Recap
In Part Five we finally got around to seeing our first calculations by looking at two important papers which used “numerical methods” – 1-dimensional models – to calculate the first order effect from CO2. And to separate out the respective contribution of water vapor and CO2.
Both papers were interesting in their own way.
The 1978 Ramanathan and Coakley paper because it is the often cited paper as the first serious calculation. And it’s good to see the historical perspective as many think scientists have been looking around for an explanation of rising temperatures and “hit on” CO2. Instead, the radiative effect of CO2, other trace gases and water vapor has been known for a very long time. But although the physics was “straightforward”, solving the equations was more challenging.
The 1997 Kiehl and Trenberth paper was discussed because they separate out water vapor from CO2 explicitly. They do this by running the numerical calculations with and without various gases and seeing the effects. We saw that water vapor contributed around 60% with CO2 around 26%.
I thought the comparison of CO2 and water vapor was useful to see because it’s common to find people nodding to the idea that longwave from the earth is absorbed and re-emitted back down (the “greenhouse” effect) – but then saying something like:
Of course, water vapor is 95%-98% of the whole effect, so even doubling CO2 won’t really make much difference
The question to ask is – how did they work it out? Using the complete radiative transfer equations in a 1-d numerical model with the spectral absorption of each and every gas?
Of course, everyone’s entitled to their opinion.. it’s just not necessarily science.
The “Standardized Approach”
In the calculations of the “greenhouse” effect for CO2, different scientists approached the subject slightly differently. Clear skies and cloudy skies, for example. Different atmospheric profiles. Some feedback from the stratosphere (higher up in the atmosphere), or not. Some feedback from water vapor, or not. Different band models (see Part Four). And also different comparison points of CO2 concentrations.
As the subject of the exact impact of CO2 – prior to any feedbacks – became of more and more concern, a lot of effort went into standardizing the measurement/simulation conditions.
One of the driving forces behind this was the fact that many different GCMs (Global Climate Models) produced different results and it was not known how much of this was due to variations in the “first order forcing” of CO2. (“First order forcing” means the effect before any feedbacks are taken into account). So different models had to be compared and, of course, this required some basis of comparison.
There was also the question about how good band models were in action compared with line by line (LBL) calculations. LBL calculations require a huge computational effort because the minutiae of every absorption line from every gas has to be included. Like this small subset of the CO2 absorption lines:
From "Handbook of Atmospheric Sciences", Hewitt & Jackson 2003
Band models are much simpler, and therefore widely used in GCMs. Band models are “paramaterizations”, where a more complex effect is turned into a simpler equation that is easier to solve.
Averaging
Does one calculation of CO2 radiative forcing from an “average atmosphere” gives us the real result for the whole planet?
Asking the question another way, if we calculate the CO2 radiative forcings from all the points around the globe and average the radiative forcing do we get the same result as one calculation for the “average atmosphere”.
This subject was studied in a 1998 paper: Greenhouse gas radiative forcing: Effects of average and inhomogeneities in trace gas distribution, by Freckleton et al. They ran the same calculations with 1 profile (the “standard atmosphere”), 3 profiles (one tropical plus a northern and southern extra-tropical “standard atmosphere”), and then by resolving the globe into ever finer sections.
The results were averaged (except the single calculation of course) and plotted out. It was clear from this research that using the average of 3 profiles – tropical, northern and southern extra-tropics – was sufficient and gave only 0.1% error compared with averaging the calculation at 2.5% resolution in latitude.
The Standard Result
The standard definition of radiative forcing is:
The change in net (down minus up) irradiance (solar plus longwave; in W/m2) at the tropopause after allowing for stratospheric temperatures to readjust to radiative equilibrium, but with surface and tropospheric temperatures and state held fixed at the unperturbed values.
What does it mean? The extra incoming energy flow at the top of atmosphere (TOA) without feedbacks from the surface or the troposphere (lower part of the atmosphere). The stratospheric adjustment is minor and happens almost immediately (there are no oceans to heat up or ice to melt in the stratosphere unlike at the earth’s surface). Later note added – “almost immediately” in the context of the response of the surface, but the timescale is the order of 2-3 months.
The common CO2 doubling scenario, from pre-industrial, is:
278ppm -> 556 ppm
And the comparison to the present day, of course, depends on when the measurement occurs but most commonly uses the 278ppm value as a comparison.
IPCC AR4 (2007) pre-industrial to the present day (2005), 1.7 W/m2
IPCC AR4 (2007) doubling CO2, 3.7 W/m2
Just for interest.. Myhre at al (1998) calculated the effects of CO2 – and 12 other trace gases – from the current increases in those gases (to 1995). They calculated separate results for clear sky and cloudy sky. Clear sky results are useful in comparisons between models as clouds add complexity and there are more assumptions to untangle.
They also ran the calculations using the very computationally expensive Line by Line (LBL) absorption, and compared with a Narrow Band Model (NBM) and Broad Band Model (BBM).
CO2 current (1995) compared to pre-industrial, clear sky – 1.76W/m2, cloudy sky 1.37W/m2
(The NBM and BBM were within a few percent of the LBL calculations).
There are lots of other papers looking at the subject. All reach similar conclusions, which is no surprise for such a well-studied subject.
Where does the IPCC Logarithmic Function come from?
The 3rd assessment report (TAR) and the 4th assessment report (AR4) have an expression showing a relationship between CO2 increases and “radiative forcing” as described above:
ΔF = 5.35 ln (C/C0)
where:
C0 = pre-industrial level of CO2 (278ppm)
C = level of CO2 we want to know about
ΔF = radiative forcing at the top of atmosphere.
(And for non-mathematicians, ln is the “natural logarithm”).
This isn’t a derived expression which comes from simplifying down the radiative transfer equations in one fell swoop!
Instead, it comes from running lots of values of CO2 through the standard 1d model we have discussed, and plotting the numbers on a graph:
Radiative Forcing vs CO2 concentration, Myhre et al (1998)
From New estimates of radiative forcing due to well mixed greenhouse gases, Myhre et al, Geophysical Research Letters (1998).
The graph reasonably closely approximates to the equation above. It’s very useful because it enables people to do a quick calculation.
E.g. CO2 = 380ppm, ΔF = 1.7W/m2
CO2 = 556ppm, ΔF = 3.7 W/m2
Easy.
Benefit of Using “Radiative Forcing” at TOA (top of atmosphere)
First of all, we can use this number to calculate a very basic temperature increase at the surface. Prior to any feedbacks - or can we? [added note, James McC kindly pointed out that my calculation of temperature is wrong and so maybe it is too simplistic to use this method when there is an absorbing and re-transmitting atmosphere in the way. I abused this approach myself rather than following any standard work. All errors are mine in this bit - we'll let it stand for interest. See James McC's comments in About this Blog)
In Part One of this series, in the maths section at the end (to spare the non-mathematically inclined), we looked at the Stefan-Boltzmann equation, which shows the energy radiated from any "body" at a given temperature (in K):
Total energy per unit area per unit time, j = εσT4
where ε= emissivity (how close to a "blackbody": 0-1), σ=5.67x10-8 and T = absolute temperature (in K).
The handy thing about this equation is that when the earth's climate is in overall equilibrium, the energy radiated out will match the incoming energy. See The Earth’s Energy Budget – Part Two and also Part One might be of interest.
We can use the equations to do a very simple calculation of what ΔF = 3.7W/m2 (doubling CO2) means in terms of temperature increase. It's a rough and ready approach. It's not quite right, but let's see what it churns out.
Take the solar incoming absorbed energy of 239W/m2 (see The Earth’s Energy Budget – Part One) and comparing the old (only solar) - and new (solar + radiative forcing for doubling CO2 values), we get:
Tnew4/Told4 = (239 + 3.7)/239
where Tnew = the temperature we want to determine, Told = 15°C or 288K
We get Tnew = 289.1K or a 1.1°C increase.
Well, the full mathematical treatment calculates a 1.2°C increase - prior to any feedbacks - so it's reasonably close.
[End of dodgy calculation that when recalculated is not close at all. More comments when I have them].
Secondly, we can compare different effects by comparing their radiative forcing. For example, we could compare a different “greenhouse” gas. Or we could compare changes in the sun’s solar radiation (don’t forget to compare “apples with oranges” as explained in The Earth’s Energy Budget – Part One). Or albedo changes which increase the amount of reflected solar radiation.
What’s important to understand is that the annualized globalized TOA W/m2 forcing for different phenomena will have subtly different impacts on the climate system, but the numbers can be used as a “broad-brush” comparison.
Conclusion
We can have a lot of confidence that the calculations of the radiative forcing of CO2 are correct. The subject is well-understood and many physicists have studied the subject over many decades. (The often cited “skeptics” such as Lindzen, Spencer, Christy all believe these numbers as well). Calculation of the “radiative forcing” of CO2 does not have to rely on general circulation models (GCMs), instead it uses well-understood “radiative transfer equations” in a “simple” 1-dimensional numerical analysis.
There’s no doubt that CO2 has a significant effect on the earth’s climate – 1.7W/m2 at top of atmosphere, compared with pre-industrial levels of CO2.
What conclusion can we draw about the cause of the 20th century rise in temperature from this series? None so far! How much will temperature rise in the future if CO2 keeps increasing? We can’t yet say from this series.
The first step in a scientific investigation is to isolate different effects. We can now see the effect of CO2 in isolation and that is very valuable.
Although there will be one more post specifically about “saturation” – this is the wrap up.
Something to ponder about CO2 and its radiative forcing.
If the sun had provided an equivalent increase in radiation over the 20th century to a current value of 1.7W/m2, would we think that it was the cause of the temperature rises measured over that period?
Update – CO2 – An Insignificant Trace Gas? Part Eight – Saturation is now published
References
Greenhouse gas radiative forcing: Effects of average and inhomogeneities in trace gas distribution, Freckleton at al, Q.J.R. Meteorological Society (1998)
New estimates of radiative forcing due to well mixed greenhouse gases, Myhre et al, Geophysical Research Letters (1998)
1.7 per sq meter/radiation due to sun per sq meter = 1.7/1365 = insignificant
John, there is something about the radiative forcing graphs which I don’t understand. When I look at the shape of the graph, it appears as though the Y axis would be ZERO when CO2 is about 250 ppm. How can there be no radiative forcing when CO2 is 250 ppm. Given that the function is logarithmic, I would expect to see the rate of increase of the radiative forcing greatest going from low very low CO2 levels up. If I remember my calculus correctly, the derivative of ln(X) = 1/X + C. So as CO2 increases the rate of change of the Y axis, or radiative forcing should be getting sharply smaller.
This formula ΔF = 5.35 ln (C/C0) also seems a bit out of whack with reality. I worked this backward using the assumption that temperature change from 1880 to 2009 was in the range of .5dC to 1.0dC. This seems to be the range of dispute between warmists and deniers. Working backward, I come up with a formula in which k is only 3.2 or so. ΔF would than equal 3.2ln(CO2n/CO2o). That change flattens out the graph lines by quite a bit. AS a result the flatter lines would cross more closely to ZERO, ZERO. What I am missing here?
See answers to your questions at the end.
John Phillips:
Insignificance can be a judgement call.
To be accurate, we need to compare the energy increase per m^2 at top of atmosphere from CO2 with the sun’s incoming absorbed energy averaged over that same area.
This means we get:
Incoming absorbed solar energy per unit surface area = S(1-A)/4
where A is albedo (=0.3)
So incoming solar absorbed energy averaged over the earth’s surface = 239 W/m^2.
(Check out The Earth’s Energy Budget – Part One if this concept doesn’t seem right).
And of course, I didn’t cover the other gases, methane, N02, tropospheric ozone..
So the cumulative effect of the various trace gases to 2005 is believed to be 2.4 W/m^2.
“The common CO2 doubling scenario, from pre-industrial, is:”
How does one get to 576ppm given
1) China hit peak coal production in 2006 and will be out of coal by 2050
3) The EU will be completely out of coal by 2050, with the UK leading the parade in 9 years
2) US ‘recoverable’ coal reserves turn out to be overstated by a factor of at least 2.
http://pubs.usgs.gov/of/2008/1202/
Science – “To be accurate, we need to compare the energy increase per m^2 at top of atmosphere from CO2 with the sun’s incoming absorbed energy averaged over that same area.”
Thanks. Good point. 2.4/239 is more significant, but still only about 1% increase. I still wonder how the complex climate system processes that increase, with negative or positive feedback.
Your posts are very good, making the fundamentals understandable to non-climate scientists.
The mention about 1% increase in solar incoming short-wave radiation got me thinking: actual measured variation in solar output is much smaller that this….but I’ve read somewhere that band-by-band it is larger (i.e. the spectrum varies more than its integral).
Is it true? and when one speak about negligeable variations in solar output, this is measured by satelites (TOA) or station (on the ground)?
If it is measured at TOA, and given there are windows in the short wave range like there is in the long wave range, what about a detailed computation of what happen for short waves from TOA to ground? Is the ground variation of incoming short waves still negligeable (<<1%), even factoring out variation in cloud cover?
s.ofd.,
The problem is the feedbacks, combined with a trivial increase of ~1%, will not get us to doom.
The problem is that the CO2 driven catastrophic changes in climate that AGW theory predicts are simply not happening. And there is no indication they will be.
The TOA, by the way, is not really where people live and weather happens, is it?
Given that the changes we’re worried about are expected to mostly take place over the next century, this is unsurprising.
Knocking down a strawman adds nothing to the argument.
On the other hand, evidence of warming is all around us. Diminishing arctic sea ice, loss of mass of the greenland and antarctic ice sheets, ranges of a large number of species moving north (insects, birds), horticultural zones in the NH moving northwards, all sorts of recorded phenomena like first bloom happening earlier (cherry blossoms in Japan, records for which go back for centuries, gardeners records in England, of which quite a few go back a century or more, some much more, etc).
We don’t live on the sun, either, therefore anything happening there can’t be important, right?
hunter:
“The problem is that the CO2 driven catastrophic changes in climate that AGW theory predicts are simply not happening.”
Well this series so far is not about that, it’s about understanding:
- the basics of CO2
- the science behind how it adds radiation to the surface
- how we quantify that radiative forcing
- quantifying its impact vs water vapor
- the evidence for its effect in the atmosphere
Many people in the thick of the debate don’t understand the basics but would like to. And so we hear many comments like:
-”water vapor is 95% of the greenhouse effect”
-”adding a few ppm to CO2 can’t possibly have any effect”
-”CO2 is already saturated and can’t have any further effect”
“it’s all made up”
Without a sound foundation anything sounds plausible.
If you have a comment, a challenge, a question on the foundations as presented, here’s your chance.
scienceofdoom,
No, the basics are fine.
Please excuse the brief answer.
Of course the basics are fine.
I did not mean to jump ahead.
So I am back, and do have some questions.
Perhaps you covered them, and if so please excuse the redundancy.
- So if there was no water vapor in the atmosphere, what would the impact be on temperatures, all else being unchanged?
- Is CO2′s impact a diminishing logarithmic effect as far as its ghg impact or not?
Thanks, and enjoy the doom song.
hunter:
If there was no water vapor?? Big question. How could there be? There would have to be no oceans..
I think that’s a question that isn’t easy to answer.
No latent heat transfer, no clouds, no ocean heat transport…
But if one day suddenly and magically all the water vapor disappeared out of the atmosphere and magically it didn’t replenish – the longwave radiation change is calculated to be – on average – a 75 W/m^2 drop in longwave radiation at the top of atmosphere.
So roughly speaking we are talking about a new average surface temperature of less than 0′C (32′F). I think. But then there would be no clouds so that would warm things up because clouds have a net cooling effect.. But no latent heat removal from the surface..
Let’s say – a lot colder but not as cold as removing the CO2 and methane as well.
Does that answer that question?
And Is CO2’s impact a diminishing logarithmic effect?
Yes, that’s in the post.
If CO2 levels go to 576ppm we will have about 3.7W/m^2 of radiative forcing at TOA, and if it quadruples we will have “only” about 7.4W/m^2.
If it was possible to double again to 8x pre-industrial levels then “only” 11 W/m^2.
However, the log function is an approximate fit to the graph of the numerical calculations (see in the post), and as the graph only goes to 1000ppm I’m not sure whether the graph still follows that shape.
I noticed that I fluffed one of the CO2 concentration numbers.
Two different pre-industrial numbers get used, but sticking with the IPCC 1750 approximation of 278ppm, doubling would be 556ppm, not 576..
So I changed the post.
Well, our host has answered hunter, so perhaps I shouldn’t, but still …
It doesn’t matter, since the earth has a lot of water, but … water vapor feedbacks are about 50% of warming, as a feedback, and this was predicted by physics-based models and those predictions have been backed up by AQUA satellite observations using the AIRS sensor system.
Observations confirm model results … imagine that!
No, it’s a constant logarithmic forcing, not a decreasing one.
You may, or may not, understand why the answer to your question is “no”.
Unfortunately, I’m burdened by having a BS in Mathematics.
scienceofdoom,
Thanks for the clarification and the patience.
So if the atmosphere had no CO2 in it, what would the impact be?
dhogaza,
I am not so burdened, so perhaps you can help me a bit more?
How is it logarithmic but not a diminishing effect?
By diminishing I am trying to understand that if a factor- forget CO2 for a second- is logarithmic and is doubled, is its impact doubled?
Hunter, perhaps I misunderstood what you were trying to say …
“By diminishing I am trying to understand that if a factor- forget CO2 for a second- is logarithmic and is doubled, is its impact doubled?”
That would be a linear, not logarithmic, relationship.
Each doubling of CO2 yields a constant increase in forcing, so each molecule of added CO2 has a diminishing effect, yes, at the concentrations we’re interested in.
dhogaza,
Thank you for the clarification.
So the impact of increasing, from what is believed to be the pre-industrial CO2 ppm level of 278, to 333ppm is greater than going from 333 to today’s 388?
scienceofdoom,
Sorry about the questions. I am trying to understand your basics.
You mentioned what I believe was something to the effect that heat would be stored up in the system for a future impact. Where would it be stored?
hunter:
No CO2
If there was no CO2 in the atmosphere the temperature would be around 10′C cooler, all other things being equal. So the average global surface temp would be around 5′C.
I don’t think you are looking for an accurate number.. just an idea?
Logarithms
On “logarithmic”, in case it’s not clear to anyone, I believe dhogaza is striving for technical clarity. But for those less used to what the idea means:
- a logarithmic relationship is a diminishing relationship, so each time you double a parameter the result only increases by a constant amount each time
- a “diminishing” logarithmic relationship is either a more descriptive way of saying logarithmic (how I believe hunter meant it), or a relationship where the output slows even more, say you double the parameter and output increases by 1, double the parameter again and output now increases by 0.9 instead of 1..
Storing of heat
Not sure what you have in mind here. I can’t see anything in this post. Can you find the comment or idea that needs explaining?
Yes. I had first interpreted hunter’s question to be in the second sense given by scienceofdoom, and after clarification came to understand that hunter meant it in the first sense.
Also, hunter, it’s log base 2, the base is implied by the “doubling”.
Very interesting series, thanks.
I am eagerly awaiting the sections on negative climate feedbacks, which have prevented a runaway heating in the past, when CO2 levels were considerably higher than in modern times.
Climate models (of the mainstream —–ist variety) are apparently tweaked toward the positive feedback end of the scale, which intuitively seems quite bass ackward.
Observed temperature trends are approximating the lower range of IPCC and GISS projections that assumed a diminishing of CO2 levels, when in fact CO2 levels continue to increase.
A moderator’s reminder:
peoplewhodontagreewithus-ists will be moderated out. Check the Etiquette
scienceofdoom and dhogaza,
Thanks. yes, irt to comparative impacts, I am looking for what my grandfather would call ‘rule of thumb’ ways to follow this. He was an MIT grad in engineering and liked to reduce issues to solid concepts that could be followed fairly clearly. It served him well in a variety of enterprises. It is a habit I cultivate.
So if I am following this properly, no H2O vapor = ~0oC, and no CO2 = ~5oC?
As to the logarithmic impact of CO2, are you saying that X00ppm of CO2 ~ Yo temp forcing, so 2(X00)ppm CO2 ~2Yo temp impact?
Or is it that X00 ppm of CO2 = Yo temp forcing, and 2(X00)ppm CO2 = <1.0(Yo) temp forcing?
Thanks,
hunter – using your notation Y0+1, not 2Y0, on the right side.
log2(2*N) = N+1
“I am eagerly awaiting the sections on negative climate feedbacks, which have prevented a runaway heating in the past, when CO2 levels were considerably higher than in modern times.
Climate models (of the mainstream —–ist variety) are apparently tweaked toward the positive feedback end of the scale, which intuitively seems quite bass ackward.”
If your first statement were correct, you might have a point, but it doesn’t require negative climate feedbacks to prevent runaway heating in the past.
Positive feedbacks can lead to a convergent series (i.e. converges to some limit), they don’t necessary lead to a divergent series (grows without limit).
As it happens, all the evidence is that feedbacks in earth’s climate lead to a convergent series, therefore there’s no runaway heating.
Unlike Venus. What’s different than Venus? Among other things, its closer to the sun, but I don’t know offhand if that was sufficient to flip it into a runaway state that didn’t end until it reached its current (very hot) temperature, water all gone, etc.
I am going to repeat your second paragraph:
“Climate models (of the mainstream —–ist variety) are apparently tweaked toward the positive feedback end of the scale, which intuitively seems quite bass ackward.”
Because it includes a very typical, yet very wrong, misconception of feedbacks in models that gets endlessly repeated.
Feedbacks *arise* from the physics built into GCMs. They aren’t “tweaked in that direction”. They’re an emergent property.
hunter:
I wasn’t sure I understood your question exactly, but check out my earlier comment for some values:
You must be on a computer. If it’s a Windows PC there will be a calculator somewhere. Put some of the numbers in and use the log function (or natural log “ln” function) and you will get a sense of the results.
Note that the formula is about the empirical relationship between CO2 levels and radiative forcing.
How does this relate to temperature? Well energy radiated is proportional to the 4th power of temperature in Kelvin.
If you look at the formula above (under the heading “Benefits of using Radiative Forcing..”) where I worked out the very approximate no-feedback surface temperature rise, you can plug in the number for 4x CO2.
Actually it works out to the same temperature rise again.
- 2x CO2 (278-556ppm) results in a radiative forcing of 3.7W/m^2 and approximately 1.1′C temperature rise (all other things being equal)
- 4x CO2 (278- 1114ppm) results in a radiative forcing of 7.4W/m^2 and approximately 2.2′C temperature rise (all other things being equal)
Al Fin:
Of course, everyone wants to jump ahead and work out the final answer. Climate models, the future, the past.. the answer!
For now let’s work on the basis that climate is very complex.
That’s why we have this series on CO2 to put the spotlight on one important element of the climate.
There are positive and negative feedbacks in the climate system. I’m sure – I hope – we have champions of both who are reading this blog.
I believe the way to consider CO2 – even if we learn nothing more – is that it has a clear effect.
It has an effect that we can quantify.
And given that we can see clearly – for many readers, at least more clearly than at the start – that CO2 has a warming effect on the surface, if there had been no increase in CO2 in the last 100 years it would almost certainly be cooler.
How much – at this stage of course we can’t say.
scienceofdoom,
Thank you. The answer was, so to speak blowing in the wind- or on your blog post. CO2′s impact, if I am understanding you correctly acts on what non-technical people would call diminshing return basis. It is simlar to building material: a 2X6 is not 50% stronger than a 2X4.
My take on CO2′s effect is that it has an impact that is quantified in the lab. But in the actual area of interest- the atmospehre- the results are far less certain. Something as complex as a 10′s of mile thick ocean of gases with aerosols, soots, water in all three states, land, ocean and ice on the surface and things like volcanos, industry, ocean outgassing/evap/ingassing, land use changes -natural or not, not to mention solar impacts, etc. is not going to lend itself to straightforward statements like ‘This = that’.
But I am jumping ahead of your excellent pacing.
On what do you base this opinion? Where is the science wrong?
You followed with a bunch of unrelated stuff that doesn’t affect that basic physics of what’s going on with CO2 alone in the atmosphere. Solar impacts? Doesn’t affect CO2 forcing. And so on with many of the things you list.
Now, a few of those things you list – land use changes, outgassing/ingassing, etc, can affect the amount of CO2 in the atmosphere, of course. BUT the actual amount of CO2 that’s in the atmosphere is easy to determine, in a way that allows scientists to totally ignore such processes – THEY MEASURE IT.
And once we know how much CO2 is in the atmosphere, the forcing can be calculated in isolation.
You are entitled to your own opinion, but my recollection is that when I took college physics, my *opinion* didn’t count for squat. Neither will yours when it comes to the physics.
You need to do your work, then show your work, that shows that the physics being presented by our host is wrong.
“seems complex to me” is known as an argument from personal incredulity, and has no persuasive power.
dhogaza:
It seems like hunter is just commenting on the amazing complexity of the rest of the climate. The sum total of CO2 and all other effects.
Well that’s how I read it anyway.
Well, this isn’t the first blog that hunter’s posted on.
And this:
Would seem to make it clear (as I thought his first graph did) that he doesn’t believe that you can work with the radiative forcing due to CO2 (without feedbacks) in isolation.
“this = that” statements like “a doubling of CO2 adds X w/m2 forcing”.
But maybe I’m wrong. If hunter says so, I’ll take hunter at his/her word.
[...] 2010 by scienceofdoom In the series CO2 – An Insignificant Trace Gas? we concluded (in Part Seven!) with the values of “radiative forcing” as calculated for the current level of CO2 [...]
Thanks again!
Just a small – maybe unrelated – question. Has anyone given any thought to the simple effect of thermal insulation of the bulk gases O2 and N2? Like, the efficiency of double glazing comes from the fact that thermal transfer in the form of kinetic energy of gas molecules is a very slow process. The heavier the molecule, the lower is the speed and the slower is the process. For example the energy elements we use in my country (where triple-glazing is a must) contains Argon gas – heavier than Oxygen.
Thus my question: how much of the warming above the “base level” is due to thermal insulation and how much is due to the “greenhouse” effect?
Now, when I am at it: The “greenhouse” effect is actually a misnomer. Greenhouses work by entrapping the warm air, preventing convection – like the walls of your house. You can build a greenhouse using thin plastic foil that doesn’t absorb or reflect IR radiation. We do it in my country regularly. Or am I wrong?
Kenneth
Kenneth:
The “greenhouse” effect is often in quotes. Every time I use it I try and put it in quotes.
For exactly the reason you describe. The “so-called greenhouse effect”, we are really saying. Greenhouses have a slight property of admitting solar radiation and blocking some infrared radiation from leaving, but mainly the glass – or any material – stops convection. CO2 and other trace gases which absorb longwave radiation are really working differently.
For the first part of the question you are really talking about conduction, which is usually very inefficient at moving heat in gases.
Most of the heat movement in the troposphere (lower part of the atmosphere) is from convection. The surface warms the lowest part of the atmosphere, so it expands and therefore rises because its density has reduced. A certain amount of heat is also from latent heat – which is evaporation of water and then condensation higher up.
About conduction and convection. This is just my point – because the air is such a bad CONDUCTOR it will function as an insulator, although it is as you say – convection is the prime factor. But still…
Another effect of the gases in the atmosphere is to cool down the surface thus decreasing the black body radiation – thus decreasing the total heat loss.
Sorry for “doodling” like this, but I assume you have the right answers!
dhogaza,
Yes we have all been on this moveable feast for awhile now.
This seems to be a fairly civilized place to stop by.
Kenneth:
I’m not totally sure of the question.
Radiation, convection, conduction and latent heat all have their place in moving heat around. Conduction is by far the worst and therefore insignificant when we talk about the atmosphere, but not when we talk about the oceans.
The gases have more than one effect on the surface. If there was no atmosphere the temperature of the surface would be around -18′C, not +15′C.
This is because they re-radiate longwave back to the earth’s surface – as described through this series. Then they remove heat by convection.
At the end of CO2 – An Insigificant Trace Gas – Part Three you can see how the temperature profile (the “lapse rate”) would look if heat didn’t move by convection compared with the effect of convection.
[...] Another Update – Part Seven – The Boring Numbers [...]
dhogaza,
My writing on this is not as clear as I would like.
What I am suggesting is that the evidence shows that saying “X amount of energy into the water ocean/atmosphere system = Y” is not going to work outside of models and labs.
[...] So far on this blog I haven’t really mentioned AGW, until now. A few allusions here and there. One very minor non-specific claim at the end of Part Seven. [...]
Thanks for your excellent series!
I have been trying to dig out facts on this subject, and how they come together, for some time now. John Houghton’s book “Global Warming” (4th Edn.) – said to be an undergrad. textbook – is an insult to readers’ intelligence by comparison.
(But maybe that’s today’s undergraduates. It does have pretty pictures, e.g. of a greenhouse, of Arrhenius himself, of a bit of Amazonian rainforest canopy, and of a golden toad. We were made of sterner stuff back in the fifties, the only pictures you got was stuff like spectrophotometers.)
Anyway,
Anyway – as I was saying when I pressed the wrong bloody key and sent you the unfinished comment – I managed to calculate from some of the info buried by Houghton in different places, that the total net global warming from 1750 to 2005, was about 0.4 degrees C. When I compared this trivial amount with the comparitively wild and erratic record of smoothed (!) global temperatures from 1850 to 2005 – which includes a FALL of this order from 1880 to 1910 – it seemed to me that something else, and a good deal of it, was going on.
I am now happy that my sums were in the right ball park, and will read the rest of your blog and further posts with great interest, and in the hope of further enlightment. And I will buy a copy of your book when you get around to it.
My thanks and regards
I should check my comments better; I meant to say the global warming calculated for CO2 ON ITS OWN, was about 0.4 C.
I thinks that’s all I wanted to say…
James McC:
Thanks for the kind comments. And I’ll make sure I put a few old-school (“real”) graphics in some of my posts..
Thank you for this series and the comments in follow up. I’m finding the series well explained with technical precision, and within the grasp for the less technically inclined, which is where I place myself.
In trying to break things down to a basic value, I’m arriving at a different figure for the net effect of doubling CO2 than 1.2C
If the total Greenhouse effect translates to roughly 30C and CO2 accounts for 26% of the Greenhouse effect, that translates to roughly 7.80C of the total Greenhouse effect that is attributed to CO2.
If we start at a ppm CO2 concentration of 0, CO2 would have doubled 9x to reach a concentration of 240 ppm. At todays level of 388 ppm, concentrations of CO2 have doubled 9.62 times.
Using 7.80C of geenhouse effect attributed to CO2, at 9.62 doublings of CO2, that translates to .81C effect per doubling of CO2.
I understand these are very back of the evelope figures, however, even if we plug in 32C as the total Greenhouse effect to account for more warming, the value per doubling of CO2 works out to .86C.
If it needs to be said, I don’t think I’ve discovered something that eluded all the scientists, I’m asking because I’m trying to make sense of the basics.
Thank you for any response and thank you too for this series.
Mark H:
Thanks for the kind comments. It’s an interesting approach you are trying – everyone has to work through the concepts in different ways to get things clear in their head. Or clearer, at least!
The logarithmic relationship is more a handy rule of thumb rather than the fundamental equation governing the result of the radiative transfer equations.
1. Let’s start with the first problem. If we start at a ppm CO2 concentration of 0, how many times do you have to double this concentration to get to 240ppm?
0x2x2x2x2x2x2x2x2x2= 0 and stays like this with yet more doubling..
2^9 =512 so maybe you didn’t start with zero but with 240/512 = 0.47?
2. The second thing to point out is that the “handy ready reckoner” of the logarithmic relationship links radiative forcing, not temperature, with CO2 concentrations. (See above).
Radiative forcing is then related to surface temperature by the “ready reckoner” of the Stefan Boltzman law. (Radiation is proportional to T^4, where T is absolute temperature).
But the real point is that the log relationship is just the rough fit to the plot of the actual results from the numerical solution to the RTE (above). Because we don’t have the values below C=280ppm it might not be such a good fit for lower concentrations.
Also the graph probably fits some other empirical relationships between the 280ppm – 1000ppm range.
I’m sure someone can find R=a x (C/Co)^b relationship (find “a” and “b” where R=radiative forcing).
Well, feel free to ask away. Absorption and re-radiation of energy through a vertical column in the atmosphere is not an easy subject to grasp, it’s not intuitive unlike gravity or wind resistance.
I have just finished reading this series. It is very interesting and it will take me a while to work though the math.
What has me confused is that looking at the radiation leaving the earth, it looks like 100% of the 15um radiation is absorbed. yet the radiative forcing graph shows that we have just started up the curve.
Gut feel says this does not make sense. More CO2 will not capture more radiation as the current amount of CO2 is already capturing it all. The absorbed energy is then radiated or transfered by kinetic energy.
I am going to go through the math to see if I can follow the logic. In that I am rusty, it will take a while.
Can anone help me bridge this?
Bingham:
Good questions. There are two parts to the answer.
The first part is covered in Part Four which shows the mathematical relationships that can be used to describe “saturation”.
Just as a note, this term saturation gets used in two ways. One by physicists in a technical way, and the other by non-physicists in a more polemic way, i.e. “CO2 is saturated so it can’t have any more effect“. It’s important to check which meaning is being used..
In the technical usage of the term, you can see (in Part Four) that the transmittance (=1-absorptance) relationship changes from approximately exp (-u) to exp (-√u).
This is because the CO2 absorption band (and any band) extends out either side in wavelength from its central absorption. So more CO2 brings more absorption, but at a slower rate.
There is a second reason. And in the long-awaited Part Eight, I will cover “saturation” as best I can, but am still trying to think of a better way to explain this second part. I am looking for inspiration..
James McC posted some comments on several parts of this series over in About this Blog
And pointed out a glaring error in my calculations of temperature rise as a result of the increase in radiative forcing.
Thanks James McC.
Take a look at them over there.. I will fix up the issues in the text and eventually figure out the answer to the conundrum.
[...] called “radiative forcing” and comes with a number of definitions you can see in Part Seven of the CO2 series (along with my mistaken attempt to do a “back of envelope” calculation of surface [...]
I think you’ll find that GCM’s don’t even use band models because they’re still too computationally intensive. They use empirically fitted equations known in the trade as parameterizations. A while back some of those parameterizations for some of the models were found to be less than accurate, but that should have been fixed by now.
For calculating the first order temperature effect of changes in CO2 and CH4, I prefer to use MODTRAN ( http://geoflop.uchicago.edu/forecast/docs/Projects/modtran.orig.html ). Pick an atmosphere and other initial conditions and set the altitude to 70 or 100 km looking down. Record Iout. Make a change in conditions and then adjust the surface temperature offset to reproduce the original Iout. It’s an iterative process, but it doesn’t take long.
At very low concentrations, the effect of CO2 is linear, not logarithmic. The plot of log(CO2) vs forcing or T starts to bend around 10 ppmv. See this graph.
I see that adding links causes moderation here too. You should see about getting CA Assistant to work here. The quicktag buttons make composing a lot easier.
I just stumbled across your site this morning and rapidly read through all seven sections of “insignificant-trace-gas”. You’ve done a spectacular job. Is it fair to say that on earth we get dF~ln(CO2) because CO2 is a trace gas and there is all this other stuff going on and that on Venus we get optical thickness ~ CO2^(1/2) because at leading order venus has a pure CO2 atmosphere?
John E. Pearson:
Thanks for the kind comments.
Unfortunately I haven’t studied Venus at all, so I have no idea of the comparison idea.
Generally, I would be cautious about the “conceptual reasons” why particular overall results work out how they do – simply because so many non-linear effects work together to produce the result.
For example, who would predict the effects of tiny changes in stratospheric water vapor? See The Strange Case of Stratospheric Water Vapor, Non-linearities and Groceries.
Ok. We can’t talk about venus. But would it be equally fair to say that we can’t extrapolate the logarithmic dependence that climate models yield for the CO2 dependence of terrestrial temperature far beyond the range over which it has been been calculated? The reason I ask is that you often hear that there is something fundamental about the logarithmic temperature dependence and that it holds over very large ranges of [CO2]. If I’ve read you correctly you’re saying that over the limited range of CO2 from say 200-1000 ppm it happens that the climate models give dT proportional to log(CO2/220ppm) over 2-3 doublings but that for CO2 much larger than 1000 ppm there is no reason whatsoever to expect the logarithmic relation to hold?
John E Pearson:
Good question. From the data I have seen your assumption about my viewpoint is correct.
Others may have seen the solutions to the problem out to higher concentrations of CO2 and this logarithmic relationship may still hold. I don’t know.
It’s true that the relationship between concentration of CO2 and absorption by CO2 is not a linear one. Increase CO2 and the absorption by CO2 will not increase as much. Roughly exp(-sqrt(amount of CO2)) once the atmosphere is optically thick at that wavelength – see CO2 – Part Four
BUT, the solution to the RTE is not trivial and has many non-linearities. The only way to get the right answer is to turn on the big computers, put in the relevant climate conditions (temperature profile, concentration profile of water vapor, CO2 etc) and calculate the change in outgoing longwave radiation.
If we could skip all of that and just look at the absorption by CO2 in isolation the answer would be much easier – but the answer comes out much different. This is why many people have reached incorrect conclusions about CO2′s effect on climate they aren’t solving the RTE, they are just working out the transmittance through a known amount of CO2. This ignores many other important factors.
[...] equations, not solvable on the pocket calculator. Part Five showed two important solutions. And Part Seven showed the current best solutions along with what “radiative forcing” actually means, [...]
ΔF = 5.35 W/m^2 (ln [383ppmV/278ppmV]) = 1.71 W/m^2
The result is applied into the formula for obtaining change of T caused by the increase of CO2:
ΔT = 1.714 W/m^2 (ln [co2/co2])/4 (σ) (Tbb) = 0.143 K
And using the thermal sensitive instead the change of radiative forcing:
ΔT = 5.35 W/m^2 (ln [co2/co2])/4 (σ) (Tbb^3) = 0.44 K
Compared with the water vapor “radiative forcing” of 7.34 W/m^2, it would be:
ΔF = 7.34 W/m^2 (ln [H2Og/H2Og] = 28.71 W/m^2
Introducing this magnitude to the formula for obtaining ΔT:
ΔT = 28.71 W/m^2 (ln [H2O/H2O])/4 (σ) (Tbb^3) = 29.4 K
Real ciphers.
[...] Part Seven – The Boring Numbers – the values of “radiative forcing” from CO2 for current levels and doubling of CO2. [...]
[...] In the past many people had slightly different approaches, so usually it is prepared in a standard way – explained further in CO2 – An Insignificant Trace Gas? Part Seven – The Boring Numbers. [...]
[...] CO2 – An Insignificant Trace Gas? Part Seven – The Boring Numbers [...]
[...] that looks very like the Beer-Lambert law of absorption! Nothing like the IPCC result shown in CO2 – An Insignificant Trace Gas? Part Seven – The Boring Numbers: Radiative Forcing vs CO2 concentration, Myhre et al [...]
[...] to show these results as radiative forcing. (You can find a more formal definition of the term in CO2 – An Insignificant Trace Gas? Part Seven – The Boring Numbers – although here it is not calculated according to the strict definition of allowing [...]
[...] basic (but hard to calculate) radiative physics – already covered in many places including CO2 – An Insignificant Trace Gas? Part Seven – The Boring Numbers (and the preceding parts of the series) – tells us that, all other things being equal, a [...]
Tom Lux on April 1, 2011 at 4:02 am:
Because the radiative forcing is with respect to an initial condition of pre-industrial CO2 concentrations of 280ppm.
By definition, at 280ppm, radiative forcing = 0.
This doesn’t mean “no radiative effect of CO2″.
The calculation is based on the “simple” physics of the radiative transfer equations AND the definition of radiative forcing – see the article.
This calculation is before the surface/troposphere comes into equilibrium.
And in any case, radiative forcing is “with all other things being equal” – usually they are not.
“Just for interest.. Myhre at al (1998) calculated the effects of CO2 – and 12 other trace gases – from the current increases in those gases (to 1995). They calculated separate results for clear sky and cloudy sky. Clear sky results are useful in comparisons between models as clouds add complexity and there are more assumptions to untangle.”
Also, just for interest.. In 1998 Dr. Sherwood IDSO (author of 500 technical publications and the founders of the Center for the Study of Carbon Dioxide and Global Change) published a paper which presented his results from eight “natural experiments” (his term) which he developed to determine the impact of increased CO2 on global warming. What makes these experiments of interest is that the results obtained by Dr. Idso using eight very different experiments to test for the relationship of CO2 to warming, all yielded results which were very close to one another. In my opinion, both believers and skeptics will find this article interesting because of the unique methods used by Idso in his effort to understand the relationship of CO2 to warming. For example, in one experiment he assesses the impact of CO2 on the warming of Venus vs Mars to arrive at an estimate of the ability of CO2 produce a greenhouse effect. In another experiment he takes an entirely different approach as he measures the impact of the daily change in atmospheric water vapor vs temperature during the advent of rainy periods in the summer in Phoenix, Az. His eight unique creative experiments are at the very least, thought provoking.
About Idso
http://en.wikipedia.org/wiki/Sherwood_B._Idso
Link to the paper…
http://www.mitosyfraudes.org/idso98.pdf
Thomas Lux:
I’ll take a look at Idso’s paper. It reminded me that the great Ramanathan has covered this topic and references to Idso – not necessarily the same data and not the same paper.
The paper is The Role of Ocean-Atmosphere Interactions in the CO2 Climate Problem, V Ramanathan, Journal of Atmospheric Sciences, 1981. Unfortunately I can’t see a free copy on Google Scholar.
Also the material from the 1981 paper is covered in a review article that is easier to understand: Trace Gas Greenhouse Effect and Global Warming, V Ramanathan, Ambio, 1998. Likewise not currently available free.
At some stage I hope to write about this topic.
The issue of back-radiation vs top of atmosphere radiation is covered to a small extent in the series Understanding Atmospheric Radiation and the “Greenhouse” Effect.
[...] questions and no doubt many people have similar ones. The definition of radiative forcing (see CO2 – An Insignificant Trace Gas? Part Seven – The Boring Numbers) is at the tropopause, which is the top of the troposphere (around 12km above the [...]
[...] a big secret, but really it’s discussed on quite a few AGN-affirming websites e.g. (here and here). If the effect of C on T_s were linear, we’d be talking about a much larger temperature [...]