a problem many have is how can 1 CO2 hiding in 2500 molecules absorb all that 15 micron radiation? we know it does, so the q is, how “wide” are the IR photons that are getting absorbed relative to the 2500 molecules in the atmosphere the CO2 molecule is hiding in?

By my rough calculations (using PV = nRT, with P = .5 atm, and T = 300) the 2500 N2s, O2s and others, take up about 2.04*10^-23 cubic centimeters, so should have one side on the order of 10^-8 cm.

So, if the “width” (the magnitude of the E and B fields?) is on the order of 15*10^-6m = 15*10^-4 cm, each IR photon would be 4 orders of magnitude “wider” than the 2500 molecules that each CO2 molecule is hiding in… so the very high absorption of 15 micron IR, as seen from satellites, would make sense…

Yes, I’ve been harassing/harassed by a denier who understands CO2 can absorb IR, but refuses to understand it happens significantly in the atmosphere…

thanks again for the site

]]>Take a look at Do Trenberth and Kiehl understand the First Law of Thermodynamics?.

A nice simple example of how internal temperatures can increase way above the external temperature.

]]>We know energy cannot be created or destroyed, therefore we can conclude that the total amount of energy that will be emitted by the GHG in the atmosphere is exactly equal to the amount absorbed.

That is, there is an upper limit on the energy that can be emitted…ever. This implies an upper limit on future temperatures. Right?

]]>The optical thickness and, hence, the thickness of the air layer, (La), (as well as the number of the consecutive air layers satisfying the condition for the optical thickness) is a function of concentration of CO2 in air. The surface layer loses energy to the adjacent air layer by conduction, convection and radiation. In the case of water we must add also evaporation, but let’s omit this problem here. The adjacent layer transports heat to the next air layer by the same mechanisms. It emits also the radiation in the direction of the surface layer. However, if the temperature of the surface layer is higher than that of the air layer, the net energy flow, F, in W/m^2, will be always in the direction from the surface to the air layer.

In the case when the difference between the temperature, Ts, of the surface layer and that, Ta1, of the adjacent air layer is relatively small, the flow of energy from the surface to the air layer might be approximated by

F = P/A = b1(Ts – Ta1) + o(Ts^4 – Ta1^4) = (b1 + b2)(Ts – Ta1) (1)

where b1, in W/(K*m^2), relates to the heat transfer via convection and conduction while b2 relates to radiation.

The outflow of energy from the surface layer will decrease its temperature Ts by

Ts – dTs =Ts – [F/(cs)(rs)(Ls)]dt (2)

where (cs) is the specific heat, (rs) is density and Ls is thickness of the surface layer. Ls increases with time t proportionally to sqrt(a*t) where a is the thermal diffusivity of the soil or water.

10% of F, ie 0.1F, is absorbed by the air layer due to CO2 molecules, which leads to the increase of the temperature Ta by

Ta1 + dTa1 = Ta1 + [0.1F/(ca)(ra)La]dt (3)

where (ca) is the specific heat at constant pressure and (ra) is density of air.

The similar equation is obtained for the heat flow from the first optically thick air layer to the next one where we have to use Ta1 for the (first) air layer and Ta2 for the second one and so on along the height of the atmosphere. Since Ta1>Ta2, the heat exchange between these layers will lead to the decrease of the temperature of Ta1 by dTa12, so that the temperature of the first optical layer changes by

Ta1 + dTa1 – dTa12 (3)

where dTa12 must take care of the change of Ta2 due to the exchange of heat between layer 2 and 3 and so on.

The increase of Ta1 leads to the increase of the radiation from the layer to the surrounding, which means that 50 % of this increase, that’s

0.5o[(Ta1 + dTa1 – dTa12)^4 – Ta1^4] = 0.5o[4*Ta1^3*(dTa1- dTa12)] (4)

should be added to the downward radiation to the surface.

This means that after time dt, Ts has changed to Ts – dTs, Ta1 has changed to Ta1 + dTa1 – dTa12, (b1 + b2) has reduced by the amount given by (4) and (1) has decreased due to all these changes.

This is clearly a tough problem for the computer enthusiasts. The problem resembles a hound trying to catch its own tail. And while the hound problem will finish when the hound had caught its tail, the heat problem will finish when Ts had “caught” Ta during the nighttime (if one believes that this can happen) or when the Sun has started to shine on our CO2 plagued world and affected the changes of Ts and Ta so that it is now Ta that is trying to “caught” the flying (increasing) Ts.

Can we draw any conclusions without performing all these (still much simplified) calculations? Well, more or less if we know La and its dependence on the increase of CO2.

For instance, we might choose dt = 1s, La = 300 m, Ts – Ta = 2K, b1 + b2 = 15 W/(K*m^2). By applying the standard thermal properties of air and water we get

dTs = 0.019 K for the water layer of thickness Ls = 3*10^(-4) m

dTa1 = 7*10^(-6) K for the air layer

while the increase of the downward radiation is below 2*10^(-5) W/m^2.

One can now compute, if one bathers, the changes during the night time respectively daytime as well as double thus calculated values if the doubling of CO2 leads to the decrease of La1 by a half.

]]>Thanks for your response; apologies for the delay in mine. I see a fundamental difference between the greenhouse effect and my stylised “bottleneck”. The greenhouse effect as espoused by IPCC reflects purely radiative means of energy transfer – GHGs block outgoing longwave and back-radiate some of it to the surface with the effect that the surface becomes warmer than it would otherwise be. Increasing GHG concentration amplifies this effect.

The bottleneck, on the other hand, reflects energy transport by molecular collision, specifically the relatively low probability of collision and energy transfer between the trace GHGs and the bulk non-radiative elements of the atmosphere. Increasing GHG concentration in this case, in contrast with the greenhouse effect, increases the probability of collision, eases the bottleneck and enhances the system’s cooling performance. Increasing CO2 concentration, the IPCC villain, thus has two opposing effects on surface temperature.

We could add a third effect (which gets a mention in Sod’s most recent article): CO2 also absorbs (and emits) in the shortwave part of the radiative spectrum, reducing the solar flux at the surface, a cooling effect. My hope is that, as Sod rolls out the current suite of articles, how the RTE takes account of these three effects becomes clear. Perhaps it alread has – I haven’t caught up as yet.

]]>I have missed your comment on January 30. I have caught sight of it this morning. You are of course correct, I have discovered it by myself, too, and have presented a modified picture in my post on February 2 at 9:46 am.

After reading your comment, I have also “googled” to find more information about Schwarzschild equation and found it at

http://www.barrettbellamyclimate.com/page45.htm “Barrett Bellamy Climate, Schwarzschild’s Equation”.

What has really surprised me most was that I have constructed (in 9:46 am) more or less the same picture of the radiative transport process as it is given in Barrett. Therefore, I must conclude that the entire climate subject must be extremely simple if I could come so close to the correct description in view of the extremely limited intellectual capacity of mine. However, even this small achievement of mine would be not possible at all without your kindly mentioning about the Schwarzschild equation (on January 28, at 8:59 pm), which I had no idea about previously (even if I had some intuitive feeling for what one might expect).

If I am allowed to bath in the light of this greatest success in my life, then I can come with some more comments (probably totally irrelevant, as usual).

The contribution of CO2 to the climate is related to the “absorption area” below the 288K Planck curve and down to the 220K one. 50% (plus minus) of the energy corresponding to this area is expected to contribute to the changing in the state of the climate system (the other part will be emitted out of the system). This amount of energy is easy to find, either by computation or by the graphical methods. One might be tempted to claim that such a found value is the evidence as to the “saturation” of the influence of CO2 on the climate, as I stated in one of my previous posts, (the “saturation” means in this connection the no more effect will be observed if adding the additional amount of CO2 to the air). However, this is not the case if the addition of CO2 is resulting in the increase of the downward radiation due to the increase of the temperature of the first optically thick layer (i.e. the layer being closest to the surface), which will increase the temperature of the surface and, hence, refer now the upward radiation to this new temperature. This will raise the “tooth” curve from 288K level to a somewhat higher one. The lower part of the absorption band will be raised, too, but the net result will be still the increase of the “absorption area”. Barrett paper presents the number 1.3K for the doubling of CO2 (with all the other effects being neglected) and is mentioning also 0.07K per decade in the tropic region as due to the increase of CO2, but I am not competent to make any comments on these numbers. How much this increase of the temperature of the air will increase the temperature of the lands and oceans is depending on the heat capacity of water and soils, their thermal conductivity and the convectional and evaporational processes in the oceans. I am tempted, however, to agree with Barrett that the total effect of the increase of CO2 must be relatively small since it is masked effectively by the observed oscillations of the average temperature of the climate system being due to the other agents.

The mentioning of the wings within the absorption band of CO2 would indicate that the enriching of the atmosphere by CO2 is leading to the broadening of the absorption band (which I have difficulty to apprehend since the broadening of the width of the band is mostly the result of the Doppler effect and molecular collisions). Or I am completely out of the track? Anyhow, the increase of the absorption area due to the wing story would certainly increase of the amount of energy being consumed by the atmosphere.

I have some more comments but my post had become already too long (as usual).

]]>Namely, what happens above the height (La) at which all the surface photons within the absorption band of CO2 have been absorbed, i.e. between La and Lt where Lt is the end of the troposphere?

Assume first that we have no CO2 molecules along the pass of propagation in the upward direction above La. The observer studying the outgoing spectrum at the level Lt will found that the intensity of the band line of CO2 corresponds to that for the radiation at the temperature at La. This is because the air within this column would allow all the radiation emitted at La to propagate up to Lt unaffected, compare the Schwarzschild equation.

If we now start to put CO2 molecules inte the region between La and Lt, then the intensity of the observed band line at Lt will start to decrease. If we fill the region with the number of CO2 corresponding to the optical thickness within the band of absorption, then the intensity of the measured band line will drop to that corresponding to the intensity at the temperature of Lt. This means that all photons within this band emitted from the level La have now been absorbed, a part of them have been thermalized, which has contributed to the increase of the temperature of the air within the layer between La and Lt. If we continue to increase air by CO2 molecules, then the optical thickness will be reached at La1, where La1<Lt, and we are now back to the same situation as we had at La but now with the start at the temperature at La1 and so on.

Conclusions? The enriching of the atmosphere by CO2 leads to two effects:

A. It moves La down, which means that the energy (within the absorption band of CO2, constituting about 10 % of the total upward radiation) delivered by the upward radiation from the surface will now heat a somewhat lesser air mass, which gives a slightly higher increase of the temperature than previously. 50% of this absorbed energy might be re-emitted down (within the wavelengths of the total spectrum of thermal emission at the new temperature) and 50% up.'

B. 10% of the energy emitted from the (imaginary) surface at La will be absorbed within the next optically thick layer for the rotational band of CO2, i.e. between La and La1, 50% being emitted down and 50% up as in the point A above, and so on until the level Lt is reached.

If this picture is correct then the saturation effect will be reached when all the atmosphere is consisting of CO2.

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