For most people who study global warming only casually it is well known that the greenhouse effect acts to increase the surface temperature of the planet (currently) by about 33 K (or 60 F) above the so-called “effective temperature”; this is the temperature value that a planet would need to have in order for the infrared energy it emits to space to balance the energy it absorbs from the sun (assuming the sun is the only important source of energy, which is true enough for Earth and neighboring planets like Venus and Mars). This is simple enough, yet there are still many popular misconceptions out there concerning the relative roles of individual greenhouse gases and the total mean climatology of the greenhouse effect, and some of these confusions have admittedly not been explicitly corrected in the literature very well.
A matter of curiosity from this point is to decide how much of the total greenhouse effect is partitioned between various radiatively active substances in our atmosphere. That is, how much of the natural greenhouse effect is fractionally supported by water vapor, by CO2, etc
There are a number of sources of confusion out there on this issue. For instance, this source claims that water vapor makes up 95% of the total greenhouse effect (in fact, it does so confidently that it actually says 95.000%, a good lesson in abusing significant figures and precision for lower-level science students, see Robert Grumbine’s post a couple years ago). Other secondary sources give numbers like 97 or 98%. Lindzen (1991, Quart. J. Roy. Met. Soc) gives an estimate in this range, although it is not clear where he gets his value from. Coby Beck here in a rebuttal to this claim asserts that “CO2 contributes anywhere from 9% to 30% to the overall greenhouse effect,” presumably giving the impression that there is a 21% disagreement amongst sources and experts out there. Still further, many people incorrectly extrapolate the effect of CO2 on the total greenhouse effect to deduce the forcing you’d expect with a doubling of CO2, or use similar arguments in relation to how we expect feedbacks to behave as the current climate warms.
Table 3 of the famous Kiehl and Trenberth (1997) [PDF] energy budget paper attempts to partition the various gases/clouds by percentage; RealClimate breaks down the contributions in this link while pointing out how water vapor is a feedback and not a forcing (see here for a summary). Values presented here are similar to Ramanathan and Coakley (1978).
Nonetheless, getting a clear account of all of this has remained elusive, especially as the most relevant source seems to be a 2005 blog posting. Some of the folks at NASA GISS including Gavin Schmidt and the radiative transfer guru Andy Lacis (along with Ruedy and Miller) have attempted to correct this situation, with a 2010 paper in JGR that is in press here [PDF]. I will attempt to summarize here.
Sorting this problem out is actually not very straightforward although it can be done with a radiation model. As an analogy, imagine having a large pile of laundry on the floor, with dirty shirts, towels, and pants. Suppose we’re interested in asking what fraction of the floor is covered by each individual item.
The total extent of the whole laundry pile has a rather well-defined value. However, asking about the individual contribution for each item is a tougher question, in part owing to the complex overlap between the various clothes. You can pull out all of the shirts (for example) from the pile and spread them on the floor individually and get an estimate for the area that they now cover. This would, however, dramatically overestimate the fractional contribution that the shirts originally had in the pile. Alternatively, you can pull out an item, and examine the extent of the new pile and you might come up with an underestimate for the importance that clothing article previously had.
Similar to the dirty laundry pile, greenhouse gases exhibit complex spectral overlap (primarily by water vapor and clouds, and in second by water vapor and CO2). The maximum effect would be if the greenhouse gas were acting individually, while the minimum effect would be when only that agent is removed, and these numbers can be quite different (as in the Coby Beck example). What’s more, if you removed two agents together (say water vapor + CO2) the effect would be different than if you remove CO2, put it back, remove water vapor and put it back, and then record the sum of those two effects (ignoring feedbacks such as water vapor dependence on temperature). In particular, the sum of the effect of each absorber acting separately is greater than if they act together.
The greenhouse effect is defined by the difference in upwelling radiation flux at surface and the flux at the top of the atmosphere. With no greenhouse effect, this difference is zero. In the present-day climate, this difference is about 155 W m-2; this atmospheric absorption and emission is what drives the ~33 K enhancement of surface temperatures above the no-greenhouse (and constant albedo) case. The authors define the change in this long wave flux reduction as their metric for the greenhouse effect, and add various gases individually to a greenhouse-free atmosphere or remove them individually from the modern (well, 1980) greenhouse atmosphere.
So what do they find?
First off, water vapor accounts for 39% of the net LW absorption if removed (so taking out the vapor would make the longwave absorption go down to about 60% of its present value), and 62% if acting alone; in that order, clouds make up 15 and 36% and CO2, 14 and 25%. All of the other greenhouse gases are very minor. In terms of the percent contributions after allowing for overlap effects when discussing the individual agents in the atmosphere, here are the numbers that should be cited:
Water Vapor: 50%
Other (ozone, methane, etc): 7%
For a cloud-free atmosphere, the numbers are 67%, 24% and 9% for H2O vapor, CO2, and others. These numbers are within a few percentage points of previously published estimates (or multiply by 155 to get the contribution in W m-2 flux reduction).
As one would expect, there is also variation over the globe. Water vapor for instance accounts for ~55% of the greenhouse effect in the tropics and ~40% at the poles where it is much drier.
The radiative forcing for a doubling of CO2 in this paper is about 4 W m-2, slightly above the detailed line-by-line calculations used in Myhre et al (1998) and cited in the IPCC 2001 and 2007 reports. The “forcing” for a doubling of water vapor would be about 12 W m-2, although clearly we don’t speak of water vapor as a forcing since its concentration is rapidly regulated by temperature. Indeed, the extra long wave absorption in the atmosphere is not 4 W m-2 when you double CO2, but more around 20 W m-2 illustrating the importance of positive feedbacks.
Some words of caution now. You cannot linearize about the greenhouse effect and project CO2’s percent contribution to the total greenhouse effect onto what you’d expect for a doubling of CO2.
To illustrate this, consider what happens if you remove all the CO2 from the current atmosphere. With no feedbacks operating, the planet would cool by ~7 K, as opposed to warm about 1 K if you double CO2.
Once you include feedbacks, removing CO2 from the current atmosphere in the GISS model at least cools the planet by ~35 K after water vapor and albedo kicks in, and triggers a snowball Earth where the whole planet is ice covered. This is consistent with other model studies (Voigt and Marotzke, 2009); in this case a snowball Earth is initiated by either reducing the solar insolation by 6-9% or by reducing the CO2 to 0.1% of its pre-industrial value, although for the CO2 this is a just a single run and they do not consider what other CO2 levels might also trigger a snowball. CO2 levels below, say, 100 ppm do not appear to be realistic in Earth’s history.
It should be noted following this that the canonical “33 K” temperature enhancement by the greenhouse effect is artificial, since it assumes the planetary albedo does not change when you add or remove the greenhouse effect. In reality, removing the greenhouse effect would greatly enhance the surface albedo from expanded ice cover allowing the planet to cool well below the “255 K” effective temperature.
Finally, all of this further reinforces the importance of feedbacks on climate, and that the very popular claim of “water vapor being the most important greenhouse gas” is a bit misguided, even if it is the largest source of infrared absorption in the current atmosphere.
Removing all of the water vapor from the atmosphere (and not replenishing it) would trigger a snowball Earth as well, but the non-condensable greenhouse gases (those which don’t precipitate from the atmosphere under current Earthlike temperature and pressures) such as CO2 would still be able to support a surface temperature of about 10 K higher than it otherwise would be. If you remove the CO2 and other GHG’s however, then you’d also lose a substantial part of the water vapor and cloud longwave effects, resulting in a near collapse of the terrestrial greenhouse effect. A significant water vapor greenhouse effect would not be sustainable without the “skeleton” provided by the non-condensable greenhouse gases, although it is obviously a significant amplification factor, both for the total greenhouse effect and its change in the future. It’s thus like the “skin” on a human or animal which needs the skeleton to hold it up, but provides the extra form and protection that we need to survive. This forcing-feedback distinction also makes CO2 the fundamental driver of global climate change (at least insofar as alterations to the optical characteristics of the atmosphere are concerned). See for example, Richard Alley’s AGU talk which focuses on CO2 as the largest control knob of climate change over geologic timescales. The water vapor is just dragged along with the temperature change, but then substantially amplifies any forcing to help provide the full magnitude of the temperature fluctuations; this is also a reason cold climates tend to be much drier than warmer ones.
All of this is moreso academically interesting than anything. Obviously we don’t live in a world where we are plucking out CO2 all together and then adding water vapor, or having a world where you can have clouds without water vapor, etc…but it should help to put into context the primary (water vapor, clouds, CO2) and secondary factors to the greenhouse effect, and put into perspective the important distinction between a forcing and a feedback.
Finally, claims that water vapor is 95% of the greenhouse effect in our atmosphere is just wrong, and the number cited in the Schmidt et al (2010, still in press) paper is so far the most explicit and detailed partitioning between the various gases/clouds (note that clouds on net cool the planet through albedo, although the study focuses on long wave greenhouse effects). The numbers might make the idea that CO2 is important to climate change more intuitive. For example, if the mean value is 20% of the greenhouse effect instead of just a percent or so, then you might think changing its concentration may be more meaningful…but keep in mind that sensitivity arguments must be evaluated on the basis of the change, and not the total greenhouse effect.
Thank you for a superb discussion on this topic. I will be adding this link and some of its information to my Impact of GHGs page.
Just when one thinks they have it correct…..
Of course, 70% of the Earths surface is covered by water.
So we can not ignore the role of CO2 in controlling the amount water in the atmosphere. On top of that, there are always the longer term feedbacks (melting of land ice and snow and changes in vegetation) as well.
Thanks for the great post; also looks like there is a new banner: nice.
The claim – a false one as Chris points out – that water vapor accounts for 95% of the greenhouse effect is an example of a spurious conclusion circulated virally on the Internet and due to a misinterpretation (possibly willful) of a legitimate article. The article (reference 5 in the first link Chris cites in his post) is: S.M. Freidenreich and V. Ramaswamy, “Solar Radiation Absorption by Carbon Dioxide, Overlap with Water, and a Parameterization for General Circulation Models,” Journal of Geophysical Research 98 (1993):7255-7264
The content of the article is accurately conveyed by its title – It assesses the contributions of water and CO2 to the absorption of solar radiation (visible, UV, near infrared red, etc.). Water absorbs in the near infrared far better than CO2, and so it accounts for most of the solar absorption. The greenhouse effect, however, is based mainly on absorption of terrestrial infrared radiation at longer wavelengths, where the contributions of water and CO2 are far more balanced, and the role of CO2 predominates because of its long term atmospheric persistence, while water operates as a feedback mechanism.
H2O is actually negative overall by the time one counts the Albedo affect of clouds. Excluding the Albedo of clouds, the net greenhouse effect is only 19K. It is illogical to count the positive impact of water vapour while excluding the negative contribution of that very same water vapour through the Albedo impact of clouds.
In fact, all the numbers should be recalculated based on the solar radiation atmospheric interception/reflection of all the different gases involved. That would present a more accurate picture which will contain greater information for the user.
The greenhouse effect is the effect of LW optical properties on climate. This doesn’t include SW (solar radiation) albedo. Thus when refering to the greenhouse effect, one cannot count the cloud albedo as a part of that, except when discussing feedbacks to some change in greenhouse forcing (in which case, other parts of the greenhouse effect can become feedbacks as well).
Cloud albedo and greenhouse effect won’t necessarily change together. An increase in cloud area will tend to increase both, but by varying amounts depending on cloud type, location, and time. Increasing the heights of cloud tops while preserving area would tend to strengthen their greenhouse effect with little effect on albedo.
The paper which is the topic of this article says that the net radiative impact of clouds including SW effects is one of cooling. Under a doubling of CO2, the paper says that the expected 1.5% increase in planetary albedo due to more clouds is equivalent to about 5 W/m² reduction in forcing. Implication: Without this effect, we’d have 25 W/m² equilibrium greenhouse effect, instead of 20 W/m². So the albedo effect of increased clouds is being included and there’s no need to recalculate.
One request, can you make these numbers add to 100%. Less explaining to do if we cite them.
Water Vapor: 50%
Other (ozone, methane, etc): 7%
Response: Yea, it’s not clear to me why they decided to total it to 101%, but I don’t want to butcher what they wrote. Some of these terms will have a few percentage points uncertainty, and it’s really hard with the overlap effects to come up with perfect numbers that add up nicely. I don’t think this will be a huge issue if quoted elsewhere– chris
After rounding, individual terms may not produce the same sum. For example:
10.7 + 80.8 + 8.5 = 100
11 + 81 + 9 = 101
As you point out in your final sentence, sensitivity arguments must be evaluated on the basis of the change, and not the total greenhouse effect. Therefore your dirty laundry model is inappropriate. Your own simulations from MODTRAN show that CO2 band saturation occurs with 50 ppm CO2. Absorption in the “wings” would be confounded by water vapor absorption at the same wavelengths. Can you use your model to differentiate the relative contributions of CO2 and water vapor? In other words, what is the incremental effect of 100ppm CO2 in the presence of normal ranges of atmospheric concentrations of water vapor. I’m thinking competition for absorption around the CO2 band will be won by water vapor except in dry/cold climates. Also, what evidence do you have that an atmosphere free of all GHG, except water vapor, could not sustain a greenhouse effect?
H2O can provide significant optical thickness in the vicinity of the CO2 band, but it is not as large as what H2O supplies at some shorter and longer wavelenths; the H2O band is not saturated near the edges of the CO2 band; stratospheric H2O is actually almost transparent over the CO2 band. It must be kept in mind that H2O, being more concentrated in the lower atmosphere, can absorb a large fraction of radiation from the surface while leaving plenty of room for other gases (or high clouds) to act on the radiative fluxes at higher levels (because the lower-level H2O is relatively warm and emits radiation upward accordingly). These features can be seen from satellites; there is a distinct dip in OLR around the CO2 band, with plenty of room for that dip to expand as CO2 optical thickness increases in the ‘wings’.
To clarify: (relative to well-mixed gases), it must be kept in mind that H2O, being more concentrated in the lower atmosphere, can absorb a large(r) fraction of radiation from the surface while leaving (even more) room for other gases (or high clouds) to act on the radiative fluxes at higher levels
Just a nit to pick here, but:
Thanks for the feedback. My question addresses what I feel is a central issue involving how to quantify the degree to which fossil fuel emissions raise global temperatures. I am not comfortable with qualitative explanations of the effect of the presence of a CO2 absorption band in atmospheric spectra. For example, what does the distinct dip in OLR around the CO2 band mean in terms of a precentage of OLR relative to common concentrations of water vapor? I read the Schmidt et al. paper which provoked two concerns. First, these are computer simulations replete with biases covering a year where the most CO2 could vary is about 6 ppm. Second, the simulation compares the sole presence or absense of each GHG. How does this translate into judging the effect of a change in CO2 on the temperature of the atmosphere?
Finally, does a lower atmosphere dominated by water vapor mean that the upper atmosphere is more capable of radiative forcing? The air is cold and thin up there.
I read the Schmidt et al. paper which provoked two concerns. First, these are computer simulations replete with biases covering a year where the most CO2 could vary is about 6 ppm. ?
Well, do you know what the biases are? (I’ve only seen the abstract.) If the biases are small than you might get small percentage errors. Limited variability of CO2 shouldn’t be a problem (see below) because, given that the central part of the band at 15 microns is saturated and given that there isn’t enough CO2 for other bands to become important, the forcing is logarithmically proportional to CO2, and the seasonal changes that occur wouldn’t do much. If the correlations among different types of clouds, water vapor, ozone, and temperature profiles are almost correct, then the radiative effects and effect of overlaps among clouds, water vapor and ozone, and more well-mixed gases should be almost correct.
Second, the simulation compares the sole presence or absense of each GHG. How does this translate into judging the effect of a change in CO2 on the temperature of the atmosphere?
It doesn’t; other work has to be done (and has been done) to evaluate the effect of a change in CO2. However, some of the same information that would go into calculating the contributions to the total greenhouse effect would also go into calculating the effect of a change in the greenhouse effect. For example, it is possible to graphically estimate the radiative forcing from a doubling of CO2 given spectra of upward, downward, and/or net fluxes, identification of the valley or hill in the spectrum caused by adding the CO2, and the knowledge that CO2 optical thickness approximately halves per every interval x of the spectrum going outward from the peak near 15 microns; the valley or hill in upward, downward, or net flux at any level will get about 2*x wider per doubling CO2 (hence the logarithmic proportionality); multiply that by the height/depth and you get a radiative forcing (specifically, the radiative forcing is the reduction in net upward flux per unit area. (Then there’s some other stuff to account for stratospheric adjustment; to a first approximation, subtract radiative forcing TOA (top-of-atmosphere) from radiative forcing at the tropopause; this is the forcing on the stratosphere; the stratosphere will cool to reduce net outward flux from the stratosphere by that amount, so that after stratospheric cooling, the remaining radiative forcing is constant from the tropopause to TOA; to a rough first approximation, the upward and downward fluxes out of the stratosphere decrease by the same amount, so the forcings at tropopause and TOA meet each other half-way. Then you get the tropopause-level forcing with stratospheric adjustment.)
Rest assured this has been calculated more thoroughly then such back-of-the-envelope work.
Biases in Schmidt et al. are mainly discrepancies in actual vs. modelled cloud considerations. (BTW, the full pdf is available at the link provided above in paragraph 5.) The authors estimate errors of around 5% without explanation.
I’m not saying limited variability of CO2 is a problem, as in controlling it. I wish we had seasonal variability of 60 ppm where a response surface methodology might be applicable. The relatively stable CO2 is an issue because what needs to be demonstrated is a definitive effect on global temperature due to increasing CO2 right now. We don’t have time to wait till 2100 to see what happens.
The logarithmic relationship of CO2 and forcing is a theoretical one. How do we know it applies in the presence of other gases through all CO2 concentration ranges from past to future? I realize actual measurement may not be realistic, but I would like to see the calculations for the effect of CO2 in the presense of the other GHGs? In other words, if we could instantaneously change the atmospheric CO2 concentration from 385 to 485 ppm, what would changes in the spectra be and how would we measure a forcing from that? The Schmidt paper only covers the case where CO2 goes from 0 to 338 ppm (1980 values).
I think the latter part of your response is beyond my comprehension at the moment, but I would like to take a look at the thorough calculations you are referring to.
The logarithmic relationship of CO2 and forcing is a theoretical one.…
Although there are available comparisons (1 the measurable change in OLR in the CO2 band, 2 interplanetary comparisons (Venus, Earth, Mars; consider OLR spectra, 3 paleoclimate), they don’t directly show the relationship (1. shows a small change from a small change in CO2, 2 requires additional information (though generally available) to show that the OLR is in agreement with the known physics; also, Venusian CO2 amounts are outside the range of a logarithmic relationship), 3 requires knowing climate sensitivity to deduce the forcing); however, they do agree with the theory, and in particular support the physical underpinnings of the relationship (we can see how OLR varies over wavelength in different conditions – including different local conditions on Earth within the same global climate state); there is so much confidence in the ability to calculate forcing that 3 is so far as I know generally used not to deduce forcing (at least not from CO2 for time periods when CO2 is known) but to use forcing to deduce climate sensitivity (and compare with models).
… How do we know it applies in the presence of other gases through all CO2 concentration ranges from past to future?
That depends on what the range of CO2 concentrations has been and will be; I don’t think we can know that it will always apply for the Earth (though it will in the context of AGW), but that’s a problem of not knowing what CO2 was or will be for all times on Earth, and perhaps it is just my own lack of knowledge with regard to that (?) (My impression is that there has always been sufficient CO2 for a logarithmic relationship thus far in Earth’s history, and if there ever was too much, I think it was only at the very beginning (?)). The logarithmic relationship is an approximation that can be used as a shortcut relative to more in depth calculations (for example: ‘line-by-line’) and the best fit coefficient may vary a bit.
Of course other conditions affect the CO2 forcing; greater overlap with clouds and/or water vapor would reduce the CO2 forcing, and temperature itself is crucial to knowing forcing, but the changes in CO2 forcing would still be logarithmically proportional to CO2.
https://chriscolose.wordpress.com/2010/03/02/global-warming-mapsgraphs-2/ (shows spectra)
https://chriscolose.wordpress.com/2010/02/18/greenhouse-effect-revisited/ (shows spectra, explains logarithmic proportionality)
(and http://www.skepticalscience.com/The-first-global-warming-skeptic.html, which shows some similar types of graphs, though they are computed for a simplified spectrum and very simplified atmosphere, but still have some resemblance to actual spectra)
and the link to ” Kiehl and Trenberth (1997) [PDF] ” above
(one of the first figures shows a calculated OLR spectrum (including the effects of H2O and CO2), which looks correct considering actual OLR; note that you can interpolate across the OLR valley of CO2 to find the OLR without the effect of CO2 (which agrees with the numbers in Table 3); to do so requires knowing that H2O or other gases, and clouds, don’t produce much of a particular valley in that part of the spectrum relative to just outside that part of the spectrum)
https://chriscolose.wordpress.com/2010/05/12/goddards-world/ (particular to Venus, where the logarithmic approximation fails because there is so much CO2 that absorption in other bands becomes important (also there may be issues with different pressure-broadenning and temperature effects on line-strength (?).)
(note the first figure, which shows the change in brightness temperature of OLR from 1970 to 1996; part of the CO2 band appears in the graph at the left edge; in this type of figure, forcing is only approximately proportional to area over a small interval of wave numbers, so you can’t directly compare the CH4 and CO2 effects in terms of W/m2 just by looking at this graph; also, part a significant part of the CO2 band is outside the range of wave numbers shown).
my series of comments mainly in response to L. David Cooke’s comments on Real Climate, “A simple recipe for GHE”; it starts here:
but that part covers many topics, so you may prefer to skip that and start here:
Total greenhouse effect (kicking off with discussion of Kiehl and Trenberth 1997), radiative forcing, and changes in radiative forcing
391 (total ghe, OLR spectrum; also, climate sensitivity depends on climate) http://www.realclimate.org/index.php/archives/2010/07/a-simple-recipe-for-ghe/comment-page-8/#comment-181122
404 (feedbacks and climate sensitivity)
http://www.realclimate.org/index.php/archives/2010/07/a-simple-recipe-for-ghe/comment-page-9/#comment-181188 (note correction at 405)
413,414(note correction in 414, and note corrections at 420, and 421 (I said 150 W/m2 in some places where it was supposed to be 155 W/m2)) (forcing depends on climate; forcing can be different between a change and the reverse change (but the feedbacks will also be different))
first part of 421: http://www.realclimate.org/index.php/archives/2010/07/a-simple-recipe-for-ghe/comment-page-9/#comment-181367
426,beginning of 427 (summing up some points; then, what is a feedback and when, and some more about climate sensitivity: see also 409) http://www.realclimate.org/index.php/archives/2010/07/a-simple-recipe-for-ghe/comment-page-9/#comment-181847
climate sensitivity (see also 430-436 below)
internal variability (see also 430-436 below)
Step by step description of radiative forcing
428 (general) http://www.realclimate.org/index.php/archives/2010/07/a-simple-recipe-for-ghe/comment-page-9/#comment-181853
429 (CO2) http://www.realclimate.org/index.php/archives/2010/07/a-simple-recipe-for-ghe/comment-page-9/#comment-181854
430,431,433-436 (Planck response and other feedbacks, climate sensitivity and change, Charney sensitivity, efficacy, the 4-dimensional climate state; also, tropopause level forcing with stratospheric adjustment) http://www.realclimate.org/index.php/archives/2010/07/a-simple-recipe-for-ghe/comment-page-9/#comment-181855
I think the latter part of your response is beyond my comprehension at the moment,
Some of the above links should help. Try drawing spectra out on paper.
last link shouldn’t have the end paranthesis as part of the website (paranthesis – is that the singular of parantheses? I don’t know…)
This post is breaking your feed because there’s a vertical tab character in “In particular, the sum of the effect” (after the first “e” in “effect”) so it’s not well-formed XML.
While a lot of this is over my head, I’m very grateful for the thorough and clear analysis and summary here and at RC. Seems to me to clear away a lot of the underbrush, and the 7% increase is something I can remember and hopefully not mis-cite.
Patrick, actually it’s parenthesis, so you’ve got the emphAsis on the wrong syllAble.
Modeling radiative transfer in the Earth’s atmosphere is a bit messy and complicated, if not outright murky and opaque. While the basic principles of radiative transfer are relatively simple and straightforward, it is having to deal with several hundred thousand absorption lines of greatly varying strengths, distributed in complex clumps across the spectrum, with line shapes and widths that depend on pressure as well as temperature, and with a unique grouping of such characteristics for each principal absorbing gas in the atmosphere.
For very weak lines, the absorption is linearly proportional to the absorber amount. For strong pressure broadened (Lorentz) lines, or large absorber amounts, absorption is proportional to the square root of absorber amount. For Doppler broadened (primarily stratospheric) lines, the absorption becomes logarithmic in absorber amount (see Atmospheric Radiation by Goody and Yung for details). Accurate calculation requires use of the so-called line-by-line method where the shape, strength, and spectral location of each line is explicitly determined, and where spectral contributions from all spectral lines of all absorbing gases are summed up at each wavelength of the spectrum. But, at each wavelength of the spectrum, radiative transfer is accurately represented by Beer’s law absorption and exponential extinction. This is where a good computer is needed to handle all the numerical work.
To facilitate radiative flux calculations for atmospheric applications, we developed a ‘correlated k-distribution’ method (Lacis and Oinas, 1991, JGR, 96, 9027-9063) whereby the spectral absorption coefficient of the different gas were regrouped in the order of their absorption strength to enable a faster way to calculate radiative fluxes without sacrificing accuracy. This is also the approach that has been adapted for use in the GISS GCM. Thus the radiative calculations in the GISS ModelE are being done explicitly (on a first principle basis) for whatever absorber and temperature distribution that happens to be encountered at each grid box of the model, to within an accuracy of about 1 W/m2 compared to line-by-line calculation.
Thus the logarithmic dependence for doubled CO2 is a model generated result, rather than some theoretical constraint that is place on the GCM radiation model. In the Hansen et al. (1988, JGR, 93, 9341–9364) paper we derived the logarithmic type formula
F(X) = log [ 1 + 1.2 X + 0.005 X2 + 0.0000014 X3 ]
where X is the atmospheric CO2 concentration in ppm. This gives formula gives the radiative forcing in terms of equivalent temperature change rather than in W/m2. Thus, for 350 ppm, F(350) = 7.0 °C (or 7.0/33.0 = 21.2% of the total terrestrial greenhouse effect), while for doubled CO2 the formula yields ΔTo = F(700) – F(350) = 1.23 °C. This particular formula was constructed using the GCM radiation model operating in a 1D mode, being run to radiative/convective equilibrium for a series of CO2 amounts ranging from zero to several thousand ppm, but with all cases using the current climate global-mean water vapor profile, global-mean temperature profile, and global-mean cloud distribution.
The above formula, and the simpler purely logarithmic formula in popular use, are useful formulations for estimating CO2 forcing without having to perform explicit model runs. For more precise results, which also include feedback interactions, there is no substitute for full atmosphere-ocean coupled climate model calculations.
The terrestrial greenhouse flux attribution calculations reported in Schmidt et al. (2010), and also in Lacis et al. (2010), are for a current climate (1980) atmospheric structure. For a year’s worth of GCM simulated atmospheric data, each constituent is either added one by one to an empty atmosphere, or subtracted one by one from the full component atmosphere, with the TOA outgoing fluxes recalculated for each case and averaged globally over the year. The fact that the sum over the individual components for both the addition and subtraction exercises does not add up to the roughly 150 W/m2 that is the greenhouse strength for the entire atmosphere, is a clear indication of non-linear overlapping absorption by the different atmospheric components. By normalizing the fractional sums we arrive at a sensible estimate for the greenhouse component attribution, i.e., the 50% water vapor, 25% cloud, 20% CO2, and 5% other minor GHG breakdown.
Note that this attribution applies only for the entire atmosphere (and more specifically, for the current climate atmosphere). Therefore, extrapolating this fractional attribution to doubled CO2, for example, is not warranted because water vapor, CO2, and clouds all exhibit different degrees of saturation. The current GISS ModelE has a climate sensitivity of about 3 °C for doubled CO2, instead of 4×1.23 °C, which might expected from the attribution results if the absorptions could be extrapolated linearly. It appears that clouds in particular may be strongly saturated with respect to responding to radiative forcing changes relative to current climate conditions, since the cloud feedback component appears to be close to zero. There is also a substantial (∼1 °C) negative feedback contribution due to moist adiabatic lapse rate change that is automatically included in the ModelE 3 °C doubled CO2 result that does not explicitly appear the total greenhouse flux attribution study.
It should also be noted that the ‘cloud feedback’ response to changing meteorological conditions can impact multiple cloud characteristics (cloud cover, cloud height, cloud life time, water/ice phase, optical depth, particle size, diurnal phase), all of which have radiative consequences, some affecting the SW more, others having greater impact on the LW fluxes (and the cloud contribution to the greenhouse effect). It is possible to have cloud changes such that the cloud SW albedo effect effectively cancels the cloud LW greenhouse effect. We are currently working to complete a more detailed flux attribution for the ModelE doubled CO2 example.
Response: Thanks for the thoughtful comment Dr. Lacis
Funny that you had this here because I did a somewhat similar post just then and didn’t even see yours.
As a meteorologist, looking at the real atmosphere, I find it inconceivable that clouds don’t have a dominant influence on surface temperatures. The albedo effect , which short-circuits any action by the greenhouse gases is grossly underestimated. Imagine what would happen if the earth had a permanent cloud cover. Temperatures would either stay the same or gradually cool. Volcanoes might provide the only warming.
The effect of clouds in the tropics—morning sunshine leads to afternoon clouds and showers to cool temperatures. Clouds then tend to dissipate during the night, allowing more cooling. If water vapor is a positive feedback, how is it that the average temperatue in a dry, desert region is hotter than a humid region at the same latitude? (Do the comparison).
As Lindzen and Spencer show, feedbacks are near zero or even negative.
Without negative feedbacks, temperatures would spin out of control.
Response: Everyone already knows clouds have a strong influence, both albedo and in the longwave greenhouse components, amounting to ~20 W/m2 cooling globally. This does influence the impact of other gases via absorption overlap issues, but not a ‘short-circuit’ (whatever that is supposed to mean). You’re just confusing the absolute magnitude of an effect with the derivative of that effect with respect to changing T. Then, your statement about positive feedbacks is just untrue.– chris
Simply stated, if SW radiation from the sun is reflected back to space, it can’t be acted on by greenhouse gases—-(short circuited) instead
of completing the whole circuit (process) of reaching and warming the earth, then re-radiating LW to be acted on by greenhouse gases.
As Lacis stated. ” It is possible to have cloud changes such that the cloud SW albedo effect effectively cancels the cloud LW greenhouse effect”.
Without the greenhouse effect where is the water vapor feedback and temperature amplification?
It’s the changes in cloud type and coverage due to changing weather patterns that can cause delta T. Spencer sugests that “The PDO can cause changes in weather patterns that affect cloud amounts. It only takes a 1-2% change in global average cloud cover to explain all the temperature changes in the last 2,000 years.
werecow’s little nit actually answers part of Chic Bowdrie’s question, since dry ice needs it to be -80C and regular ice and snow just needs 0C.
The CO2-less world would be a snowball (or snowy – with maybe some open water – at about -18 C until the albedo caught up and then much colder), the water-vaporless world would be if it got cold enough a dry-iceball, but wouldn’t get that cold. Unless you stabilize at -80C. It would be too cold for us to live, probably – and what we’d live on is a good question. But anyway, most of the water vapor would freeze and snow out in a CO2-less atmosphere, and that wouldn’t happen in the vaporless atmosphere (basically nitrogen, CO2 and oxygen). So it only makes sense that your stable point for a CO2-less atmosphere is lower than for a vaporless atmosphere, since in the case of the vaporless atmosphere, you still have CO2 gas (and a greenhouse effect) until you get past -80C.
So the true answer is you can’t treat H20 in gas form and CO2 as identical, just as you can’t treat them as identical to N and O, and also, you can’t model it without including feedbacks. Where would the snow come from? and if your earth doesn’t get 80 below you don’t get dry snow. So the H20-less Earth would only have dry ice at the poles.
I’ve been impressed that some of your comments about the error in Goddard’s argument that pressure per se can explain increased temperature are less biased than many and appear to show an essential understanding of spectra . I take it you are a PhD student in Madison . I have a permanent climbing injury from Devil’s lake .
Frankly , I find the understanding of the most basic relevant physics pathetic on both sides of the debate . It is my strong impression that you can get a PhD in “climate science” without ever even learning how to calculate the temperature of a radiantly heated colored ball . Am I wrong ?
Certainly the field seems retarded compared to other areas of applied physics such as electrodynamics . Only when students of the problem come forward who seek to truly understand the phenomena rather than “prove” a particular outcome will a Chandrasekhar level analysis of the energy structure of planetary atmospheres be achieved .
But how can you possible defend the bull shit notion that the green house effect is 33k ? I defy you to show me a spectrum which produces that temperature .
This is the retarded sort of amateur math which makes me doubt you and your peers even know what the difference in temperature between a light or dark gray ( flat spectrum ) ball ?
If you do understand this , given your knowledge of , and access to , available and appropriate spectral data you can pick up $300 and almost certainly some publications by collaborating on extension and application of my array language implementation , http://cosy.com/Science/TemperatureOfGrayBalls.htm , of the basic StefanBotzmann and Kirchhoff relations for gray balls to full spectra , ie , colored balls . You supply the spectra , I’ll calculate the experimentally testable equilibrium temperature .
To me , that’s the way physics advances .