In our summary of IPCC AR1 (1990) on radiative forcing, I noted that the logarithmic relationship and 4 wm-2 values were attributed to: Hansen et al (1988), which in turn cited Lacis et al 1981; and Wigley (1987) which is not presently available to me (or to Wigley himself) and appears not to have been peer-reviewed (FWTW). Feedback analysis primarily relied on Cess et al 1989. I’ll examine those references at some point, but today I’ll continue the review through two supplements to IPCC (1990), published in 1992 and 1994.
Climate Change 1992
A few pages (6-8,45-47,57-59, 63-70) of Houghton et al, Climate Change 1992: The Supplementary Report to the IPCC Scientific Assessment are online at Google here, but the sections of interest here are not. [Update 2015 – the entire report is online at IPCC here.)
Chapter A2 (Radiative Forcing) starts by focusing on ozone and sulphate aerosols, saying that there have bee “significant advances in our understanding” of their impact on radiative forcing. CO2 results are not mentioned in the Executive Summary of this chapter. On page 53, it re-capitulates the definition of radiative forcing, but I did not locate any fresh analysis of CO2. Their analysis of aerosols is primarily of sulphate aerosols, where they report negative sulphate aerosol forcing, stating:
A very important implication of this estimate is that the net anthropogenic radiative forcing over parts of the NH during the past century is likely to have been substantially smaller than was previously believed.
They note high geographic variability of sulphate aerosol forcing, with their Figure A2.3 showing high values only over North America and Europe-Asia.
Climate Change 1994: Radiative Forcing of Climate Change and an Evaluation of the IPCC 1992 IS92 Emission Scenarios
Again a few pages of this report (1-27, 157-160, 167-170, 190), this time including a little bit of interest in this post, are online here . (Update 2015 – Google book excerpts is much more extensive but still incomplete. It contains 168,170,172, 174, 178-179, 181-182 among others, but not Figure 4.1. Strangely this report is not included in list of IPCC assessments here, which is otherwise complete.)
This report, published in June 1995, contains a discussion of the “saturation” argument that one sometimes sees by “skeptics” and which was the subject of a contemporary exchange (1994-early 1995) in Spectrochimica Acta between “skeptic” Jack Barrett and, on the other side, John Houghton and Keith Shine (among others).
First they spend a couple of pages distinguishing instantaneous forcing from no-feedback forcing – a distinction that is not material to the derivation of 4 wm-2 or the logarithmic relationship. They report results for doubled CO2 from a 1-D model of Rind and Lacis 1993 (presumably a descendant of the 1-D Lacis et al 1981 model cited in AR1):
(170) The utility of radiative forcing will be the subject of Section 4.8, but it is useful here to illustrate the potential importance of the adjustment process using 1-dimensional radiative-convective results reported by Rind and Lacis (1993) see Table 4.1. …For a doubling ..of CO2 the stratosphere cools so that the adjusted forcing is about 6% less than the instantaneous.
Table 4.1 Surface temperature changes using a a 1-D radiative -convective model (Lacis and Rind 1993)… (Note that surface temperature changes would be about 1 to 4 times larger if climate feedbacks were included – see IPCC 1990). The changes in radiative properties used here are meant to be illustrative and do not necessarily represent actual or projected changes. Results below are for doubling CO2 from 300-600 ppmv.
Item Impact Surface temperature change (ΔT_0) 1.31 K Radiative forcing at tropopause, instantaneous (ΔF_i) 4.63 wm-2 Radiative forcing at tropopause, no feedback (ΔF_o) 4.35 wm-2 Climate sensitivity parameter, instantaneous (λ_i) 0.28 K/ wm-2 Climate sensitivity parameter, no feedback λ_o 0.30 K/ wm-2
They introduce section 4.2 (Greenhouse Gases) as follows:
(p. 171:) Our understanding of the enhanced greenhouse effect is dependent on two broad areas. First we need to understand the fundamental radiative properties (“spectroscopy”) of the gases involved. Next, these spectroscopic data need to be included in radiative transfer models to calculate radiative forcing due to changes in gas concentration, for a given atmospheric profile of temperature, water vapour and other trace gases, and cloudiness. In this section the discussion will concentrate on the radiative forcing of greenhouse gases as a result of direct emission of that gas. This is referred to as the direct greenhouse forcing.
Their section 4.2.1 ( Spectroscopy) introduces the HITRAN and GEISA databases, mentioning “uncretainties” in the water vapor continuum, without elaboration:
In the thermal infrared (approximately 4-500 μm) molecules absorb and emit radiation by changing the energy with which they vibrate and/or rotate the wavelengths of the vibration/rotation transitions occur over narrow spectral intervals. Laboratory and theoretical studies are required to determine the wavelengths, strengths and widths of these transitions”¬⤮
The main databases of spectral parameters of atmospheric gases are subject to periodic update; the two main catalogues, HITRAN (Rothman et al, 1992) and GEISA (Husson et al., 1992) have both been substantially revised since IPCC (1992). These revisions are based on improvements to both laboratory measurements and theoretical techniques… A detailed assessment of the effect of these revisions has not yet been reported. Fomin et al. (1993) report that the net irradiance at the tropopause, evaluated for a mid-latitude clear-sky atmosphere, changes by less than 1% between using the 1986 and 1992 versions of HITRAN. It seems unlikely that the effect of these revisions on radiative forcing will be greater than 5% but there is a need to assess both the effect of these changes and the potential impact of remaining uncertainties.
Continuum absorption, especially by water vapour. Is also of importance in calculating radiative forcing. In spite of recent progress in describing the effect, further theoretical and laboratory investigations are required to resolve remaining uncertainties.
Next section 4.2. Calculating the Radiative Forcing , sketches how the HITRAN line strength information gets translated into models: essentially, for computational reasons, the infrared spectrum is divided into “bands” and an average absorption is assigned to each band. Bands may be “narrow” (at that time about 10 cm-1) or “broad”. IPCC 1994:
A whole hierarchy of different radiative transfer schemes are available to compute the radiative forcing, ranging from line-by-line models through to so-called wide-band models (Ellingson et al 1991). In addition the results from such models can be represented by relatively simple empirical formulae, such as those presented in IPCC (1990) and Shi (1992) to allow rapid and reasonably accurate computation of forcing.
Many details of the radiation schemes (such as methods of handling clouds, spectral overlap of gases, treatment of water vapour continuum) affect the radiative forcing and are not handled in the same way by all schemes (see Ellingson et al 1991)
The ultimate test of such models is their ability to reproduce observed irradiances, given the observed state of the atmosphere. Until recently, the quality of observations was generally inadequate to assess the models; now high-quality experimental data (see e.g. Ellingson et al. 1992) are becoming available and should provide valuable checks on the realism of radiative models. The radiative forcing due to changes in concentration of CO2, CH4, N2O, CFC-11 and CFC-12 presented in IPCC (1990) have been re-assessed by Kratz et al (1993) and Shi and Fan (!992), although neither set of authors accounted for stratospheric adjustment …
Despite the general agreement between the earlier IPCC reports and more recent calculations, a similar agreement is not found for radiative transfer calculations performed in GCMs used for climate prediction. Cess et al (1993) report an intercomparison of instantaneous clear-sky radiative forcing due to a doubling of CO2 from 15 different GCMs. The results deviated by as much as 20% from reference line-by-line calculations; some of the difference was due to neglect of some minor absorption bands, and in particular those near 10 μm, The size of the deviation should not be taken to indicate the uncertainty in calculating the CO2 forcing; it is more indicative of the weakness in the radiative transfer schemes used in some GCMs.
The Ellingson et al 1991 study mentioned here is an interesting one. Ellingson et al did an intercomparison of GCMs noting a wide variation in infrared codes, many of which he said were simply incorrect. Regardless of whether their code was erroneous or not, the GCMs in the survey all agreed quite closely on the impact of doubled CO2, provoking an arch comment from Ellingson et al about “tuning”.
Box: THE GREENHOUSE EFFECT OF INCREASED CONCENTRATIONS OF CARBON DIOXIDE
Next IPCC 1994 has an interesting discussion of how the enhanced greenhouse effect actually works – which, to my knowledge, is by far the most explicit such discussion in the entire IPCC corpus, which is, in part, a response to an exchange between skeptic Jack Barrett and John Houghton in Spectrochimica Acta in 1994. I’ve repeated it in full below.
(174) “It is sometimes stated that, because there is so much CO2 already in the atmosphere, it is “saturated” and extra CO2 can have no additional greenhouse effect. The purpose of this box is to present a simplified explanation as to why this is a misconception.
When gases are present in small concentrations (the halocarbons are examples), the radiative effect of a gas is almost linear in concentration: doubling the concentration of, for example, CFC-11 will approximately double its greenhouse effect. This is not the case for greenhouse gases in larger concentrations, for well-understood reasons (see e.g. Goody and Yung, 1989). Doubling the concentration of CO2 from its present day concentrations leads to a 10-20% increase in the total greenhouse effect due to CO2 ”¬’ this effect is well-understood and has been included in climate models for several decades.
Figure 4.1 illustrates aspects of the increased greenhouse effect of CO2 using a detailed radiative transfer model (see footnote below for details ). Figure 4.1a shows the spectral variation in the net infrared irradiance (“flux”) at the tropopause in Wm-2/cm-1. The shape of the curve is dictated by two factors. First, the Planck function determines the maximum amount of energy that can be emitted at a given wavelength and temperature. At typical atmospheric temperatures, the maximum lies between 10 and 15 μm; at wavelengths short than 5 μm little can be emitted. The second factor is the absorbing properties of the atmosphere, which is dictated by the presence of greenhouse gases (of which water vapour is the most important, followed by CO2) and clouds.
If the troposphere were transparent to infrared radiation, then the irradiance reaching the tropopause would be the same as that leaving the surface. However, greenhouse gases and clouds absorb the radiation emitted by the surface over a range of wavelengths they emit energy in all directions, but since the temperature generally decreases with altitude in the troposphere, less on average is emitted upwards than is absorbed from below, so less reaches the tropopause. The downward radiation from the stratosphere into the troposphere is also an important factor.
CO2, like many other gases absorbs and emits radiation by changing the energy at which it vibrates and rotates, The wavelengths of CO3 absorption are grouped into bands (see e.g. Goody and Yung, 1989) with a strong absorption band centred near 15 μm (Figure 4.1b) The centre of the 15 μm absorption band is so strong that the radiation reaching the tropopause comes from very close to the tropopause and more importantly the CO2 in the stratosphere emits as much downwards as the troposphere emits upwards – the net irradiance is thus very close to zero (see Fig 4.1a – note the feature at about 10 μm is mainly due to ozone.)
Figure 4.1c shows the modelled effect of an instantaneous change in CO2 on the net irradiance at the tropopause. (The change in concentration between 1980 and 1990 is chosen for the purposes of illustration.) All other factors, such as cloudiness and temperature are held fixed. This plot indicates significant change in irradiance. At the centre of the 15 μm band the increase in CO2 concentration has almost no effect – the CO2 absorption is indeed saturated at these wavelengths. Away from the band centre CO2 is less strongly absorbing so that an increase in CO2 concentration does have an effect, The net irradiance at the tropopause decreases – this corresponds to positive radiative forcing that would tend to warm the climate system. As more and more CO2 is added to the atmosphere, more of its spectrum will become saturated – but there will always be regions of the spectrum, which remain, unsaturated and capable of enhancing the greenhouse effect if CO2 concentrations are increased. An example is the 10 μm band system. As shown in Figure 4.1b, it is about 1 million times weaker than the peak of the 15 μm band, but its contribution to the irradiance change in the lower frame is much higher than might be anticipated; as CO2 concentrations increase, the 10 μm band would increase in its importance relative to the 15 μm band.
The saturation effect is partly responsible for the fact that CFC molecules are bout 10,000 times more effective at enhancing the greenhouse effect than molecules of CO2. However, for every extra CFC molecule in the atmosphere since pre-industrial times, there are around 70,000 more CO2 molecules – thus, the relative weakness of CO2 per molecule is more than compensated by the large absolute increase in the number of CO2 molecules in the atmosphere.
Figure 4.1: An illustration that additional amounts of CO2 in the atmosphere do enhance the greenhouse effect- the details of the calculations are given in the footnote to the box. (a) Net infrared irradiance (Wm-2/cm-1) at the tropopause from a standard radiative transfer code using typical atmospheric conditions; (b) Representation of the strength of the spectral lines of CO2 in the thermal infrared: note the logarithmic scale [not bolded in original]. (c) Change in net irradiance at the tropopause (in Wm-2/cm-1) on increasing the CO2 concentration from its 1980 to 1990 levels, whilst holding all other parameters fixed. Note the change in irradiance at the wavelength of maximum absorption, as shown in (b) is essentially zero, while the most marked effects on the irradiance are at wavelengths at which CO2 is less strongly absorbing. Note:The radiative transfer calculations were performed using the standard narrow band code of Shine (1991), which has a spectral resolution of 10 cm-1. The atmosphere used is Northern Hemisphere mean for January, including the effect of clouds, water vapour, ozone carbon dioxide and a number of other gases, although the above argument is non sensitive to the details. The spectrum in the middle frame is the sum of the line strengths in each of the 10 cm-1 intervals at a temperature of 250 K, using the HITRAN database (Rothman et al., 1992); the units are cm-1/(kg m-2). In the lower frame, the irradiance change is the instantaneous forcing.
I’m not going to comment on this argument right now as I want to collate a couple of other thoughts first, but will return to it.
Climate Change 1995 (SAR)
Next came the IPCC Second Assessment Report (SAR) also published in 1995. SPM here ; some sections from Google online here (1-73, 117- 119, 127, 142-148) with a bit of the radiative forcing chapter online (65ff). They re-state their definition of radiative forcing:
(109ff:) the detailed rationale for using radiative forcing was given in IPCC (1994). .. The definition of radiative forcing adopted in previous IPCC reports (1990, 1992, 1994) has been the perturbation to the net irradiance (in Wm-2) at the tropopause after allowing for stratospheric temperatures to re-adjust (on a time-scale of a few months) to radiative equilibrium, but with the surface and tropospheric temperature and atmospheric moisture held fixed …
Their discussion of greenhouse gases is shorter than IPCC (1994); much of the emphasis at this time seems to be on the non-CO2 impacts. IPCC section 2.41 (Greenhouse gases):
Estimates of the adjusted radiative forcing due to changes in the concentration of the so-called well-mixed greenhouse gases (Co2, CH4, N2O and the halocarbons) since pre-industrial times remain unchanged from IPCC (1994); the forcing given there is 2.45 Wm-2 with an estimated uncertainty of 15%. CO2 is by far the most important of the gases, contributing about 64% of the total forcing. .
The basic understanding of the ways in which greenhouse gases absorb and emit thermal infrared radiation (e.g. Goody and Yung, 1989) is supported by abundant observations of the spectrally resolved infrared emission by the clear-sky atmosphere (e.g. Kunde et al., 1974; Lubin 1994)). Barrett (1995)’s suggestion that greenhouse gases are unable to emit significant amounts of infrared radiation is contradicted by these observations.
Again, no readers should doubt that greenhouse gases can emit significant amounts of infrared radiation; downwelling IR radiation can be measured and is not a theoretical construct.
From our limited objective here, nowhere so far has there been a thorough explication by IPCC of how AGW actually works. The Box in IPCC (1994) is the longest discussion in the corpus, but it’s hardly a thorough exposition. I presume that IPCC’s position is that providing such an explication is baby food – however, I think that that’s an unjustifiable position for them to take, as there are many earnest readers, including many CA readers, who looked to IPCC for an explication of how AGW worked in some detail. Or if they weren’t going to do so themselves, they could have cited texts that did so to IPCC satisfaction in their list of references, so that people inquiring into the topic would not be thrashing.
References:
Ellingson et al 1992. The intercomparison of radiation codes used in climate models. Long wave results. JGR 96, 8929-8953. pdf
IPCC, 1994. Radiative Forcing of Climate Change and an Evaluation of the IPCC 1992 IS92 Emission Scenarios, Google book excerpts contains 168,170,172, 174, 178-179, 181-182 among others,
Rind, D., and A. Lacis (1993), The role of the stratosphere in climate change, Surv. Geophys., 14, 133-165. Abstract
Climate Audit 
84 Comments
The base reference for the log effect of CO2 forcing at absorption saturation seems to be “Goody and Yung, 1989.” This reference is to a book, Goody, R. M., and Y. L. Yung, 1989: Atmospheric Radiation, Theoretical Basis. 2d ed. Oxford University Press, 519 pp., unfortunately, making it harder to check.
My present understanding — I haven’t seen the actual derivation — is that the log effect of forcing represents absorption moving down the exponential tail of the Gaussian absorption band, as atmospheric CO2 concentration increases.
The skeptic ‘staturation’ argument as I understand it is simply a statement of the logarithmic relationship between CO2 and temperature. This logarithmic relationship means that each additional injection of CO2 will cause less warming than its predecessors. The IPCC and RC arguments confirm this relationship while they refute the so called ‘saturation’ argument. These arguments give me the impression that ‘saturation’ is a convenient strawman for AGW advocates.
Steve: no it’s different than that. be patient, I’ll review it – it’s a non-issue.
I’m going to get saturation in a little more detail after I canvass some more materials – so I’d prefer that people don’t opine on it right now. I copied some relevant sections from Goody and Yung a couple of years ago and will refer to them in my notes.
According to this exposition, the saturation proposition has two orthoginal components to it:
1. The change in temperature attributable to radiation within a particular frequency range
2. Change in radiation across the frequency spectrum, as the individual bands saturate
Either or both could lead to a logarithmic pattern of saturation response of Temp vs CO2. The shape of the latter is going to depend on the shape of the spectrum.
More to the point. The technical documentation should be separating out these independent effects, not conflating them. Obviously one needs to read Goody & Lung to see if they conflated them as well. Again, another reason why an engineering-quality report would be helpful. Instead of blogospheric speculation from all sides. (How many IPCC reviewers even bothered to read canonical Goody & Lung?)
Oops. Crosspost. Although I did try to tie it back to the IPCC process.
#1 You are correct that for saturated absorption band the width of these bands grows in a log like fashion. For a Gaussian distributed absorption coefficient, I found the width to grow with sqrt(log(CO2 concentration)). For a Cauchy distribution I found the width to grow with sqrt(CO2 concentration). I presented the details to Steve. I think he wants to tie in a few more topics before presenting the derivation. A log function lies in between these two curves so if you have a mix of Gaussian and Cauchy distributed bands that a logarithmic model makes sense. Of course this is a simplistic model and does not account for line mixing.
What I found interesting about the original post is the talk of stratospheric readjustment and that the net radiative flux at the tropapause is close to zero. What I wonder is, if most of that downward flux from the stratosphere is due to the black body emission of the stratosphere or if it is due to the solar input from the sun.
As CO2 concentrations increase, the total effect does indeed saturate (i.e. the probability that a thermal IR photon from the surface will make it to space is so low that adding more CO2 doesn’t substantially change that.). However, the RealClimate types have a point that this is irrelevant. This is because adding more CO2 is like adding another blanket. There will be radiative equilibrium between the layers and the surface. Adding another layer will definitely increase the surface temperature.
Steve: I’ve asked people not to discuss saturation until I post up more material, as it is a complete non-issue although the IPCC argument is, IMO, far from the most relevant one.
http://spacescience.nrl.navy.mil/introupatmsci.html
I find the above figure interesting. Why is the upper atmosphere so hot?
Steve: It’s because ozone in the stratosphere absorbs some of the incoming solar. This graph is one of the ones that I’m going to come to in discussing the “the higher the colder” napkin argument used by Houghton and the IPCC. It doesn’t mean that their point is necessarily wrong, only that it’s nuanced. Again it’s not that the authors aren’t aware of the nuance. To some extent, it’s because they try to be too cute when they do try to explain things.
#9, John Creighton:
I think it’s due to UV absorption by the ozone, isn’t it?
What definition of temperature do they use? Do they define the temperature based on statistical properties of the emission spectrum like the mean frequency and compare it to the black body distribution? The whole idea of heat flowing from a cold spot to a hot spot bugs me even though I know it is possible. Perhaps the gas particles do have the high temperature but not the photons in the surrounding vacuum as the system is not in equilibrium.
I’m trying to think of how such a high temperature can be possible yet not violate Stephan Boltzmann’s law. Thinking in terms of Boltzmann’s law we know the input energy which is absorbed from the sun but can the effective emission area be less then the surface area of the gas. Perhaps this could result in a distribution like that at a higher temperature but with less intensity? If my idea of an effective emission area makes sense, then I wonder how the time ratio of the time between emissions to the the time between collisions effects this effective area.
11, John Creighton:
– I’m sure they use the gas temperature, related to the random kinetic energy of the molecules.
– This is not heat conduction, but radiative transfer. If you put something hot near something cold, photons will go in both directions, but the net flux will be towards the cold.
– Stefan-Boltzmann doesn’t really apply: This is a gas that is being zapped by UV photons coming from the sun, at roughly 6000-K. It’s not an equilibrium situation; and also, the gas is rather tenuous. I don’t think the optical density goes much beyond 1, the radiation intensity doesn’t have much space in which to thermalize with the gas.
Think about the brightness of the sun. Then take a cupful of sun and isolate it in space. Even at the same temperature, I bet you couldn’t see it. It’s different when you have a solid opaque object: an iron ball the temperature of the Sun would be just as bright as the Sun.
I think that the average emission spectrum should reflect the average kinetic energy of the gas. I agree Boltzman’s law doesn’t apply, but I think that the emission spectrum sill might closely follow a plank distribution except that it will be scaled so as to output less power then Stephan Boltzmann’s law would imply.
I think though that we can deduce the power output because the emitted power must equal the absorbed power. The following should let us deduce how much power is absorbed per volume:
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JCPSA6000110000022010749000001&idtype=cvips&gifs=yes
Thus when we know how much power is absorbed per volume we should be able to scale the plank distribution to give the correct power output. This is relevant because it will give us both the power and spectrum of the radiation emitted from the upper atmosphere.
I find this relevant because according to the above stuff which Steve posted the net radiation flux between the troposphere and stratosphere is almost zero. As a consequence the area above the troposphere is important when considering radiative balance. I think that the reason the temperature may fall off exponentially in the thermosphere is that as particles travel upwards in the thermosphere kinnetic energy is converted into potential energy.
#13, John Creighton:
This is a radiative transfer issue, it’s not going to look the same as the surface of a blackbody.
At a given frequency, you need enough gas to look into an optical depth somewhat greater than 1, all at the temperature of interest. Then you will get the BB intensity at that frequency. Frequencies for which the OD is much smaller than 1 won’t give you much.
I don’t have any of my books with me, but maybe you can look around for radiative-transfer and thermal radiation topics.
Doesn’t that suggest the temperature in the lower troposphere should be increasing at a faster rate than land? Is that the case? And since oceans cover ~75% of the earth’s surface and have huge capacities to store heat, are oceans absorbing this heat from the troposphere? Doesn’t liquid water have a much higher capacity to store heat than gas (water vapor)? So many questions.
I hope this is not considered OT
I can see greenhouse grasses resulting in a cooler tropopause temperature because if more radiation gets absorbed before the tropopause then the energy will need to be transfered though convection but when warm air rises it cools adiabatically. This is the reason for the lapse rate in the troposhere.
Steve: John, this is not correct.
This may be another simpleton observation, but since the earth is essentially round with x circumference, at say 1km up there will be x volume. At 10 km up the volume increases. Wouldn’t logic dictate the rising heat would be more dispersed the higher up it goes because as the volume increases the temperature would diminish accordingly? How is this calculated?
#17, I have thought of that before. However, the hight of the troposphere is small in comparison to the radius of the earth.
Folks, please don’t spend a whole lot of energy on expounding your own bright ideas on this or trying to reinvent the wheel unless you are very familiar with the literature. The literature is very comprehensive and naive presentations, as opposed to familiarizing yourself with the available literature, simply gives third parties a bad impression of the site here. If you want to describe a published article for the benefit of others, fine, but please no expositions of personal theories of how the atmosphere works.
I know it’s fun to play theorist, but I suggest we all curb our urges to speculate beyond our knowledge and experience. Yes, me included. Remember this is Steve’s lab notebook. Let’s try not to fill out with junk.
Well, here’s what I find so far then:
Fundamentals of radiative transfer Chapter 2
Click to access JM_02.pdf
#21, John Creighton: Reference on radiative transfer
Great, now look at eqn. 2.8:
It shows that the intensity of a beam of photons starts out as the intensity of the initial beam (of course); and as the beam passes through the medium, the optical depth (tau) gradually wipes out the “memory” of the initial intensity, while gradually adding in the intensity of the black-body function at that frequency. For larger and larger values of the optical depth, only the most recent gas really counts.
So as the beam propagates through the gas, from ground level upwards, the intensity becomes appropriate to other temperature of the gas, and the temperature of the ground becomes irrelevant. If the gas is getting colder with height, the relevant gas (the most recent gas) is colder.
This is why I was saying that the interesting point is the photosphere, where OD = 1 (as measured coming down from space): the intensity of the outwards-going beam is determined by the temperature of the gas in the neighborhood of the photosphere. The higher up the photosphere, the colder it is up there (adiabatic lapse rate), the smaller the blackbody radiation intensity, so the less IR actually escapes.
Since the incoming solar radiation is not affected, this upwards move in the photosphere creates the radiative power imbalance which is the GHE. (Because the reason the photosphere moved up was because we added more GHG to the atmosphere.)
A pity he doesn’t do the calculation explicitly, but the result is implicit in eqn. 2.8.
The reason I’m always complaining about the “all the photons are already blocked by saturated C-O2” issue: That idea depends on the first term in 2.8, the original intensity dying away. It neglects the second term, which adds the photons back, albeit at intensity appropriate to gas temperature.
There is a saturation effect, but it has to do with the calculation of the optical depth, so that the dependence of OD on gas density and distance is not linear. This does not seem to be discussed here, and I don’t remember much about it.
>> Because the reason the photosphere moved up was because we added more GHG to the atmosphere
I’m sorry if you’ve already gone over this, but I’m not clear on how the photosphere gets “moved up” by GHGs.
#22 I agree with you but with regards to equations 2.7 and 2.8 they look wrong to me. I’m sure I’m missing something but the forced response to a linear system is the convolution of the impulse response, with the forcing term.
http://en.wikipedia.org/wiki/Convolution
The point is that one of the functions get flipped. Consequently shouldn’t (2.7) be:
I meant to say:
Gunnar, this may help.
http://www.nasa.gov/centers/goddard/news/topstory/2004/0315humidity.html
#26, John Creighton:
No, I think the equations are right as done in the text.
#23, Gunnar:
The radius of the photosphere is the distance at which the optical depth = 1, when measured starting from infinity and heading towards the center of the Earth. When there is more GHG, there is more GHG at higher altitudes, so the optical depth will reach the value 1 sooner (farther out from the Earth).
#3 to Steven McIntyre:
Before you go in the subject of saturation I have the following comment:
Saturation is a wrong term in this connection. Saturation occurs when a very strong laser beam is going through a volume of absorbing gases. The radiated energy fluxes from the Earth are weak and can not cause saturations effects. An excellent (a simple) textbook description of this can be found in The Quantum Theory of Light by Rodney Loudon (Third edition, Chapter 1 and 2). At the same place a detailed and clear description of the absorption process can be found together with expressions of the important attenuation coefficient.
Another and a more fruitful way to describe what is going on in an absorbing media (with weak incoming energy fluxes) is to consider the atmosphere as a blotting paper in the frequency space. The thickness of the blotting paper in a certain frequency range is determined by the density of absorbing lines, the density of the absorbing gases and the extend of the gas layer (the height of the atmosphere).
The blotting paper of water vapour is fairly thick even at very moderate concentration (>1000ppm), and has only few holes in the Planck radiation spectrum of the Earth at standard temperature, which means that most (if not all) of the emitted energy flux is absorbed. Only in frequency areas where water vapour has no absorption lines, other absorbing gases can trap the emitted photons from the Earth. The CO2 blotting paper is not as thick as the water vapours, due to the concentration (300-600ppm) and it absorptions lines is overlapping those of water vapour, and has beside, large holes in the frequency space. Even if CO2 has concentration of 1000ppm or more it would not matter: The available energy flux cant be absorbed twice!
Now, if this explanation is acceptable (and can be proved rigorously; what I think it can and is working on) the climate has been in balance with the water vapour content most of the life span of the Earth, and CO2 is only an additional player which content does not matter at all, even at very high concentrations.
John Creighton in #24
You are missing nothing and you are right while 2.7 is wrong .
That the equation 2.7 is wrong can be easily checked by differentiating I .
If you differentiate the right expression that you have given (convolution product) you get dI / d tau = – I + J what is the right equation .
If you differentiate the expression given by 2.7 you don’t get the right equation .
One has always to be careful because it is not by writing “text book” on a paper that it becomes automatically correct .
#29, Tom Vonk; #24, John Creighton: My mistake
Pardon me, when I was looking at your correction it was late at night, and I didn’t work out the special cases (tau near 0, tau near end-point) properly. Unfortunately, there now seems to be a problem with the file, so it doesn’t download properly: Maybe someone’s fixing it?
#28, Arne Skov Jensen: Blotting paper model
What I believe your model to be missing is the fact that the absorbed photons are re-radiated. If this were not true, one could block all outgoing radiation by adding enough gas. But this cannot be true, because eventually at the “outer surface” of the gas (the photosphere), there must be some radiation because the temperature is not absolute zero. Your model, if true, should apply to the Sun: from what I recall of stellar structure, the source of the photons is in the center of the Sun, so they have to get out via radiative transfer. The optical depth from the center to the photosphere is quite large, so there’s quite a lot of blotter paper. So why isn’t the Sun dark?
In actuality, the solar photons are absorbed and replaced by other emitted photons many times over; and this is what is described in the radiative-transfer equation under discussion.
#29 Tom Vonk
Yes, the absorbed energy is re-emitted as spontaneous and simultaneous emitted light; but why should the blotting prevent this from happning?
#30 Im not sure what is wrong with my correction. Id be grateful for any insight.
#29 I think what I could be missing is the definition of Tau. If we think of Tau as a dependent variable in a one dimensional differential equation then the formula in the text looks wrong. However, if we think of Tau is the distance between the point of interest and each radiative source then I dont think its wrong. I dont think the latter definition of Tau was given upfront in the text but it might be implied with some of the derivation that will follow later.
Whereas clearly identifying and auditing the theoretical basis for the radiative forcing assumptions of AGW is important, it is more important to ensure that this basis is grounded in observational and experimental evidence. Except for spectral parameters, all the graphs and numbers shown in this article are calculated, where is the data?
#29 Tom Vonk
We are talking about a stationary radiation process in the frequency space? For me, time is not present explicit or implicit in a radiation balance. So the processes dont happened many times.
#31, #34: Arne Skov Jensen:
As I understand your blotting-paper analogy, once the photon is absorbed, it’s “out of circulation”. Therefore, the outgoing “beam” of IR photons would fall to zero, as the photons get picked off one by one in heading out to space.
If that were true, the Sun would be dark.
#32, John Creighton:
– Your #25 is OK.
– tau is defined in eqn. 2.4. It depends upon your choosing a straight-line path along the direction of a beam of radiation. Think of a flashlight beam headed through the fog: tau = 0 at the flashlight, and increases along the beam. The initial intensity is due to the flashlight, but as you go along the beam, the flashlight visibility fades away; what you start to see will reflect the BB radiation at that frequency (not much, for optical frequencies in a London fog).
– Of course, the flashlight is optional. You could just pick a direction: from the Earth to the sky, define a beam at 15 microns in the IR, and you have the GHG problem.
#35 Neal J. King
Maybe my English is bad, so I dont express the meaning with the modeled clearly. The answers both you and #29 have given seem to imply that. Please, read #29, #31 and #34 once more. How can you deduce that, #31 should imply that the sun would be dark? The photons is by the way out of circulation until they are re-emitted, but not permanently
Do you understand what I mean with frequency space and stationary processes?
Arne,
Please describe what you expect the “blotting paper” to do.
Another way of asking the question: A beam of IR radiation at 15 microns (in the C-O2 IR absorption band) starts at ground level and is headed towards the sky. Tell me about the intensity of the IR in that beam as you follow its path to infinity.
What happens to a beam at a frequency that is not absorbed by anything? Another that is strongly absorbed?
The definition of temperature in physics is an interesting one. It is a measure of average energy and is commonly given as 11,605 deg K per electron volt (eV).
Where things get interesting (and confusing to a lot of educated physics guys) is where you have a mono-energetic beam. Say the beam was at that same 1 eV. It would be described as having a temperature of 11,605 deg K. And yet it behaves differently (re: things like quantum tunneling) because you do not have a distribution of energies.
When the gas density gets thin it is very important to distinguish particle speed (eV is one measure of that given a known mass) from gas temperature. This is important where thermal equilibrium is not a given (i.e., a net motion in a specific direction).
In plasma physics there is a lot of confusion between equilibrium and non-equilibrium situations. Radiation losses are not the same in the two situations despite the fact that they can both be described by the same “temperature”.
#37
Neal
Ok, but I have not imaged that this should be so difficult, but I think I have point here. Usual I am not good to explain what I see in mathematical equations, and this is apparent also the case here.
As a start, my point is that the Log behavior of the forcing equation is not a saturation effect. Only very strong light sources give saturation as state earlier. I will look at one absorption line, for instance, in water vapor with a certain bandwidth and try to see what happed when we increase the content of water vapor. The light source is the radiate energy flux from the Earth, with an intensity given by the Plancks radiation law for the frequency bands in question..
1) First, with zero content of water vapor all the radiation is escaping to space, this is trivial..
2) Secondly we have a content of 10ppm water vapor: A part of the emitted photons are annihilated or absorbed, the rest is escaping to space. The (rotational) exited water vapor is emitting photons spontaneously i.e. the photons are emitted in all direction with no memory the source field. Besides a small part are emitted simultaneous i.e. in the same direction as the incoming beam and with the same phase. The energy flux of the simulated and spontaneous emitted photons is equal to the previous absorbed energy flux.
3) Third, the content of water vapor is 1000ppm or more. All the photons from the source are absorbed, and nothing is escaping to space. The exited water vapor emits photons simultaneous and simulated in an amount equal to the absorbed energy flux.
4) Now, assuming that CO2 has the same or nearly the same absorbing line as water vapor above, and that we add an arbitrary amount of CO2. Does this change the picture in 3)?. No, no photons are escaping to space all are absorbed and re-emitted. The only difference is the that both water vapor and CO2 are sharing the photons.
Now, this means that the CO2 forcing is zero in this limit. If the CO2 was alone, as IPCC assumes, you will get an approximated Log-like behavior for the forcing as a function of the CO2 concentration. However, since we need an asymptotic behavior, the Log behavior can not be correct for all concentration. From computations I have found the total simulated energy flux for CO2 goes as a-b*Ln(x)/x is a better curve fit that IPCCs a*Ln(x)+b, where x is the CO2 concentration. But again, if sufficient water vapor is present all radiation flux is absorbed, and the CO2 forcing becomes zero.
Now, I hope this is satisfying, without using the blotting paper analogy. You should also notice that time not has been used in this context, that we are operation strictly with stationary pictures and in the frequency space, nothing is moving, and the sun is still shining.
#40 Arne Skov Jensen:
Does this not depend on the temperature of the gas? What happens if the gas is too cool for the molecules to emit at the required rate?
#40, ASJ:
Step 3) is where I have a definite disagreement with you: As the photons are leaving the surface of the earth and then (in your picture) getting absorbed by the water vapor, how can you assume that none escape to space? Photon absorption implies that the water molecules are excited; when they are de-excited, they radiate in ALL directions. So some of them also go outward into space.
In fact, the amount that go out into space should depend upon the temperature of the gas at the surface (photosphere).
#41
pochas
Yes, it depend on the temperature at the actual location where the photons are emitted. The dependence come via the local spectrum of the absorbing line, which has a Lorentz shape with a half width give by the temperature dependent collision boarding. This is the main temperature dependence, but the Einstein A-coefficient which characterize the absorbing line has a weak temperature dependence. But now we are going into details.
Arne:
Thank you for your Information. I have had no trouble understanding your explanation from the start.
39, do you have a link to that? Lucia and I were going around a few weeks ago over the question of whether or not temperature was even defined for single molecules and other particles. If that’s true, I was right.
#42 Neal
Yes, half of the spontaneous emitted photons are going to space. The is exactly what the greenhouse effect is about, and the point is that these photons are going in all directions, whereas the incoming light is emitted from the Earth in one direction. With respect to the number of directly escaping photons, precise computation has to be done. The presented description should be considered as picture.
I hope you can see the analogy to the blotting paper though we not are talking about ink!.
#41 Actually it does not depend on temperature. This comes from what I was saying before. The confusion of particle energies with Maxwellian radiation. A particle that absorbs radiation will re-emit it. The frequency of re-emission is dependent on how the energy is distributed in the particle (rotation – electron energy levels – collisions before re-emission etc.).
There is a lot of confusion between the particular case and the average case.
Funny my point should be so well made just a few posts after putting it up.
Larry,
Energy 1 ev = 1.60217653E-19J/ev
Boltzman’s Constant = 1.3806505E-23J/deg K
I think you can work it out from there.
Arne,
Here you say:
But here you say:
How do you reconcile these two statements?
#50 Neal
The photons from the source are in a certain spatial mode, in 3) these are not escaping to space.
The spontaneous emitted photons are not in the same mode as the incoming light. For instance, if you propagate a narrow beam through a gas of sufficient thickness, all incoming photons are absorbed and the beam is destroyed. The re-emitted spontaneous light is propagating in all directions with no memory of the original beam. This illustrate the problem you have if you want look at the Earth from outside or looking out from the Earth in the infrared area.
The time in Europe is 2 a.m. and I am going to sleep
#51, Arne:
OK, but in that case, as you say (#43), the intensity of the radiation (into all directions) depends upon the local temperature.
So now if the ground is at one temperature, and we consider the situation far above the ground (where the original upward “beam” has faded out), the temperature at that point is lower, so fewer photons will be heading upwards than were in the original “beam” at ground level. Right? I’ll wait for your response to go to the next question.
(Actually, it was not really a beam, it was the thermal emission, into the vertical direction, of the ground.)
Give Arne Skov Jensen and Vonk a thread and we will have this greenhouse gas idea explained!
This paper looks like it might be interesting:
http://adsabs.harvard.edu/full/1968ApJ…153..917H
Pat,
So correct!
Let me add that if the atoms/molecules are tenuous enough so that they are not exchanging significant energy over a short enough time span (the time from absorption to re-radiation) you will not get a Boltzmann distribution of radiation vs “temperature”. The measure should probably be mean time between collisions (i.e. mean free path – which is density related and mean velocity which is “temperature” or better energy related) and relaxation time for energy radiation of an excited species.
The Boltzmann Law is only true when the density is high enough. Thus we look at the sun and its temperature is around 6000K despite the fact that the less dense parts outside the radiating layer are above a million deg K.
Where this came up in my recent field of study (plasma fusion) is a famous paper which showed that a certain kind of reactor couldn’t work because of the “temperature” of the reactants. The paper was refuted about a decade after publication when it was shown that the concept of radiation “temperature” did not apply in the situation of a specific reactor design.
As I said. Even physicists (and an awful lot of them at that) get confused by not thinking clearly about the problem.
In some cases the relaxation time to re-radiation is in the milliseconds. This was known in the very early 1930s. In fact had some one put the idea of stimulated emission together with the idea of relaxation time we could have had gas lasers around that time. They had the technology. All they lacked was ideas on how to put together what they already knew.
Let me also add that in thermodynamics a population with an inversion (a significant population above the ground state) has a negative temperature.
Steve,
Pardon the use of the forbidden word. I hope no one follows up on that. 😉
@Pat– for 53. 🙂
@M.Simon– for 56. 🙂 🙂
OK, add Simon and a couple others. There’s so much expertise here, I wish it could all be melded somehow.
Arne:
I’m still waiting for your response to #52.
We can continue the discussion from that point.
#61, M. Simon:
On the thread:
http://www.climateaudit.org/?p=2567#comment-192306
at #14, I discovered this same effect while looking for a physical interpretation for the mechanism by which the radiation imbalance created by the additional GHG creates warming at the ground level.
My analysis convinces me that the radiative imbalance is there, and results in more IR photons raining from the sky. The simplest way to interpret this is to say that the GHG added to the photosphere creates a shell which “bounces” outgoing IR photons back downward.
The analogy with your nuclear-physics example is worth thinking about. If you take a ball of uranium, neutrons are spewing out from the surface; in particular, neutrons originating at or very close to the surface escape.
Now, add a spherical layer of the same material to that ball. Neutrons that would previously have escaped can no longer do so, they are bounced back inward, so the level of neutron activity goes up. Keep adding material, and the ball could go critical.
This illustrates how adding a barrier to escape leads to a build-up of intensity. The analogy is not perfect, because neutrons are conserved, but IR photons are not; however, the total energy of the photons is conserved, and their energies don’t change that much, so it doesn’t matter much.
#61, M. Simon: continuation of #63
So, it’s not necessary for the GCMs to explicitly take the reflection behavior into account: It’s implicit in the equations of radiative transfer that are the foundation of the GHE.
Anyway, I hope my main point is not lost in this discussion. If the thermo sphere was 1000 Kalvin as the above figure suggests then according to Stephan Boltzmann’s law the earth would radiate more power then it receives from the sun.
Well I haven’t proven the 1000 Kalvin temperature impossible since non black bodies radiate less power then a body which follows Stephan Boltzmann’s law it strikes me as odd since the net result is that the energy of earth is leaving the surface moves against a very large temperature gradient. This leads me to wonder if the 1000 Kalvin is based on the thermodynamic definition of temperature or simply based on the average kinetic energy.
I may have more to say on this in just a sec
I found a good text on Ozone in the stratosphere:
http://www.ccpo.odu.edu/SEES/ozone/class/Chap_5/index.htm
Has this site ever reviewed or discussed the paper by Gerhard Gerlich and Ralf D. Tscheuschner:
“Falsifcation Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics” arXiv:0707.1161v1 [physics.ao-ph] 8 Jul 2007
They basically give the entire concept of ‘greenhouse effect’ a once over. quite interesting. If necessay I can upload the doc, but don’t have a link.
Roger
Im responding to DeWitt Paynes comment here because we should try to keep conversations about readiatitive transfer to the two threads which Steve created for it.
http://www.climateaudit.org/?p=2572#comment-193507
I found your comment very interesting and Im glad that LTE calculations hold up to 100km altitude. I dont think though that LTE calculations are necessary though although they may be convenient and computationally efficient.
http://en.wikipedia.org/wiki/Maxwell-Boltzmann_statistics
With respect to non equilibrium, a sensible assumption might be that within a given system collisions transfer a fixed amount of energy per time and the probability of it being transferred to any state is equally likely. This should converge to as t->oo to the equilibrium solution.
64 Roger
G & T ist verboten hier — at least for now.
#64 The book can be found here:
Click to access Falsification_of_CO2.pdf
It looks kind of long, maybe I’ll look at it later.
Re: #65
John,
The existence of LTE is important for radiative transfer calculations because Kirchhoff’s Law (absorptivity = emissivity) only holds if LTE exists. Note that Kirchhoff’s Law does not demand that emission and absorption are equal. If there is an energy source, like sensible or latent heat transfer, emission can exceed absorption by the amount of heat introduced and the converse is true as well.
I agree with the fish wrap comment about the G&T paper in another thread.
68
DeWitt
I agree with most of this, but not the first sentence. I think a better way to look at it is as follows:
– Detailed balance/LTE means that emissivity equals absorptivity
– The value of Emissivity and absorptivity is a basic property of the surface and does not depend on LTE
– Emission is not the same as emissivity, E (and same for absorption). As you say, emission can and does exceed absorption if the surface is warmer than the temperature of the surface it is looking at, but that is because emission goes as E*T^4.
Re: #69
Pat,
I was talking about LTE and Kirchhoff’s Law as applying to emission and absorption by molecules in a gas not emission/absorption at a surface. So the emission/absorption spectrum of a molecule is a fundamental property of the molecule, modified by doppler and pressure broadening, isotope effects, etc. But the population of the excited states is determined, at LTE, by the temperature of the surrounding gas through inelastic collisions (the Boltzmann distribution, IIRC). For high optical density, emission becomes limited by the value of the Planck function at the wavelength of interest. Stefan-Boltzmann only applies to grey or black bodies, so unless absorption/emission is saturated at all wavelengths (which can happen at high enough humidity and temperature), the temperature dependence is not well described by a T^4 dependence.
I agree you need equilibrium to apply Kirchhoffs Law but I’m not convinced that you need a high optical density.
You don’t nee high optical density for Kirchhoff’s Law. I was just pointing out that the emitted spectrum could look like a black body if the optical density is high enough. To see an example, use the MODTRAN calculator for a tropical atmosphere, look up at an altitude of zero, set the relative humidity constant and start cranking up the surface temperature. At an offset of 30 degrees, there is only a slight deviation from a 330 K blackbody spectrum.
70 DeWitt
True, but that’s the microscopic viewpoint, which is apples and oranges when you compare it to the macroscopic viewpoint, such as the S-B equations and Kirchoff’s Law.
The same microscopic viewpoint also applies to a solid surface, it’s a fundamental property of the way the atoms are coupled together and lattice-vibration excitations modified by anharmonicity, nonlinear dipole moments, isotope effects, etc……The IR spectrum has lines and peaks and valleys much like the absorption spectrum of a gas.
So there isn’t much difference between a gas and a solid, conceptually. A mm thickness of gas probably has the same number of atoms as the first few microns of a solid surface.
73
That should be:
#73, #74: Pat Keating
The difference between a gas and a solid is that photons intersecting a solid HAVE to interact in some way.
Whereas in passing through a thin gas, the photons can avoid interaction, and thus avoid becoming thermalized. When the Optical Depth gets up to about 1, this issue goes away; at that point, the intensity approximates the blackbody intensity for that frequency.
Neal
It depends on what you mean by ‘interact’. Photons can certainly pass through a solid without absorption. If by ‘interact’ you mean that the photon is influenced by fields due to the atoms, photons in gases also HAVE to interact with atomic/molecular fields.
70:
My understanding is that this is correct (but I’m certainly no thermo expert). What I keep wondering is how does the 98 + percent O2 and N2 affect the emission/absorption of IR by the trace amounts of GHGs. Thermalization of all those molecules HAS to have a profound effect on the energy levels of the GHGs. I wonder just how much rocking and rolling the CO2 and HOH molecules are doing in the presence of N2 and O2.
#72 is there anywhere I can find the code for that calculator?
Phooey on THEORY! Phooey on “black bodies” Fie on T^4, on emissivity.
Experiment and measurements “trump” theory.
http://junkscience.com/blog/2008/01/12/processing-33-years-of-ir-longwave-data/
76, Pat Keating:
It’s a question of degree & amount.
If you take the same kind of atoms (say, gold) and disperse them as a cloud of vapor vs packing them into a solid, 1 cm of travel through each of these cases will experience dramatically different total absorption.
Re #77
The presence of the N2/O2 does indeed have a profound effect on the energy levels of the GHGs in the lower troposphere, in the case of CO2 molecules excited in the 15 micron band the vibrational energy increase is ~8kJ/mole, this is almost completely removed by collisions with the surrounding molecules at a timescale much shorter than the emission timescale.
80 Neal
Sure, that’s why I used the word “conceptually” in post #73:
I felt that posts 70 and 75 were assigning too big a conceptual difference between molecules in a gas and ‘molecules’ (e.g., unit-cells) in a solid, as far as IR radiative effects are concerned.
Pat Keating #73
But there are .
Solids (and plasmas) have free electrons what gives them very special characteristics while gazes don’t .
Solids present a sharply defined interface while gazes don’t .
Solids (and plasmas) exhibit reflection at their interface while gazes scatter .
Also solids (and dense plasmas) can be approximated by a black bodies while gazes can’t .
It is not the number of atoms that counts but their structure and presence of free electrons .
So conceptually the interaction of electromagnetical waves with solids and with gazes is treated in a quite different manner .
Solids can be treated like a phonon/photon interaction while gazes can’t .
#82, Pat Keating:
But I thought we were talking about the real impact on radiation. The difference is going to be quantitative: radiation coming from the earth’s surface is going to be a lot stronger than coming from a bit of gas.