The Logarithmic Effect of Carbon Dioxide

Guest post by David Archibald

The greenhouse gasses keep the Earth 30° C warmer than it would otherwise be without them in the atmosphere, so instead of the average surface temperature being -15° C, it is 15° C. Carbon dioxide contributes 10% of the effect so that is 3° C. The pre-industrial level of carbon dioxide in the atmosphere was 280 ppm. So roughly, if the heating effect was a linear relationship, each 100 ppm contributes 1° C. With the atmospheric concentration rising by 2 ppm annually, it would go up by 100 ppm every 50 years and we would all fry as per the IPCC predictions.

But the relationship isn’t linear, it is logarithmic. In 2006, Willis Eschenbach posted this graph on Climate Audit showing the logarithmic heating effect of carbon dioxide relative to atmospheric concentration:

And this graphic of his shows carbon dioxide’s contribution to the whole greenhouse effect:

I recast Willis’ first graph as a bar chart to make the concept easier to understand to the layman:

Lo and behold, the first 20 ppm accounts for over half of the heating effect to the pre-industrial level of 280 ppm, by which time carbon dioxide is tuckered out as a greenhouse gas. One thing to bear in mind is that the atmospheric concentration of CO2 got down to 180 ppm during the glacial periods of the ice age the Earth is currently in (the Holocene is an interglacial in the ice age that started three million years ago).

Plant growth shuts down at 150 ppm, so the Earth was within 30 ppm of disaster. Terrestrial life came close to being wiped out by a lack of CO2 in the atmosphere. If plants were doing climate science instead of us humans, they would have a different opinion about what is a dangerous carbon dioxide level.

Some of the IPCC climate models predict that temperature will rise up to 6° C as a consequence of the doubling of the pre-industrial level of 280 ppm. So let’s add that to the graph above and see what it looks like:

The IPCC models water vapour-driven positive feedback as starting from the pre-industrial level. Somehow the carbon dioxide below the pre-industrial level does not cause this water vapour-driven positive feedback. If their water vapour feedback is a linear relationship with carbon dioxide, then we should have seen over 2° C of warming by now. We are told that the Earth warmed by 0.7° C over the 20th Century. Where I live – Perth, Western Australia – missed out on a lot of that warming.

Nothing happened up to the Great Pacific Climate Shift of 1976, which gave us a 0.4° warming, and it has been flat for the last four decades.

Let’s see what the IPCC model warming looks like when it is plotted as a cumulative bar graph:

The natural heating effect of carbon dioxide is the blue bars and the IPCC projected anthropogenic effect is the red bars. Each 20 ppm increment above 280 ppm provides about 0.03° C of naturally occurring warming and 0.43° C of anthropogenic warming. That is a multiplier effect of over thirteen times. This is the leap of faith required to believe in global warming.

The whole AGW belief system is based upon positive water vapour feedback starting from the pre-industrial level of 280 ppm and not before. To paraphrase George Orwell, anthropogenic carbon dioxide molecules are more equal than the naturally occurring ones. Much, much more equal.


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436 Comments
March 10, 2010 8:28 pm

Willis Eschenbach (13:23:52) :
Frank (08:39:47)

2) The absorptions of carbon dioxide, water vapor and other greenhouse gases overlap, making it misleading to say that carbon dioxide contributes only 10% of the greenhouse. As one goes up in altitude (and temperature drops), the relative importance of water vapor and carbon dioxide to the greenhouse effect changes dramatically. Since most heat is removed from the earth’s surface by evaporation (latent heat) and convection to the upper troposphere – NOT by direct radiative cooling to space.

No most surface heat loss is via radiation.
Only the upper troposphere cools mostly by radiation and there CO2 is the most important greenhouse gas. (See Lindzen’s 2007 article.)
Frank, I agree. You can’t just give a single figure. I just went to MODTRAN, which gives the following figures for standard conditions (the ones that MODTRAN opens with except holding relative humidity steady);
Cooling if we remove all GHGs: ~25.2°C
Cooling if we remove CO2: ~12°C
Cooling if we remove H20: ~15.3°C
As you point out, the bands overlap, so removing both gives less than the sum of the individual coolings.
Finally, as you point out this does not include any losses in the system from evaporation or convection.
In other words, on a theoretical Earth, if there were no CO2 in the atmosphere, we’d be about 7°C colder.

Why 7ºC and not ~12°C? And of course according to C-C equation the water vapor would drop to ~65% of its former value (@288K) which of course would cause a further drop in T, let’s say a further 4ºC, now the water vapor’s down to ~50% so it gets a bit cooler, etc. Of course if the initial drop is actually 12ºC then T really plummets!
Well, that is, we would be that much colder if there were no thermostatic mechanism regulating the earth’s temperature.
Well it’s called CO2, we just don’t want too much of it!

Editor
March 10, 2010 9:37 pm

Phil. (20:28:12)

Willis Eschenbach (13:23:52) :

In other words, on a theoretical Earth, if there were no CO2 in the atmosphere, we’d be about 7°C colder.

Why 7ºC and not ~12°C?

Because my mind was on vacation while my fingers were busy working overtime … I’ve fixed it, thanks.
w.

Editor
March 10, 2010 9:41 pm

George E. Smith (17:54:21) : edit


I do appreciate those little (here) thingies you scatter around, specially that one for water emissivity;

Thanks for that. I’m a scientist, I provide citations whenever I can.

March 11, 2010 3:58 am

Henry James
I agree with your last comment 100%. We don’t really know. I have yet to see any proof that CO2 is a greenhouse gas, i.e that the cooling caused by CO2 is less than the warming…..see argument below….
Henry Phil.
I believe we had this argument before.
here is the famous paper that confirms to me that CO2 is cooling the atmosphere by re-radiating sunshine (12 hours per day).
http://www.iop.org/EJ/article/0004-637X/644/1/551/64090.web.pdf?request-id=76e1a830-4451-4c80-aa58-4728c1d646ec
they measured this radiation as it bounced back to earth from the dark side of the moon. Follow the green line in fig. 6, bottom . Note that it already starts at 1.2 um, then one peak at 1.4 um, then various peaks at 1.6 um and 3 big peaks at 2 um.
This paper here shows that there is absorption of CO2 at between 0.21 and 0.19 um (close to 202 nm):
http://www.nat.vu.nl/en/sec/atom/Publications/pdf/DUV-CO2.pdf
There are other papers that I can look for again that will show that there are also absorptions of CO2 at between 0.18 and 0.135 um and between 0.125 and 0.12 um.
We already know from normal IR that CO2 has big absorption between 4 and 5 um.
So, to sum it up, we know that CO2 has absorption in the 14-15 um range causing some warming (by re-radiating earthshine, 24 hours per day) but as shown and proved above it also has a number of absorptions in the 0-5 um range causing cooling (by re-radiating sunshine). This cooling happens at all levels where the sunshine hits on the carbon dioxide same as the earthshine. The way from the bottom to the top is the same as from top to the bottom. So, my question is: how much cooling and how much warming is caused by the CO2? How was the experiment done to determine this and where are the test results? If it has not been done, why don’t we just sue the oil companies to do this research? (I am afraid that simple heat retention testing will not work here, we have to use real sunshine and real earthshine to determine the effect in W/m3 [0.04%]CO2/24hours)
I am going to state it here quite categorically again that if no one has got these results, then how do we know for sure that CO2 is a greenhouse gas?

Francisco
March 11, 2010 5:51 am

Henry Pool (03:58:24) :
I am going to state it here quite categorically again that if no one has got these results, then how do we know for sure that CO2 is a greenhouse gas?
===================
I’ve recently read an article arguing the opposite: i.e. that ALL atmospheric gases are in a sense “greenhouse” gases simply because they are all heated by contact with the surface and then by convection. And anything that is heated (above absolute zero) radiates energy (“heat”) back. The article is here.
http://www.americanthinker.com/2010/02/the_hidden_flaw_in_greenhouse.html
Well I suppose there must be some abysmal reasoning flaws in that article, but the following sounds like a fun thought exercise. Let’s say you eliminate the two main components of the atmosphere, nitrogen and oxygen, plus any trace gases that are transparent to infrared radiation. Now you have an atmosphere whose thickness and density are a tiny fraction of the real one, and is composed only of orthodox greenhouse gases. What would the effect of this radical thinning be on surface temperature? Would it not be a lot cooler?

March 11, 2010 6:51 am

Henry@Francisco
Thanks! Interesting article. I liked it. It makes sense to me. I would indeed argue the same points and possibly evaluate the (so-called) greenhouse gases individually at various concentrations against a constant backround of 20% oxygen and 80% Nitrogen. For my testing there would not be much point in removing that same backround because the reality is that it is here. I think you are right though. My instinct also tells me it would be a lot cooler in the atmosphere without the oxygen and nitrogen.

cba
March 11, 2010 7:02 am

“”
Francisco
… Well I suppose there must be some abysmal reasoning flaws in that article, but the following sounds like a fun thought exercise. Let’s say you eliminate the two main components of the atmosphere, nitrogen and oxygen, plus any trace gases that are transparent to infrared radiation. Now you have an atmosphere whose thickness and density are a tiny fraction of the real one, and is composed only of orthodox greenhouse gases. What would the effect of this radical thinning be on surface temperature? Would it not be a lot cooler?
“”
Eliminate the o2 and n2 and basically, you’ve got Mars. Actually, Mars has more like 40 times the amount of co2 in a column as does Earth’s atmosphere. That’s 5 additional doublings worth of it. The actual Martian warming is under 10 deg C relative to a gray body of the same albedo. That value may be under 5 deg C. The albedo does vary from place to place and potentially time to time. What is going on here though is that the lower total atmospheric pressure is far less and results in far less line broadening which makes the absorption lines narrower and able to capture less total power. Of course, that goes on way up in our atmosphere too where t he pressure is less but not nearer the surface.
The non IR emitting atoms and molecules are doing two things. First, they provide pressure which broadens the lines and permits greater power absorption (and emission). Second, they help store energy temporarily and help disperse it around the general area and to other ghg molecules. Note that there is very little storage capacity in the atmosphere compared to the radiative and convective heat flow.
Ultimately, one has the problem of the geometry. One side (at the bottom) is heated by the surface (via all mechanisms) and on the other side (at the top) it is heated by space radiatively at a temperature of under 3 K. Any slab of air in between with ghgs will absorb some power and it will radiate outward at a rate related to both its absorption ability and its temperature. Were space to be at the same temperature as the surface, then the whole atmosphere would reach thermal equilibrium at that same temperature and there would be absorption from the outbound in a slab as well as the same amount of inbound absorption which would equal the radiated power inbound and outbound from the slab. However, with space effectively at 0 K we get a thermal gradient because energy (power = energy / time) must balance so what comes in from below (plus back radiation from above – if any) must equal what radiates outbound plus what radiates inbound and that means the temperature must be less.

Spector
March 11, 2010 8:58 am

RE: David Archibald (17:17:30) : “That is a very good point. Perhaps the physical chemists amongst us could put that graph together.”
This is an example of the type of chart I had in mind, perhaps zoomed in on the critical 5 to 20 micron range, the Earth thermal radiation band. I believe a linear frequency scale would be the best indicator as radiated energy is proportional to the frequency bandwidth.
http://www.globalwarmingart.com/images/7/7c/Atmospheric_Transmission.png

Francisco
March 11, 2010 9:03 am

I must say after years of following these kinds of discussions from the perspective of a curious layman with some scientific background, that our actual ability to quantify the effect, if any, of a given increase in atmospheric CO2 concentrations — putatively attributed to humans — this ability is just about non-existent at present. This is the only rational conclusion I can reach from the stunningly wide range of divergent opinions and approaches by all kinds of people with a solid background in these matters. I see nothing remotely resembling a “consensus” on ANY of the countless aspects of this puzzle. What I DO see very clearly, is that at every single step of this tottering tower, a particular hypothesis has been selected among many by the official custodians, and that the only guiding principle of each selection is to provide the necessary prop to the next step. Once that’s done, the previous step is canonically considered as “settled”. But nothing at all seems anywhere near settled or well understood, not even the very core of the assumptions. And empirical experiments are conspicuously absent, partly because some of them may be unfeasible, and partly because the high priests are not interested in setting them up. The effect of the whole thing is rather dizzying. I cannot think of any science, except perhaps sociology, endowed with such evanescence and theoretical prestidigitation.
The bottom line is that the core question of this science is the *ideal* question for the construction of an inexhaustible and indestructible BS generating machine, cloaked as Science, if only because a conclusive demonstration that CO2 emissions pose no grave danger seems as impossible as a conclusive demonstration that imps don’t exist. And as long as there remains a political will at the decision making centers, this may just go on and on and on indefinitely.

March 11, 2010 9:35 am

Spector (08:58:04) :
RE: David Archibald (17:17:30) : “That is a very good point. Perhaps the physical chemists amongst us could put that graph together.”
This is an example of the type of chart I had in mind, perhaps zoomed in on the critical 5 to 20 micron range, the Earth thermal radiation band. I believe a linear frequency scale would be the best indicator as radiated energy is proportional to the frequency bandwidth.

Already done, the plot on the top left shows the complete spectrum and the other plots show the result of progressively removing each gas, thus showing the individual contributions:
http://i302.photobucket.com/albums/nn107/Sprintstar400/Atmos.gif

March 11, 2010 9:42 am

cba (07:02:43) :
Eliminate the o2 and n2 and basically, you’ve got Mars. Actually, Mars has more like 40 times the amount of co2 in a column as does Earth’s atmosphere. That’s 5 additional doublings worth of it. The actual Martian warming is under 10 deg C relative to a gray body of the same albedo. That value may be under 5 deg C. The albedo does vary from place to place and potentially time to time. What is going on here though is that the lower total atmospheric pressure is far less and results in far less line broadening which makes the absorption lines narrower and able to capture less total power. Of course, that goes on way up in our atmosphere too where t he pressure is less but not nearer the surface.

As an illustration of that effect are the comparative partial CO2 spectra at Earth/Mars surface conditions:
http://i302.photobucket.com/albums/nn107/Sprintstar400/Mars-Earth.gif

Doug S
March 11, 2010 9:45 am

Well said Francisco. I’m in the same boat with a mere 4 yr. Physics degree, an interested layman at best. The science seems to be far from settled, in fact, it appears to me there is a tremendous value in the ongoing discussion of the science. Those that persist in claiming the “science is settled” are engaging in advocacy politics and not science.

cba
March 11, 2010 10:27 am

Phil,
is that some sort of measured values for Earth vs Martian conditions or is that a synthetic or calculated spectrum from a Hitran database or something similar? Also, is there a particular reason for choosing an 85nm window around 13 microns?
Admittedly, I’ve not looked closely at 13um before and I don’t do frequencies as I prefer wavelengths. I find the Martian graph rather believable. I’m a bit concerned over just how broad the lines are for Earth. They look a little too broad. In fact, they look more like what I would expect in the visible on a scale of maybe 2nm, not 85 nm. That raises the question of is this a one dimensional model or merely a zero dimension, everything at 1 atm pressure, type of model?

March 11, 2010 11:44 am

Henry@Francisco
I agree with your comments 100%. The science on carbondioxide is far from settled.
They always refer to the warming properties and forget or ignore about the cooling qualities. To tell you the truth, if they ever will do the right kind of testing, they will properly find that CO2 causes as much cooling as it causes warming.
I see Phil. did not take my bait again.
But to me it does not really matter anymore. The debate is pointless and unnecessary..
I started my own investigations on global warming in October last year and I already compiled my final report. If you are interested in reading this, here are the results of my investigations/conlusions:
FOR MY CHILDREN, & FAMILY AND FRIENDS LIVING IN THE NORTHERN HEMISPHERE
You may not know this. For a hobby I did an investigation to determine whether or not your carbon footprint, i.e. carbon dioxide (CO2), is really to blame for global warming, as claimed by the UN, IPCC and many media networks. I guess I felt a bit guilty after watching “An inconvenient truth” by Al Gore, so I had to make sure for myself about the science of it all. If you scroll down to my earlier e-mails you will note that I determined that, as a chemist, I could not find any convincing evidence from tests proving to me that CO2 is indeed a major cause for global warming. As my investigations continued, I have now come to a point where I doubt that global warming is at all possible…. Namely, common sense tells me that as the sun heats the water of the oceans and the temperatures rise, there must be some sort of a mechanism that switches the water-cooling system of earth on, if it gets too hot. Follow my thinking on these easy steps:
1) the higher the temp. of the oceans, the more water vapor rises to the atmosphere,
2) the more water vapor rises from the oceans, the more difference in air pressure, the more wind starts blowing
3) the more wind & warmth, the more evaporation of water (evaporation increasing by many times due to the wind factor),
4) the more evaporation of water the more humidity in the air (atmosphere)
5) the higher the humidity in the air the more clouds can be formed
6) Svensmark’s theory: the more galactic cosmic rays (GCR), the more clouds are formed (if the humidity is available)
7) the more clouds appear, the more rain and snow and cooler weather,
8) the more clouds and overcast conditions, the more radiation from the sun is deflected from the earth,
9) The more radiation is deflected from earth, the cooler it gets.
10) This cooling puts a brake on the amount water vapor being produced. So now it is back to 1) and waiting for heat to start same cycle again…
Now when I first considered this, I stood in amazement again. I remember thinking of the words in Isaiah 40:12-26.
I have been in many factories that have big (water) cooling plants, but I realised that earth itself is a water cooling plant on a scale that you just cannot imagine. I also thought that my idea of seeing earth as a giant (water) cooling plant with a built-in thermostat must be pretty original….
But it was only soon after that I stumbled on a paper from someone on WUWT who had already been there, done that …. well, God bless him for that!
i.e. if you want to prove a point, you always do need at least two witnesses!
Look here (if you have the time):
http://wattsupwiththat.com/2009/06/14/the-thermostat-hypothesis/
But note my step 6. The Svensmark theory holds that galactic cosmic rays (GCR) initiate cloud formation. I have not seen this, but apparently this has been proven in laboratory conditions. So the only real variability in global temperature is most likely to be caused by the amount of GCR reaching earth. In turn, this depends on the activity of the sun, i.e. the extent of the solar magnetic field exerted by the sun on the planetary system. We are now coming out of a period where this field was bigger and more GCR was bent away from earth (this is what we, skeptics, say really caused “global warming”, mostly).
But apparently now the solar geomagnetic field is heading for an all time low.
Look here:
http://wattsupwiththat.com/2010/01/07/suns-magnetic-index-reaches-unprecedent-low-only-zero-could-be-lower-in-a-month-when-sunspots-became-more-active/
Note that in the first graph, if you look at the smoothed monthly values, there was a tipping point in 2003 (light blue line). I cannot ignore the significance of this. I noted similar tipping points elsewhere round about that same time, (e.g. in earth’s albedo, going up). From 2003 the solar magnetic field has been going down. To me it seems for sure that we are now heading for a period of more cloudiness and hence a period of global cooling. If you look at the 3rd graph, it is likely that there wil be no sun spots visible by 2015. This is confirmed by the paper on global cooling by Easterbrook:
http://wattsupwiththat.com/2008/12/29/don-easterbrooks-agu-paper-on-potential-global-cooling/
In the 2nd graph of his presentation, Easterbrook projects global cooling into the future. These are the three lines that follow from the last warm period. If the cooling follows the top line we don’t have much to worry about and the weather will be similar to what we had in the previous (warm) period. However, indications are already that we have started following the trend of the 2nd line, i.e. cooling based on the 1880-1915 cooling. In that case it will be the coldest from 2015 to 2020 and the climate will be comparable to what it was in the fifties and sixties. I survived that time, so I guess we all will be fine, if this is the right trendline.
Note that with the third line, the projection stops somewhere after 2020. So if things go that way, we don’t know where it will end. Unfortunately, earth does not have a heater with a thermostat that switches on if it gets too cold. Too much ice and snow causes more sunlight to be reflected from earth. Hence, the trap is set. This is known as the ice age trap. This is why the natural state of earth is that of being covered with snow and ice. This paper was a real eye opener for me:
http://wattsupwiththat.com/2009/12/09/hockey-stick-observed-in-noaa-ice-core-data
However, man is resourceful and may find ways around this problem if we do start falling into a little ice age again. As long as we are not ignorant and listen to the so-called climate scientists whose agenda’s depend on money. A green agenda is still useless if it has the wrong items on…
Obviously: As Easterbrook notes, global cooling is much more disastrous for humans than global warming.

Francisco
March 11, 2010 1:03 pm

Henry,
Yes, that the system must be governmed by negative rather than positive feedbacks seems to be supported by the relatively narrow range of temperature fluctuations in the past, in the face of great fluctuations in other factors, including a much dimmer earlier sun etc.
If you have not seen it, the following half-hour talk by Richard Lindzen makes the main points very well.

Reading a couple of Lindzen papers was in fact how I began to get interested in this topic a few years ago.
There are further basic aspects of the whole thing that I seldom see discussed because they are assumed to be essentially correct, but I have many doubts. The carbon cycle for example, and the modelling assumption that the small amount of human emissions (i.e. small with respect to the total transfers between the different parts of the system) will not be taken by the huge sinks, seems hard to understand.
Consider some more or less official figures of the carbon cycle from the following NASA chart (I should add I once saw a similar IPCC chart with similar figures, and the disclaimer that the expected errors were in the order of more than 20%
http://nasascience.nasa.gov/earth-science/oceanography/ocean-earth-system/ocean-\
carbon-cycle
that chart gives the following totals for carbon in the system:
the atmosphere 760 PgC (increasing at a rate of about 3 PgC per year)
the ocean surface layers 800 PgC
the deep ocean 38,000 PgC
plants and soils 2,000 PgC
We see that the human contribution of 6.5 Pg per year is a very small fraction of the total turnover between the atmosphere and the soil/plants and between the atmosphere and the oceans, according to the chart. (And it is only 0.015% of the total carbon in the system.)
It is well know that the plants do take extra CO2 if it becomes available. That’s why you get this
http://wattsupwiththat.com/2008/06/08/surprise-earths-biosphere-is-booming-co2-the-cause/
Yet they apparently model all this by assuming that the biomass intake of CO2 is static. This is like assuming a herd of animals will always eat exactly the same amount of food, regarding of how much is available. It is beyond absurd, if true.
Regarding the oceans. I still don’t understand well the extent to which Henry’s Law should be strictly applied to the atmosphere-ocean system. But if it is applied, well then you have a current distribution of 38,800 Pg in the oceans vs 760 in the atmosphere, according to the chart above. That is about 50 to 1. Or 98% in the oceans and 2% in the atmosphere. Assuming this arrangement represents partial pressure equilibrium, then any additional CO2 released in the atmosphere will find itself distributed in the same way (eventually) at roughly the current temperature. I suppose the only question is to find out what “eventually” means. Much is made of the fact that the oceans will release CO2 when warmed up, but the attempts I have seen at quantifying this show it is very little. Lubos Motl had a post some time ago where he calculated roughly that you need a huge 8 deg C increase in temperature to produce something like 100 ppm increase in CO2. So this is clearly insignificant. So roughly 98% of any human released CO2 will eventually find its way to the oceans (assuming there are no plants who also want a piece of the pie.) Or, put another way, a permanent doubling of atmospheric CO2 would require (eventually) a doubling of ocean CO2 – which is a physical impossibility: there simply isn’t enough carbon around.
It seems to me that we are assuming the trickle of a dripping human faucet will not go through the huge sinks of that vast pool. If you’ve ever seen one of those long-tongued, insect-eating animals, it seems to me the system will treat our CO2 contribution with the same calm disregard as those animals swallow a little mosquito within reach of their tongue – and without a second thought.
Again, if the total amount of available fossil fuels in the ground (gas, oil and coal) is 5,000 Pg (according to the same chart above), where are we going to get the extra 39,000 Pg of carbon needed to double the amount in the oceans, if the atmospheric concentration is to be also permanently doubled.? Where indeed?
Further, it is perfectly possible that natural variations in the CO2 cycle are of a magnitude larger than our contribution. Much is made of the human “signature” based on the proportion of C13 and so on. But I’ve seen comments (one by Roy Spencer, I think) saying this signature is not necessarily ours.

March 11, 2010 1:17 pm

cba (10:27:51) :
Phil,
is that some sort of measured values for Earth vs Martian conditions or is that a synthetic or calculated spectrum from a Hitran database or something similar? Also, is there a particular reason for choosing an 85nm window around 13 microns?

Hitran, I chose a small enough window to show the individual lines.
Admittedly, I’ve not looked closely at 13um before and I don’t do frequencies as I prefer wavelengths. I find the Martian graph rather believable. I’m a bit concerned over just how broad the lines are for Earth. They look a little too broad. In fact, they look more like what I would expect in the visible on a scale of maybe 2nm, not 85 nm. That raises the question of is this a one dimensional model or merely a zero dimension, everything at 1 atm pressure, type of model?
As listed at the side of the plots it’s at surface conditions pathlength 1km.
I just reran it to see if I’d goofed on any of the parameters, seems OK.

Colin Davidson
March 11, 2010 1:35 pm

Phil wrote at 20:24:16, 9th March:
“Bad math(s) and physics, it isn’t only the radiant energy that can return to the surface, it all can! So more correct accounting is:
390+24+78= 492 out
324=66% back
So as far as the atmosphere is concerned, it gets its energy from the surface in the following proportions:
Latent Heat: Three Fifths 16%
Conduction: One Fifth 5%
Radiation: One Fifth 79%
When the surface warms, the Radiation proportion decreases increases as T^4 and the Latent Heat proportion increases as e^(4900/T).

I think we are arguing semantics. However there is a point.
The NET flux into the atmosphere due to photon absorption is, on these numbers, 26W/m^2.
This enters the atmosphere at a different level to the other two fluxes: Conduction enters at ground level. Latent heat enters at cloud level. But the majority of absorption of surface radiation is in the first 250m of the atmosphere – more close to the ground and roughly exponentially less the higher you go. Similarly the back radiation mostly originates from this close to the ground layer. (One can quibble with this – obviously this is not true for the “wings” – but it is true for all major emission lines. The greenhouse effect is pretty much done and dusted by 500m as far as the surface is concerned.)
As the surface temperature goes up, so evaporation increases and the NET radiation from the surface decreases. For an increase of 3DegC, the latent heat transfer increases between 6 and 16 W/m^2 (depending on who one believes for the rate of evaporation increase). The NET radiation decreases by the same amount (otherwise the surface enegy fluxes don’t balance).
So as the surface temperature rises, the net energy flux into the very lowest portion of the atmosphere (conduction+radiation) drops by between 12% and 32%, and the energy flux into the clouds increases by between 6% and 20%.
I didn’t understand the comment: “it isn’t only the radiant energy that can return to the surface, it all can!”, I wonder if Phil could expand that thought.

DeWitt Payne
March 11, 2010 2:52 pm

Re: cba (Mar 11 10:27),

is that some sort of measured values for Earth vs Martian conditions or is that a synthetic or calculated spectrum from a Hitran database or something similar?

I can get similar spectra using Spectracalc, which does use the HITRAN 2004 database. But I was only able to replicate his Mars spectrum at a path length of 1,000,000 cm, not the 100,000 that appears next to his graph. And the Earth graph was 100 cm.

Spector
March 11, 2010 3:32 pm

For the moment, rather than get involved in complex transmission calculations, I would like to concentrate on just how CO2 just affects the basic transparency of the atmosphere in the critical band for radiating heat from the Earth’s surface.
On the Bill O’Reilly show, for example, a few weeks back Bill Nye presented a linear darkening model which implied that each parcel of CO2 added to the atmosphere was having a uniform additive effect over the whole band.
On the other hand, what I see from absorption data plots is that CO2 only blocks transmission at specific frequency or wavelength bands and at these bands we already have zones of 100% absorption of IR emitted from the surface. It appears that all we are getting from added parcels of CO2 is a minor and diminishing increase in the width of these blocking bands.

cba
March 11, 2010 3:39 pm

Phil,
Hitran is a line database. I didn’t think it had any internal line width calculations etc. What software did you use to create a spectrum? Also, using a 1km single pressure thickness layer is not going to provide accurate results.

DeWitt Payne
March 11, 2010 8:07 pm

David Archibald,
You know, if you have a logarithmic response, you really shouldn’t use a linear plot.
I calculated Iout and surface temperature required for Iout to be equal to that at 375 ppmv CO2 with MODTRAN for CO2 levels ranging from 0.01 to 2000 ppmv using the 1976 standard atmosphere and constant relative humidity, 100 km altitude looking down, all other conditions default. Plotting both using a logarithmic axis for the CO2 concentration gives this graph. As you can see, the response isn’t logarithmic at all concentrations. Nor would one expect it to be. At low concentrations, less than 0.1 ppmv, the response is nearly linear. It becomes logarithmic by 10 ppmv and the slope is constant to 2000 ppmv. That doesn’t qualify as “tuckered out” to me. The temperature sensitivity to doubling the concentration is 1.22 degrees for 10 ppmv to 2000 ppmv. The change in forcing for doubling CO2 is 2.86 W/m2. That’s less than the IPCC value because this is calculated for the top of the atmosphere rather than at the tropopause, clear sky conditions and the stratosphere has not been allowed to equilibrate to the change in CO2, as is done to calculate the IPCC forcing.
Re: cba (Mar 11 15:39),
Those line widths are valid for the surface pressure only.

cba
March 11, 2010 8:29 pm

spector,
it’s an extremely complex situation in some ways. Nye is doublessly full of it. depending upon the overall pressure and the total amount of ghg atoms in the atmospheric column, there are effects. At low presures, the individual lines are quite narrow and tall. at higher pressures, the bands widen out with less of a peak. they differ by line as to just how wide the line is and how tall it tends to be. Many are quite potent requiring only a few cm of length to block practically all of the power at the peak. THere are thousands of these lines, some forming bands. The net result is pretty much described. At the tropopause, one loses an additional 3.7w/m^2 for a doubling of co2. At higher altitudes, some of that loss is made up. This is only relevent to clear sky paths which is less than half of the total.
some factors that seem not to be taken into account include that when clouds are present, one has the re-emission of a continuum from the top level. This is above most all of the h2o vapor, some of the co2, and a fair amount of the highest pressures.
that co2 absorbs in the atmosphere (and it also emits) is not really where there are problems. The real factors are associated with the sensitivity and with cloud & h2o vapor cycle contribution. One can see there is about 150 w/m^2 of blocked outgoing radiation and that this is associated with 33 deg. C of temperature rise. That amounts to a very low sensitivity. factors like cloud albedo tosses in a great deal of unknown into many facets.

March 11, 2010 8:56 pm

DeWitt Payne (14:52:37) :
Re: cba (Mar 11 10:27),
is that some sort of measured values for Earth vs Martian conditions or is that a synthetic or calculated spectrum from a Hitran database or something similar?
I can get similar spectra using Spectracalc, which does use the HITRAN 2004 database. But I was only able to replicate his Mars spectrum at a path length of 1,000,000 cm, not the 100,000 that appears next to his graph. And the Earth graph was 100 cm.

That’s odd, I ran it again through Spectralcalc using the same parameters and got the same results.
cba (15:39:30) :
Also, using a 1km single pressure thickness layer is not going to provide accurate results.

I didn’t do the calculation to simulate a full vertical traverse through the atmosphere, I just did it to contrast the broadening of the spectral lines on Mars and Earth, for which it’s adequate.
Spector (15:32:27) :
For the moment, rather than get involved in complex transmission calculations, I would like to concentrate on just how CO2 just affects the basic transparency of the atmosphere in the critical band for radiating heat from the Earth’s surface.

That’s what I showed you, it results in an ~log response.

Glenn Tamblyn
March 12, 2010 12:02 am

davidmhoffer (20:11:38)
“The argo buoys have been sampling ocean heat for four years now and show a decline in each year. That’s some lag”
Actually they have been sampling reliably since 2003. And deployment of them started earlier. Prior to that we had sampling from XBT’s going back several decades. See Domingues et al 2008
As to the supposed cooling reported, that was reported in Levitus et al 2009. There study only looked at the top 700m of the ocean. Von Schuckmann et al 2009 looked at Argo data down to 2000 m since 2003 and showed continued warming for that body of water. The upper layers may have plateaued of dropped a little but the total down to 2000m is still warming.
George E Smith (19:25:01)
“I would aprpeciate a citation”
Try this discussion over at RealClimate by RayPierre Humbert:
http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument-part-ii/
“The assumptions are mind boggling. Surface emitted LWIR is uniform and constant all over the earth, and CO2 distribution is the same all over the earth, and nothing else has any say in what the Temperature of the atmosphere is, and somehow the Temperature of the atmosphere sets the surface temperature of the earth. Meanwhile the most common molecule on the planet, just sits by and lets all that happen”
And exactly how do you know what the assumptions used in climate models actually are? Simple question. Are you critising something based on how you THINK it is done, rather than ACTUAL KNOWLEDGE of how it is really done. And if you have actual knowledge of how they do it, care to share your sources.
General rule; Chinese Whispers from the Blogosphere doesn’t count as knowledge. A lawyer would dismiss it as uncorroberated hearsay.

March 12, 2010 8:36 am

Francisco
“Much is made of the fact that the oceans will release CO2 when warmed up, but the attempts I have seen at quantifying this show it is very little. Lubos Motl had a post some time ago where he calculated roughly that you need a huge 8 deg C increase in temperature to produce something like 100 ppm increase in CO2”.
Henry@Fransisco
I doubt this. We were taught at college that to get rid of CO2 in the water you have to boil it.But I am sure just a bit of heat would do the trick. Remember that the heat is transferred from the top to below, so the temp. of the top layer may well be initially a lot higher, releasing CO2. There is also the effect of wind and storms, causing release of CO2 in the atmosphere due to vacuum boiling…etc.
There was a prof. in Australia who charted the lagging of CO2 increases after warming, I think his name is Bob Carters or Carteres. His studies were quite convincing.
There is also my question whether a general increase in the salinity of the oceans ( for example, also more carbonates) due to human activities, could trap more heat in the oceans? I don’t know. Have not seen any studies on it and certainly nobody has ever mentioned to me this possibility, as a reason for global warming. I doubt that conductivity of the oceans has been measured on a scale as temperature has.