How We Know the Effect of CO2 on Global Temperature

How We Know The Effect of CO2 on Global Temperature: Part 1

When studying the topic of climate change, once one understands the idea that an increase in CO2 is supposed to be responsible for an increase in global temperature, one may sensibly ask the questions:

  1. How much warming will a given increase in CO2 give? and,
  2. How do we know that it does?

This post is meant to address precisely these questions.

It is a bit of a lengthy read but I suggest you stick through it until the very end, where it is revealed exactly how it is that the mainstream scientific community with its scientific consensus knows empirically, definitively, without a doubt that an increase in CO2 levels results in an increase global temperature.

As a hint, the alternate title for this post is “Genealogy of a Hoax:wink: .

Starting with Google

As an example starting point only, if we google “How much of global warming is caused by CO2?” we get as the first link an article from 2013 titled Carbon dioxide causes 80% of global warming:

Carbon dioxide, mainly from fossil-fuel-related emissions, accounted for 80 per cent of global warming since 1990 according to the World Meteorological Organization’s (WMO) latest report from November 2013. Between 1990 and 2012 there was more than a 25 per cent increase in radiative forcing – the warming effect on our climate – because of carbon dioxide (CO2).

So, Mr. Reinhold Pape, reporting for, knows that CO2 causes temperature increase because the World Meteorological Organization reported that it does.

The World Meteorological Organization

How does the World Meteorological Organization know? Let’s look at their report from 2013, WMO statement on the status of the global climate in 2013.

The first pages are all measurements of increased temperatures, which of course don’t in and of themselves indicate CO2 was responsible. On page 17-18 in the section “Greenhouse Gases and Ozone Depleting Substances” we have an explanation of how they know:

Globally averaged levels of CO2 reached 393.1±0.13 parts per million (ppm), 41 per cent above pre-industrial levels (before 1750). […] As a result, the NOAA Annual Greenhouse Gas Index for 2012 was 1.32, representing a 32 per cent increase in total radiative forcing (relative to 1750) by all long-lived greenhouse gases since 1990.

So, the World Meteorological Organization knows because that is what the NOAA Annual Greenhouse Gas Index says.

The National Oceanic and Atmospheric Administration

How do the compilers of the NOAA Annual Greenhouse Gas Index know? Let’s take a look at their methodology, reported at “The NOAA Annual Greenhouse Gas Index (AGGI)” (which was “Updated Spring 2022”)


Increases in the abundance of atmospheric greenhouse gases since the industrial revolution are mainly the result of human activity and are largely responsible for the observed increases in global temperature [IPCC 2014]. Because climate projections have large model uncertainties that overwhelm the uncertainties in greenhouse gas measurements, we present here an observationally based index that is proportional to the change in the direct warming influence since the onset of the industrial revolution (also known as climate forcing) supplied from these gases.

Radiative Forcing Calculations

To determine the total radiative forcing of the greenhouse gases for the AGGI, we have used IPCC [Ramaswamy et al., 2001] recommended expressions to convert changes in greenhouse gas global abundance relative to 1750, to instantaneous radiative forcing (see Table 1).

So, the National Oceanic and Atmospheric Administration knows that CO2 increases the global temperature, because the IPCC in 2014 reported that it does, and provided a formula that anybody could use to determine the effect, which the IPCC provided in 2001.

Note well this point — the reported increases of global temperature due to CO2’s “direct warming influence” are based on a formula derived from the measure CO2 concentrations.

In other words, any increase in CO2 is directly attributed to be increasing the world temperature, because of the IPCC’s “recommend expressions” to convert it from one to the other.

Now we’ve answered our 1st question – “How much warming will a given increase in CO2 give?”, but we still need to answer the far more important 2nd question – “How do we know that it does?”

In other words, how did the IPCC arrive at these “recommended expressions”?

The Intergovernmental Panel on Climate Change – 3rd party explanation

The full 2001 report is 27.3MB and 893 pages, so instead of reading it all let’s first try to find someone who explains how the IPCC knows.

As an example only, we can take a look at the “Science of Doom” website, which according to their subtitle is created for the purpose of “Evaluating and Explaining Climate Science”.

They posted a series “CO2 – An Insignificant Trace Gas?”, where in Part Seven “The Boring Numbers” they go into details on this matter:

In Part Five we finally got around to seeing our first calculations by looking at two important papers […] The question to ask is – how did they work it out?

Exactly the question!

The 3rd assessment report (TAR) [i.e. IPCC 2001] and the 4th assessment report (AR4) [i.e. IPCC 2007] have an expression showing a relationship between CO2 increases and “radiative forcing” as described above:
ΔF = 5.35 ln (C/C 0**)**
C0 = pre-industrial level of CO2 (278ppm)
C = level of CO2 we want to know about
ΔF = radiative forcing at the top of atmosphere.

This is the formula referred to by NOAA above – which appears to not have changed between 2001-2007. How is it derived?

This isn’t a derived expression which comes from simplifying down the radiative transfer equations in one fell swoop!

Thank goodness!

Instead, it comes from running lots of values of CO2 through the standard 1d model we have discussed, and plotting the numbers on a graph:

Oh… it’s gotten by more calculations. Ok… how do we know the calculations reflect physical reality?

After a few more paragraphs about calculations and how the equation can be used we get to the conclusion:

We can have a lot of confidence that the calculations of the radiative forcing of CO2 are correct.

Ok, how do we know they are correct?

The subject is well-understood and many physicists have studied the subject over many decades.

Ok, in that case it should be easy to point to exactly how everyone has determined the calculations reflect reality.

Calculation of the “radiative forcing” of CO2 does not have to rely on general circulation models (GCMs), instead it uses well-understood “radiative transfer equations” in a “simple” 1-dimensional numerical analysis.

Ok, he is saying the calculations rely on simpler models rather than more complex computer models. How do we know the simpler models reflect reality?

The immediate next sentence is:

There’s no doubt that CO2 has a significant effect on the earth’s climate – 1.7W/m2 at top of atmosphere, compared with pre-industrial levels of CO2.

Ok, so we literally go from a series of calculations directly into a result that there is “no doubt” that CO2 has a “significant effect”! There is no sleight of hand here and anyone can visit the initial links to see that I didn’t leave anything out.

The next sentences are:

What conclusion can we draw about the cause of the 20th century rise in temperature from this series? None so far! How much will temperature rise in the future if CO2 keeps increasing? We can’t yet say from this series.

That is, the author draws a distinction between the radiative forcing per se, and the direct effect on the climate, and claims agnosy as to the precise relation between one and the other. But it is clear the author has “no doubt” that this (calculated) forcing is real and has a warming effect:

Something to ponder about CO2 and its radiative forcing.

If the sun had provided an equivalent increase in radiation over the 20th century to a current value of 1.7W/m2, would we think that it was the cause of the temperature rises measured over that period?

Going to the Source – The Intergovernmental Panel on Climate Change (AR6, 2021)

As the Science of Doom website didn’t explain how the IPCC knows the calculations reflect reality, let’s go directly to the source.

To give it the best chance of making the most compelling point, we should of course start with the very latest publication that has the most up to date methods and evidence, the 2021 IPCC, also known as the Sixth Assessment Report (AR6), specifically the “Working Group 1: The Physical Science Basis” which working group’s reports is what has been cited above.

This report is 404MB (!) (with a ‘small’ version available for only 265 MB) and 2,409 (two thousand four hundred and nine) pages long.

“Annex III” is titled Radiative Forcing so that is a promising starting point:

Annex III presents, in tabulated form, data related to historical and projected changes in greenhouse gas (GHG) mixing ratios and effective radiative forcing (ERF) of all climate forcers as assessed and used throughout Chapters 1–7.

Perfect, exactly what we’re looking for. On page 3 of the annex / page 2141 of the full report we have the effective radiative forcing listed for CO2 as “2.16 W/m^2” with the following note d:

d: ERF (2019–1750) from Chapter 7.

So our hunt continues onto Chapter 7, titled “The Earth’s Energy Budget, Climate Feedbacks and Climate Sensitivity”, where we find the following:

Executive Summary
Earth’s Energy Budget
[…] Changes in atmospheric composition and land use, like those caused by anthropogenic greenhouse gas emissions and emissions of aerosols and their precursors, affect climate through perturbations to Earth’s top-of-atmosphere energy budget. The effective radiative forcings (ERFs) quantify these perturbations […]

Here we see the key role of “effective radiative forcings” or ERFs – they quantify the perturbations to Earth’s “top-of-atmosphere energy budget”.


Since AR5, the accumulation of energy in the Earth system, quantified by changes in the global energy inventory for all components of the climate system, has become established as a robust measure of the rate of global climate change on interannual-to-decadal time scales.

So we see that these ERFs that quantify the perturbations have resulted in a “robust measure” of “the accumulation of energy in the Earth system” that has been “established” as such since AR5.


How the climate system responds to a given forcing is determined by climate feedbacks associated with physical, biogeophysical and biogeochemical processes. These feedback processes are assessed, as are useful measures of global climate response, namely equilibrium climate sensitivity (ECS) and the transient climate response (TCR) […]

How is the “equilibrium climate sensitivity” determined? From Box 7.1:

The equilibrium climate sensitivity, ECS (units: °C), is defined as the equilibrium value of ΔT in response to a sustained doubling of atmospheric CO2 concentration from a pre-industrial reference state. The value of ERF [effective radiative forcing] for this scenario is denoted by ΔF2xCO2, giving ECS = –ΔF2xCO2/α from Equation 7.1 applied at equilibrium.

This confirms the central relevance of the concentration of CO2 with regards to global temperature change. Although the radiative forcings give us a change measured in Wm^-2 and not in global temperature (i.e. °C) per se, they are then plugged into a formula that adjusts this ERF by a factor of (1/α) to then result in the global temperature change. (α is defined in Box 7.1 as well: “The feedback parameter, α (units: W m–2 °C–1) quantifies the change in net energy flux at the TOA for a given change in GSAT [global surface air temperature]”.)

Thus the climate sensitivity is defined as the response to a doubling of CO2 – and this equation directly uses the values of radiative forcing of CO2 that we are looking to determine the validity of. This is just to confirm that the reported values of increased global temperature due to CO2 increase, is indeed based on this calculated radiative forcing.

Which brings us back to the main point – what are these ERFs exactly, and how are they calculated?

With a little digging we can see that actually the ERF is a “concept” not a “measure” per se. From figure 7.1 we see that ERFs are “An improved radiative forcing concept from better understanding of adjustments” relative to AR5. Further from 7.3.1 we see that "ERF extended the SARF concept […]" to account for further “adjustments”, which we see from was introduced in AR5 (“The AR5 introduced the concept of effective radiative forcing (ERF) and radiative adjustments […]”)

Ok, concepts can still be useful though, if they reflect an underlying physical reality. How are these “effective radiative forcings” calculated and how do we know they reflect physical reality such as to be able to result in a “robust measure” of the change in global temperature?

Effective Radiative Forcing
For carbon dioxide, methane, nitrous oxide and chlorofluorocarbons, there is now evidence to quantify the effect on ERF of tropospheric adjustments […] The assessed ERF for a doubling of carbon dioxide compared to 1750 levels (3.93 ± 0.47 W m–2) is larger than in AR5.

Ah wonderful, we now have “evidence” to quantify the effect of tropospheric adjustments on ERFs. This presumably refers to the improvements since AR5. But, how do we know the ERFs were good to begin with?

The total anthropogenic ERF over the industrial era (1750–2019) was 2.72 [1.96 to 3.48] W m–2. This estimate has increased by 0.43 W m–2 compared to AR5 estimates for 1750–2011. […] {7.3.2, 7.3.4, 7.3.5}

Ok, they refer to section 7.3.2, so the evidence must be there.

First, in Section 7.3 we have:

7.3 Effective Radiative Forcing
ERF is determined by the change in the net downward radiative flux at the TOA (Box 7.1) after the system has adjusted to the perturbation but excluding the radiative response to changes in surface temperature. This section outlines the methodology for ERF calculations (Section 7.3.1) and then assesses the ERF due to greenhouse gases (Section 7.3.2) […]

Wonderful, let’s see what the methodology is…

7.3.1 Methodologies and Representation in Models: Overview of Adjustments
As introduced in Box 7.1, AR5 (Boucher et al., 2013; Myhre et al., 2013b) recommended ERF as a more useful measure of the climate effects of a physical driver than the stratospheric temperature adjusted radiative forcing (SARF) adopted in earlier assessments.

Ok, the ERF is a “measure” that is “more useful” than measures used in earlier assessments – which are used as the key part of and constitute a “robust measure” of the Earth’s global energy budget that has “become established” by 2021.

How do we know it’s a valid measure? This goes into how it’s calculated:

[…] The ERF for a particular forcing agent is the sum of the IRF [instantaneous radiative forcing] and the contribution from the adjustments [(i.e. those changes caused by the forcing agent that are independent of changes in surface temperature)] […] There have been two main modelling approaches used to approximate the ERF definition in Box 7.1 […]

Ok, so the ERF is calculated with models… how do we know the models are right?

7.3.2: Greenhouse Gases
High spectral resolution radiative transfer models provide the most accurate calculations of radiative perturbations due to greenhouse gases (GHGs), with errors in the instantaneous radiative forcing (IRF) of less than 1% (Mlynczak et al., 2016; Pincus et al., 2020). […]

Ok, this particular type of model provides the best calculations of radiative perturbations due to greenhouse gases - with errors of “less than 1%” - but, errors compared to what? How do we know the calculations reflect reality?

The high-resolution model calculations of SARF [stratospheric-temperature-adjusted radiative forcing] for carbon dioxide, methane and nitrous oxide have been updated since AR5, which were based on Myhre et al. (1998).

Now they’re talking about SARFs not ERFs… how are they related?

This assessment therefore estimates ERFs from a combined approach that uses the SARF from radiative transfer models and adds the tropospheric adjustments derived from ESMs [Earth System Models].

Hmm… so it appears the ERF is estimated by combining the SARF models with some other ESM models. So it’s a model plus a model. Let’s focus on what appears to be the main component which is the SARF.

How do we know the SARF models are right? We saw they have been “updated since AR5” – meaning they must have been right in AR5 and now they are even more right. If we look into how they were updated, that should shine some light on the matter.

The SARF for carbon dioxide (CO2) has been slightly revised due to updates to spectroscopic data and inclusion of the absorption band overlaps between N2O and CO2 (Etminan et al., 2016)

Ok, so the latest revisions are due to Etminan et al. 2016. How do they know their calculations match reality? Let’s go to the source…

Etminan et al. 2016

The paper is titled Radiative forcing of carbon dioxide, methane, and nitrous oxide: A significant revision of the methane radiative forcing. In the abstract we have:

Abstract. New calculations of the radiative forcing (RF) are presented for the three main well‐mixed greenhouse gases, methane, nitrous oxide, and carbon dioxide.

In the “Introduction” we have:

The radiative forcing (RF) due to changes in concentrations of the relatively well mixed greenhouse gases (WMGHGs) is the largest component of total RF due to human activity over the past century [Myhre et al., 2013a]

The headline RF values for CO2, CH4, and N2O presented in recent Intergovernmental Panel on Climate Change (IPCC) assessments [e.g., Myhre et al., 2013a] are calculated using simplified expressions presented in the IPCC Third Assessment Report [Ramaswamy et al., 2001, section 6.3.5]. These were largely based on the work of Myhre et al. [1998, henceforth MHSS98]. […] The purpose of this letter is to update these expressions in a number of important ways.

So it’s just an update of the work of Myhre et al 1998, which the AR6 also refers to the AR5 as having used (re-quoted from AR6 above: “The high-resolution model calculations of SARF for carbon dioxide, methane and nitrous oxide have been updated since AR5, which were based on Myhre et al. (1998).”)

How did they update it? In “Methods” we have (emphasis added):

The RF calculations use the Oslo line‐by‐line (OLBL) code […] OLBL code is based on the GENLN2 LBL code […] It is coupled to a 16‐stream Discrete Ordinate code [Stamnes et al., 1988] to compute irradiances […] The shortwave RF part of OLBL is now updated to be representative for global simulations. Solar radiative transfer simulations are per-formed forfive solar zenith angles […] Present‐day natural and anthropogenic aerosols are included using the OsloCTM2 simulations […] Absorption data from HITRAN 2008 edition [Rothman et al., 2009] are adopted both for the longwave and shortwave RF calculations.

It should be clear from this that the only updates the paper did are based on models and calculations.

Ok, but it’s based on earlier work, and improves upon it, so surely as the earlier work had some empirical basis, if we see how the earlier work knows the calculations are correct, we should have our empirical evidence, non?

The Intergovernmental Panel on Climate Change (AR5, 2018)

Before going to the earlier papers, let’s stop by the 2018 IPCC report to see if there’s anything else there.

It is titled “Climate Change 2013: The Physical Science Basis”. The relevant chapter is Chapter 8, titled “Anthropogenic and Natural Radiative Forcing

Here we have:

Executive Summary
It is unequivocal that anthropogenic increases in the well-mixed greenhouse gases (WMGHGs) have substantially enhanced the greenhouse effect, and the resulting forcing continues to increase.

Great! It is “unequivocal”! How do we know?

As in previous IPCC assessments, AR5 uses the radiative forcing (RF) concept, but it also introduces effective radiative forcing (ERF). […] A total aerosol–cloud interaction is quantified in terms of the ERF concept […]

Interestingly, the fact that ERF is a “concept” is present directly in the executive summary in AR5, and explicitly mentioned as a “concept” numerous times, while in AR6 it’s only mentioned occasionally and in such a way that one could miss it on the first read-through.

Nevertheless, concepts and models and calculations can be useful as long as they are based in physical reality. So, how do we know this concept is a physically valid one?

8.1 Radiative Forcing
There are a variety of ways to examine how various drivers contribute to climate change. In principle, observations of the climate response to a single factor could directly show the impact of that factor, or climate models could be used to study the impact of any single factor. In practice, however, it is usually difficult to find measurements that are influenced by only a single cause, and it is computationally prohibitive to simulate the response to every individual factor of interest. Hence various metrics intermediate between cause and effect are used to provide estimates of the climate impact of individual factors, with applications both in science and policy. Radiative forcing (RF) is one of the most widely used metrics, with most other metrics based on RF

Hmmm, here we see that it’s “difficult” to find measurements – which measurements wouldn’t show cause and effect anyway as you need a physical experiment to demonstrate that. Therefore “various metrics” are developed which are intermediate between cause and effect! These metrics provide “estimates” of the impact, and “radiative forcing” is one of these metrics!

So not only is radiative forcing a “concept”, but it’s a “metric” used to act as an “intermediate” between cause and effect – because it is difficult to observe and measure it, even though observations and measurements only can’t demonstrate cause and effect anyway – and this metric thus “estimates” the impact of a factor (with “most other metrics” being based on this one).

8.1.1 The Radiative Forcing Concept
RF is the net change in the energy balance of the Earth system due to some imposed perturbation. […] Though usually difficult to observe, calculated RF provides a simple quantitative basis for comparing some aspects of the potential climate response to different imposed agents, especially global mean temperature, and hence is widely used in the scientific community.

It should be clear that the “Equilibrium Climate Sensitivity” of the AR6 from further above is therefore showing nothing but an estimate based on a metric based on a concept used in lieu of the difficult-to-measure and impossible-to-demonstrate causality that would actually demonstrate such a thing, which is “widely used in the scientific community” because it is “simple”.

Ok, the ice is really starting to thin here… but surely the concept is at least based on something empirical!! Even if we can’t measure cause and effect, we can infer it, can’t we?

Hope remains strong. Let’s continue to see how they determine that this concept measures something useful, something real in the physical world.

As CO2 is clearly of primary focus let’s just drill down on how exactly it’s computed for CO2.

8.3 Present-Day Anthropogenic Radiative Forcing
[…] In this section we determine the RFs for WMGHGs and heterogeneously distributed species in fundamentally different ways […]
8.3.2 Well-mixed Greenhouse Gases
[…] Carbon Dioxide
[…] Using the formula from Table 3 of Myhre et al. (1998), and see Supplementary Material Table 8.SM.1, the CO2 RF (as defined in Section 8.1) from 1750 to 2011 is 1.82 (1.63 to 2.01) W m–2.

Ok, as we found earlier above, the AR5 WG1 report does indeed use this Myhre 1998 paper’s results. The next step is clear - how does Myhre know that this is an effective metric?

Myhre et al. 1998

This paper is titled “New estimates of radiative forcing due to well mixed greenhouse gases”.

From the Abstract we have (emphasis added):

We have performed new calculations of the radiative forcing due to changes in the concentrations of the most important well mixed greenhouse gases (WMGG) since pre-industrial time. Three radiative transfer models are used.

Ok, it looks like this paper also consists entirely of calculations using models.

How do they know the new calculations reflect reality?

The differences between our model results and the expressions from IPCC and Hansen et al. [1988] for CO2, N20, and CH4 are illustrated for a wide range of concentrations in Figure 1. […] It is an overall good agreement between the NBM [narrow-band model] and BBM [broad band model] calculations and the IPCC expressions with new coefficients for CO2, CH4, and N20, with poorest agreement for large concentrations of the three WMGG [well mixed greenhouse gases]. Based on the NBM and BBM calculations as well as the LBL [line-by-line] calculations our best estimates for new coefficients to the IPCC expressions are shown in Table 3. For CO2 we have chosen the coefficients based on the BBM calculations, which is lower than the one derived from the NBM, due to inclusion of solar absorption by CO2 only in the BBM.

Here is figure 1 for reference:

In other words they refine the calculations and find good agreement with some, while they choose updated coefficients on others based on their “best estimates” resulting from their multiple model calculations.

In essence they are basing the correctness of the calculations – their reflectance of physical reality – based largely on the correctness of the previous calculations, done in Hansen (1988) and IPCC (1990).

In that case, our evidence will surely lie with those publications!

The Intergovernmental Panel on Climate Change (AR4, 2007)

Before going to those publications directly, we check out the AR4 to see if they have any additional information.

The AR4 WG1 report is titled “AR4 Climate Change 2007: The Physical Science Basis”.

In Chapter 2, titled “Changes in Atmospheric Constituents and in Radiative Forcing”, we have:

2.2 Concept of Radiative Forcing
The definition of RF from the TAR and earlier IPCC assessment reports is retained. Ramaswamy et al. (2001) [i.e. AR3] define it as ‘the change in net (down minus up) irradiance (solar plus longwave; in W m–2) at the tropopause after allowing for stratospheric temperatures to readjust to radiative equilibrium, but with surface and tropospheric temperatures and state held fixed at the unperturbed values’.

Following the reference of “Ramaswamy et al.” shows that it’s a reference to the AR3 report:

Ramaswamy, V., et al., 2001: Radiative forcing of climate change. In: Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change [Houghton, J.T., et al. (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, pp. 349–416.

So the AR4 essentially just refers to the AR3.

Radiative forcing is used to assess and compare the anthropogenic and natural drivers of
climate change. […] it has proven to be particularly applicable for the assessment of the climate impact of LLGHGs (Ramaswamy et al., 2001)

They refer to AR3 having “proven” it to be “particularly applicable”.

The simple formulae for RF [radiative forcing] of the LLGHG [long-lived greenhouse gases] quoted in Ramaswamy et al. (2001) are still valid. These formulae are based on global RF calculations where clouds, stratospheric adjustment and solar absorption are included, and give an RF of +3.7 W m–2 for a doubling in the CO2 mixing ratio.

Ok, then we can simply go to AR3 next.


How We Know The Effect of CO2 on Global Temperature: Part 2

The Intergovernmental Panel on Climate Change (AR3, 2001)

The AR3 WG1 report is titled “TAR Climate Change 2001: The Scientific Basis”.

In Chapter 6, titled “Radiative Forcing of Climate Change”, we have:

Executive Summary
Radiative forcing continues to be a useful tool to estimate, to a first order, the relative climate impacts […] due to radiatively induced perturbations.

So despite what AR4 said, AR3 isn’t proving that radiative forcing is “particularly applicable” per se but rather saying that it “continues to be” useful. That means its usefulness must have been already demonstrated earlier.

We get some new information from this 2001 report, though:

The practical appeal of the radiative forcing concept is due, in the main, to the assumption that there exists a general relationship between the global mean forcing and the global mean equilibrium surface temperature response (i.e., the global mean climate sensitivity parameter, λ) which is similar for all the different types of forcings.

That is, we find out that the concept of radiative forcing (as a metric to estimate that which cannot be experimentally demonstrated) arises due to an assumption that there is a relationship between this calculated value and the surface temperature!!!

Note the progression as we go forward in time:

  • AR3 (2001): a “concept” based on an “assumption” that there is a relationship between forcing and surface temperature, that is already “well established” (see further below)
  • AR4 (2007): a “concept” that AR3 had supposedly “proven to be particularly applicable”
  • AR5 (2013): a “metric” based on a “concept”, leading to the development of a new “concept” of ERF
  • AR6 (2021): (now ERF) a “concept” that is a “measure” that is made “more useful” than those RF metrics/concepts used in earlier assessments by combining it with yet other models, that constitutes a “robust measure” of Earth’s global energy inventory

The most remarkable aspect of this progression is that there is no new experimental cause-and-effect evidence to provide any reason for this evolution! Instead each increasingly-certain rephrasing refers to previous reports and/or papers that themselves are either newly done calculations or models (i.e. no additional documentary/experimental evidence) that are in-line with earlier ones, or refer to earlier work! Meanwhile all the while it is firmly established, proven to be useful, etc… yet without providing any new evidence for it!

In any case, maybe AR3 will at last provide some concrete evidence. Maybe by 2007 it was already so well-known that it didn’t even need to be stated.

6.1 Radiative Forcing
6.1.1 Definition
We find no reason to alter our view of any aspect of the basis, concept, formulation, and application of radiative forcing, as laid down in the IPCC Assessments to date and as applicable to the forcing of climate change. Indeed, we reiterate the view of previous IPCC reports and recommend a continued usage of the forcing concept to gauge the relative strengths of various perturbation agents […]

Ok, they just refer to the AR2 essentially. So, no new evidence for how this measure reflects physical reality.

How does the AR3 report how to calculate the effect of increasing CO2 concentration?

6.3.5 Simplified Expressions
IPCC (1990) used simplified analytical expressions for the well-mixed greenhouse gases based in part on Hansen et al. (1988).
The already well established and simple functional forms of the expressions used in IPCC (1990), and their excellent agreement with explicit radiative transfer calculations, are strong bases for their continued usage, albeit with revised values of the constants, as listed in Table 6.2

That is, it uses “expressions” that are “already well established”. That means the proof for why they are valid must exist in the past.

There are new constants in Table 6.2. How do we know the constants are right?

They provide three alternatives for CO2, first:

∆F= α ln(C/C0) , with α=5.35
[…] The constant in the simplified expression for CO2 for the first row is based on radiative transfer calculations with three-dimensional climatological meteorological input data (Myhre et al., 1998b) […]

This refers to the Myhre paper above, which we saw just consists of updated calculations based on IPCC 1990 and Hansen 1988, giving it “three-dimensional climatological meteorological input data”. But we have yet to see how we know these calculations are valid.

∆F= α ln(C/C0) + β(√C − √C0), with α=4.841, β=0.0906
∆F= α(g(C)–g(C0)) where g(C)= ln(1+1.2C+0.005C^2 +1.4 × 10^−6 C^3), with α=3.35
[…] For the second and third rows, constants are derived with radiative transfer calculations using one-dimensional global average meteorological input data from Shi (1992) and Hansen et al. (1988), respectively. […]

So these also rely on calculations, referring directly to Hansen 1988.

Instead of diverging to Shi (1992), let’s move on with IPCC 1990 and Hansen 1988 which appear to be more central, and in any case should be valid in and of themselves since they are recommended to be used (and “already well established” by 2001).

The Intergovernmental Panel on Climate Change (AR2, 1995)

Before going to 1990 and 1988 we stop by 1995 when the AR2 report came out.

The 1995 AR2 WG1 report is titled “AR2: The Science of Climate Change

Chapter 2 is titled Radiative Forcing of Climate Change. We have that:

The use of global mean radiative forcing remains a valuable concept for giving a first-order estimate of the potential climatic importance of various forcing mechanisms.

Ok, it “remains” a valuable concept – meaning by 1995 it must have already been proven to be a valuable concept. This means the proof is in the past. Let’s look for any mentions of this proof…

2.4 Radiative Forcing
The detailed rationale for using radiative forcing was given in IPCC (1994). It gives a first-order estimate of the potential climatic importance of various forcing mechanisms. […] There are, however, limits to the utility of radiative forcing as neither the global mean radiative forcing, nor its geographical pattern, indicate properly the likely three-dimensional pattern of climate response; the general circulation models discussed in Chapters 5 and 6 are the necessary tools for the evaluation of climate response.

Interestingly this 1995 report actually provides a fairly direct criticism against using the radiative forcing – which by later reports was still “widely used” because it is “simple”, and which in the 2021 report no longer has any mention of limitations at all (while the reports from 1995 up to then all have some amount of paying-lip-service to the limitations of radiative forcing). However this criticism has vanished in future reports. Note the “Equilibrium Climate Sensitivity” in AR6 unconditionally relied on the radiative forcing calculations. Also, even though the AR6 metric of “effective radiative forcing” is “radiative forcing” plus an adjustment derived from ESMs (Earth System Models) which models are the successors of the GCM (general circulation models), it still results in a simple formula relating the forcing to climate response and therefore doesn’t address the criticism here.

In any case let’s stick to the point of finding the rational basis for this conceptual metric (which we now know is based on an assumption).

Estimates of the adjusted radiative forcing due to changes in the concentrations of the so-called well-mixed greenhouse gases (CO2 […]) since pre-industrial times remain unchanged from IPCC (1994); the forcing given there is 2.45 Wm^-2 with an estimated uncertainty of 15%. CO2 is by far the most important of the gases […]

So they refer to IPCC 1994.

The Intergovernmental Panel on Climate Change (Special Report, 1994)

This report is titled “Radiative Forcing of Climate Change and An Evaluation of the IPCCIS92 Emission Scenarios”.

1 What is Radiative Forcing?
A change in average net radiation at the top of the troposphere (known as the tropopause). because of a change in either solar or infrared radiation, is defined for the purpose of this report as a radiative forcing. […] For example, an increase in atmospheric CO2 concentration leads to a reduction in outgoing infrared radiation and a positive radiative forcing. For a doubling of the pre-industrial CO, concentration, in the absence of any other change, the global mean radiative forcing would be about 4 Wm^-2. For balance to be restored, the temperature of the troposphere and of the surface must increase, producing an increase in outgoing radiation. For a doubling of CO2 concentration, the increase in surface temperature at equilibrium would be just over 1 °C, if other factors (e.g., clouds, tropospheric water vapour and aerosols) are held constant. Taking internal feedbacks into account, the 1990 IPCC report estimated that the increase in global average surface temperature at equilibrium resulting from a doubling of C02 would be likely to be between 1.5 and 4.5 °C, with a best estimate of 2.5 °C.

So it refers to the 1990 IPCC report. Also note it directly translates this radiative forcing into a temperature change value, just like the AR6 does.

In Chapter 4 “Radiative Forcing” we have:

The concept of radiative forcing
Global-mean radiative forcing is a valuable concept for giving at least a first-order estimate of the potential climatic importance of various forcing mechanisms. […]
Greenhouse gases
The direct global-mean radiative forcing due to changes in concentrations of the greenhouse gases […] is essentially unchanged from previous IPCC assessments.

So just like in 1995 where it “remains” a valuable concept, here in 1994 it is a valuable concept which is “essentially unchanged” from previous reports.

There is no evidence provided for why the calculations here are valid, we are only referred to a previous report.

Let’s move on. The 1990 report is the very first assessment report, so surely this must have the evidence we are ready to hear at this point!

The Intergovernmental Panel on Climate Change (AR1, 1990)

The AR1 WG1 report is called “FAR Climate Change: Scientific Assessment of Climate Change” and it came out in 1990.

Chapter 2 is called “Radiative Forcing of Climate”.

Executive Summary
1 The climate of the Earth is affected by changes in radiative forcing due to several sources […]
2 The major contributor to increases in radiative forcing due to increased concentrations of greenhouse gases since pre industrial times is carbon dioxide […]
3 The most recent decadal increase in radiative forcing is attributable to CO2 […]
4 Using the scenario A ("business-as-usual case) of future emissions derived by IPCC WG3, calculations show the following forcing from pre industrial values (and percentage contribution to
total) by the year 2025. […] The total, 4.6 Wm^-2 corresponds to an effective CO2 amount of
more than double the pre-industrial value.

Ok, it used emission predictions (i.e. to predict the quantity of CO2 emitted) from a separate working group report. We would need to see why those predictions are valid also. But let’s stick to just the forcing calculations. How was the forcing calculated? And how do we know they are sensible calculations?

2.2 Greenhouse Gases
2.2.1 Introduction
[…] The strength of the greenhouse effect can be gauged by the difference between the effective emitting temperature of the Earth as seen from space (about 255K) and the globally-averaged surface temperature (about 285K).

Ok, this refers to the flat-non-rotating-weakly-insolated Earth calculation… not the most promising starting point.

Also of note is that this type of explanation is absent from the more recent reports…

In any case, does the calculation of the radiative forcing of CO2 really all depend on this blackbody flat-Earth assumption? Let’s see…

[…] Here we are primanly concerned with the impacts of changing concentrations of greenhouse gases. A number of basic factors affect the ability of different greenhouse gases to force the climate system […]
From this introduction it is clear that an assessment of the strength of greenhouse gases in influencing radiative forcing depends on how that strength is measured. There are many possible approaches and it is important to distinguish between them.

Although they do list many possible approaches, later they go on to say:

2.2.4 Relationship Between Radiative Forcing and Concentration
To estimate climate change using simple energy balance climate models […] it is necessary to express the radiative forcing for each particular gas in terms of its concentration change . This can be done in terms of the changes in net radiative flux at the tropopause:

ΔF = f(C0,C)

where ΔF is the change in net flux (in Wm^-2) corresponding to a volumetric concentration change from C0 to C.

Ok now we are getting a familiar form of the function as presented by NOAA much further above. As the progression indicates, this has remained essentially unchanged since this report came out in 1990.

Direct-effect ΔF-ΔC relationships are calculated using detailed radiative transfer models. Such calculations simulate […]

Ok, and it’s calculated using a model… as we already know. So, how do we know the model reflects reality?

Table 2.2 shows the radiative forcing approximation for CO2:

ΔF = 6.3 ln (C/C0)

With the note:

Functional form from Wigley (1987), coefficient derived from Hansen et al (1988).



Hansen et al (1988) is clearly a seminal paper as AR5 referenced Myhre et al. 1998 which also referenced Hansen et al, as well as AR3 referencing it directly.

We are really getting close now! This 1988 paper must be what definitively demonstrated the validity of this radiative forcing calculation approach.

Hansen et al. 1988

This paper is titled “Global Climate Changes as Forecast by Goddard Institute for Space Studies Three-Dimensional Model”.

In the “Introduction” we have:

Studies of the climate impact of increasing atmospheric CO2 have been made by means of experiments [sic!] with three-dimensional (3D) climate models in which the amount of CO2 was instantaneously doubled or quadrupled […] These models all yield a large climate impact at equilibrium for doubled CO2, with global mean warming of surface air between about 2°C and 5°C.

Oh boy… this paper is just yet another model! And not a particularly realistic one either (with CO2 “instantaneously” doubling or quadrupling - later they write their simulation has “no feedback of climate change on ocean heat transport”!). Also note the conflation of running climate models with “experiments” (i.e. control setup done with real life measurements taken).

From section 2. “Climate Model”:

The equilibrium sensitivity of this model for doubled CO2 (315 ppmv → 630 ppmv) is 4.2°C for global mean surface air temperature (Hansen et al. [1984], hereafter referred to as paper 2).

Ok, they refer to an earlier paper of theirs for the equilibrium sensitivity. But how do they know this 1988 or 1984 model reflects realty?

4 Radiative Forcing in Scenarios A, B, C
4.1 Trace Gases
The net greenhouse forcing, ΔT0, for these scenarios is illustrated in Figure 2; ΔT0 is the computed temperature change at equilibrium (t → ∞) for the given change in trace gas abundances, with no climate feedbacks included [paper 2].
[…] we anticipate that the climate response to a given global radiative forcing ΔT0 is similar to first order for different gases, as supported by calculations for different climate forcings in paper 2. Therefore results obtained for our three scenarios provide an indication of the expected climate response for a very broad range of assumptions about trace gas trends. The forcing for any other scenario […] can be compared to these three cases by computing ΔT0(t) with formulas provided in Appendix B.

Ok, this appears sensible. They made a model which is presumed to be accurate by relying on results from an earlier “paper 2”. The model was only run for three specific scenarios, but they provide a formula to interpolate for other scenarios in Appendix B. This latter formula is what appeared in the first IPCC report in 1990.

Let’s first see how the formula is derived, and then we can finally validate all of these calculations empirically!

Appendix B: Radiative Forcings
[…] Radiative forcings for a variety of changes of climate boundary conditions are compared in Figure B1, based on calculations with a one-dimensional radiative-convective (RC) model [Lacis et al., 1981]. The following formulae approximate the ΔT0 from the 1D RC model within about 1% […]

ΔT0(x) = f(x) - f(x0)
f(x) = ln ( 1 + 1.2x + 0.005x^2 + 1.4x10^-6x^3);
x0 = 315 ppmv, x <= 1000 ppmv

Ok, so Hansen et al either created or re-presented a formula to approximate the results of a model from Lacis et al. 1981. This formula was then simplified in AR1 1990 but in a way that preserves the results, presumably.

Let’s see what we find at this 1981 paper…

Lacis et al. 1981

The paper is called “Greenhouse Effect of Trace Gases, 1970-1980”.

Abstract. Increased abundances were measured for several trace atmospheric gases in the decade 1970-1980. […] The combined warming of CO2 and trace gases should exceed natural global temperature variability in the 1980’s and cause the global mean temperature to rise above the maximum of the late 1930’s.

Ok, how do they know?

Observed Trace Gas Abundances
[…] We recognize that more precise future measurements [of our planet’s atmospheric composition] may substantially modify the estimated changes of specific trace gases. Therefore, we give analytic expressions for the computed greenhouse warmings, so the results can be adjusted in accord with more accurate data.

1-D Radiative-Convective Model
The 1-d RC model uses a […] The radiative flux is obtained by integrating the radiative transfer equation […] The radiative calculations are made with a method […]

Ok, so it’s just a model with more calculations. How do they know the model is right?

Observed Atmospheric Temperature Trend

Recent analyses agree that the Northern Hemisphere surface air and troposhperic temperatures increased by about 0.1-0.2°C in the 1970’s ([…] Hansen et al., 1981). The latter authors [i.e. Hansen et al.] also analyzed the global mean temperature trend, for which they found a similar increase in the 1970’s.
Normal fluctuations of the smoothed global mean temperature are of the order of 0.1°C for decadal time scales. […] Therefore, although the observed global temperature change in the 1970’s is consistent with that expected from increased trace gas abundances, the change is too small to be confidently ascribed to the greenhouse effect.

Uhm… wow. So the answer is, the author’s of this 1981 paper don’t know that the model calculation reflects reality. They just happened to make a model that matched observed temperatures… that could also be attributed to different things…

Ok, but these calculations matched what Hansen et al found in their “paper 2”. So, this must be where the real evidence lies!

Hansen et al. 1984

This paper is titled “Climate Sensitivity: Analysis of Feedback Mechanisms”.

It should be clear by now that everything relies on this paper’s results. All paths from the most recent AR6 lead backwards towards the 1988 Hansen et al. paper, which is a model that bases the validity of its predictions on this 1984 paper. All the radiative forcing calculations throughout the past four decades rely on the empirical validity of this formula, which so far we have seen only to be based on calculations which one other author indicated could not even account for the calculated effect with certainty.

Everything is on the line here… but as the scientific consensus has been so well-established and peer-reviewed for these past four decades, this must be the rock-hard, firm foundation atop which all of climate science lies!

Abstract. We study climate sensitivity and feedback processes in three independent ways :
(1) by using a three dimensional (3-D) global climate model for experiments [sic] in which solar irradiance S0 is increased 2 percent or C02 is doubled, (2) by using the CLIMAP climate boundary conditions to analyze the contributions of different physical processes to the cooling of the last ice age (18K years ago), and (3) by using estimated changes in global temperature and the abundance of atmospheric greenhouse gases to deduce an empirical climate sensitivity for the period 1850-1980.

Ok, points 1 and 2 are a bit alarming as they are also just models and calculations.

But finally, we get to the nub of the issue! They link the result of the model calculation to an empirically-measured climate sensitivity! Finally we can see how they determined the validity of these calculations.

They detail this 3rd approach here (emphasis mine):

The temperature increase believed to have occurred in the past 130 years (approximately 0.5°C) is also found to imply a climate sensitivity of 2.5-5°C for doubled C02 (f = 2-4). if (1) the temperature increase is due to the added greenhouse gases, (2) the 1850 C02 abundance was 270 +/- 10 ppm, and (3) the heat perturbation is mixed like a passive tracer in the ocean with vertical mixing coefficient k - 1 cm2 s-1.

And the Oroborous is complete.

WTF !! !! !! !! !! !! !! !! !! !! !!

There you have it. Four decades of research, calculations, models, and scientific consensus around measuring the effect of increased CO2 concentration on global temperature… and it is all based on a 1984 assumption that the (“believed”) temperature rise from 1850-1980 was due to that very effect being calculated, namely increased CO2 concentration (further based upon a starting-point “choice” of one of five values for 1850 CO2 abundance).

There are no further references. The buck stops here. All paths lead to this 1984 paper, which the seminal 1988 paper is based on. The single and solitary validation of the models and calculations reflecting physical reality, proving that increasing CO2 → leads to increasing temperatures in physical reality (and not just in models and calculations), that has been given in these four decades, is that it matches an assumption made in 1984 that an increase in CO2 led to an increase in temperatures.

In other words, the mainstream, scientific consensus is nothing other than forty years of circular reasoning. Each updated report only re-affirms and re-assures that the calculations are established, well-founded, proven effective, and simply refers to earlier works that say the same thing!


The following article by David A. Burton on is highly informative, titled “Hansen et al 1988, retrospective”:

Reviewing the predictions of a seminal climate modeling paper, thirty years later
In 1988 NASA’s James Hansen and seven co-authors wrote a highly influential, groundbreaking climate modeling paper entitled, Global Climate Changes as Forecast by Goddard Institute for Space Studies Three-Dimensional Model (pdf). […]
They predicted (src) a “warming of 0.5°C per decade” (or “nearly two degrees F higher in 20 years”) if emissions growth was not curbed (though their graph showed only about 0.37°C per decade).
Now, I would agree that +0.5°C/decade would be something to worry about! Fortunately, it was nonsense.
Even so, climate alarmists frequently claim that the NASA GISS model was “remarkably accurate.” Only in the massively politicized field of climatology could a 200% error be described as remarkably accurate. Even economists are embarrassed by errors that large.
In fact, it wasn’t just their temperature projections which were wrong. Despite soaring CO2 emissions , even CO2 levels nevertheless rose more slowly than their “scenario A” prediction, because of the strong negative feedbacks which curbed CO2 level increases, a factor which Hansen et al did not anticipate. Although CO2 emissions increased by an average of 1.97%/year, CO2 levels increased by only about 0.5%/year.
It is impossible to imagine that Dr. Hansen, his seven co-authors, the peer-reviewers, and the JGR editors, were all ignorant of those already-existing treaties. So there’s no excuse for the paper nevertheless projecting exponential increases in CFCs, in any of their scenarios. They knew CFC emissions would be falling, not rising, yet they promoted a “scenario” as “business as usual,” which they knew was actually impossible.
In other words, Hansen et al 1988 [i.e. the seminal paper detailed above] was wildly wrong about almost everything.)

Why did they write it, then?

IPCC founded

Most scientists are cautious about making predictions which are apt to embarrass them in the future. But Hansen et al 1988 had a purpose. It was the basis for Dr. Hansen’s famous June 23, 1988 Congressional testimony. 5½ months after that testimony, and 3½ months after the paper was published, the United Nations created the Intergovernmental Panel on Climate Change, to combat the perceived threat — a threat which turns out to have been much ado about very little.
So, even though the authors got just about everything wrong in their paper, it was nevertheless a great success, because it accomplished what it was intended to accomplish [emphasis added].

Incidentally the following is a very interesting snippet regarding the context of that June 23, 1988 testimony, an excerpt from “The Climate Fix: What Scientists and Politicians Won’t Tell You About Global Warming” (emphasis added):

In the summer of 1988, global warming first captured the imagination of the American public. In early June of that summer Senator Al Gore (D-TN) organized a congressional hearing to bring attention to the subject, one that he had been focusing on in Congress for more than a decade. The hearing that day was carefully stage-managed to present a bit of political theater, as was later explained by Senator Tim Wirth (D-CO), who served alongside Gore in the Senate and, like Gore, was also interested in the topic of global warming. “We called the Weather Bureau and found out what historically was the hottest day of the summer. Well, it was June 6th or June 9th or whatever it was. So we scheduled the hearing that day, and bingo, it was the hottest day on record in Washington, or close to it. What we did is that we went in the night before and opened all the windows, I will admit, right, so that the air conditioning wasn’t working inside the room.”

The star witness that day was Dr. James Hansen, a NASA scientist who had been study climate since the 1960s. […]
Looking back many years later one observer remarked that the 1988 Gore-Hansen hearing in the summer of 1988 “sparked front page coverage across the globe and touched off an unprecedented public relations war and media frenzy, marks the official beginning of the global warming policy debate.” […]

Indeed, Hansen, with his 1984 and 1988 papers, set out to do precisely that which he (along with Al Gore, Tim Wirth, and others) accomplished in 1988, together with a little help of con-artistry of picking the hottest day in summer and turning off the air conditioning during a testimony about global warming: the eventual creation of the IPCC and the birth of a worldwide hoax.

Final Notes

As a final note, the following is relevant when considering the reported historical and recent temperature trends: a series by Jennifer Marohasy titled “Hyping Daily Maximum Temperatures”. It starts as follows:

There is more than one way to ruin a perfectly good historical temperature record. The Australian Bureau of Meteorology achieves this in multiple ways, primarily through industrial scale remodelling (also known as homogenisation – stripping away the natural warming and cooling cycles that correspond with periods of drought and flooding), and also by scratching historical hottest day records, then there is the setting of limits on how cold a temperature can now be recorded and also by replacing mercury thermometers with temperature probes that are purpose-built, as far as I can tell, to record hotter for the same weather.


That is a magnificent piece of writing @claudiu !

Though reclining, I was emotionally “on the edge of my seat”.

Thanks for taking the time to share!!!

It has me singing Black Sabbath

“Generals gathered in their masses, just like witches at black masses”.

A black body mass, as it turns out.

That Hansen bloke is the one I found to have claimed in his book (apologies for forgetting it’s name) that the Stefan-Blotzmann equation is accurate in a simulation, by, wait for it…by using the Stefan-Blotzmann equation!