Guest essay by Dr. Antero Ollila

WUWT previously published my essay on the Semi Empirical Climate Model’ on the 21^st of November. In that essay I used the term “IPCC climate model” and I received some comments saying that the “IPCC has no climate model”. I understand this argument, because IPCC should not have any models according to its mission statement.

In this essay I analyze in detail the evidence of the IPCC climate model, its properties, and its usefulness in calculating the warming values according to the IPCC science. I reckon that some readers shall also argue that there is no such thing as “IPCC science”. The mission statement says role of the IPCC…

“…is to assess on a comprehensive, objective, open and transparent basis the scientific, technical and socio-economic information relevant to understanding the scientific basis of risk of human-induced climate change, its potential impacts and options for adaptation and mitigation. IPCC reports should be neutral with respect to policy, although they may need to deal objectively with scientific, technical and socio-economic factors relevant to the application of particular policies.”

The mission statement above guides IPCC to concentrate to assess human-induced climate change issues and it means that the natural causes have a bystander role. IPCC must summarize the assessment results and to compose concise presentations based on the thousands of scientific papers. The outcomes of this work can be found in the IPCC’s reports. Finally, we have presentations like Radiative Forcings (RF) of greenhouse gases, Transient Climate Sensitivity (TCS), and Equilibrium CS (ECS). The IPCC has composed these presentations based on few scientific papers or even on its own task forces like in the case of Representative Concentration Pathways (RCPs). Therefore, it is justified to call this work “IPCC science”. It is not typically based on any individual scientific work alone, but it is based selections and combination work of IPCC.

It is true that the IPCC does not openly manifest that “this is the IPCC simple climate model”, because it would be clearly against its mission. But, it can be found in the IPCC Assessment Reports. I refer to 3^rd, 4^th, and 5^th Assessments Reports using the acronyms TAR, AR4, and AR5. The oldest reference to the IPCC climate model can be found in TAR, chapter 6.2.1:

The climate sensitivity parameter (global mean surface temperature response dTs to the radiative forcing dF) is defined as (I have changed the Greek symbols into English ones). Equation 6.1:

dTs /dF = CSP

(Dickinson, 1982; WMO, 1986; Cess et al., 1993).

Equation 6.1 is defined for the transition of the surface-troposphere system from one equilibrium state to another in response to an externally imposed radiative perturbation. In the one-dimensional radiative convective models, wherein the concept was first initiated, CSP is a nearly invariant parameter (typically, about 0.5 K/(Wm−2); Ramanathan et al., 1985) for a variety of radiative forcings, thus introducing the notion of a possible universality of the relationship between forcing and response.

The same equation can be found chapter 2.2 of AR4 and on page 664 of AR5 in the form of equation 1 below

dT = CSP * RF

…where RF means Radiative Forcing.

The value of CSP is 0.5 K/(W/m2) according to TAR, and there is reference to the paper of Ramanathan et al. (1985). I read this paper, and I found Table 8, in which eight CSP values are tabulated from 0.47 to 0.53. One of the values was that of Ramanthan et al., and it is 0.52. The average value of these eight CSPs is 0.5. So, it looks like that the reference of TAR is not accurate. The oldest reference is to the paper of Wanabe & Wetherald (1967) and it may be the oldest reference to equation 1.

Another essential equation in the IPCC climate model is the RF formula by Myhre et al. (1989) for carbon dioxide (CO2) is equation 2 below

RF = k * ln (CO2/280)

where k is 5.35 and CO2 is the CO2 concentration (ppm). IPCC selected this equation bases on the assessment in TAR, section 6.3.5. The closest rivals were the equations of Hansen et al. and Shi. IPCC has calculated the CO2 forcing in the AR5 according to equation (2) (AR5, p. 676). The RF value of CO2 concentration of 560 ppm according to equation 2 is 3.7 W/m2. In Table 9.5 of AR5 is tabulated the same 560 ppm RF values of 30 AOGCMs (Atmosphere-Ocean Global Circulation Model also known as ‘coupled atmosphere-ocean models’), and the average value is 3.7 W/m2. It is well-known that equation (2) has been commonly used practically in all GCMs, and probably that is why Gavin Schmidt et al. (2010) calls it a “canonical estimate”.

IPCC describes its equation 6.1 like this:

Equation (6.1) is defined for the transition of the surface-troposphere system from one equilibrium state to another in response to an externally imposed radiative perturbation.

The word “equilibrium” is not a proper expression for this equation, because it could mean that this equation is applicable only for equilibrium states as defined by the specification of ECS. The basic difference between the TCS and ECS is in the positive feedbacks.

In AR5 chapter 12.4.5.1, Atmospheric Humidity there is this text:

“A common experience from past modelling studies is that relative humidity (RH) remains approximately constant on climatological time scales and planetary space scales, implying a strong constraint by the Clausius–Clapeyron relationship on how specific humidity will change.”

It is well-known that all IPCC referred climate models apply the positive water feedback and it is inherently in the value of CSP, if the value is 0.5 K/(W/m2) or greater. In ECS calculations also other positive feedbacks are taken into account like the snow and ice albedo decrease.

IPCC summarizes the differences of ECS and TCR (IPCC has changed the term TCS to TCR (Transient Climate Response)) in AR5 like this (page 1110):

“ECS determines the eventual warming in response to stabilization of atmospheric composition on multi-century time scales, while TCR determines the warming expected at a given time following any steady increase in forcing over a 50- to 100-year time scale.”

And further on page 1112, IPCC states that “TCR is a more informative indicator of future climate than ECS”. I will show later that all the IPCC calculations for future scenarios for this century are based on the TCS/TCR approach, i.e. only the positive water feedback has been applied.

In Table 9.5 are the average values of ECS and TCR of 30 AOGCMs and the values are 3.2 C and 1.8 C. According to equation 1 it is impossible to get ECS value of 3.2 K by multiplying the RF value of 3.7 W/m2 by the CSP value of 0.5 K/(W/m2) as the explanation by IPCC could insist. In Table 9.5 the average CSP is 1.0 for calculating the ECS value. The TCR value calculated according to equation 1 would be 0.5 * 3.7 = 1.85 K, which is practically the same as the average value of 30 AOGCMs. My conclusion is this: the expression “one equilibrium state to another” for equation 1 and the CSP value of 0.5 K/(W/m2) does not mean the equilibrium between the equilibrium climate sensitivity (ECS) states but equilibrium states according to TCR calculations.

We can combine equations 1 and 2 into one formula (equation 3) for CO2

dTs = CSP * k * ln(CO2/280)

If the CSP value is 0.5 K/(W/m2) and the k = 5.35, I call equation 3 the IPCC climate model. Equation 3 cannot be found in any original research paper. If somebody can do so, then I will change my mind.

IPCC has carried out the following selections:

1. The elements of the equations
2. The value of CSP is 0.5 K/(W/m2) (IPCC’s own value, not Ramanathan et al.)
3. The RF formula for CO2 forcing.

IPCC has carried out scientific work by assessing the original research papers and selecting the elements for its model. I have done the same thing. My selection for the model elements is the same but the value of CSP is 0.27 K/(W/m2) and the value of parameter k is 3.12. It is a common practice to call my model the Ollila’s climate model and in the same way we can call the selections of IPCC to be IPCC climate model.

Even though equation 1 is as simple as possible, it is very good and accurate expression about the dependency of the surface temperature change needed to compensate the decrease of the outgoing longwave radiation (OLR) at the top of the atmosphere (TOA) originally caused by the increased absorption of CO2 concentration increase. The evidence is shown in Figure 1.

I have calculated the OLR changes using the spectral calculations applying the average global atmospheric conditions for three CO2 concentrations namely 393, 560 and 1370 ppm. There is no model applied in these calculations except the complicated absorption, emission, and transmission equations of the LW radiation emitted by the Earth’s surface in the real atmospheric conditions.

The dependency between RF change and the surface temperature change is essentially linear. This can be noticed by comparing the red curve calculated using the CSP value of 0.27 k(W/m2) to the blue curve of the spectral calculations. The TCS/TCR value of 0.6 C degrees can be read directly from Figure 1.

As shown above, the TCS/TCRds value of 1.8…1.9 C degrees is the same calculated by the IPCC’s climate model or by the AOGCMs. The warming values of RCP scenarios are originally calculated by the AOGCMs as well. IPCC tries to muddle the water by calculating the warming values of RCPs from the period 1986-2005 to the period 2081-2100, and not for the period 1750-2100 what is the specification of RCPs:

“The RCPs are named according to radiative forcing target level for 2100. The radiative forcing estimates are based on the forcing of greenhouse gases and other forcing agents. The forcing levels are relative to pre-industrial values and do not include land use (albedo), dust, or nitrate aerosol forcing.”

The warming of RCP8.5 for this period is 3.7 C degrees according to AR5 time span above. The warming from 1750 to 2000 has been 0.6 C degrees per IPCC. Thus, the total warming according to the RCP original specification from 1750 to 2100 is about 0.6 + 3.7 = 4.3 C degrees. Applying the IPCC’s climate model, the result is 0.5 * 8.5 = 4.25 C degrees, which is close enough.

The dependency between the CO2 concentration and the RF value is: RF = k * ln(CO2/280), where k is 3.12, In Figure 2, note that the equation starts from the CO2 concentration of 280 ppm onward, where the curve is slightly non-linear.

Usually I do not approve of the essential results of IPCC, but I do approve of this statement found in Chapter 6.2.1 in TAR:

“The invariance of CSP has made the radiative forcing concept appealing as a convenient measure to estimate the global, annual mean surface temperature response, without taking the recourse to actually run and analyse, say, a three-dimensional atmosphere-ocean general circulation model (AOGCM) simulation.”

Using equations (1) and (2) it is easy to calculate the TCS/TCR values (ECS values are not needed during this century and they are not real anyway) and the temperature effects of RCPs. For example, the temperature effect of RCP8.5 according to IPCC in 2100 is simply 0.5*8.5 = 4.25 C degrees, because the number 8.5 means RF value in 2100. The RF value of 8.5 W/m2 corresponds to the CO2 concentration of 1370 ppm, and according to my model the warming impact would be only 1.3 C. Eq. (1) is applicable for warming calculations, if a RF value is known. The RF values of GH gases can be calculated by equation 2, if equivalent CO2 values are known. But I do not recommend the CSP and k values of IPCC.

Why IPCC does not openly show that they have this simple climate model, which is very easy to apply, and which gives the same results as very complicated AOGCMs?

One reason could be that they are little bit shy to call it IPCC model, because they should not have it. Another reason could be that openly using it would decrease the image of climate change science, if it turns out that actually AOGCMs are not needed for calculating global warming values, which are very important in the tool box of IPCC.

There is a supposition that it is an unwritten rule among the climate change scientists that the values of the IPCC model and average GCMs should give essentially the same global values. The facts show that this is the case.