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:
- How much warming will a given increase in CO2 give? and,
- 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” 
.
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 airclim.org, 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”)
Introduction
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:
Recap
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**)**
where:
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:
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”.
Further:
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.
Further:
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 7.3.5.1 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
[…]
8.3.2.1 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.
