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.
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.
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.
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.
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.
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.
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.