Guest post by John Kehr from: The Inconvenient skeptic
There are many times when I am putting together articles that I need to compare the results of my research to the models of the theory of Anthropogenic Global Warming (AGW). In this manner I can contrast the results and predictions directly. This way I understand how the different views relate to each other.
Recently I was trying to find the total amount of energy (forcing) that the warmists claim CO2 is responsible for in the atmosphere. The reason I wanted this is because I have recently completed my full analysis of absorption and I wanted to compare my results to the warmist views. While this article is not about my results, it will focus on some interesting results that I found using their models. Because I was searching for the warmist views about energy I was using information from their sites (and citations of course). While that might seem strange, they generally have lots of good information there.
The starting point is the basic equation they use to determine the forcing caused by a change in CO2 concentration.
CO2 Forcing Equation
This equation provides the amount of energy in W/m2 that a difference in two CO2 concentrations should cause.
While looking for the total forcing of CO2 in the atmosphere, I found an interesting article on the Skeptical Science (SkS) site that had an answer to my question (citation). They state that the radiative flux caused by CO2 is 32 W/m2. I will use the information from that article several times. When I compare the energy calculated by the forcing equation using CO2 levels of 1 ppm and 390 ppm I get a result of 31.9 W/m2. So far things are looking consistent for the theory of AGW. Here is a chart of the forcing from 1 ppm to over 1000 ppm.
Proposed Model of CO2 Forcing
The next step is to determine how much warming this energy causes. For this I use the next important equation that the AGW model uses. That is the climate sensitivity.
Climate Sensitivity: Warming caused by Forcing
Again I found lots of discussion and references at the SkS website (Hansen et al. 2006) where they provide their views about climate sensitivity. This equation is straightforward and simple to decipher. They generally calculate it by looking at a period of time with a temperature change and then estimate the change in forcing. For example if increasing CO2 caused a forcing of 2 W/m2 and the observed temperature change was 5 °C, then the climate sensitivity would simply be 2.5 °C /(W/m2).
One thing to be aware of is that the sensitivity is usually not shown directly. Most warmist publications display the results in terms of temperature change that will happen as a result of forcing. For example the most commonly used quantity for climate sensitivity is 3.0 °C for a doubling of CO2. To determine the climate sensitivity they are using it is simply:
λ = (3°C / 3.7 W/m2 ) = 0.81 °C/(W/m2)
I am going to use the direct climate sensitivity instead of the temperature effect that a forcing will cause. This will make my numbers look a little different, but here is the conversion.
Proposed Range of Climate Sensitivity
When comparing climate sensitivity it is very important to know exactly which form is being used. I will be using the actual climate sensitivity instead of the CO2 doubling form. The best way to check is to look at the units being used.
The most common estimate is the 0.81 °C/(W/m2). That is what corresponds to the 3 °C temperature increase for a doubling of CO2. The full range is what I have shown in the table. Some estimates do go a little higher or lower, but the 0.43-1.13 °C/(W/m2) is the most widely accepted range.
SkS puts the climate sensitivity at the 0.81-0.92 °C/(W/m2). I am going to use the 0.81 °C/(W/m2) as the default value for the warmists as it is the most commonly used value.
So far all of this seems perfectly reasonable and hopefully acceptable. This is also where the wheels start to come off.
I decided to look at another method to determine the climate sensitivity. I am troubled by the method normally used because it is very hard to know the exact forcing and cause of the temperature change. So I decided to use what should be a less controversial method, but somehow I doubt it works out that way.
I decided to use the total Greenhouse Effect (as the ΔT) and then the energies involved. The total Greenhouse Effect is perhaps the least controversial aspect of the Global Warming debate. I will use the normally accepted value of the Greenhouse Effect as 30 °C.
Now by using the climate sensitivity value it is possible to compare what portions of the Greenhouse Effect (GHE) are caused by different components. Since the accepted forcing value for CO2 is accepted as 32 W/m2 it is now possible to determine the total impact that CO2 has on the total GHE.
ΔT = (0.81°C/(W/m2)) * 32 (W/m2) = 25.9 °C
While that might not immediately seem unreasonable. The entire stated effect of the GHE is 30 °C. So according to the accepted climate sensitivity and CO2 forcing equations, CO2 accounts for 86% of the total GHE.
So all other factors in the Earth’s climate account for 14% of the GHE and CO2 by itself accounts for the other 86%. This can also be compared to the number of CO2 doublings that take place from 1 ppm to 390 ppm. That is roughly 8.6 CO2 doublings (1,2,4,8,16,32,64,128,256,390 ppm). Using 8.6 doublings from 1 ppm gives 25.8 °C. So their model is coherent, but saying that CO2 causes 86% of the GHE is extremely incorrect.
This means that the methods being used for determining temperature change based on forcing and climate sensitivity are flawed. Any result that puts CO2 at 86% of the GHE is wrong. Earlier I showed that the forcing model and the accepted total forcing have a good match. That would indicate that the problem is with (at least partially) the estimated climate sensitivity.
So I worked backwards. Assuming that the total temperature change caused by the GHE is 30 °C and then the total energy inputs are the total forcing. The total GHE is not very controversial. Very few people will argue that the Earth is not warmer as a result of the atmosphere. Without the atmosphere the Earth would be around -15 °C and with the atmosphere it is currently about 15 °C. That 30 °C difference is caused by the insulative effect caused by the atmosphere.
That leaves forcing as the problem in determining the correct climate sensitivity. The same article that stated CO2 as 32 W/m2 also stated that water vapor causes a forcing of 75 W/m2. If I assume that water vapor and CO2 are the ONLY factors I get a total forcing of 107 W/m2. This would indicate:
λ(30%) = (30°C /107W/m2) = 0.28 °C/(W/m2)
Already using very poor assumptions the climate sensitivity is already much lower (by almost 3x) than the accepted value. This still puts CO2 at 30% of the total GHE, so even this estimate for climate sensitivity is still too high.
The normally discussed range of CO2 effect on the GHE is 9-26%. Assuming that the 32 W/m2 remains accurate for the forcing magnitude of CO2 results in climate sensitivities of:
λ (9%) = (30°C / 356 W/m2 ) = 0.08 °C / (W/m2 )
λ (26%) = (30°C / 123 W/m2 ) = 0.24 °C / (W/m2 )
At 9% of the GHE the climate sensitivity must be 10x lower than what is currently accepted. There is one more possible scenario that I want to cover.
If I look at the Radiation Budget (Kiehl, Trenberth 1997) I get a total forcing from the surface to the atmosphere of 452 W/m2. That would include the energy from evaporation, convection and radiative transfer and subtracting out the open window of 40 W/m2. If I use the 32 W/m2 for CO2 with that total energy then CO2 accounts for 7% of the total GHE. Then the climate sensitivity is:
λ (total energy) = (30°C / 452 W/m2 ) = 0.066 °C / (W/m2 )
That is what the real lower limit of the climate sensitivity is. The flaw in the estimates for climate sensitivity is the assumption that all temperature change is caused by the greenhouse gas forcing. If the climate was as sensitive as the much higher estimates currently in use are, the Earth would be a very unstable place as small changes in energy would cause large changes in temperature.
Using the total GHE determined climate sensitivities, here are the CO2 doubling effects on the climate.
GHE Determined Climate Sensitivities
What this shows is that trying to determine the climate sensitivity from a change in measured temperature and then assuming it was caused by a particular forcing is incompatible from the determination of climate sensitivity from the actual GHE. In choosing between methods it is the GHE that is a known quantity. Since the measurements have been done to determine the individual parts of the GHE, that seems to be a much more reliable method than “assuming” that a particular forcing caused a certain change in temperature.
The IPCC and the general AGW method of determining climate sensitivity is about an order of magnitude different than the method of using the total GHE and then calculating the components. This is a significant scientific disparity.
The difference the climate sensitivity makes to the temperature projections based on increasing CO2 concentrations are significant. Assuming the same CO2 forcing while using the different climate sensitivity values results in the following effects of CO2 on the global temperatures.
Red: The AGW accepted climate sensitivity of 0.81 (3C for doubling) Green: Climate sensitivity of 0.28 (1C for doubling) Blue: Climate sensitivity of 0.066 (0.24C for doubling)
The total GHE of 30 °C is incompatible with the currently accepted IPCC values of climate sensitivity and CO2 forcing. In order for the GHE to be compatible, the total effect of the greenhouse would have to be closer to 100 °C which would result in a global temperature of ~85 °C. This strong overstatement of the climate sensitivity substantially weakens the idea that CO2 could cause measurable change in the Earth’s climate, much less the type of danger that is often being stated.
This does not mean that CO2 is not a significant portion of the Earth’s greenhouse, but it does limit the role that it plays in the total GHE. The climate sensitivity is what prevents the sum of the parts from being greater than the whole and the sum of the parts cannot be greater than the total observed GHE. If the current estimates of CO2 forcing and climate sensitivity do not fit within the parameters of the total GHE effect, those estimates must be incorrect.
For Tim and Dave, Re water absorption.
The IR Handbook gives some good data for seawater.
Seawater is MOST absorptive at and around 3.0 Microns (solar spectrum; not thermal). The Absorption coefficient is about 9,000 cm^-1 which means attenuation to 1/e (37%) in about 1.1 microns; which would be 99% absorbed in 5.5 microns. It then drops considerably to as low as 200 cm^-1 at 4 microns; beyond which only 1% of sunlight remains, and reaches the second highest peak of maybe 2000cm^-2 at 6.3 microns, and then drops to about 900 at 700 microns from where it rises slowly to a final max of about 3200 cm^-1 at about 15-20 microns; right where the CO2 peak is and water’s best LWIR peak.
From there is drops about linearly on a log log plot to maybe 300 cm^-1 at 100 microns. So 1000 would give a 1/e depth of 10 microns so 50 microns absorbs 99%.
So definitely not a monomolecular layer by any stretch; but a very thin layer for the LWIR thermal spectral range. The linear log-log plot continues all the way out to 10 cm which is 3GHz, where the slope about doubles as water gets more transparent to radio-waves.
I think for the bulk of the 5.0 to 80 micron surface or atmospheric thermal spectrum, 2,000 cm^-1 is good number which is a 5 micron 1/e depth or 25 micron 99% absorption depth (1 mil).
That to me is a thin layer that can easily heat sufficiently to evaporate profusely.
In contrast at the sunlight peak of around 470 nm , the absorption coefficient is 0.0001 cm^-1 which is a 100 metre 1/e depth, and 500 metres for 99%.
Actually in a lot of sea waters; biologicals in the water; will cause more losses; but you get the idea that solar energy is deposited deep in the ocean; while the downwelling LWIR from the atmosphere is stopped in a mil of water.
Dave Springer says: October 27, 2010 at 9:22 am
The albedo of desert sand is 40% whereas that of a rainforest is 10%. The surface of the desert is absorbing 30% less energy from the sun than the rainforest yet the mean desert temperature is higher.
So here’s a perfect moment to ask: What’s Up With That?
My first suspicion would be that the cloud cover is the main difference.
I checked into the Amazon basin and found a credible link that suggests that area has a 70% – 80% cloud cover (http://mclean.ch/climate/Cloud_Amazon.htm). I didn’t find a similar estimate for the Sahara, but I strongly suspect it is closer to 10% – 20%.
* If 80% of the sunlight reaches the surface in the Sahara and 60% of that is absorbed, that results in 48% of the total that gets absorbed.
* If 30% of sunlight reaches the surface of the rain forest and 90% of that is absorbed, that results in 27% of the total.
These are of course rough numbers, but it clearly shows that rain forests could easily absorb less total solar energy (and hence be cooler on average).
@Tim
Yes sir. The water cycle (clouds are a part of it) is the big Kahuna when it comes to surface temperature on a water world. CO2’s only important role (other than plant food!) is keeping it warm enough for the water cycle to be active. Evidently we don’t have quite enough CO2 because warm spells like the Holocene interglacial only last about 15,000 years then there’s 100,000 years of glaciers and sea ice covering everything all year round from 40 to 90 degrees latitude. That’s been the cycle for the last several million years. I don’t think humans can possibly pump enough CO2 into the atmosphere by burning fossil fuels to break that cycle. At best maybe delay the inevitable by no more than a few centuries. That might be enough time to figure out and put in place some other artificial means of preventing the next glacial period.
George E. Smith says: October 28, 2010 at 11:40 am
The IR Handbook gives some good data for seawater….
Thanks for the post. I had seen a similar graph and come to similar conclusions about penetration depths.
The one conclusion I don’t completely agree with is “That to me is a thin layer that can easily heat sufficiently to evaporate profusely”
It seems (and I could be wrong) and you and Dave are thinking that the ~300 W/m^2 of downwelling IR from the atmosphere is simply going to evaporate away the ocean surface without heating the deeper layers. But since there is also ~ 400 W/m^2 upwelling LWIR from the ocean; all the downwelling LWIR can really do is keep the surface from cooling too quickly. Of course, the solar IR also mostly affects the surface layer, so midday I would not be surprised to see net heating of this thin layer and enhanced evaporation.
———
Perhaps the most important conclusion is that we do not have the data nor the time (nor the expertise, I suspect) to really answer these questions here. This blog is fantastic for learning about the various opinions and concerns about GW, but it is really not effective for learning about the science, and it is even less effective for coming to new conclusions.
That is why people make careers out of tackling problems like this. That is why there is peer review of new ideas by others who have the knowledge to offer informed criticism. That is why people develop elaborate computer programs to take into account more and more of the variables we are musing about.
As a friend once said — if it was so easy that you could figure it out the first time around, they wouldn’t call it “re-search”. 🙂
MODERATOR:
It looks like I missed the “” in the previous post after the second line:
” The IR Handbook gives some good data for seawater… ” 🙁
Even weirder — my formatting comment to the moderator left out the symbols in the quotation marks! I missed the ending html italic tag, but even typing the symbols with spaces between them didn’t work. C’est la vie.
@george
Thanks for the IR optical depth data in seawater!
I knew it was a very thin layer. Elsewhere I read the observed action all takes place in the first millimeter even though complete absorption takes place in just a few microns.
Evaporation however is a surface event. In a boiling fluid (vaporization pressure equals environmental pressure) vaporization can occur anywhere. In evaporation where the vaporization pressure is only a fraction of environmental pressure it occurs in the top layer of molecules as they have less binding energy than molecules completely surrounded by other water molecules.
In the real world there is going to be some other processes going on due to impurities in the water which are not subject to phase change. It’s unclear to me if there are any real world conditions where IR impinging on a water surface could possibly raise its sensible temperature. It would seem that at the least this would require non-moving saturated air at the interface like in a fog bank. All I know for sure is that when evaporation is occuring it is removing sensible heat from the surface and the vapor itself doesn’t have a higher temperature than the bulk liquid it leaves behind because the heat it carries away is latent which won’t have any heating effect on the surrounding environment until the vapor changes phase back to a liquid and that usually occurs at some significant altitude so the net effect is like an express elevator mechanically carrying heat away from the surface and dumping it thousands of feet higher up in the troposphere or maybe even in the stratosphere when a convective cell gets wound up really tight.
@Tim
“The one conclusion I don’t completely agree with is “That to me is a thin layer that can easily heat sufficiently to evaporate profusely””
There seems to be some confusion here. No “heating” is required. Temperature is an average of the individual motion of an exceedingly large number of molecules. In all this motion a few molecules will be moving much faster than the bulk and a few moving much slower. The fastest moving molecules in the bulk are the ones ripe for a phase change to vapor with just a little extra nudge. When the phase change happens it’s like a rubber band snapping and all the potential energy in the stretched rubber gets packed into the vapor molecule as latent heat (potential energy not the energy of motion which a thermometer can sense). The unvaporized molecules at the other end of the broken rubber band suddenly lose a lot of energy of motion – about a thousand times as much energy of motion as is contained in the latent (potential) energy being carried away by the vapor molecule.
The action at the individual molecule is more or less new to me. Engineers usually work with bulk properties of materials and statistical mechanics. Unless the engineer is working with something very very tiny like features on integrated circuits there’s never any need to consider what happens at quantum scales. I have a passing engineering interest in steam engines and have studied them from the first ones (which were invented to evacuate water from mine shafts) to present day construction. Steam is still used a lot today in industry because of its unique material properties the most attractive of which is its huge latent heat of vaporization which means you can move lots of energy from place to place with a small volume of an abundant non-polluting material. Along with steam engines I have a passing fascination with Carnot cycle engines in general. A convective cell is a heat engine which performs a lot of work moving large masses of air around and lifting a lot of water from the surface to high in the air and sometimes violently rearranging heavy objects on the surface like trees and homes and cows and automobiles.
The bottom line for “sensitivity” to CO2 concentration is not simple thing. If the water cycle is stopped due to freezing temperatures then the sensitivity is very high and extraordinarily high for the first 0-50ppm where its greenhouse efficiency increases in a more linear fashion with increasing concentration. Much less sensitive to increases above 200ppm where it efficiency increases are inversely exponential.
The earth without any greenhouse gases would have an average temperature well below freezing. CO2’s most significant role by far (excluding plants needing it) is in raising the surface temperature from below freezing to above freezing. Once that happens the water cycle is activated and as long as the temperature remains above freezing the water cycle controls the climate and CO2 does little to nothing. In the big picture then one might CO2 as a limiting factor in how far the average temperature can drop and the water cycle is a limiting factor in how far the average temperature can rise. Since the earth still periodically gets covered by glaciers for 100,000 years with brief respites lasting about 15,000 years then as far as civilization is concerned the “pre-industrial” CO2 level of 280ppm is too little as that doesn’t stop the recurring glacial epics. Maybe if we can manage one or two doublings from pre-industrial level by burning fossil fuels to get a CO2 concentration of 1000ppm (which will make green plants much happier too) it might be enough to break the glaciation cycle. What it won’t do is result in any excessive warming because the water is what limits warming. Sensitivity to CO2 doublings is essentially zero when and where the water cycle is active.
The “correct” sensitivity is thus not anywhere near a fixed number but rather varies tremendously depending on the activity level of the water cycle which in turns depends only on surface temperature being on average above freezing.
I don’t think sensitivity can be easily or convincingly explained to the average person. It doesn’t require any knowledge or skills that most people had when they managed to get passing grades on final exams in high school science classes. The thing of it is that most people forget that stuff very quickly because it isn’t needed in most cases to get along well in life. What the average person is good at and the skill grows with age and experience is knowing when someone is being dishonest and figuring out the ulterior motives that spawn the dishonesty. The public is becoming increasingly aware that catastophic climate disruption, or whatever the most popular name for it is today, is a big lie with a range of ulterior motives behind it mostly having to do with money and political power and keeping a largely useless cottage industry of climate related research alive and growing. I believe Climategate was the straw that broke the camel’s back. The average person might understand and accept that “trick” can just refer to a clever and useful way of doing something but when the trick is connected to “hide the decline” they understand that the trick in that case is a clever way of lying.