1. Al Tekhasski says:

The author writes:
"The heat the Earth must radiate for balance is 240 / (1 – a/2), where a = the radiation absorption fraction. If the absorption is 75 percent, when a is 0.75, then the value for the Earth’s radiation is 240 / (1 – 0.375) or 384 with 75 percent or 288 being absorbed, and one half or 144 being sent back to Earth."

So, the author's model describes the "sent back" radiation as 144 W/m2. However, this quantity is routinely measured by meteorologists in many places on Earth, for example: http://www.urbanclimate.net/matzarakis/papers/Izi
See Table 2, or Fig.7 or many other figures.

Here is a standard precision tool to conduct these measurements of "downwelling longwave irradiance", http://www.eppleylab.com/PrdPrecInfRadmtr.htm

It appears that the measured radiation varies with weather and is in the range of 200-450W/m2. These are the data for several particular sites. Some other climatologists researched the subject and found the global average as being about 333W/m2. This experimentally obtained number is 2.3X bigger than Mr. Petschauer's theory suggests. I wonder how the author is willing to re-conciliate this substantial discrepancy with reality?

Seriously, the presented work is a primitive account of earliest models of radiative equilibrium, 1-layer model, where the absorbed radiation gets emitted "half-way up" and "half-way down". It is well-known that it is absolutely inadequate to reality and cannot be used for any serious estimations of climate sensitivity. It is only used as educational tool in classrooms of sophomores for illustrative purposes only.

2. TomVonk says:

Mr Petschauer

I will only comment on the Figure 4 because it concentrates many of the confusions due to a wrong interpretation of "saturation" that are quite common.

You wrote:
Now it can be seen that only the CO2 region above the water vapor line will make any change in the total heat absorbed, thereby reducing the increase of absorption with increasing amounts of CO2.

This is very incorrect.
To see why, one has to think 5 minutes what the Y Axis means.
It is a percentage of absorbed energy for a given thickness of the atmospheric layer.
Clearly this percentage is not the same if you consider a layer of 1 µm or 1 km.
So let's suppose that the Figure 4 was established for 1m – it is not important how much it really is, it is only important that this thickness is some number.

So does that mean that because after 1m H20 is able to absorb 100% of energy for some wavelength , CO2 absorbs none of this wavelength ?
Obviously it doesn't.
It is enough to just consider the first mm of the 1 m layer and the wave length of 18 µ.
In this first mm H20 will absorb much less than 100%, let's say only 1%.
That leaves more than enough radiation, namely 99% for the CO2 to absorb.
CO2 will of course absorb much less than the 1% that H2O absorbs but it will absorb whatever it must.

So now proceed to the second mm.
There is still enough of the original (the one coming from the ground) radiation at 18µ for both H2O and CO2.
On top, as you rightly said in the beginning of the paper emissivity = absorptivity so to the "original" radiation adds the radiation that has been emitted both by the CO2 and H20 of the first mm layer.
As you go up mm by mm, you notice that every mm layer has always enough of 18µ radiation to be absorbed (and remitted!) both by H20 and CO2.
When you arrive at last at the 1000th mm layer for which the Figure was established you will observe that there is indeed nothing left from the "original" radiation (e.g all photons originating from the ground have been absorbed) yet you have still the same amount of 18µ photons to be absorbed but originating from reemissions in the layers 1 through 999.

Actually without surprise you will observe that the total 18µ radiation 1m up from ground is the same as it was on the ground.
The 100% number on the Figure has nothing to do with some "saturation", it just means that the original photons finish all by being absorbed after some length.
But as they are replaced by reemitted photons of the same wavelength, the Figure 4is without much interest and certainly doesn't mean that … only the CO2 region above the water vapor line will make any change in the total heat absorbed

3. Richard Petschauer says:

Background
First some background on this paper. I did not write it for climate scientists, but for the public especially for those with a technical background. The reason was to inform them about some basic facts on the role of carbon dioxide relative to global warming to counteract the bad information passed on by main stream media from so called scientists. Things like impending tipping point in a few years unless we take immediate action. The “350 Club” that claims we must very soon reduce global CO2 concentration to 350 ppm. Al Gore claiming the planet has a fever and the science is settled that man made global warming will cause irreversible damage very soon, etc. That CO2 is forming a heat trapping blanket that will soon raise surface temperatures to levels never seen before. Pictures of smoke stacks belching dark gray clouds next to an article about CO2, the images implying that perhaps black carbon is being emitted, when CO2 is invisible and odorless. My main objective was to counteract an incorrect and misleading mental picture the media was creating.
There are two messages in the paper: one is qualitative, the other quantitative. Please judge my paper on each separately.

Qualitative Picture of CO2 "Heat Trapping”
My paper shows that rather than a blanket that covers the complete atmosphere and capturing a major portion of the heat leaving the surface, it is limited to about 20% of the spectrum and over about 90% of that range it is already absorbing all of it. This is depicted in Figures 1 and 2. Based on what I had heard, it was an eye opener to me! When I doubled the CO2, the difference was so small that a separate line showing the added absorption in Figure 2 could not be seen. So I added Figure 3 expanding the scale around the 15 micron wavelength region to show the relative small absorption with increased CO2 for several doublings, demonstrating the well known approximate log relation of absorption or forcing with CO2 concentration. Figure 4 then shows the overlap with water vapor, another significant factor. I have not seen this action so clearly shown any other place. Please tell me what is wrong with Figures 1 to 4. Or did you stop reading before that?

Quantitative Evaluation of CO2 Warming
First, if a person reads the paper it does show that water vapor feedback is included. Not included are negative lapse rate feedback, that IPCC estimates is somewhat larger than that of positive feedback from albedo and CO2 itself. Clouds were handled in a different way, and there is not agreement if clouds cause positive feedback as IPCC estimates.

The statement “Data shows that present concentrations of CO2, a strong absorber, are already well above the saturation value at its principal wavelength, so increases in it have a relative small affect.”, may have been misunderstood, but in the same sentence it says there are still increases. Perhaps the wording should be “above where saturation begins”. But I think this is nit picking. In discussing Figure 1 from Wikipedia this is clarified and again shown clearly in Figure 3.

Regarding the back radiation of only 140 Wm-2, the reason this value was selected is explained below.
Granted, the method used here is a simple one. It considers only a clear-sky case, with cloud action estimated separately later. We estimate about 74% combined absorption from water vapor and CO2. A total of 77% absorption results from assumed 3% being added by other greenhouse gases. In the Kiehl
and Trenberth 1997 paper on the Earth’s Annual Global Mean Energy Balance, they estimate 99 of 390 Wm-2 through the atmospheric window with clear skies, corresponding to about 75% absorption. The one half of the absorbed radiation being sent back to the surface and one half being transmitted to space was selected to provide a surface radiation of 390 Wm-2, corresponding to the present 15C estimate of global temperature and a net incoming solar radiation rounded to 240 Wm-2 (compared to the IPCC estimate of 236 Wm-2).
This method ignores atmospheric shortwave absorption including in clouds and sensible and latent heat transfer from the surface. Part of this heat and back radiation from clouds are not included which accounts for less longwave back radiation than actual values in the range of 324 Wm-2. According to the Kiehl and Trenberth 1997 paper and a 2009 update, the actual fraction of the total heat absorbed by the atmosphere radiated back the surface including that from clouds is about 66%, compared to the 50% used here. Again 50% was used here to provide surface temperature close to the estimated actual value. My estimate of 0.55 C including feedback for 2x CO2 is low, but I am convinced it is a lot closer to the real value than the IPCC central value of 3.2C. My current estimate is about 0.8C based on my latest much more complete model that uses the estimates from Kiehl and Trenberths of 1997 and 2009 as the starting point with forcing perturbations of various types applied. A significant factor now being ignored is the negative feedback caused by surface evaporation latent heat being moved to the atmosphere.

The Saturation Problem
TomVonk provided some thoughtful comments regarding the “saturation” of CO2 and my Figure 3. As stated in the paper it is for a 10 km path in a standard atmosphere at an angle of 45% representing a typical path. It only shows initial absorption, not upward reemission and absorption of “later generations” of which I was aware. My thinking was that only radiation back from the atmosphere that reaches the surface can cause warming and this would be proportional to initial absorption. In other words there is a bidirectional property of absorption and transmission in the path. That is if there is a probability, p, that a certain photon is absorbed in traveling from the surface to some point in the path, then the same probability p applies to an emission starting at that point and reaching the surface.

Also in TomVonks description of what happens in stating that after 10000 m the same number of 18 micron photons remains, I assume he would agree that in the atmosphere with a decreasing temperature with altitude that the number would have to be reduced. Otherwise increasing CO2 would not reduce the amount of heat leaving the planet and greenhouse gases would be a heat conductor from the surface to outer space.

But, it is interesting to consider that greenhouse gases in absorbing heat also transmit it, almost like a conductor. For example in gas fired water boilers, following combustion completion, the gases are passed through metal tubes that are immersed in the water to be heated, both water vapor and CO2 are key in transferring the heat from the gas to the tube walls. Of course the amount of these gases present here is much higher than that in the atmosphere.

4. Al Tekhasski says:

Richard wrote @5:

"… they estimate 99 of 390 Wm-2 through the atmospheric window with clear skies, corresponding to about 75% absorption. The one half of the absorbed radiation being sent back to the surface and one half being transmitted to space was selected …"

I think this phrase explains where this approach (to energy balance) is wrong. This is a depiction of isothermal "glass slab" gray atmosphere. In reality there is no half and half. The atmosphere is a non-isothermal body, which has two effective boundaries, top and bottom, and also has through holes. Bottom is warm, top is quite colder. Different IR wavelengths have vastly different level of absorption. Some wavelengths are absorbed within 100m of bottom air ( see "Gas Cell Simulator" at http://www.spectralcalc.com/calc/spectralcalc.php and try 620-720 cm-1 for CO2 at sea level and 400ppm). This means that these photons are emitted “back” from “air body" that has a temperature corresponding to 100m height, where it is just half-degree colder than at the surface. Therefore these pressure-broadened lines and bands of spectrum emit back about the same radiation as air absorbs. The top emits similarly, but it is much colder. This difference is balanced by convection and latent heat transport within the body of atmosphere. That’s why there is no “half-and-half”.

While some radiation gets totally absorbed in 100m, some other wavelengths are not absorbed at all, and the emitter (surface) sees the outer space directly, through a whole window or through the picket fence of lines, and cools off accordingly. One can take an average of this, and it is what the IR radiometer does. The radiometer is an integrating device, it does not differentiate which radiation came from where. If it sees "333W/m2", it means it. However, the interpretation of this might be tricky.

In short, if you are calculating right, this approach should give you the same result as AGW. The AGW says that CO2 doubling will invoke the radiative imbalance of 3.7W/m2. They admit that the result comes solely from the sides of 14-16um absorption band, not from the “saturated” inner part, and nothing comes from the IR transparency window.

Now look at what you have in Figure 3, in 13um area. Effectively this side of absorption band becomes wider by 0.1um, so it “blocks” more of outgoing IR. With all other things equal (aka instant no-feedback forcing in climatology-speak), this should decrease OLR to space and cause the infamous AGW imbalance. How much energy is blocked by 0.1um? Look at spetralcalc blackbody calculator, or at equivalent Figure7 in G4. The spectral irradiance at 13um is 7W/m2/sr/um, or 21W/m2/um. For 0.1um you have 2W/m2 less of OLR, which is exactly half of AGW number (because it is only one side of blocking band). Therefore, your calculations should yield the same AGW number, with all corresponding logic.

But I agree that other permanent factors are reducing this effect. As you noted, the 16-17um side is permanently covered by water vapor that always is in the air, so changes in CO2 contribute nothing in this area. The other factor is clouds. They are made of water droplets, and therefore have continuous spectrum, and block the other, 13um edge of CO2 band. Cloud cover is 66-70%, therefore this should reduce the 13-um effect to 1/3 of 2W, or 0.6-0.7W/m2. So we are getting about right picture. If we account for stratospheric cooling, the imbalance should be even smaller. I believe there are other factors that reduce this alleged imbalance further.

BTW, it seems to be very difficult to come by an experimental OLR spectrum for cloudy weather on the web. Climatology really must dislike the inconvenience of clouds, all their constructions seems to be focused on easy part, “clear sky”. Pretty sad I would say.

5. TomVonk says:

Also in TomVonks description of what happens in stating that after 10000 m the same number of 18 micron photons remains, I assume he would agree that in the atmosphere with a decreasing temperature with altitude that the number would have to be reduced. Otherwise increasing CO2 would not reduce the amount of heat leaving the planet and greenhouse gases would be a heat conductor from the surface to outer space.

Yes , there is lapse rate and decreasing density , so what happens at 10 k is not the same as in the first m (what I was talking about) .
The point is that there is ALWAYS enough (reemitted) IR for the CO2 to absorb regardless whether the Figure 4 says that H2O absorbs 100% or not .
This is true in the first m , 1 k , 5 k etc .
There is neither saturation , nor "saturation" .
LTE condition makes sure of that .

I didn't understand the second phrase . Conduction and radiation are 2 completely different things . The outgoing radiation , as long as one believes that the Earth is in radiative equilibrium , depends only on the Sun and can't be "reduced" by CO2 or whatever else .

6. Leonard Weinstein says:

@ 10 Tom,
The outgoing radiation can be slightly reduced if the temperature is continually increasing, as that implies a continual increase in the ocean/atmosphere storage. Once the temperature levels out (on the average) the outgoing again balances the incoming. Since the temperature has been flat (on the smoothed average) for the last 10 or so years, we should be in a balance of outgoing with incoming at the present time.

7. TomVonk says:

Leonard
The outgoing radiation can be slightly reduced if the temperature is continually increasing,

Yes , of course . If the temperature is not constant then there is no equilibrium and outgoing radiation is not equal to incoming .
This is what happens all the time and everywhere on the real Earth anyway .

As I wrote above , my comments are only valid for radiative equilibrium .
Even if this is not the reality , this is how every calculation is done .
But as the point was to show that this "saturation" concept doesn't make any sense and that Figures like 4 were irrelevant , it is not a problem to restrict the system to equilibrium .

8. Richard Petschauer says:

This paper written in early 2008 for some of the reasons stated in Comment # 5
I have read and learned much since then. My current estimates regarding some aspects on climate sensitivity and the role of CO2 are included in two posts here.

G10. Improved Simple Climate Sensitivity Model
This is a shorter and simpler version of post G7 and its main purpose was to present why I think surface evaporation causes negative feedback even though it is now ignored even by the skeptics. It also shows how to calculate climate sensitivity and feedback issues.
Compared to IPCC’s estimate for doubling CO2, including all feedbacks, that ranges from 2 to 4.5 C, this paper shows 0.69 to 97 C if cloud feedback is positive as IPCC believes it is, or from 0.54 to 0.71C if cloud feedback is negative of the same magnitude. All these assume a forcing (heat unbalance) caused by doubling CO2 equal the generally accepted value of 3.71 Wm-2. I am currently working on an improved version of this paper to help better justify evaporation cooling and generalize the method of calculating it.

Does the Tropopause Limit Carbon Dioxide Heat Trapping?
This paper has new estimates based on spectra analysis of the pre-feedback value of radiative forcing caused by doubling CO2 using the online tools available from the spectralcalc.com website. The results here show a forcing of 2.53 Wm-2 compared the generally accepted value of 3.71 Wm-2, a 32% reduction. This would reduce both the pre-feedback and post feedback temperature rise values by this same percentage including the values cited above from Post G10.

Other work in progress
I have begun using the same tools as in the above paper to estimate water vapor feedback assuming that water vapor content will increase to maintain constant RH, the present assumption that some models also show. This is a separate issue from some recent reports that indicate that at high altitudes water vapor content has not been increasing as surface temperatures have risen.

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