I wanted to let people know that P. N. Keating, aka “PatK” has published a “Simple radiative models for surface warming and upper-troposphere cooling” in “The International Journal of Climatology”. The paper describes a simple model for the enhanced greenhouse effect and compares the model predictions to temperature observations.
The abstract reads:
Abstract
A simple model of greenhouse-gas radiative processes intended to make the surface-warming effect of water-vapour and CO2 absorption more readily understandable leads to a conclusion that the greenhouse gases also cool the upper troposphere. The results from the simple model are compared with experimental observations, and a functional form for the decline of vertical convection and water-vapour radiation near the tropopause is derived from previously unexplained high-altitude cooling-trend data. A possible reason why global climate models do not show the observed upper-troposphere cooling trend is tentatively suggested.
I’m a bit swamped right now, so I’m not going to give a detailed overview. However, since portions will interest readers, and the model predictions appear to be in qualitative accord with some temperature observations, I’ll describe the organization of the paper and post quotes of what appear to be some of the major results.
The organization of the paper
Introduction: The zero dimensional view of radiative heat transfer from earth is.
IR Photon Absorption: The radiative properties of water and CO2 are discussed.
Simple Model – Lower and Mid Troposphere: The zero dimensional model is extended, dividing the troposphere into three sections. Keating also defines three classes of photons based on their wavelength relative to the absorption bands of water and CO2 and relates these classes to radiative transport in the three sections of the troposphere.
Based on this section, Keating discusses the surface warming effect of GHG’s
Upper Troposphere and Tropopause: This section describes an analytical treatment of the simple model. The equation averse might want to focus on the final two paragraphs, which describes the effect of CO2 on the temperature distribution in the atmosphere given the simplifications provided above. The final two paragraphs read:
In summary, the above analysis provides a basis for our hypothesis that the upper troposphere near the tropopause is warmed because of the decline in natural upward convection and water-vapor emission, which causes IR emission by CO2 molecules to become the critical mechanism there for thermal-energy removal. Any increase in CO2 enhances this transfer, and thereby cools by reducing the need for warming. Emission from the wings of the band is most important because of the need to penetrate the temperature inversion in the stratosphere.
While CO2 molecules act in the lower-troposphere to help water-vapor warm the Earth by absorption of surface-emitted photons of type A, we see that they also act to cool the top of the troposphere by the emission of type B, C photons from that level
Comparison with Experiment and Other Work: In this section, Keating places his model in context of experimental work. In particular, Keating focuses on suspected cooling of the upper troposphere which would be consistent with the behavior predicted by his simple model. Keating notes:
All four datasets (Fig. 1 of Douglass et al , 2008) clearly indicate that there is a cooling trend at the top of the troposphere which the GCMs generally fail to reproduce, though some have attempted to suggest that it is the observed data which is in error (Sherwood et al, 2005). However, all four datasets show a similar behavior as a function of altitude. A number of explanations for the cooling trend have been offered, including atmospheric and ocean circulation patterns (Hurrell and Trenbeth, 1996; Brown et al, 2000b), ozone loss (Brown et al, 2000a), and volcanic activity (Brown et al, 2000b). The observed lack of a significant ozone loss-trend in the tropics, where the cooling is most pronounced, indicates that it is not ozone depletion.
Figure 1: Variation of Temperature With ElevationOur analysis in the previous section has suggested a more direct cause. Natural vertical convection and water-vapor radiative emission, which move heat upward independently of CO2, decline near the tropopause and upward heat transfer becomes very dependent on photon emission from the wings of the CO2 band. This bottleneck causes upper-troposphere warming, and any enhancement of the transfer process by adding CO2 offsets that and thus results in cooling. By matching the observed high-altitude cooling data, our analysis yields a functional form for f(p), representing a rather sharp cut-off of the other upward transfer mechanisms at the tropopause (Fig. 3).
What do you think?
I’ll be reading this paper in more detail over the next week. In the meantime, feel free to chat. If we are lucky, Keating (aka PatK) himself might drop by. Also, maybe Phil, who knows much more about the details of radiative transport in the atmosphere will stop by too. (Anyone else is welcome too.)
In the mean time, while I’m focusing on “real work”…. feel free to provide comments so we can all put this in context.
31 thoughts on “Simple radiative models for surface warming and upper-troposphere cooling”
$30 US seems a bit steep for one article. I’ll pass at the moment.
DeWitt–
Try your interlibrary loan. It might take a week, but lots of libraries can get these for you. It’s much wiser than paying.
DWP, we have an institutional access. Where I can mail you a .pdf?
Looks interesting but I will have to wait untill it is available free of charge .
Or if you have it , could you send me a pdf at my mail adress ?
The crucial role of the wings reminds me of the J.Nicol paper .
Also coupling correctly convection with radiation is major what J.Nicol wrote too (and no , as I exchanged many mails with him for the revision of his paper , not everything he wrote was right in my opinion) .
If the surface heating is easy to derive , upper troposphere cooling is not .
H2O/CO2 radiative coupling is not either .
What makes me skeptical is the question how a “simple” 0/1 dimensionnal model could get the radiation/convection coupling right when the mature full 3D multimillion line GCMs managed by hundreds of scientists can’t .
Especially as we have been told for years that precisely this was one aspect of the models where they all agreed (qualitatively) .
But it shall have to wait untill I read it .
I downloaded Keating08 as a .pdf and can email it to avid readers. Just mail me – the address is EWCZ at seznam.cz
Maybe somebody can compare and contrast the model with Essenhigh’s:
Thanks to lucia and PatK I now have a preprint of the paper without anyone violating copyright. More later after I’ve had a chance to study the paper.
Argh !
I have almost been put off already at the first page because of this same old error that people keep repeating .
.
At one line it is correctly said that the “effective emitting temperature is 255 K .”
This is the temperature that would have an isothermal spherical body in radiative equilibrium with another body at infinity .
Of course everybody knows that no planet in the solar system is an isothermal spherical body in radiative equilibrium with the Sun regardless if it has an atmosphere or not .
However even if isothermal planets don’t exist and can’t exist , one can’t forbid people to write equations for them as long as they precise that the equations apply to a system that can’t exist .
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Yet right in the following line it is written “In other words the surface would be around 33°C colder than what it is if the atmosphere was tranparent to IR”
So suddenly the “effective emitting temperature of 255 K .” became “the average temperature .” .
This is clearly wrong because the average of the 4th power is not the 4th power of the average .
It is also wrong because a planet without water , atmosphere , cryosphere would not have neither the same albedo neither the same surface emissivity as a planet that has all of the above .
On top this wrong statement is not even necessary for what comes after .
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So yes I actually read farther despite the bad impression of the beginning .
Tom–
Of course everyone, including Pat, know there are no spherical isothermal planets. That idea is a baseline for all simplified models. The paths of starting form the most complicated end and moving simpler and starting from simpler and getting progressively more complicated are both well respected.
Some people don’t like simplified models used to develop understanding of processes. But others do, and I think they give valuable insights. Yes, the model neglects water, continents, ice etc. And the atmosphere is simplified.
The goal is to see whether by extending the simplified models (like those in text books like McGuffy Hendrick-Sellers) one can predict a puzzling feature: the apparent cooling of the tropical tropopause.
I have no problem withh simplified processes .
I have a problem with WRONG statements and I was mentionning sofar only the page 1 .
This : “In other words the surface would be around 33°C colder than what it is if the atmosphere was tranparent to IR†is a wrong statement .
It is not an approximation or an argument – it is not even a guess .
One can turn around it as often as one wants and say whatever one wants , it won’t make the statement right .
It is perhaps right in a parallel universe with isothermal planets but not in ours .
When people do idea experiments or simplified models they always choose systems that are supposed to exist at least as approximations even if the probability is very low .
I can’t remember a single example where is choosen a system that can’t exist in our universe .
It’s beyond me what can be helpful in taking an isothermal planet (which will never exist) in radiative equilibrium (which doesn’t exist) and saying that the average of 4th power is the 4th power of an average (which is wrong) .
I’d say that any conclusion drawn from the set of assumptions above would be at best irrelevant to the real world .
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But as I said I am still reading what follows this unnecessary and wrong first page .
Tom–
I’ve done the correction for non-isothermal. It exists, but it’s not large. The planet would be even colder if we account for the non-isothermal nature and the greenhouse effect is larger.
I disagree with you that this sort of simplification is useless. It’s useful to ignore the variations with latitude and longitude to get an idea of the specific features with height. But… if you don’t like this sort of separate effects sort of thinking, I guess that’s fine. It has a long history in both science and engineering. (There is also a long history of people who hate these things. But… well… there ya’ go!)
Lucia writes:
“I’ve done the correction for non-isothermal. It exists, but it’s not large. The planet would be even colder if we account for the non-isothermal nature and the greenhouse effect is larger.”
I don’t think this is the important part of the Tom’s remark. The important part is that Teff is not the surface temperature of an atmosphere free mass of “rock”. Teff is the temperature of a contained, ideal-gas under those conditions. Consequently the “eff” refers to the effective temperature as if the object were an ideal-gas, not any temperature that can be measured from the object itself in the sense of statistical mechanics.
TomVonk
I am unfamiliar with the J. Nichol paper that you mentioned. Do you have a link to it?
There is a kind of analog of the Heisenberg Uncertainty Principle regarding
accuracy and clarity: in order to make a complex point very clear and understandable, one must drop a lot of qualifications and riders;
a statement that is highly accurate requires a lot of conditional “if”
clauses to keep it accurate and muddies the explanation.
As you say, the “zero-dimensional”, isothermal model is very much an idealization, and represents the clearer-but-less-accurate end of the above scale. The word “around” was included in the sentence relative to the 33C to recognize the idealization’s inaccuracy. However, the idealization helps many people understand the basic energy-balance issue, and serves as a useful starting point.
It is fair to say that the Earth without water-vapor and CO2 in its atmosphere would be a great deal colder than it is. As Lucia pointed out, the isothermality assumption does not introduce a huge error — and that is partially offset by the much-reduced albedo which would result from eliminating water-vapor.
Someone please correct me if I’ve misinterpreted something in my cursory reading of the Nicol paper cited above, but it looks like he ignored the line wings in his calculation. It’s true that in the center of the line, further increases in concentration past a certain point have no effect, but it’s not true for the wings. The equivalent width of the line continues to increase with increasing concentration, but at a slower rate. For an isolated line, the equivalent width increases as the square root of the concentration in the strong line limit. Something similar should also be true for a band of overlapping lines.
DeWitt
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No . J.Nicol precisely argues that wing radiation is very important because the mean free path is very different from the one at the peak of the band .
There were 2 other points I had issues with an discussed them at large with J.Nicol some 10 months ago but didn’t follow if he dealt with it .
PatK
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The J.Nicol paper is rightly linked by DaveB . As I had other things to do , I didn’t follow up the evolution with J.Nicol so don’t know if there are updates .
As you rightly say a planet without everything (Jon is calling it a “mass of rock”) would very probably have an average temperature lower than the Earth (depending on rotation , orbital parameters , the property of rock etc) .
But I’d prefer the use of a hand waving argument saying f.ex that “the night side is at equilibrium with 3 K while the day side is around 380 K and therefore the average temperature is below 288 K”
The day side is much hotter than the real Earth but the night side is much , much cooler – so the average of much and much much is a bit cooler .
Of course the argument could be made better than only handwaving rather easily if necessary .
Lucia has said somewhere that something that violates the laws of physics is unphysical .
Well an isothermal planet at equilibrium with the Sun violates the laws of physics so is uphysical .
And I share with Heisenberg the dislike of unphysical systems because a system that violates the laws of physics can’t validly demonstrate something about the laws of physics .
That’s why Equation 2 is strange – why should aT1 + bT2 be equal to a constant and more specifically to 255 K which has nothing to do with A or B photons ?
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Anyway the interesting part of the paper is not this one but the one dealing with the upper troposphere .
Qualitatively it looks reasonable and as here the equations used are local , the same critics like for the 1st part doesn’t apply .
Appendix 1 is classical LTE pure radiation transfer uncoupled to convection .
You then couple it to convection and H20 by Equation 5 .
Apparently you consider that the coupling is linear and there are no terms of the type h(Tp,p,nu) . This is an important assumption .
Clearly Equation 8 is also important for the conclusions . I don’t have an idea yet if that assumption is reasonable .
Tom Vonk
“Apparently you consider that the coupling is linear and there are no terms of the type h(Tp,p,nu) . This is an important assumption .”
There is upward thermal transfer by radiation transfer and by convection, so it is natural to treat them as contributing separately and additively to the overall transfer for a first approximation in an initial treatment of the issue. Are there interactions between the two? Most probably, but these represent higher-order effects and elaborations which would certainly add a great deal of complication to the analysis and tend to obscure the core physics. My aim was simplicity, to pull out the core of the problem.
(As a former manager of research, I often felt that a common sin in theoretical research attempts was to over-analyze and over-complicate a problem, making it intractable and opaque — it is good to remember KISS).
Given my approach, Eq. (8) is an Ansatz, chosen to be as simple as possible (Occam’s razor) consistent with what is known. As discussed prior to Eq. (6), there is little doubt that f(p) is known to fall off as we approach the tropopause, the radiosonde data suggest that it should fall off quite rapidly, and we know that it must be less than 1 everywhere. My ansatz meets all four criteria, I believe, but other expressions could also be used. An alternative might be to use a polynomial fit or, better, to use a fluid-flow analytical result, although at the likely cost of adding more parameters.
Re the first part of the paper, I agree that models must not be unphysical (in fact, my best-known work is based on showing that a model proposed by Max Born failed to satisfy rotational invariance requirements, and then producing an alternative model which did — but that’s another story). However, while I have no desire to waste effort defending it, it is fairly clear that the Lorius “zero-dimensional” picture could be made physical fairly easily and the main point would remain.
I appreciate your review of the paper and your thought-provoking comments and look forward to more of them. Perhaps you yourself might take my hypothesis a step further along by replacing some of the assumptions I have made with better ones.
Tom Vonk: As you rightly say a planet without everything (Jon is calling it a “mass of rockâ€) would very probably have an average temperature lower than the Earth (depending on rotation , orbital parameters , the property of rock etc) .
But I’d prefer the use of a hand waving argument saying f.ex that “the night side is at equilibrium with 3 K while the day side is around 380 K and therefore the average temperature is below 288 Kâ€
The day side is much hotter than the real Earth but the night side is much , much cooler – so the average of much and much much is a bit cooler .
The lump of rock which shares our distance from the sun has a mean surface temperature (day) of 107°C and a mean surface temperature (night) -153°C. That averages out to ~250 K which is rather close to the predicted value for Earth without an atmosphere, of course it has a rather lower albedo (0.12) as opposed to ~0.3 for earth (largely due to clouds).
TomVonk (Comment#7190) December 8th, 2008 at 4:54 am,
I’ll have to read the Nicol paper more closely then. It’s not obvious to me that there can be a limit to the greenhouse effect from CO2 when the short wavelength side of the 15 micrometer band borders on the atmospheric window at low altitude and both wings of the band are visible in the high altitude emission spectrum. That would seem to imply that an increase in CO2 will always result in higher emission from the atmosphere to the surface and less emission from the atmosphere to space at constant temperature and lapse rate (and can be easily demonstrated to do that using MODTRAN).
Nicol’s population inversion argument is a straw man. One can easily absorb a very high percentage of incident photons without causing a population inversion. That’s how absorption spectrophotometry works. Also, collisional energy transfer works both ways. In fact it has to for Kirchhoff’s Law to work. Sorry for going off topic, but I wasn’t the one to link the Nicol paper to this thread.
Look at Figure 1 in Nicol’s paper and then look at the observedIR emission spectrum of the atmosphere from space or from the surface. Note the features of the CO2 band centered at 667 cm-1. Nicol’s assertion that CO2 only absorbs radiation and does not emit because of collisional deactivation is clearly falsified by observation. This fundamental error invalidates the rest of the paper. I don’t understand why so many otherwise intelligent people fall into this error.
The lump of rock which shares our distance from the sun has a mean surface temperature (day) of 107°C and a mean surface temperature (night) -153°C. That averages out to ~250 K which is rather close to the predicted value for Earth without an atmosphere, of course it has a rather lower albedo (0.12) as opposed to ~0.3 for earth (largely due to clouds).
Well that would be fascinating if true considering that liquid water covers 70% of the earth and has an emissivity of 0.67 and soil has an emissivity of around 0.38, whereas the moon is primarily silica with an emissivity of 0.88–larger even because of the fine lunar powder. So much so that the original measurements in 30s mistook the moon to be very close to a black-body!
Claiming that an atmosphere-free Earth and the Moon have similar emissivities is a point requiring substantiation.
Jon (Comment#7213) December 8th, 2008 at 10:48 pm,
I don’t know where you’re getting that emissivity data but this reference for example has the emissivity in the thermal IR band of the various substances comprising the surface of the earth ranging from 0.89 to 0.99.
Or here’s another:
The concept of brightness temperature is extremely useful for remote sensing at infrared and microwave wavelengths. For example, at thermal IR wavelengths, most land and water surfaces and dense cloud layers have an emissivity epsilon approximately equal to 1.
Grant Petty, A First Course in Atmospheric Radiation.
DeWitt
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Where have you seen “population inversion” problems ?
That is clearly not an issue and I don’t remember J.Nicol mentionning this point .
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Your remark about collisionnal energy transfer is valid . I made the same to J.Nicol several months ago and we spent considerable time dealing with it .
Indeed the view that GHG “warm” non GHG by collisions is shared by many but a more precise calculation in LTE conditions is necessary because the translationnal and vibrationnal degrees of freedom stand in equilibrium too .
I do not know if J.Nicol included this modification in a new version .
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There is also the question whether the phi in equation 26 is a constant in first approximation .
Tom,
I may be misinterpreting what Nicol is saying, but here’s the quote from the last paragraph on page 25 of the pdf linked by DaveB (Comment#7164) December 6th, 2008 at 3:24 pm above:
In each case, the proportion of energy contained as excitation of a Greenhouse gas, compared to that released through collisions to heat the surrounding gases, will remain essentially the same unless the density oof the radiation were sufficient to saturate the corresponding resonant transitions. This is demonstrably not the case, since the rapid transfer of molecular excitatin energy to thermal kinetic energy takes place in much less than a microsecond. The CO2 molecules in only 10 m3 on the other hand, if half were simultaneously excited, would be holding 660 Joules of energy, an amount which could only be radiated by the earth in about 2 seconds.
As Emily Litella (played by Gilda Radner on the old Saturday Night Live TV show) would say: Never mind. Obviously (well obvious now that I have read it carefully), he’s making the argument for local thermal equilibrium. But I don’t know with whom he’s disputing the point. Standard greenhouse radiative transfer theory requires LTE because Kirchhoff’s Law only applies to a gas when it’s in LTE. The definition of LTE is that collisional energy transfer occurs far more often than radiative energy transfer.
deWitt
Well yes . Sure . You say the same thing and J.Nicol is disputing nothing with anybody . He’s just saying what happens .
I still don’t see where the “population inversion” you mentionned comes from .
I don’t know where you’re getting that emissivity data but this reference for example has the emissivity in the thermal IR band of the various substances comprising the surface of the earth ranging from 0.89 to 0.99.
I’m getting my data from the Handbook of Chemistry and Physics tabulation of total emissivity–the numbers you cite look like spectral emissivity (i.e., narrow-band adjustments suitable for calibrating an instrument). In our context, we’re not interested in estimating the temperature of an object by observation so spectral emissivity is not the appropriate concept. Total emissivity should be used when modeling radiative heat-flux. Please let me know if I’ve been wrong-footed in someway. I do not have your reference at-hand.
Tom,
“…if half were simultaneously excited…” That would be a population inversion, I think, since normally well over 90% of the CO2 molecules are in the ground state for the 15 micrometer band.
PatK,
I’m having a problem with this statement in section 4 (page numbers would have been nice).
The net energy transfer rate due to type A photons is proportional to the local temperature gradient and therefore slows and then reverses direction above the tropopause to a downward flow of thermal energy.
Considering that pressure broadening is decreasing rapidly with altitude as well as number density, the proportion of type A photons is shrinking so fast in the stratosphere that it overwhelms the effect of the positive temperature gradient and the net energy transfer is still upward (cooling to space). At the tropopause temperature minimum, there is maximum interaction with emission from above and below so the net energy transfer from CO2 to the atmosphere is slightly positive, but above and below this altitude, CO2 radiates energy away.
“the proportion of type A photons is shrinking so fast in the stratosphere that it overwhelms the effect of the positive temperature gradient and the net energy transfer is still upward”.
DeWitt
At the tropopause, there are still a lot of type-A photons from the center of the band (see the bottom half of Table I) and these are the ones that provide a downward flow [I said “The net energy transfer rate due to type A photons…slows and then reverses direction above the tropopause…”]. I agree that the TOTAL energy from all photons is a net upward flow, but the type A portion is downward just above the troposphere.
This can, I believe, be seen in the detailed line-by-line results of Clough and Iacano (1995) for the center of the CO2 band at the tropopause, as I discuss in Section 5.3 of my paper.
deWitt
“…if half were simultaneously excited…†That would be a population inversion, I think, since normally well over 90% of the CO2 molecules are in the ground state for the 15 micrometer band.
OK I see . Technically it is not a population inversion because a gas in LTE can never go above 50 % of excited states . To get a population inversion NON equilibrium conditions must be created .
The excited 15µ levels in LTE are in reality only about 5 % fast decreasing with altitude .
I think that J.Nicol wanted to take an example to say that even with the maximum allowable value of excited states (50%) there would be no “saturation” .
I find it quite obvious and that’s why I didn’t pay much attention to this statement that could be , in my opinion , left out without changing anything .
$30 US seems a bit steep for one article. I’ll pass at the moment.
DeWitt–
Try your interlibrary loan. It might take a week, but lots of libraries can get these for you. It’s much wiser than paying.
DWP, we have an institutional access. Where I can mail you a .pdf?
Looks interesting but I will have to wait untill it is available free of charge .
Or if you have it , could you send me a pdf at my mail adress ?
The crucial role of the wings reminds me of the J.Nicol paper .
Also coupling correctly convection with radiation is major what J.Nicol wrote too (and no , as I exchanged many mails with him for the revision of his paper , not everything he wrote was right in my opinion) .
If the surface heating is easy to derive , upper troposphere cooling is not .
H2O/CO2 radiative coupling is not either .
What makes me skeptical is the question how a “simple” 0/1 dimensionnal model could get the radiation/convection coupling right when the mature full 3D multimillion line GCMs managed by hundreds of scientists can’t .
Especially as we have been told for years that precisely this was one aspect of the models where they all agreed (qualitatively) .
But it shall have to wait untill I read it .
I downloaded Keating08 as a .pdf and can email it to avid readers. Just mail me – the address is EWCZ at seznam.cz
Maybe somebody can compare and contrast the model with Essenhigh’s:
http://pubs.acs.org/doi/abs/10.1021/ef050276y?prevSearch=&searchHistoryKey=
Thanks
Thanks to lucia and PatK I now have a preprint of the paper without anyone violating copyright. More later after I’ve had a chance to study the paper.
Argh !
I have almost been put off already at the first page because of this same old error that people keep repeating .
.
At one line it is correctly said that the “effective emitting temperature is 255 K .”
This is the temperature that would have an isothermal spherical body in radiative equilibrium with another body at infinity .
Of course everybody knows that no planet in the solar system is an isothermal spherical body in radiative equilibrium with the Sun regardless if it has an atmosphere or not .
However even if isothermal planets don’t exist and can’t exist , one can’t forbid people to write equations for them as long as they precise that the equations apply to a system that can’t exist .
.
Yet right in the following line it is written “In other words the surface would be around 33°C colder than what it is if the atmosphere was tranparent to IR”
So suddenly the “effective emitting temperature of 255 K .” became “the average temperature .” .
This is clearly wrong because the average of the 4th power is not the 4th power of the average .
It is also wrong because a planet without water , atmosphere , cryosphere would not have neither the same albedo neither the same surface emissivity as a planet that has all of the above .
On top this wrong statement is not even necessary for what comes after .
.
So yes I actually read farther despite the bad impression of the beginning .
Tom–
Of course everyone, including Pat, know there are no spherical isothermal planets. That idea is a baseline for all simplified models. The paths of starting form the most complicated end and moving simpler and starting from simpler and getting progressively more complicated are both well respected.
Some people don’t like simplified models used to develop understanding of processes. But others do, and I think they give valuable insights. Yes, the model neglects water, continents, ice etc. And the atmosphere is simplified.
The goal is to see whether by extending the simplified models (like those in text books like McGuffy Hendrick-Sellers) one can predict a puzzling feature: the apparent cooling of the tropical tropopause.
I have no problem withh simplified processes .
I have a problem with WRONG statements and I was mentionning sofar only the page 1 .
This : “In other words the surface would be around 33°C colder than what it is if the atmosphere was tranparent to IR†is a wrong statement .
It is not an approximation or an argument – it is not even a guess .
One can turn around it as often as one wants and say whatever one wants , it won’t make the statement right .
It is perhaps right in a parallel universe with isothermal planets but not in ours .
When people do idea experiments or simplified models they always choose systems that are supposed to exist at least as approximations even if the probability is very low .
I can’t remember a single example where is choosen a system that can’t exist in our universe .
It’s beyond me what can be helpful in taking an isothermal planet (which will never exist) in radiative equilibrium (which doesn’t exist) and saying that the average of 4th power is the 4th power of an average (which is wrong) .
I’d say that any conclusion drawn from the set of assumptions above would be at best irrelevant to the real world .
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But as I said I am still reading what follows this unnecessary and wrong first page .
Dan
Thanks for the link. Here is Essenhigh’s previous article on climate:
Does CO2 really drive Global Warming?” Energy & Environment, 2001
Tom–
I’ve done the correction for non-isothermal. It exists, but it’s not large. The planet would be even colder if we account for the non-isothermal nature and the greenhouse effect is larger.
I disagree with you that this sort of simplification is useless. It’s useful to ignore the variations with latitude and longitude to get an idea of the specific features with height. But… if you don’t like this sort of separate effects sort of thinking, I guess that’s fine. It has a long history in both science and engineering. (There is also a long history of people who hate these things. But… well… there ya’ go!)
Lucia writes:
“I’ve done the correction for non-isothermal. It exists, but it’s not large. The planet would be even colder if we account for the non-isothermal nature and the greenhouse effect is larger.”
I don’t think this is the important part of the Tom’s remark. The important part is that Teff is not the surface temperature of an atmosphere free mass of “rock”. Teff is the temperature of a contained, ideal-gas under those conditions. Consequently the “eff” refers to the effective temperature as if the object were an ideal-gas, not any temperature that can be measured from the object itself in the sense of statistical mechanics.
TomVonk
I am unfamiliar with the J. Nichol paper that you mentioned. Do you have a link to it?
There is a kind of analog of the Heisenberg Uncertainty Principle regarding
accuracy and clarity: in order to make a complex point very clear and understandable, one must drop a lot of qualifications and riders;
a statement that is highly accurate requires a lot of conditional “if”
clauses to keep it accurate and muddies the explanation.
As you say, the “zero-dimensional”, isothermal model is very much an idealization, and represents the clearer-but-less-accurate end of the above scale. The word “around” was included in the sentence relative to the 33C to recognize the idealization’s inaccuracy. However, the idealization helps many people understand the basic energy-balance issue, and serves as a useful starting point.
It is fair to say that the Earth without water-vapor and CO2 in its atmosphere would be a great deal colder than it is. As Lucia pointed out, the isothermality assumption does not introduce a huge error — and that is partially offset by the much-reduced albedo which would result from eliminating water-vapor.
PatK,
I believe the John Nicol paper that Tom mentions can be downloaded from
http://www.ruralsoft.com.au/ClimateChange.doc
Someone please correct me if I’ve misinterpreted something in my cursory reading of the Nicol paper cited above, but it looks like he ignored the line wings in his calculation. It’s true that in the center of the line, further increases in concentration past a certain point have no effect, but it’s not true for the wings. The equivalent width of the line continues to increase with increasing concentration, but at a slower rate. For an isolated line, the equivalent width increases as the square root of the concentration in the strong line limit. Something similar should also be true for a band of overlapping lines.
DeWitt
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No . J.Nicol precisely argues that wing radiation is very important because the mean free path is very different from the one at the peak of the band .
There were 2 other points I had issues with an discussed them at large with J.Nicol some 10 months ago but didn’t follow if he dealt with it .
PatK
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The J.Nicol paper is rightly linked by DaveB . As I had other things to do , I didn’t follow up the evolution with J.Nicol so don’t know if there are updates .
As you rightly say a planet without everything (Jon is calling it a “mass of rock”) would very probably have an average temperature lower than the Earth (depending on rotation , orbital parameters , the property of rock etc) .
But I’d prefer the use of a hand waving argument saying f.ex that “the night side is at equilibrium with 3 K while the day side is around 380 K and therefore the average temperature is below 288 K”
The day side is much hotter than the real Earth but the night side is much , much cooler – so the average of much and much much is a bit cooler .
Of course the argument could be made better than only handwaving rather easily if necessary .
Lucia has said somewhere that something that violates the laws of physics is unphysical .
Well an isothermal planet at equilibrium with the Sun violates the laws of physics so is uphysical .
And I share with Heisenberg the dislike of unphysical systems because a system that violates the laws of physics can’t validly demonstrate something about the laws of physics .
That’s why Equation 2 is strange – why should aT1 + bT2 be equal to a constant and more specifically to 255 K which has nothing to do with A or B photons ?
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Anyway the interesting part of the paper is not this one but the one dealing with the upper troposphere .
Qualitatively it looks reasonable and as here the equations used are local , the same critics like for the 1st part doesn’t apply .
Appendix 1 is classical LTE pure radiation transfer uncoupled to convection .
You then couple it to convection and H20 by Equation 5 .
Apparently you consider that the coupling is linear and there are no terms of the type h(Tp,p,nu) . This is an important assumption .
Clearly Equation 8 is also important for the conclusions . I don’t have an idea yet if that assumption is reasonable .
Tom Vonk
“Apparently you consider that the coupling is linear and there are no terms of the type h(Tp,p,nu) . This is an important assumption .”
There is upward thermal transfer by radiation transfer and by convection, so it is natural to treat them as contributing separately and additively to the overall transfer for a first approximation in an initial treatment of the issue. Are there interactions between the two? Most probably, but these represent higher-order effects and elaborations which would certainly add a great deal of complication to the analysis and tend to obscure the core physics. My aim was simplicity, to pull out the core of the problem.
(As a former manager of research, I often felt that a common sin in theoretical research attempts was to over-analyze and over-complicate a problem, making it intractable and opaque — it is good to remember KISS).
Given my approach, Eq. (8) is an Ansatz, chosen to be as simple as possible (Occam’s razor) consistent with what is known. As discussed prior to Eq. (6), there is little doubt that f(p) is known to fall off as we approach the tropopause, the radiosonde data suggest that it should fall off quite rapidly, and we know that it must be less than 1 everywhere. My ansatz meets all four criteria, I believe, but other expressions could also be used. An alternative might be to use a polynomial fit or, better, to use a fluid-flow analytical result, although at the likely cost of adding more parameters.
Re the first part of the paper, I agree that models must not be unphysical (in fact, my best-known work is based on showing that a model proposed by Max Born failed to satisfy rotational invariance requirements, and then producing an alternative model which did — but that’s another story). However, while I have no desire to waste effort defending it, it is fairly clear that the Lorius “zero-dimensional” picture could be made physical fairly easily and the main point would remain.
I appreciate your review of the paper and your thought-provoking comments and look forward to more of them. Perhaps you yourself might take my hypothesis a step further along by replacing some of the assumptions I have made with better ones.
Tom Vonk: As you rightly say a planet without everything (Jon is calling it a “mass of rockâ€) would very probably have an average temperature lower than the Earth (depending on rotation , orbital parameters , the property of rock etc) .
But I’d prefer the use of a hand waving argument saying f.ex that “the night side is at equilibrium with 3 K while the day side is around 380 K and therefore the average temperature is below 288 Kâ€
The day side is much hotter than the real Earth but the night side is much , much cooler – so the average of much and much much is a bit cooler .
The lump of rock which shares our distance from the sun has a mean surface temperature (day) of 107°C and a mean surface temperature (night) -153°C. That averages out to ~250 K which is rather close to the predicted value for Earth without an atmosphere, of course it has a rather lower albedo (0.12) as opposed to ~0.3 for earth (largely due to clouds).
TomVonk (Comment#7190) December 8th, 2008 at 4:54 am,
I’ll have to read the Nicol paper more closely then. It’s not obvious to me that there can be a limit to the greenhouse effect from CO2 when the short wavelength side of the 15 micrometer band borders on the atmospheric window at low altitude and both wings of the band are visible in the high altitude emission spectrum. That would seem to imply that an increase in CO2 will always result in higher emission from the atmosphere to the surface and less emission from the atmosphere to space at constant temperature and lapse rate (and can be easily demonstrated to do that using MODTRAN).
Nicol’s population inversion argument is a straw man. One can easily absorb a very high percentage of incident photons without causing a population inversion. That’s how absorption spectrophotometry works. Also, collisional energy transfer works both ways. In fact it has to for Kirchhoff’s Law to work. Sorry for going off topic, but I wasn’t the one to link the Nicol paper to this thread.
Look at Figure 1 in Nicol’s paper and then look at the observed IR emission spectrum of the atmosphere from space or from the surface. Note the features of the CO2 band centered at 667 cm-1. Nicol’s assertion that CO2 only absorbs radiation and does not emit because of collisional deactivation is clearly falsified by observation. This fundamental error invalidates the rest of the paper. I don’t understand why so many otherwise intelligent people fall into this error.
The lump of rock which shares our distance from the sun has a mean surface temperature (day) of 107°C and a mean surface temperature (night) -153°C. That averages out to ~250 K which is rather close to the predicted value for Earth without an atmosphere, of course it has a rather lower albedo (0.12) as opposed to ~0.3 for earth (largely due to clouds).
Well that would be fascinating if true considering that liquid water covers 70% of the earth and has an emissivity of 0.67 and soil has an emissivity of around 0.38, whereas the moon is primarily silica with an emissivity of 0.88–larger even because of the fine lunar powder. So much so that the original measurements in 30s mistook the moon to be very close to a black-body!
Claiming that an atmosphere-free Earth and the Moon have similar emissivities is a point requiring substantiation.
Jon (Comment#7213) December 8th, 2008 at 10:48 pm,
I don’t know where you’re getting that emissivity data but this reference for example has the emissivity in the thermal IR band of the various substances comprising the surface of the earth ranging from 0.89 to 0.99.
Or here’s another:
Grant Petty, A First Course in Atmospheric Radiation.
DeWitt
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Where have you seen “population inversion” problems ?
That is clearly not an issue and I don’t remember J.Nicol mentionning this point .
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Your remark about collisionnal energy transfer is valid . I made the same to J.Nicol several months ago and we spent considerable time dealing with it .
Indeed the view that GHG “warm” non GHG by collisions is shared by many but a more precise calculation in LTE conditions is necessary because the translationnal and vibrationnal degrees of freedom stand in equilibrium too .
I do not know if J.Nicol included this modification in a new version .
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There is also the question whether the phi in equation 26 is a constant in first approximation .
Tom,
I may be misinterpreting what Nicol is saying, but here’s the quote from the last paragraph on page 25 of the pdf linked by DaveB (Comment#7164) December 6th, 2008 at 3:24 pm above:
As Emily Litella (played by Gilda Radner on the old Saturday Night Live TV show) would say: Never mind. Obviously (well obvious now that I have read it carefully), he’s making the argument for local thermal equilibrium. But I don’t know with whom he’s disputing the point. Standard greenhouse radiative transfer theory requires LTE because Kirchhoff’s Law only applies to a gas when it’s in LTE. The definition of LTE is that collisional energy transfer occurs far more often than radiative energy transfer.
deWitt
Well yes . Sure . You say the same thing and J.Nicol is disputing nothing with anybody . He’s just saying what happens .
I still don’t see where the “population inversion” you mentionned comes from .
I don’t know where you’re getting that emissivity data but this reference for example has the emissivity in the thermal IR band of the various substances comprising the surface of the earth ranging from 0.89 to 0.99.
I’m getting my data from the Handbook of Chemistry and Physics tabulation of total emissivity–the numbers you cite look like spectral emissivity (i.e., narrow-band adjustments suitable for calibrating an instrument). In our context, we’re not interested in estimating the temperature of an object by observation so spectral emissivity is not the appropriate concept. Total emissivity should be used when modeling radiative heat-flux. Please let me know if I’ve been wrong-footed in someway. I do not have your reference at-hand.
Tom,
“…if half were simultaneously excited…” That would be a population inversion, I think, since normally well over 90% of the CO2 molecules are in the ground state for the 15 micrometer band.
PatK,
I’m having a problem with this statement in section 4 (page numbers would have been nice).
Considering that pressure broadening is decreasing rapidly with altitude as well as number density, the proportion of type A photons is shrinking so fast in the stratosphere that it overwhelms the effect of the positive temperature gradient and the net energy transfer is still upward (cooling to space). At the tropopause temperature minimum, there is maximum interaction with emission from above and below so the net energy transfer from CO2 to the atmosphere is slightly positive, but above and below this altitude, CO2 radiates energy away.
“the proportion of type A photons is shrinking so fast in the stratosphere that it overwhelms the effect of the positive temperature gradient and the net energy transfer is still upward”.
DeWitt
At the tropopause, there are still a lot of type-A photons from the center of the band (see the bottom half of Table I) and these are the ones that provide a downward flow [I said “The net energy transfer rate due to type A photons…slows and then reverses direction above the tropopause…”]. I agree that the TOTAL energy from all photons is a net upward flow, but the type A portion is downward just above the troposphere.
This can, I believe, be seen in the detailed line-by-line results of Clough and Iacano (1995) for the center of the CO2 band at the tropopause, as I discuss in Section 5.3 of my paper.
deWitt
“…if half were simultaneously excited…†That would be a population inversion, I think, since normally well over 90% of the CO2 molecules are in the ground state for the 15 micrometer band.
OK I see . Technically it is not a population inversion because a gas in LTE can never go above 50 % of excited states . To get a population inversion NON equilibrium conditions must be created .
The excited 15µ levels in LTE are in reality only about 5 % fast decreasing with altitude .
I think that J.Nicol wanted to take an example to say that even with the maximum allowable value of excited states (50%) there would be no “saturation” .
I find it quite obvious and that’s why I didn’t pay much attention to this statement that could be , in my opinion , left out without changing anything .