudonym Eli Rabbett?
Bugs, when Dixy Lee Ray (a marine biologist) was appointed to chair the Atomic Energy Commission, a friend asked if she knew anything about nuclear energy. Her response was “give me a week”. This world still is occasionally blessed with such renaissance women and men.
Only a week? I guess I’ll just have to trust you on that.
You don’t need to be able to build a reactor from scratch in order to know enough to regulate those who do.
Ref 24 AK said “Well above the tropopause. In fact emissions to space and to Earth are effectively equal at all heights, the important point is that it can emit more than it absorbs due to the very low density.”
I disagree,interaction with h20 and other molecules decreases with altitude as air density decreases. At roughly 17 Kilometers, the angle tangent to the horizon becomes significant. With virtually no interaction with h20 at this point, the window to space is much larger. The up down models of CO2 are not very accurate unless they consider the average for each layer of the atmosphere.
Re: #30 captdallas2 says:
You need to remember that at these very low angles a layer is mostly interacting with itself. The conversion from a vertical ray to integration over a (hemi)sphere should technically take account of the sphericity, but the error involved is probably much smaller than that from assuming a layer with a comparatively large thickness is thin.
Just because one of the outputs of the Archer MODTRAN interface program is the energy measured looking up or down doesn’t mean the program doesn’t correctly calculate emission and absorption at all angles. If you select save text and than look at the complete output, there’s a whole lot more data than what appears in the graphical output.
Ref 32 DeWitt
Yep, But the model is up and down. Angle tangent to the Earth is fixed at 180 degrees. For the sub Arctic winter there appears to be a questionable notation about slant angle 70. I would have to get with David to find out what that means. It is an up/down as best I can determine. The wind is blowing for the next few days so I may play with it.
Ref 31 AK Low angle in two dimensions is one thing, in three they can be more significant. We have two spheres, one huge one small. The horizon of the huge one will become significant at some point. Where is that point?
Re: #33
The horizon at the stratopause is roughly 1/15 radian below horizontal. This means a tangential ray travels ~15 times as far passing through its own layer as it does vertically. If the layer is radiating significantly at some wavelength, it will also absorb (below the thermosphere), so the effect of radiation at that angle will already have been reduced. (A ray from the middle of the stratosphere pointing horizontally will travel several hundred Km before it exits the stratosphere.)
The effect of sphericity is certainly present, but I doubt it’s significant for calculations below the thermosphere.
I don’t need to know how to work a lathe to know you’re not at it, or that the resulting table leg looks horrible or breaks when put under stress. I don’t need to know the subject to know you’re boring the students, or that it’s clear you have no idea at all what you’re talking about. I don’t need to know how the game of basketball works to see your team’s score is 20 and the other’s is 570 and know they won. I don’t need to know the specifics of how a nuclear reactor is cooled to know what cools it and what may happen if it’s not cooled.
I don’t need to know exactly how and to what extent CO2 aborbs IR to know it does.
Re #35
Scores from a Cross country meet: Team A 35, Team B 25, which team won?
ref 34 AK In the tropics and mid latitudes it would be insignificant. The sub arctic may be another matter. That 1/15 radian change to the horizon results in roughly a twenty percent reduction in radiance incident to Earth. Insignificant at the Stratopause. A ten percent reduction at the poles due to horizon angle plus the lower altitude of the Tropopause (no H2O to interact with)may be significant (as in a percent or two).
Nothing Earth shattering, but since the poles aren’t following the game plan as predicted, maybe something worthy of considering.
“You don’t need to be able to build a reactor from scratch in order to know enough to regulate those who do.”
Isn’t that my point? Steve is trying to rebuild the whole science from the top down. (Rather than the bottom up, which would be the logical way to do it.)
Captdallas2 #30
That is an extremely important point to be understood in order to understand the role of CO2 (or any other GHG) in an atmosphere .
Unfortunately few people understand that and even less try .
It involves actually no PDE and no complicated maths – only quantum mechanics .
CO2 has 3 vibrationnal modes . 1 of them does not interact with with IR radiation , the other 2 do .
From those 2 who do , 1 is triply degenerated (the one absorbing at 15µ) .
So the partition function at equilibrium tells us that if only the first vibrationnaly excited states exist (very good assumption for low temperatures) then :
20 % of the excited states are in the IR inactive mode
20 % of the excited states are in the small IR active mode
60 % of the excited modes are in the 15 µ mode
That already explains why the 15 µ band is so intense compared to other absorption/emission bands .
Now how many excited states are there (always at equilibrium) ?
We have from the MB distribution of quantum states at equilibrium N(Ei) / N(Ej) = exp ( – (Ei – Ej) / kT)
Ei – Ej is the difference between the ground state and the 15µ state so 13.2 10^-21 J .
kT is 4,14 10^-21 for 300 K
kT is 3.12 10^-21 for 220 K (typically the -50 °C in the stratosphere)
By applying the MB distribution we see that there are only 5 % of the states in the 15µ excited mode at 300 K and 1% at 220 K .
That justifies a posteriori the validity of the hypothesis that only the first states are excited and puts to rest the idea of great number of excited CO2 states .
For all practical purposes the CO2 molecules are in the ground state at equilibrium and the already small fraction of excited states farther decreases when the temperature decreases .
Now what about the “warming potential” even if this denomination is not very clearly defined ?
In the area of interest here (below 50 km) the equilibrium is dominated by collisions .
In the low atmosphere we have some 5 10^9 collisions /sec .
In the stratosphere we have typicaly 10 times less .
So not only the proportion of excited states is 5 times less but the number of collisions is 10 times less .
The absorbed energy is also less because there are less absorbing molecules per volume unit .
Folllows that the main part of the CO2 IR business happens in the low atmosphere and its contribution decreases very fast with altitude because both temperature and pressure are dropping .
Word of caution : the above is only valid for EQUILIBRIUM conditions . Above some 70 km the collisions no more dominate and we are no more in LTE . The CO2 above this altitude behaves mostly radiatively through absorption/emission .
Tom Vonk,
Thank you very much for that. That is an explanation I have been looking for for a while.
Bugs,
Sometimes one is just trying to understand the science. Separate the science from the kool aide as it were. Reading press reports and snarky blogs like RealClimate doesn’t cut it for everybody.
Wanting to know the equations involved in a prediction is working from top down??????
If you don’t understand the basic physics it is. He needs to start with a university course and work his way up.
#42. Bugs, why do you assume that I don’t understand the basic physics?
The behavior seems trollish.
(psst, bugs, finding out how to get to 2.5C is working from the bottom up)
Phil. : I don’t know who won the track meet. Did the scoring start at zero and work its way to a number of points per win, or did it start at some number and get some number of points subtracted per loss?
You’ve phrased the question badly.
Golfer A got 50 and golfer B got 60, who won? You can’t tell; were they playing with golfer C and D and with some number of points per hole for first second or third, did they play 110 holes and count number of holes with a lower score, or did they play regular golf on 9 holes and shoot a 50 and 60?
Basketball games usually start with both teams at 0. Any other system would have to be mentioned if it’s a special circumstane, like a free-shoot contest or something between players etc.
Obviously, if the system being looked at is poorly or not understood, clarifying questions woul dhave to be asked. But if I’m watching a normal game on TV, I think I’d get the scoring system in the game.
Why don’t you ask me if a car can run me over while I’m on an airplane? 🙂
Re #44
It was a Cross country meet not a track meet and the point was that some basic information about the competition is necessary to interpret the result, contrary to your earlier assertion.
Just like in CO2 absorption where the logarithmic dependence requires a quite sophisticated background.
Bugs, knowing the equations is basic physics.
ref 39 Tom Vonk,
Excellent post, thank you.
Phil. Ah, so. Yes. Cross country. Lower score.
I don’t think I asserted you don’t need any information about the competition, just that you didn’t have to be an expert at a task to do it. You just have to find out the basics online or in a book, watch the sport for a while, take a look at the materials used by the judges, ask some spectators, etc. In fact, I didn’t look it up, because (besides mixing it up with track!) I assumed if you asked it, it was a question in which typically the low score wins. Which is why I used golf as my first example.
I don’t need to know any of the specifics of how carbon dioxide absorbs to know doubling it is estimated to cause a positive forcing of somewhere between 1 and 5 (pretty much), and that nobody knows what it will actually do in the actual system. The only way to know the reality is would be to hold everything else stable and get the reading to 800 ppmv, hold it for 30 years and calcuate the anomaly. Or in other words, there’s no way to know what it would actually do. However, we can model that and get various estimates.
I don’t need to be a graphics artist to be the boss of one, or a piano player to have one in my band, or a nuclear engineer to know what’s cooling a reactor. That’s all I’m sayin’.
Re: #39
Some additions:
Not all collisions are inelastic. The estimates I have seen is that the proportion of inelastic collisions resulting in energy transfer is less than 1 in 10,000. This is important for determining the lifetime of an excited molecule and its probability of undergoing stimulated or spontaneous emission before it is returned to the ground state by inelastic collision.
Energy transfer by collision between CO2 and O2 is very efficient so CO2 is considered to be in LTE up to 100 km.
Absorption of IR emitted by the surface is indeed only important in the troposphere. Emission of IR by CO2 in the stratosphere, however, is quite important in determining the temperature profile of the stratosphere.
Re: #49
So, AFAIK, is absorption by CO2 in the stratosphere of IR emitted by the Troposphere.
Re: #50
No. The optical density is too low and the line width too narrow (no pressure broadening to speak of) to absorb a significant amount of energy compared to emission. When you look at an IR spectrum taken from orbit you see an emission peak in the middle of the CO2 band at 15 micrometers, not an absorption dip. The stratosphere is optically thin in the IR and emission dominates. It’s optically thick in the far UV, though. This is the opposite of the case in the lower atmosphere leading to the opposite effect, i.e. adding CO2 lowers the temperature of the stratosphere.
Re: #51
My understanding was that pressure broadening doesn’t reduce the absorption cross section at the center of the band. Am I mistaken?
Yes. That emission peak shows that a significant part of the radiation is coming from the warmer upper stratosphere. However, AFAIK thermal collisions still dominate in the stratosphere, which means emission will be determined by temperature. Thus if there’s enough CO2 to radiate to space, there’s enough to absorb some of what’s coming from below. Of course, the emission dominates, for purposes of calculating net heating rate, but you still have to add in the absorption of 14.7 micron radiation from below, even though it’s a smaller number. Don’t you? Wouldn’t increasing the CO2 in the troposphere alone also tend to cool the stratosphere?
45 Phil
Do you have any references or links to earth radiance data in the 20-100u (100-500cm-1) region?
Has anyone check the output of Archer’s modtran model?? The peaks of his black body plots don’t match Wien’s Displacement Law. For instance, 300k blackbody should peak at around 1000 wavenumber (10 microns) not ~600. Also his plots don’t compare to some of my references for spectral radiance when looking up.
Re: #54
Wein’s displacement law is for wavelength not frequency or cm-1. Reciprocal centimeters (cm-1) is effectively frequency. The Planck equation written for frequency rather than wavelength is a quite different looking expression. Look it up in Wikipedia. Also, the energy is in W/cm-1 rather than W/micrometer. The end result is that a radiation plot in cm-1 looks different and the MODTRAN plots are correct, as far as they go.
Re: DeWitt Payne (#55),
Phil B:
DeWitt:
Now, come on. Black body radiation DOES peak around 10 µm for 300 K. If in doubt, please look it up in Wikipedia. You may also use your favorite Black Body Radiation applet (I suggest this one). The wavelength of 10 µm corresponds to 1000 cycles/cm, and not to 600 cycles/cm (as Dave’s applet erroneously claims). If you don’t believe it’s 1000, please consider the following:
The IR atmospheric window extends:
from 13 to 8 µm, or
from 770 to 1250 cycles/cm, or
from 4738 to 7854 cm-1,
cf. Simmons, Infrared radiation studies of the winter marine antarctic atmosphere. You can now play with these numbers (if you want to verify units) and fit the BBR maximum at 10 µm into this window. It will land at 1000 cycles/cm, not at 600 cycles/cm.
Still not enough? So note that Dave places the black body radiation maximum at 600 cycles/cm and the major CO2 absorption line – at (approximately) 650 cycles/cm (the corresponding value in reciprocal cm, which he gives in one of the figures, is wrong, but this is not crucial). The CO2 position of 650 cycles/cm rougly read from the applet’s output in cycles/cm is fine (e.g., Wikipedia CO2 data sheet quotes 667 cycles/cm, and so does Simmons). 667 cycles/cm correspond to 15 µm, which – as far as I can tell – is indeed the correct position center of the major CO2 absorption band. BUT: 15 µm photons have LOWER energy than 10 µm photons. That is, if we plot things as a function of cycles/cm, the CO2 band centered at 15µm wavelength should be on the LEFT hand side of the black body radiation maximum (centered at 10 µm), and not on the right hand side (as it is in the diagrams produced by the applet).
Something is wrong, no doubt.
And this mistake may have a significant effect on the estimate of the temperature response. I guess the response will be larger, because it seems that he effectively assumed black body radiation for much too cold Earth. His Earth was at about 174 K instead of 300 K. This translates into 9-fold increase of thermal flux if the correct temperature is used. (But I did not verify the spectral energy densities, in principle they may be arbitrarily affected if something is wrong in the code).
BTW, ten years ago Heinz Hug measured (not very precisely, it seems) the absorption band of CO2 around 15 µm and concluded that the contribution from the broadening of the peak (this is the effect responsible for the global temperature response to the changes in CO2 concentration) is 80 times smaller than usually assumed. I don’t know about more exact measurements. Hug may well be an order of magnitude off, judging from the quality of his data acquisition and data analysis; still, 80 times is not a joke. But if Dave’s applet assumes at the same time a wrong shape of the absorption line, these two errors (his and – possibly – Hug’s) may roughly cancel out, resulting in the correct prediction.
What about other models?
Re: Jarek (#69),
Get the Planck equations in frequency and wavelength form. Plot them for a black body at 300 K. Just to make it easy, I’ll do it for you. Wavelength. Wavenumber. See the difference? Yet both integrate over the full frequency or wavelength range to 459 W/m2. The important difference is that the Y axis is W m-2 micrometer-1 for the wavelength plot and W m-2 cm-1.
I’m sorry but I can’t resist being a little snarky here. Do you really think people who do this for a living are that stupid?
Re: #53
Come to think of it, I’m not sure. Looking it up in Petty didn’t make it any clearer. I think, but I can’t prove it, that broadening increases total absorption of energy by a line. I come to this conclusion because it can be easily shown that a line with zero width won’t absorb any energy at all.
There will be some absorption, but I’m pretty sure it can be neglected. Emission from CO2 in the stratosphere results primarily by collisional excitation and increases with temperature, but emission and absorption don’t have to be equal because there is another source of the thermal energy from solar UV absorption by oxygen and ozone. Of course, ozone has a strong line at 10.5 micrometers so it emits as well as absorbs. IIRC though, the loss of ozone from CFC’s was supposed to cool the stratosphere because the net result of ozone was energy absorption.
For an instantaneous doubling, maybe, but not very much, IMO. Downwelling IR from the stratosphere has an effect on the troposphere, but upwelling IR from the troposphere should have little or no effect on the stratosphere because the energy involved is insignificant compared to the absorption of incident solar UV. For forcing calculations they do it the other way. They equilibrate the stratosphere to the new CO2 level and then calculate the effect on the troposphere.
Re #52
Try this as a start: FarIR
Re #56
The warming of the stratosphere by O3 occurs from ~400mb to ~20mb (and therefore the reduction of O3 leads to cooling) whereas cooling of the upper stratosphere is mainly by emission by CO2 from ~100mb upwards
Re #55, thanks Dewitt, all of my references have plots that are in wavelength.
I will do some further checking.
Re#51, DeWitt:
Do you look at “IR spectrum taken from orbit” averaged over night/day?
(45% of solar radiation at Earth orbit is IR).
57
Thanks, Phil, much appreciated. That doesn’t have what I want (which may not exist yet), but it should help me get as far as is possible.
Re #60
No need to, the solar IR is at a lower wavelength than the IR from earth and is easily separated.
re Phil. 62, You say-
The peak intensities are widely separated in wavelength/energy. However, that does not mean they can be easily separated. What is the intensity of incoming solar in the 10-14 um band (for example) compared with the intensity of thermal emission from Earth in the same band?
Re #63
If we assume blackbodies then the Earth’s contribution would be about 500x the solar.
DeWitt Payne in #56:
It would appear that you have a picture of the troposphere/stratosphere radiative process(es) fixed sufficiently well in your mind that you can make replies to comments here almost instantaneously. What you say generally makes sense to me. My problem is that when I view these separate processes I have a problem integrating them into a complete and an understandable radiative process. The cartoon models while informative say little (to me) about the individual processes and the controlling physics for them.
I think my needs and perhaps others reading and posting here are threefold: (1) a layout of the controlling individual processes that includes the differences in absorbing and emitting species and some explanations of what can be ignored as a small or non effect, (2) tying these processes into a overall view of the radiative process and finally (3) outlining how this process is handled by climate models.
Would you feel comfortable presenting such an outline here at CA — even in an abbreviated form in a long post?
Just a comment on the “rigid atmospheric profile”. I have used a Process plant simulation package (AspenPlus) to calculate lapse rates as a function of relative humidity. Ground temperature was 20C. The results show changes of lapse rate that would be significant for radiation balance analysis. I can show the results if someone can tell me how to copy an Excel graph to this site.
Gary, I use imageshack for posting Excel graphs at CA. It will provide you with a link to your graph stored at Imageshack to use in your post.
http://imageshack.us/
Gary, to be more complete I copy the Excel graph to Paint and save it in the form of a gif file. I then copy the Imageshack information in the site box to a CA post starting from img and ending with .gif”.
Yes, you are right. Since in one case Y is dW/dLambda, and the other it is dW/d(1/Lambda), there is an additional Lambda which must be accounted for in the density, and this displaces the maximum. In other words, it is not simply a change of units, but a nonlinear change of variables. I missed that. Sorry.
Still, this does not explain the tone of your reply. Do you really think that the others are that stupid? Let me apologize, but I can’t resist making this remark; from the fact that you are more familiar with the subject than your guest happens to be it does not follow that you cannot give polite replies to polite questions. It is not rude to point out a possible mistake, but it is pretty rude to suggest that the question is stupid.
Now, could you please be so nice and comment on Hug’s measurements?
The reason I am asking (and the reason for my interest in the whole business) is that someone asked me and I tried to figure out how does the climate change model work. That’s how I arrived to Dave’s applet – and the rest you know: since I could not reproduce his shape of black body radiation on my computer, I could not trust the rest of the theory. Accidentally, I am a physicist myself and am not used to accepting things for granted. Particularly, not models. I used to construct models myself and know pretty well how easy it is to put together a model which reproduces the observation but fails to make reasonable predictions. I am sure you know this as well.
Re: Jarek (#71),
My German is a tad rusty. But from what I could make out on a first pass, he’s measuring the spectrum of a synthetic mixture of CO2 and water vapor at 357 and 714 ppmv in a 10 cm path length cell. The problem I see here is that his path length is too short and the spectrometer resolution is not high enough to accurately measure the weak lines on the wings of the band.
If you look at observed atmospheric emission spectra, the CO2 band looks very much like that calculated by MODTRAN (observed 1, observed 2, calculated). I can’t duplicate the Barrow spectrum exactly because I can’t adjust the lapse rate in MODTRAN to reflect the strong temperature inversion that was present at Barrow. The MODTRAN calculations are traceable more or less to the HITRAN database. More or less because MODTRAN is a band model, not a line by line model.
Another place to look to get spectral data is Spectracalc. You can do limited calculations of transmission spectra (one molecule at a time and maximum spectral width is 100 cm-1, e.g.). By selecting the right path length and pressure, you can approximate the amount of CO2 in the atmosphere from the ground to deep space. It won’t be completely accurate because pressure and Doppler broadening vary with altitude, but I found the width of the absorption band to be comparable to MODTRAN and the observed spectra. You can also get plots of the lines in the HITRAN database for a particular molecule over the same maximum spectral range. Here, for example is a plot of the CO2 lines from 660 to 674 cm-1. Here are calculated transmittance plots for a 10 cm cell with 0.48 mbar and 0.96 mbar CO2 at 0.1 cm-1 resolution. If I did my sums right, that would be equivalent to Hug’s experiment minus the H2O and at higher resolution. The free version won’t let me change resolution.
Re: DeWitt Payne (#72)
Re: Phil. (#73)
Thanks. This was also my feeling.
This leads to a related question. Let’s we assume that the whole transmission of heat goes via a direct radiative transport path (by “direct” I mean that there is only absorption, and re-emission at the same wavelength). Let’s also ignore all feedback effects. We are now left with only water and about 360 ppm CO2, both with some average distribution in the atmosphere that is in some average state. How much surface temperature increase would such a naive model yield on doubling of the CO2 concentration, given – say – the HITRAN spectra?
_________________________
PS. I do not think that a layman who wants to learn something is able to ask a question or rise a doubt that could be offensive to an expert. OK, but that’s about approaches to education :D. Since this may be a sensitive subject, let’s drop it. What matters is that none meant any offence.
Re: Jarek (#71),
He didn’t assert that you were stupid but that it was offensive to suggest that professionals in the area were making the kind of mistake that you claimed!
E.g.
Now, come on. Black body radiation DOES peak around 10 µm for 300 K.
Something is wrong, no doubt.
And this mistake may have a significant effect on the estimate of the temperature response.
Now, could you please be so nice and comment on Hug’s measurements?
A cursory glance would suggest that they were done at a much too low resolution to be of any use, here’s a small part of the CO2 wing from HITRAN:
I am legally blind, even so I have look at some of Novack’s stuff and yours…
I was under the impression the co2 bands wouldn’t broaden as much as they claim at realclimate.
Tonight i run across this on a google search Radiative heat transfer By Michael F. Modest
http://books.google.com/books?id=lLT-aKLTxkQC&pg=PA305&lpg=PA305&dq=10+cm-1+narrow-band+radiative+transfer&source=bl&ots=7jaTxlo66l&sig=vBpvNtlNKRl6Y137i1OH4WeXNVs&hl=en&ei=JQOHTNCICon2tgPxo7jSCg&sa=X&oi=book_result&ct=result&resnum=8&ved=0CDYQ6AEwBw#v=onepage&q=10%20cm-1%20narrow-band%20radiative%20transfer&f=false
It shows a clip of the Book. I cannot read a book.Page 305 the sample :
“if the totsl presure is raised one bar. shown in center of frame, lines become strongly broadened, leading to substantial line overlap and a smoother variation in the coefficient(with considerably lower minima)”
sentence or two before references Fig 10-9
any thoughts?
Regards, bnwild
Click to access Mod5CLassWrapperForMODTRAN.pdf
read.pudn.com/downloads118/ebook/500884/ProjectPlanningfinal.pdf
Haven’t followd up to find any downloadable code but projects for a Mathlab interface are around.