Energies 2020, 13, 1365; doi:10.3390/en13061365 www.mdpi.com/journal/energies
How Much Human-Caused Global Warming Should
We Expect with Business-As-Usual (BAU) Climate
Policies? A Semi-Empirical Assessment
*, Michael Connolly
, Robert M. Carter
and Willie Soon
Dublin D11, Ireland; firstname.lastname@example.org
Center for Environmental Research and Earth Sciences (CERES), Salem, MA 01970, USA;
Queensland 4000, Australia; email@example.com
* Correspondence: firstname.lastname@example.org
† RMC was a retired professor and independent scientist, but passed away on 19 January 2016.
Received: 17 February 2020; Accepted: 11 March 2020; Published: 15 March 2020
Abstract: In order to assess the merits of national climate change mitigation policies, it is important
to have a reasonable benchmark for how much human-caused global warming would occur over
the coming century with “Business-As-Usual” (BAU) conditions. However, currently, policymakers
are limited to making assessments by comparing the Global Climate Model (GCM) projections of
future climate change under various different “scenarios”, none of which are explicitly defined as
BAU. Moreover, all of these estimates are ab initio computer model projections, and policymakers
do not currently have equivalent empirically derived estimates for comparison. Therefore, estimates
of the total future human-caused global warming from the three main greenhouse gases of concern
, and N
O) up to 2100 are here derived for BAU conditions. A semi-empirical approach is
used that allows direct comparisons between GCM-based estimates and empirically derived
estimates. If the climate sensitivity to greenhouse gases implies a Transient Climate Response (TCR)
of ≥ 2.5 °C or an Equilibrium Climate Sensitivity (ECS) of ≥ 5.0 °C then the 2015 Paris Agreement’s
target of keeping human-caused global warming below 2.0 °C will have been broken by the middle
of the century under BAU. However, for a TCR < 1.5 °C or ECS < 2.0 °C, the target would not be
broken under BAU until the 22nd century or later. Therefore, the current Intergovernmental Panel
on Climate Change (IPCC) “likely” range estimates for TCR of 1.0 to 2.5 °C and ECS of 1.5 to 4.5 °C
have not yet established if human-caused global warming is a 21st century problem.
Keywords: climate change mitigation; climate sensitivity; airborne fraction; Paris Agreement;
climate policies; business-as-usual
Since the late-1960s and early-1970s, computer model simulations of the Earth’s climate have
been predicting that increasing concentrations of “greenhouse gases” (chiefly, carbon dioxide or CO
in the atmosphere from human activity should be causing substantial global warming at the Earth’s
surface and in the lower atmosphere [1,2]. In the 1960s  and 1970s , estimates of global surface
temperature trends (which mostly were confined to the Northern Hemisphere since there is less long-
term data for the Southern Hemisphere) suggested, if anything, a global cooling trend. However,
during the 1980s, the cooling trend reversed and, by the late-1980s, the long-term linear trend since
the (relatively cold) late-19th century was warming [5–7]. This prompted several researchers to argue
that the long-term warming trend was in fact the “enhanced greenhouse warming” originally
predicted by the computer models, e.g., [8–10]. To distinguish this predicted “enhanced greenhouse
warming” due to increasing greenhouse gas concentrations from a naturally occurring global
Energies 2020, 13, 1365 2 of 53
warming trend which might have occurred anyway, the term “Anthropogenic Global Warming”
(AGW) is often used. These claims garnered a lot of media attention and public concern, e.g., .
Ultimately, this led the United Nations to set up the United Nations Framework Convention on
Climate Change (UNFCCC) with the goal of facilitating international negotiations to achieve the “(…)
stabilization of greenhouse gas concentrations in the atmosphere at a level that would prevent dangerous
anthropogenic interference with the climate system” . To work in parallel with the political work of
the UNFCCC, the United Nations also co-founded, with the World Meteorological Organization, a
separate body called the Intergovernmental Panel on Climate Change (IPCC) to provide amongst
other things “a comprehensive review (… on) the state of knowledge of the science of climate and climatic
In the ensuing years, the computer models have continued to predict that increasing greenhouse
gas concentrations should be causing substantial global warming. Indeed, based on the results of
simulations with one of the NASA Goddard Institute of Space Studies (GISS)’ computer models, Lacis
et al. (2010) concluded that “atmospheric CO2 (… is the) principal control knob governing Earth’s
temperature” . Largely on the basis of comparing the results of such computer models to global
temperature trends, the IPCC’s most recent complete Assessment Report (2013) concluded that, “It is
extremely likely that human influence has been the dominant cause of the observed warming since the mid-
20th century”  (Emphasis in original). Although a competing series of reports has been published
by the Nongovernmental International Panel on Climate Change (NIPCC), which contradicts many
of the IPCC’s findings, e.g., NIPCC (2013)  and (2019) , the IPCC reports are widely cited and
have been highly influential among both the scientific community and policymakers.
Meanwhile, the efforts of the UNFCCC have led to a series of major international treaties and
agreements to try to reduce greenhouse gas emissions, from the Kyoto Protocol (1996)  to the
Paris Agreement (2015) . In particular, the Paris Agreement specifically aims to encourage
national and international policies to reduce greenhouse gas emissions with the view to, “Holding the
increase in the global average temperature to well below 2 °C above pre-industrial levels and pursuing efforts
to limit the temperature increase to 1.5 °C above pre-industrial levels” . Although the United States has
decided to withdraw from the Paris Agreement , most nations are currently signed up to the
voluntary Paris Agreement.
The selection of a specific “global average temperature” in °C as an international “goal” is a
remarkably arbitrary and subjective process, e.g., see Mahoney (2015) . Hence, there has been
some debate over whether a target of 1.5 or 2 °C is better, e.g., [22–25], and whether or not such targets
in terms of global temperature are helpful, e.g., [26–30]. However, there is a more fundamental
question—what specifically should an individual nation do differently in order to “(keep) the global
average temperature to well below 2 °C above pre-industrial levels (or even) 1.5 °C”? If the motivation of
the Paris Agreement was to encourage individual nations to significantly alter their national policies
relative to “Business-As-Usual”, then it is important to know how much Anthropogenic Global
Warming to expect under “Business-As-Usual” conditions.
In other words, what is the “human-caused global warming baseline” against which efforts to
meet the Paris Agreement are to be assessed? This is the question we will attempt to answer in this
paper. However, while the question might initially seem fairly reasonable and straightforward, as we
will discuss, it is remarkably challenging to answer satisfactorily. In essence, it depends on the
answers to four separate questions:
• Question 1. What would future greenhouse gas emissions be over the coming century under
• Question 2. For each of the greenhouse gases, what is the relationship between emissions
and actual changes in atmospheric concentrations?
• Question 3. How different would global average temperatures be at present if greenhouse
gases were still at “pre-industrial concentrations”? In other words, how do we define the
“pre-industrial levels” of global average temperatures to which the Paris Agreement refers?
• Question 4. How “sensitive” are global average temperatures to increases in the atmospheric
concentrations of greenhouse gases?
Energies 2020, 13, 1365 3 of 53
With each of these questions, there is considerable debate in the scientific literature. However,
the relevant literature for each subject comes from quite different academic disciplines. The first
question is typically addressed by economists, political scientists, environmental governance
researchers, etc. The second question is mostly the realm of biologists, ecologists, geochemists,
oceanographers, etc. The third and fourth questions are both climate science problems, but even
within these topics, there are separate bodies of literature from, e.g., computer modelling research
groups, groups evaluating climate records, statisticians evaluating results from a meta-analysis
In other words, many researchers who might be familiar with the debates in one relevant branch
of the literature are often completely unaware of the debates in other relevant branches. In our
personal experience in dealing with these four questions, we have found that researchers with
expertise on one aspect are frequently delighted to have a robust scientific discussion on the
controversies within that specific aspect. However, as soon as the discussion shifts to one of the other
aspects, the researcher will typically tell us that they are “getting outside of their comfort zone” or that
they are “not very familiar with that subject”, and that they “would have to spend more time reading the
literature before continuing this discussion”.
We totally appreciate the discomfort felt by those researchers and recognize that many readers
might share this discomfort. However, we suggest that unless the scientific debate over all four of
these questions are simultaneously considered, it is unlikely that truly satisfactory answers will be
achieved to the over-arching question, “How much human-caused global warming should we expect with
Business-As-Usual (BAU) climate policies?” With that in mind, we will discuss all four of these sub-
questions in turn, including a brief review of the key relevant literature, before attempting to answer
the main question. Specifically, we will consider Question 1 in Section 2; Question 2 in Section 3;
Question 3 in Section 4 and Question 4 in Section 5. In Section 6, we will combine the answers to all
four questions to develop a set of Business-As-Usual projections.
2. What Would Future Greenhouse Gas Emissions Be Under “Business-As-Usual” Conditions?
As can be seen from Table 1, the Earth’s atmosphere is largely composed of nitrogen (~78%),
oxygen (~21%), argon (~1%) and some water vapor (~0.33% by mass, ~0.53% by volume). However,
when Tyndall (1861)  studied the infrared activity of the atmospheric gases, he noted that nitrogen
and oxygen were largely inactive with respect to infrared activity (argon was not discovered until
1894, but also is infrared-inactive). On the other hand, he noted that water vapor, and also some of
the trace gases (e.g., CO2 and CH4) were strongly infrared-active, i.e., they are what we now call
“greenhouse gases”. On this basis, he argued that if the dramatic climatic changes between glacial
and interglacial periods were due to changes in atmospheric composition (a theory that was popular
at the time), then changes in water (rather than CO2) would be a plausible candidate .
Table 1. Key statistics on the Earth’s atmospheric composition. The fraction by volume and total mass
figures are adapted from Table 1 of Hartmann (1994) . Calculated “Global Warming Potential
(GWP)” values are taken from Table 8.7 of the Intergovernmental Panel on Climate Change (IPCC)
Working Group 1’s 5th Assessment Report (2013 ). One ppmv is one part per million (by volume),
i.e., 0.0001% and one ppbv is one part per billion (by volume), i.e., 0.0000001%.
Volume of Dry
Air in 1990
(g) in 1990
Total Atmosphere 28.97 5.136 × 1021
Dry Air 28.964 100.0% 5.119 × 1021
Nitrogen N2 No 28.013 78.08% 3.876 × 1021
Oxygen O2 No 31.999 20.95% 1.185 × 1021
Argon Ar No 39.948 0.934% 6.59 × 1019
Water Vapor H2O Yes N/A 18.015 - 1.7 × 1019
Carbon Dioxide CO2 Yes 1 44.01 353 ppmv ~2.76 × 1018
Neon Ne No 20.183 18.2 ppmv 6.48 × 1016
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Krypton Kr No 83.80 1.14 ppmv 1.69 × 1016
Helium He No 4.003 5.24 ppmv 3.71 × 1015
Methane CH4 Yes 28 16.043 1720 ppbv ~4.9 × 1015
Xenon Xe No 131.30 87 ppmv 2.02 × 1015
Ozone O3 Yes 47.998 Variable ~3.3 × 1015
Nitrous Oxide N2O Yes 265 44.013 310 ppbv ~2.3 × 1015
“F-compounds” Various Yes >1000 Various ~1 ppbv <<1 × 1015
Several decades later, Arrhenius (1896) argued that because atmospheric water vapor
concentrations were more immediately responsive to air temperatures (e.g., warmer temperatures
lead to more evaporation from water-enriched surfaces and oceans), carbon dioxide was a better
candidate—even though by volume the average concentration of water vapor is more than 10 times
that of carbon dioxide . Although Arrhenius’ arguments were disputed by, e.g., Ångstrom (1901)
 and Simpson (1929) , the theory has remained popular. Moreover, Callendar (1938) 
argued that human activities since the Industrial Revolution (chiefly the use of fossil fuels) were
probably increasing the atmospheric concentration of CO2 and thereby leading to human-caused
global warming. We will briefly discuss the debate which this provoked in later sections. However,
for here it is sufficient to note that this theory was incorporated into the early computer climate
models, e.g., refs. [1,2], and as described in Section 1, this ultimately led the UN to argue that the
international community needed to dramatically reduce emissions of greenhouse gases in order to
minimize any future (human-caused) global warming that would occur if the world continued
In this paper, we are trying to quantify what the expected (human-caused) global warming from
“business-as-usual” would be. In this section, we deal with the first step of this process, which is to
quantify what future greenhouse gas emissions would be under business-as-usual. As can be seen
from Table 1, the most common of the greenhouse gases in the Earth’s atmosphere (by an order of
magnitude) is water vapor. However, like Arrhenius (1896) , the current computer climate models
assume that water vapor concentrations respond to changes in climate rather than drive climate
change, e.g., Lacis et al. (2010) . Moreover, the emissions of water vapor from human activity are
a relatively minor contributor to the hydrological cycle.
Therefore, in terms of the expected (human-caused) global warming, the chief “anthropogenic
greenhouse gas” of concern is CO2. However, various human activities can also lead to emissions of
other infrared active gases, and so the UNFCCC’s Kyoto Protocol (1996)  also included several
other greenhouse gases as being of potential concern: methane (CH4), nitrous oxide (N2O, also known
as “laughing gas”) and three halogenated gases that are collectively known as the “F-gases” (as they
all are fluorine-containing compounds).
There are many other trace gases which could also be regarded as “greenhouse gases”. However,
according to the latest IPCC assessment reports  and computer models (e.g., Ref. ), three
greenhouse gases—CO2, CH4 and N2O—together account for more than 90% of the expected
anthropogenic global warming under business-as-usual . With that in mind, we will confine our
analysis to just these three gases.
As we will discuss in Section 3, all three of these gases are naturally occurring gases that are
essential for life as we know it on this planet. Therefore, there are many natural sources and sinks of
these gases, e.g., photosynthesis requires CO2 and aerobic respiration releases CO2, while anaerobic
respiration releases CH4. However, various human activities are known to contribute to additional
emissions of these gases. In this section, we will look in turn at various estimates and projections of
the magnitude of the annual “anthropogenic emissions” of the three gases, and extrapolate from these
estimates how these annual emissions would be expected to change if things continued business-as-
usual. The estimates and projections used are listed in Table 2.
Energies 2020, 13, 1365 5 of 53
Table 2. Sources used in this study for emissions data.
Emissions Type Dataset Ref.
Historical CO2 Emissions
(fossil fuels/industry) Global Carbon Budget (2019), https://www.globalcarbonproject.org/ 
(Alternative Source) CDIAC, https://doi.org/10.3334/CDIAC/00001_V2017 
CO2 Emissions (Land
use/Land Cover) Global Carbon Budget (2019), https://www.globalcarbonproject.org/ 
(Alternative Source) Smith and Rothwell (2013), CDIAC, https://cdiac.ess-
Historical CH4 and N2O
Gütschow et al. (2019): The PRIMAP-hist national historical emissions time
series (1850-2017). v2.1. GFZ Data Services.
IPCC AR1 Projections IPCC Working Group 3, 1st Assessment Report (1990). There are 5 scenarios:
A, B, C, D and D* 
IPCC AR2 Projections IS92 Emissions Scenarios. The scenarios are A, B, C, D, E and F. Source:
IPCC AR3 and AR4
Special Report on Emissions Scenarios (“SRES”). This comprises more than
40 different scenarios, but six are recommended as “representative
scenarios”, i.e., A1, A1G, A1T, A2, B1 and B2. Source:
IPCC AR5 Projections
Representative Concentrations Projections (“RCP”) Database (Version 2.0.5).
This comprises four scenarios each of which is named in terms of the
expected increase in radiative forcing in W/m2 by 2100, i.e., 2.6, 4.5, 6.0, and
8.5. Source: http://www.iiasa.ac.at/web-apps/tnt/RcpDb
IPCC AR6 Projections
The Shared Socioeconomic Pathways (“SSP”) scenarios are paired with a
slightly extended range of the RCP projections (increases in radiative forcing
of 1.9, 3.4 and 7.0 W/m2 are also considered). Hence, they are sometimes
referred to as “SSP/RCP”. Nine scenarios have been recommended for use by
the CMIP6 climate modelling groups, i.e., SSP1-19, SSP1-26, SSP2-45, SSP3-70
(Baseline), SSP3-70 (LowNTCF), SSP4-34, SSP4-60, SSP5-34-OS, and SSP5-85
(Baseline). The naming format is SSPn-xx, where n is the pathway and xx is
the projected increase in radiative forcing by 2100 (× 10). Source:
2.1. Some Notes on Units and Acronyms
In order to minimize the use of large and cumbersome numbers, emissions are usually reported
in units of, e.g., gigatons of carbon dioxide (Gt CO2), teragrams of methane (Tg CH4), etc. Moreover,
since much of the focus is on carbon dioxide emissions, for brevity, carbon dioxide emissions are
frequently reported in terms of the carbon component of carbon dioxide, i.e., gigatons of “carbon”
(Gt C) instead of Gt CO2. This is a simple arithmetic calculation of dividing the mass of CO2 by 3.6675
(i.e., the molecular weight of CO2/molecular weight of C = 44.01/12 = 3.6675). For convenience, here
is a summary of the main relevant relationships for the three main anthropogenic greenhouse gases:
• 1 Gt C = 1 Pg C = 1000 Tg C = 3.6675 Gt CO2 = 3.6675 × 1012 kg of CO2 = 3.6675 × 1015 g of CO2
• 1 Mt CH4 = 1 Tg CH4 = 1 × 109 kg of CH4 = 1 × 1012 g of CH4
• 1 Mt N2O = 1 Tg N2O = 1 × 109 kg of N2O = 1 × 1012 g of N2O
Although emissions are usually described in terms of the mass of the gas, measurements of the
atmospheric concentrations are usually reported in fractions by volume. Therefore, in order to
consider the relationship between the emissions of a particular gas and the actual changes in
atmospheric concentrations of that gas (as we will do in Section 3), it is useful to convert the emissions
into an equivalent atmospheric concentration or vice versa. This can be approximated by using the
values of the atmospheric composition in 1990 listed in Table 1. For instance, given that the
atmospheric concentration of carbon dioxide of 353 ppmv (0.0353% by volume) in c. 1990 represents
a total mass of ~2.76 × 1018g CO2 = ~2760 Gt CO2 = ~752.6 Gt C, 1ppmv of CO2 is equivalent to ~7.8 Gt
CO2 or 2.13 Gt C. We can approximate the relationships for both CH4 and N2O similarly:
Energies 2020, 13, 1365 6 of 53
• 1 ppmv of CO2 ≅ 7.8 Gt CO2 or 2.13 Gt C
• 1 ppbv of CH4 ≅ 2.85 Tg CH4
• 1 ppbv of N2O ≅ 7.42 Tg N2O
We appreciate that there are many different acronyms, abbreviations, and shorthands repeatedly
used in this article. Therefore, we have listed them in Table 3 for quick reference.
Table 3. List of acronyms, abbreviations, and shorthands used in this article.
AGW Anthropogenic, i.e., human-caused Global Warming
CMIPn Coupled Model Intercomparison Project, phase n, where n=3, 5 or 6
CO2 Carbon dioxide
ECS Equilibrium Climate Sensitivity
GCM Global Climate Model. Note that historically this acronym originally referred to General
Circulation Models, i.e., early climate models
Gt Gigatonne, i.e., 1015 g
GWP Global Warming Potential
IPCC Intergovernmental Panel on Climate Change
IPCC ARn The nth IPCC Assessment Report (where n = 1−6)
IS-92 Projections used for IPCC AR2 (1995)
n × CO2 A climate model simulation that is run assuming atmospheric CO2 is n times that of
present (where n is typically 1, 2 or 4)
N2O Nitrous oxide, "laughing gas"
NASA GISS NASA Goddard Institute of Space Studies, based in New York, USA
Pg Petagram, identical to gigatonne, i.e., 1015 g
ppbv parts per billion by volume
ppmv parts per million by volume
RCP Representative Concentrations Projections, projections used for IPCC AR5 (2013)
RF Radiative Forcing
SRES Special Report on Emissions Scenarios, projections used for IPCC AR3 (2001) and AR4
Shared Socioeconomic Pathways. (Often described with an accompanying
Representative Concentrations Projection), projections to be used for the upcoming
IPCC AR6 report
TCR Transient Climate Response, a type of climate sensitivity estimate
Tg Teragram, i.e., 1012 g
UNFCCC United Nations Framework Convention on Climate Change
2.2. Carbon Dioxide (CO2) Emissions
The largest source of human-caused CO2 emissions comes from fossil fuel use and industrial
processes (e.g., cement production). Boden et al. (2017) have compiled estimates of the national and
global emissions from these processes from 1751 to the near present , and this is the main dataset
used by most researchers—either directly or indirectly (through using a dataset which is based on
the Boden et al. dataset). For convenience we use Friedlingstein et al. (2019)’s updated version of this
dataset, which was compiled as part of the “Global Carbon Budget” project .
The annual emissions since 1850 to the near present (2018) are plotted in Figure 1a. We can see
that since the end of World War 2, i.e., post-1945, there has been a substantial and almost continuous
growth in annual emissions. The solid black line represents a linear extrapolation of the data from
1946–2018 up to 2100, and therefore represents one estimate of “business-as-usual” growth in
emissions. However, as discussed in the Introduction, since the late-1980s, there has been
international interest in reducing CO2 emissions due to the concerns raised by the UNFCCC and
IPCC. Therefore, arguably the linear extrapolation for the period post-1990 (dashed line) is a better
period for estimating “business-as-usual” growth. Ironically, the extrapolation from 1990-2018
Energies 2020, 13, 1365 7 of 53
implies a slightly higher rate of growth. At any rate, we will use the linear extrapolations from both
periods as an upper and lower bound for business-as-usual growth in CO2 emissions from fossil fuels
and industrial usage.
There is a second source of indirect CO2 emissions that is human-caused, however. These are
emissions which occur from changes in land use or land cover, e.g., deforestation. Unfortunately,
these indirect emissions are rather hard to quantify, and there are multiple different estimates, e.g.,
refs. [41,49–52]. We had initially considered just using one of the more widely cited of these estimates
for extrapolating future emissions from changes in land use/land cover under BAU. However, often
these estimates imply opposing trends, e.g., the Houghton and Nassikas (2017)  estimate implies
that there has been a slight decreasing trend in annual emissions since 1997, while Hansis et al.
(2015)’s “BLUE” estimate implies a slight increasing trend over the same period . However, we
note that Friedlingstein et al. (2019) have compiled both these estimates and 15 different model-based
estimates for the post-1958 period as part of the “Global Carbon Budget” project . Therefore, for
our analysis in this paper, we have calculated the mean and standard errors of all 17 of these
estimates. We then use a linear extrapolation of the upper and lower bounds of the error bars as our
projection of BAU emissions from changes in land use/land cover up to 2100—see Figure 1b.
In Figure 1c, we have summed the two separate components together to develop a BAU
projection of the total annual human-caused CO2 emissions up to 2100. In Figure 2, we then compare
this projection to the various emission scenarios that have been considered by each of the IPCC
reports. Figure 3 shows the equivalent comparisons for the two separate components from the IPCC’s
2nd Assessment Report (1995), but such a breakdown was not available for the 1st Assessment Report
(1990)’s emissions scenarios.
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Figure 1. Historical and projected "Business-As-Usual" CO2 emissions for: (a) fossil fuel and industry
usage; (b) changes in land use/land cover; (c) the sum of both components. The horizontal axes
correspond to years. Each of the plots for the historical period in (b) represents a different estimate of
the CO2 emissions since 1959, as compiled by the Global Carbon Budget project. The acronyms of
these estimates are provided in the legend below (b), but for further details on each of these estimates,
we refer the reader to Friedlingstein et al. (2019) and references therein. However, for the analysis in
this paper we will use the mean ± twice the Standard Error of all these estimates, which is shown with
a thick solid red line (with light red envelope).
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Figure 2. Comparison of the new “Business-As-Usual” projections of future total CO2 emissions with
the various projections considered by the IPCC's (a) 1st Assessment Report (AR1, 1990); (b) the 2nd
Assessment Report (AR2, 1995); (c) the 3rd Assessment Report (AR3, 2001); the 4th Assessment Report
(AR4, 2007); (d) the 5th Assessment Report (AR5, 2013); and (e) the upcoming 6th Assessment Report
Energies 2020, 13, 1365 10 of 53
(AR6, due c. 2021/2022). The horizontal axes correspond to years. Details on the projections are
provided in Table 2.
Figure 3. Comparison of the new "Business-As-Usual" projections of future CO2 emissions for (a–d)
fossil fuel and industry usage and (e–h) changes in land use/land cover with the various projections
considered by the IPCC’s Assessment Reports. Note that the vertical axes for (e–h) have a different
scale than for (a–d). The horizontal axes correspond to years. Details on the projections are provided
in Table 2.
Comparing our BAU projection to the various IPCC scenarios, we see from Figure 2a, that
Scenario A from the 1st Assessment Report (1990)  was actually a fairly good match for BAU.
However, all the other scenarios implied a continual decrease in emissions post-1990 which did not
occur. For the 2nd Assessment Report (1995) , our BAU projection is intermediate between
scenarios IS92-F and IS92-A/IS92-B—see Figure 2b—but they also considered a much higher-growth
scenario as IS92-E and two scenarios with a more modest emissions rate from 1995 up to present than
has been observed and which imply a steady decrease in emissions from about 2025 until the end of
The “SRES” projections that were developed in a special IPCC (2000)  report were used for
both the 3rd (2001)  and 4th (2007)  Assessment Reports. These included more than 40 different
Energies 2020, 13, 1365 11 of 53
scenarios, but six of these (“A1”, “A1G”, “A1T”, “A2”, “B1”, and “B2”) were chosen as being
representative of the full range of available scenarios. We compare them to our BAU projection in
Figure 2c. None of these six “SRES” scenarios match well with our BAU projection. “A1G” and “A2”
both imply a growth in emissions that is considerably higher than BAU. This is broadly consistent
with the findings of McKitrick et al. (2013)  as well as the earlier critique by Castles and Henderson
(2003) , which led to considerable debate, e.g., [59–62]. Meanwhile, the rest of the scenarios imply
changes that are considerably less than BAU. “A1” and “A2” match our BAU projection reasonably
well up to 2050, but then they diverge in opposite directions (“A1” increasing faster than BAU and
Figure 2d compares our BAU projections to the four Representative Concentrations Projections
(RCP) scenarios  considered by the most recent 5th Assessment Report (2013) . As for the SRES
projections, none of them match well. The RCP 8.5 scenario implies a growth in emissions much
greater than BAU. This agrees with several recent articles pointing out that RCP 8.5 substantially
overestimates CO2 emissions relative to BAU, e.g., [63–66]. Meanwhile, all of the other scenarios
imply that emissions are substantially decreasing relative to BAU over the 21st century.
In preparation for the upcoming 6th Assessment Report, the RCP scenarios have been updated
and elaborated on with a series of “Shared Socioeconomic Pathways” (SSP) [48,67,68]. Nine of these
combined SSP/RCP scenarios have been recommended to the CMIP6 modelling groups, and we
compare these to our BAU projection in Figure 2e. Two of these recommended scenarios actually
match quite well to BAU, i.e., the two “SSP3-70” scenarios. However, the “SSP5-85 (Baseline)”
scenario implies much higher growth in emissions over the 21st century than BAU, while the other
scenarios imply much lower emissions than BAU.
2.3. Methane (CH4) Emissions
Historical estimates of past CH4 and N2O appear to have been much less studied so far.
However, recently, Gütschow et al. (2016)  have published version 2 of the “PRIMAP-hist national
historical emissions time series”. We have used their 2019 update (version 2.1)  to extrapolate CH4
annual emissions up to 2100 in this section and the equivalent extrapolations for N2O in Section 2.4.
Version 2.1 of the dataset estimates emissions up to 2017, and also provides an upper and lower
bound. Therefore, we applied our 1946–2017 and 1990–2017 linear extrapolations to both the upper
and lower bound. The results are shown in Figure 4a. We use the lowest and highest extrapolations
from these four extrapolations as the upper and lower bound for BAU annual emissions up to 2100.
In Figure 4b–f, we again compare our BAU projections to the scenarios used by each of the IPCC
reports. We note that all the scenarios for the 1st Assessment Report start at a much higher annual
emission rate than observed—see Figure 4b. This thereby implies much greater emissions over the
21st century than our BAU projection. However, this seems to be because they apparently mistakenly
included several natural sources of CH4 emissions in their total annual human-caused emissions.
For subsequent reports, these naturally occurring emissions appear to have been separated out.
As a result, the starting point for the later IPCC report scenarios matches quite well with the historical
human-caused emission estimates (and therefore also with our BAU projection). However, for the
2nd Assessment Report, scenarios and the SRES projections used in the 3rd and 4th Assessment
Reports, CH4 emissions were projected to increase at a much higher rate than was observed up to
present and continue to increase at a rate much higher than BAU for much of the 21st century—see
Figure 2c,d. Some of the projections imply lower annual emissions than BAU by 2100, but this appears
to be because it is assumed that there will be active policy-driven reductions in CH4 emissions in the
second half of the 21st century.
On the other hand, several of the scenarios in both the RCP scenarios—Figure 4e—and the new
SSP/RCP scenarios—Figure 4f—imply that CH4 emissions will be much less than our BAU projection.
Although, again, the RCP 8.5 scenario overestimates BAU CH4 emissions, as do several of the
SSP/RCP scenarios over most of the century, i.e., “SSP3-70 (Baseline)”; “SSP5-85 (Baseline)” and
Energies 2020, 13, 1365 12 of 53
Figure 4. (a) Historical and projected "Business-As-Usual" CH4 emissions. (b–f) A comparison of said
Business-As-Usual projections to the projections considered by the various IPCC reports. The
horizontal axes correspond to years. Details on the projections are provided in Table 2.
Energies 2020, 13, 1365 13 of 53
2.4. Nitrous Oxide (N2O) Emissions
Figure 5 presents the equivalent analysis for annual N2O emissions. For brevity, we will not
comment in too much detail on the comparisons, but we will note a key point difference. As for CH4,
the starting point for annual N2O emissions seems to have been higher than the current estimates of
historical emissions. However, there appears to have been much more inconsistency in the estimates
of current emissions between reports. The scenarios used by both the 1st and 5th Assessment Reports
imply higher annual emissions at the start of their projections than the current estimates, while those
used by the 2nd, 3rd, and 4th Assessment Reports imply lower annual emissions. On the other hand,
the starting annual emissions implied by the latest SSP/RCP scenarios match well with the current
estimates of historical emissions.
Energies 2020, 13, 1365 14 of 53
Figure 5. (a) Historical and projected "Business-As-Usual" N2O emissions. (b–f) A comparison of said
Business-As-Usual projections to the projections considered by the various IPCC reports. The
horizontal axes correspond to years. Details on the projections are provided in Table 2.
Energies 2020, 13, 1365 15 of 53
3. What Is the Relationship between Greenhouse Gas Emissions and Actual Changes in
It is the atmospheric concentrations of these gases that the computer model simulations predict
should be influencing global temperatures [1,2,8–10], rather than the rates of anthropogenic
emissions. However, CO2, CH4, and N2O are all naturally occurring gases. They also each play
important roles in many biological processes. In particular, CO2 is consumed by photosynthesis and
released by (aerobic) respiration, and therefore is a key component for all life on this planet. Hence,
there are many natural fluxes into and out of the atmosphere for these gases. For convenience, a flux
out of the atmosphere is usually referred to as a “sink” and a flux into the atmosphere as a “source”.
Therefore, in order to estimate how much human-caused global warming the projected BAU
emissions in Section 2 could potentially cause, we need to estimate what fraction of the emitted gases
will remain in the atmosphere, i.e., what will the “airborne fraction” of the emitted gases be? Given
the many uncertainties associated with the natural sources and sinks for each of the three gases, we
argue that currently the best way to estimate this is to consider how the airborne fractions have
behaved since continuous records of atmospheric concentrations began (in 1958/59 for CO2; 1978/79
for CH4 and N2O). In this section, we will calculate the airborne fractions by comparing the
anthropogenic emissions described in the previous section to the observed changes in atmospheric
concentrations using the datasets listed in Table 4.
Table 4. Sources for atmospheric greenhouse gas concentration data used in this study.
Emissions Type Dataset Reference
CO2, CH4 and N2O
NOAA ESRL Global Monitoring Division,
(Alternative Source) The NOAA Annual Greenhouse Gas Index (AGGI)
N2O (Alternative Source) Combined Nitrous Oxide data from NOAA ESRL
Law Dome, Antarctic Ice
NOAA NCEI Paleoclimatology Data,
IPCC AR5 Projections RCP Database (Version 2.0.5), http://www.iiasa.ac.at/web-
3.1. The Airborne Fraction of Carbon Dioxide (CO2) Emissions
Figure 6a shows the observed annual atmospheric CO2 concentrations as recorded at Mauna Loa
observatory in Hawai’i (solid green line) since systematic measurements began in early-1958 and also
globally averaged estimates from multiple observatories around the world since 1979 (dashed blue
line). Although the globally averaged curve is slightly below the Mauna Loa curve, they both almost
overlap each other. Therefore, since the Mauna Loa record is longer, for the rest of this paper, we will
treat it as being representative of “global atmospheric CO2 concentrations”. It can be easily seen
that—as discussed earlier—atmospheric CO2 concentrations have been steadily rising at a rate of
roughly ~1.5 ppmv per year since at least 1959, i.e., the start of the record. Antarctic ice core estimates
of pre-historic atmospheric CO2 concentrations suggest that up until the 19th/20th centuries,
concentrations had remained fairly constant since the end of the last glacial period more than 10,000
years ago , only fluctuating within the range 271–285 ppmv . This small range of “pre-
industrial variability” is shown by the grey band in Figure 6a, with the dashed black line
corresponding to the mean value of 280 ppmv.
We will discuss below some of the scientific debate over exactly how reliable the Antarctic ice
core estimates are. Nonetheless, if we assume for now that the Antarctic ice core estimates are reliable,
we can see why it is widely believed that the rise in atmospheric CO2 from ~280 ppmv to ~410 ppmv
today (a 46% increase) is largely human-caused and due to human-driven CO2 emissions. However,
as can be seen from Figure 6b, there is a challenging complication. The lower green curve represents
the annual change in atmospheric CO2, i.e., the increase in atmospheric CO2 from each year to the
Energies 2020, 13, 1365 16 of 53
next. As discussed in Section 2.1, we can convert the anthropogenic (i.e., human-caused) annual CO2
emissions determined in Section 2.2 from Gt C/year into the equivalent annual change in atmospheric
concentrations. This is the upper curve (solid red line with a surrounding envelope) of Figure 6b. The
two vertical axes are scaled so that they are directly interchangeable, i.e., an annual change of 1 ppmv
on the left-hand vertical axis is equivalent to 2.13 Gt C/yr on the right-hand axis.
Figure 6. (a) Changes in annually averaged atmospheric CO2 concentrations since direct and (almost)
continuous measurements began in 1959. Estimates of pre-industrial concentrations derived from the
Antarctic Law Dome ice core are shown with a grey band for comparison. (b) A comparison of the
annual anthropogenic CO2 emissions (red band) with the observed annual changes in atmospheric
CO2 (green line). (c) The “airborne fraction” for CO2, i.e., the fraction of anthropogenic CO2 emissions
that remained in the atmosphere for each year since 1960. The horizontal axes correspond to years.
Although both curves have generally increased over time, the lower curve corresponding to the
observed atmospheric changes has been consistently below the curve corresponding to
anthropogenic emissions. In other words, only a fraction of the anthropogenic CO2 emissions remains
in the atmosphere from year-to-year. The so-called “airborne fraction”, i.e., the ratio of atmospheric
change to anthropogenic emissions is plotted in Figure 6c.
The reason that there is not an exact 1:1 relationship between anthropogenic CO2 emissions and
atmospheric CO2 concentrations is that CO2 is a naturally occurring gas. Moreover, it is one of the
most important gases biologically speaking. Life as we know it on Earth is carbon-based, and this
carbon in living organisms largely comes from the photosynthesis of atmospheric CO2 by plants and
other photosynthetic organisms. As a result, as well as the anthropogenic sources for CO2, there are
Energies 2020, 13, 1365 17 of 53
also natural sinks and sources for CO2. In fact, current estimates for the annual anthropogenic CO2
emissions are ~12 Gt gC/year, but the current estimates for the emissions from natural sources are
~200 Gt C/year, and it is also estimated that natural sinks absorb ~200 Gt C/year of CO2 from the
atmosphere . Therefore, the exact relationship between anthropogenic CO2 emissions and actual
atmospheric CO2 concentrations depends on the many complex interactions between the various
natural and anthropogenic CO2 sources and sinks, known collectively as “the carbon cycle”.
The annual changes in atmospheric concentrations show quite a lot of variability from year-to-
year, which is not apparent from the annual anthropogenic emissions, and the airborne fraction
actually varies quite a bit from year-to-year, as has been noted by others (e.g., refs. [74–82]). This
suggests that natural variability actually plays quite a substantial role in atmospheric CO2
concentration trends. On the other hand, if the Antarctic ice core estimates are reliable, then it implies
that atmospheric CO2 has been almost constant for more than 10,000 years, making it very difficult to
see why the steady increase since at least 1959 is not a recent and human-caused phenomenon.
Moreover, if it were to transpire that all (or even most) of the recent increase in atmospheric CO2 were
a natural phenomenon, then this would completely undermine the entire basis for claiming that
society’s CO2 emissions are causing “human-caused global warming”. Therefore, whenever a
researcher publishes an analysis suggesting that some or all of the recent increase could be natural in
origin, such as the references cited above [76,78–82] and also refs. [74,75,77,83–89], their arguments
are attacked with a particular vehemence, e.g., [90–99].
In Kuhn’s 1962 book, “The structure of scientific revolutions” , he argued that for the vast
majority of what he called “normal science”, i.e., the day-to-day work of most researchers, scientists
carry out their research implicitly relying on one or more paradigms that are assumed to be
indisputable. Although the specific paradigms within one discipline might be different from a
separate discipline, and that they change over time, he argued that “normal science” implicitly relied
upon these paradigms being correct. As a result, Kuhn proposed that whenever a researcher
questions a key paradigm within a discipline, they are immediately attacked or ridiculed by their
peers. On the other hand, he noted that over time an increasing number of “anomalies” that are
difficult to explain may arise within that paradigm, and during “revolutionary science”, the
community may undergo a shift to a replacement paradigm. Ultimately, Kuhn argued that science
progresses over time through both processes.
We refer to this Kuhnian approach to viewing science here because in our opinion, a lot of the
(often acrimonious) debate between researchers on this particular topic, as well as several of the
topics we will discuss later (Sections 4.1, 4.2 and 5) can be best understood in terms of competing
paradigms. With regards to the debate over the relationships between natural and human-caused
sinks and sources of CO2, we have identified four distinct paradigms:
• Paradigm 1—the “anthropocentric” approach. It is assumed that any natural sinks and
sources of CO2 are effectively balanced, and that all human-caused CO2 emissions will
contribute to human-caused global warming. This was originally proposed by studies before
the Mauna Loa observations had begun or had only recently begun, e.g., refs. [37,101–103].
It also seems to be implicit among researchers who consider carbon dioxide (CO2) to be a
“pollutant”, even though it is a naturally-occurring gas, e.g., the US EPA’s 2009 so-called
“Endangerment finding” .
• Paradigm 2—the “airborne fraction” approach. Like Paradigm 1, it is assumed that any
natural sinks and sources are roughly balanced from year-to-year. However, given the fact
that the airborne fraction is <1, it is acknowledged that the natural sinks and sources are not
exactly balancing each other. Instead, it is assumed that some of the natural sinks (chiefly,
the oceans and terrestrial vegetation) are absorbing some of the anthropogenic emissions.
Within this paradigm, there is ongoing debate over whether these sinks will continue to take
up a fraction of this anthropogenic CO2 at the same rate they have been since 1959, e.g., refs.
[105–107], or whether the airborne fraction is going to start increasing towards 1 in the near
future, e.g., refs. [39,108,109].
Energies 2020, 13, 1365 18 of 53
• Paradigm 3—the “sinks and sources” approach. Within this paradigm, it is recognized that
anthropogenic emissions are a new source of CO2, but that there is also significant variability
in the magnitudes of the natural sinks and sources. In particular, it is widely acknowledged
that increasing temperatures should increase the natural CO2 emissions from soil respiration
[110,111] as well as reducing the solubility of CO2 in the upper oceans  (which could
potentially lead to net outgassing of CO2 into the atmosphere). For this reason, several
researchers have argued that some component of the observed increase in atmospheric CO2
since 1959 could be a result of a natural global warming trend (i.e., the opposite of the
human-caused global warming theory), e.g., refs. [16,17,74,75,77,79–81,85,113]. Importantly,
this paradigm does not rule out a contribution from anthropogenic emissions in the recent
increase—rather, anthropogenic emissions are treated as an additional source that needs to
be taken into account.
• Paradigm 4—the “resilient Earth” approach. This is similar to Paradigm 3, except that it is
disputed whether there is anything unusual about the increase since 1959. Within this
paradigm, it is argued that the Antarctic ice core estimates are unreliable and that similar
CO2 concentrations to present may well have occurred in the decades and centuries before
the Mauna Loa record began. Instead, it is argued that most (if not all) of the rise in CO2
over the Mauna Loa record was natural in origin (due to natural global warming), e.g., refs.
Notice that the four paradigms cannot all be correct. As a result, proponents of one paradigm
may consider proponents of competing paradigms to be not just wrong, but scientifically
incompetent. However, once the existence of different paradigms is appreciated and respected, it
may be possible for fruitful discussions to take place between competing paradigms. Indeed, it is
worth noting that the Mauna Loa observations were largely initiated in order to resolve the debate
 between proponents of Paradigm 1 (e.g., refs. [37,101–103]) and Paradigm 4 (e.g., Revelle and
Suess (1957) ). Yet, ironically, as explained below, the “airborne fraction” results implied by the
Mauna Loa record, i.e., Figure 6c, actually point towards either Paradigm 2 or 3.
Let us consider the evidence for and against each of these paradigms. First, if Paradigm 1 were
correct, then we would expect the airborne fraction to be 1 (or at least nearly 1). That is, we would be
expecting most of the emitted anthropogenic CO2 to remain in the atmosphere. On the other hand, if
Paradigm 4 were correct, then we would expect the airborne fraction to be near-zero on average, i.e.,
we would be expecting the changes in atmospheric CO2 to be largely independent of anthropogenic
emissions. However, as can be seen from Figure 6c, the airborne fraction has been fairly constant with
a mean of 0.44 ± 0.04 over the entire record. This appears to rule out Paradigms 1 and 4, leaving either
Paradigm 2 or 3.
Now, let us consider the reliability of the Antarctic ice core estimates. If these estimates are
correct and atmospheric CO2 was almost constant for nearly 10,000 years up to the 19th century
[38,72], then that seems to rule out much room for naturally occurring trends of more than a dozen
ppmv. In other words, it appears to rule out Paradigms 3 and 4. However, in this context it is worth
noting that several estimates of past CO2 concentrations derived from the stomata of fossilised leaves
imply considerably more variability during the pre-industrial era than that implied by the Antarctic
ice cores, see refs. [117–127]. Moreover, Greenland ice cores imply increases of ~20–30 ppmv more
than the Antarctic ice cores during relatively warm periods in the pre-industrial era, although it has
been argued that the Antarctic ice cores are more reliable, e.g., refs. [128–130].
If the greater variability implied by the stomatal-based estimates (or even the Greenland ice
cores) are accurate, then this could provide support for Paradigm 3. For instance, Kouwenberg et al.
(2005) suggest that atmospheric CO2 could have dropped as low as 260 ppmv and risen as high as
320 ppmv several times over the last millennium , while the Antarctic ice cores suggest that CO2
remained within the range 271–285 ppmv . However, it should be stressed that the current
concentrations of ~410 ppmv are still higher than those stomata-based estimates, which suggests that
anthropogenic emissions have significantly increased concentrations above natural variability, i.e.,
Energies 2020, 13, 1365 19 of 53
disagreeing with Paradigm 4. Moreover, the stomata-based estimates have been disputed by
supporters of the Antarctic ice core estimates [129,131].
Others have also suggested that the Antarctic ice core estimates are problematic and unreliable,
e.g., refs. [83,84,87–89], and Beck has suggested that early measurements of atmospheric CO2 before
the Mauna Loa observations began implied atmospheric concentrations above 400 ppmv in the 1940s
as well as in the early 19th century [87–89]. This would be very consistent with Paradigm 4, but, again,
all of these studies have been vehemently disputed by advocates for Paradigm 2 [98,99].
What does this tell us about the relationship between anthropogenic CO2 emissions and changes
in atmospheric CO2 up to 2100? Well, if Paradigm 4 were correct, then there should be no relationship
(or at best a weak one). In that case, arguably the rest of the analysis in this paper would be largely
redundant, and we could say that there should be no (or very little) human-caused global warming up
to 2100 [82–84,87–89,114], although it would not preclude the possibility of natural global warming.
However, as explained above, this would also imply an average airborne fraction of 0 or close to 0.
Similarly, we can rule out Paradigm 1, as this would imply an average airborne fraction close to 1.
If Paradigm 3 is correct, then at least some of the observed increase in atmospheric CO2 over the
Mauna Loa record is anthropogenic in origin, and therefore we argue that “business-as-usual”
conditions imply that the airborne fraction will remain fairly constant. Within Paradigm 2, there is
some debate over whether some of the sinks that are currently reducing the airborne fraction might
become “saturated”, e.g., refs. [39,105–109]. However, given that the annual airborne fraction has
remained fairly constant since the Mauna Loa record began in 1959, we will define “business-as-
usual” conditions to mean this will remain constant with a mean of 0.44 ± 0.04. In Section 3.4, we will
compare this assumption to the airborne fractions implicit in the IPCC RCP scenarios. But, first, let
us consider the other two relevant gases.
3.2. The Airborne Fraction of Methane (CH4) Emissions
Figure 7 shows the equivalent results for CH4. Although the CH4 observational records are not
as long as for CO2, there are more than 40 years of measurements (compilations of various flask
measurements beginning in 1978, and more systematic measurements beginning in 1984 ).
Unlike for CO2, the airborne fraction of anthropogenic emissions has been almost zero (0.07 ± 0.02)
over the entire record, and for a few years even went slightly below zero, i.e., atmospheric
concentrations decreased even though anthropogenic emissions continued.
Antarctic ice core estimates of atmospheric CH4 before the instrumental record  suggest pre-
industrial concentrations of less than half the current concentrations, i.e., 624–737 ppbv (0.624–0.737
ppmv) compared to ~1850 ppbv today . Furthermore, during the 1980s, atmospheric
concentrations were still rising. This led many researchers to suggest that anthropogenic CH4
emissions were significantly altering atmospheric concentrations of CH4 as well as CO2. Therefore,
CH4 was included as one of the six greenhouse gases considered under the 1996 Kyoto protocol .
Indeed, as Ganesan et al. (2019)  note, attempting to reduce anthropogenic CH4 emissions is one
of the main goals of the 2015 Paris Agreement . However, during the 1990s and early 2000s, the
rise in CH4 concentrations began to slow down and even plateaued for several years. It is only after
2006 that concentrations began to rise again. Over this entire period, anthropogenic emissions have
continued and even increased—see Figure 7b.
This has been a puzzle for researchers who had been assuming something like the Paradigm 2
we described in the previous section applied to CH4 emissions, e.g., refs. [133,135]. As a result,
researchers working on the “Global Methane Budget” are recognizing that there is significant
variability in many of the natural sinks and sources of methane, and that this natural variability may
be a major factor for the unexpected trends in atmospheric CH4—see Saunois et al. (2016) , which
builds on the work of Kirschke et al. (2013) .
Unlike CO2, where most of the anthropogenic emissions have tended to come from developed
nations with relatively high GDPs [137,138], most of the anthropogenic CH4 and N2O emissions
apparently come from agricultural processes (e.g., rice paddies and cattle production) in developing
nations—especially in Asia and South America, e.g., Tian et al. (2015) . However, Zhang et al.
Energies 2020, 13, 1365 20 of 53
(2020) have recently shown that the contribution of rice paddies in monsoon Asia has declined since
2007 , suggesting that other changes in sources and sinks are probably involved in the post-2006
Although Saunois et al. estimate that anthropogenic emissions (approximately 540–568 Tg
CH4/year) comprise about 60% of the total annual CH4 emissions, they caution that the uncertainties
over the natural sources appear to be much larger than for anthropogenic sources . The
variability in the natural sources and sinks remains poorly understood, e.g., Bastviken et al. (2011)
estimated that freshwater lakes, reservoirs, streams, and rivers could be contributing at least 103 Tg
Figure 7. (a) Changes in annually averaged atmospheric CH4 concentrations since direct and (almost)
continuous measurements began in 1979. The estimates of pre-industrial concentrations derived from
the Antarctic Law Dome ice core are shown with a grey band for comparison. (b) A comparison of
the annual anthropogenic CH4 emissions (red line) with the observed annual changes in atmospheric
CH4 (green line). (c) The “airborne fraction” for CH4, i.e., the fraction of anthropogenic CH4 emissions
that remained in the atmosphere for each year since 1980. Note that the airborne fraction was below
0 on three years (2001, 2004 and 2005). The horizontal axes correspond to years.
If the Antarctic ice core estimates of past atmospheric CH4 are inaccurate, then on the basis of
the very low airborne fraction of 0.07 ± 0.02 over the instrumental record, it is quite plausible that
most of the apparent trends in atmospheric CH4 are due to variability in the natural sinks and sources.
In that case, it would suggest that anthropogenic CH4 emissions might not be influencing
atmospheric concentrations, in which case they probably could be removed as a potential source of
human-caused global warming. We suggest that this possibility should be considered and we
encourage more research into identifying and quantifying the variability in the various natural
sources and sinks, perhaps building on the work of Saunois et al. (2016) , but explicitly
Energies 2020, 13, 1365 21 of 53
considering Paradigms 3 or even 4 as relevant for CH4. However, for the purposes of this analysis,
we will define BAU to imply that anthropogenic emissions are increasing the atmospheric
concentration, but with an airborne fraction of only 0.07 ± 0.02 up to at least 2100. As we will discuss
in Section 3.4, this is actually assuming a higher airborne fraction for CH4 than most of the IPCC RCP
3.3. The Airborne Fraction of Nitrous Oxide (N2O) Emissions
Figure 8 shows the equivalent results for N2O. The N2O observational record is of a similar length
to that of CH4. However, unlike CH4, the airborne fraction has been quite high, although there seems
to have been quite a bit of interannual variability with three years being above 1 (implying
atmospheric concentrations increased more than was emitted anthropogenically) and one year being
below 0 (i.e., the atmospheric concentration slightly decreased in spite of anthropogenic emissions).
Averaged over the entire record, the airborne fraction has remained fairly constant at 0.65 ± 0.09. This
suggests that anthropogenic N2O emissions are responsible for much (if not all) of the fairly steady
increase in atmospheric concentration (with a rate of +0.75 ppbv/year).
Figure 8. (a) Changes in annually averaged atmospheric N2O concentrations since direct and (almost)
continuous measurements began in 1979. The estimates of pre-industrial concentrations derived from
the Antarctic Law Dome ice core are shown with a grey band for comparison. (b) A comparison of
the annual anthropogenic N2O emissions (red line) with the observed annual changes in atmospheric
N2O (green line). (c) The “airborne fraction” for N2O, i.e., the fraction of anthropogenic N2O emissions
that remained in the atmosphere for each year since 1980. Note that the airborne fraction was below
0 in one year (1987) and above 1 in three years (1982, 1986 and 1989). The horizontal axes correspond
Energies 2020, 13, 1365 22 of 53
Having said that, the airborne fraction has been quite variable, and well below 1. Therefore, there
does seem to have been quite a bit of variability in the natural sinks and sources. Davidson and Kanter
(2014)  estimate that 65%–69% of the annual N2O emissions are natural in origin. However, there
is still a lot of ongoing research into quantifying different natural sources, e.g., refs. [143,144]. We
suggest that a similar attempt to quantify the natural sinks and sources for N2O to what Saunois et
al. (2016)  have been doing for the Global Methane Budget project would be helpful (perhaps
building on studies such as Davidson and Kanter (2014) . We would recommend following the
lead of Saunois et al. (2016) who seem to have been approaching the Global Methane Budget from
Paradigm 3, rather than the Paradigm 2 approach used by Friedlingstein et al. (2019)  for the
Global Carbon Budget. In the meantime, as for the other two gases, we will define BAU to imply that
the experimentally observed airborne fraction for N2O of 0.65 ± 0.09 will continue up to at least 2100.
3.4. Comparison of “Business-As-Usual” AirborneFfractions with the RCP Scenarios
In Figur e 9, we compare t he hist orical ai rborne fractions up to present and our projected constant
airborne fractions up to 2100 with the equivalent airborne fractions used in the IPCC’s four RCP
scenarios for (a) CO2, (b) CH4, and (c) N2O.
Figure 9. Comparison of the future airborne fractions implied by each of the IPCC AR5’s RCP
scenarios to our projected “Business-As-Usual” ranges for: (a) carbon dioxide (CO2); (b) methane
(CH4); and (c) nitrous oxide (N2O). The horizontal axes correspond to years. Details on the projections
are provided in Table 2.
For CO2, one of the scenarios (RCP 2.6) predicts a rapid decline in the airborne fraction becoming
negative after 2050. This scenario predicts that society will develop and implement technologies to
Energies 2020, 13, 1365 23 of 53
allow substantial carbon sequestration, leading to “negative CO2 emissions”, such as those
considered by Fuss et al. (2018) . On the other hand, for RCP 8.5, it is predicted that the airborne
fraction will gradually increase over the century (which would thereby increase the rate at which
atmospheric CO2 concentrations would increase). The other two scenarios imply a fairly constant
airborne fraction up to the middle of the century, but RCP 6.0 predicts a slight increase from 2040–
2070, followed by a slight decrease to 2100, while RCP 4.5 predicts a rather sharp drop in airborne
fraction (associated with “negative CO2 emissions”) from 2060 to 2080 followed by an increase to
2100. In comparison, our BAU projection lies in between the two intermediate scenarios (RCP 4.5 and
6.0) for the entire 21st century.
For CH4, all of the RCP scenarios except 8.5 predict that the airborne fraction will be lower than
our BAU projection. Even with RCP 8.5, the airborne fraction is predicted to decrease towards 0 from
2050 onwards. As a result, by 2100, our BAU projection, which is already very modest (as discussed
in Section 3.2) is higher than all four RCP scenarios. In other words, our BAU projection predicts a
slightly greater fraction of anthropogenic CH4 emissions will remain in the atmosphere than the RCP
As for N2O, all four of the RCP scenarios assume a starting airborne fraction of 0.45 in 2000,
which is lower than the historical airborne fraction of 0.65 ± 0.09. As a result, even though RCP 8.5
predicts a relative increase from 2010 to 2040 and RCP 6.0 predicts a slight increase from 2030 to 2050,
all four scenarios predict a lower airborne fraction than our BAU projection for the entire 21st century.
3.5. Projected Greenhouse Gas Concentrations up to 2100 under “Business-As-Usual” Airborne Fractions
Let us now combine the results of the previous sections in order to estimate future greenhouse
gas concentrations up to 2100 for our three gases assuming (a) that anthropogenic emissions continue
to grow “business-as-usual” and (b) that the observed airborne fractions for the gases remain constant
“business-as-usual”. In that case, the increase in atmospheric concentration for each of our gases for
each year is equal to the projected emissions for that year multiplied by the airborne fraction. The
results are plotted with black dashed lines in Figure 10, along with the equivalent projections for the
four RCP scenarios (in colored dashed lines) , the historical values (in red solid line), and the
range of “pre-industrial” variability implied by the Antarctic ice cores (in black dotted line) . Since
both our projected emissions and the average airborne fractions have uncertainty ranges associated
with them (see previous sections), the resulting concentration projections have a combined
uncertainty range shown with a gray bounding envelope.
Although the concentrations of both CH4 and N2O are still projected to be several orders of
magnitude lower than that of CO2 by 2100 (e.g., CH4 and N2O being reported in units of parts per
billion by volume and CO2 in parts per million by volume), according to the current computer models
(e.g., ) and the IPCC assessment reports (e.g., ), they are both expected to cause much more
global warming on a molecule-by-molecule basis than CO2. Specifically, it is argued that these gases
have a much greater “Global Warming Potential” (GWP) than CO2. The exact values of these GWP
calculations have changed between IPCC reports and depending on the timescale used (e.g., 20 years,
100 years or 500 years). However, if we use the 100-year GWP values from the more recent IPCC
Assessment Reports, i.e., Table 8.7 of the IPCC Working Group 1’s 5th Assessment Report (2013 ),
CH4 apparently has a “Global Warming Potential (GWP)” 28 times that of CO2 and N2O has a GWP
265 times that of CO2 (see Table 1). This means that 100 ppbv of CH4 is “equivalent to” 1.02 ppmv of
CO2 in terms of GWP and that 100 ppbv of N2O is equivalent to 25.21 ppmv of CO2. We have shown
these “CO2 equivalent” scales on the right-hand vertical axes of Figure 10b,c. For interested readers,
in the Supplementary Materials, we compare the total projected greenhouse gas concentrations under
BAU (in CO2 equivalent concentrations) to alternative projections that used the projected airborne
fractions implied by the RCP scenarios.
Comparing our projected CO2 concentrations to those of the RCP scenarios, it is actually quite
similar to the RCP 6.0 scenario, and indeed the RCP 6.0 scenario curve just about fits within the gray
bounding envelope of our projection up to 2100. This suggests that the CO2 concentrations of the RCP
6.0 scenario are actually a reasonable estimate of “Business-As-Usual” for the 21st century. This is
Energies 2020, 13, 1365 24 of 53
consistent with several recent articles that argue that RCP 8.5 implies a dramatic increase in CO2
emissions relative to “Business-As-Usual”, e.g., [63–66]. Readers might wonder why the RCP 6.0 CO2
concentrations match so well with our BAU projection when the RCP 6.0 emissions projections curve
in Figure 2d was lower than our BAU projection. This seems to be a consequence of the slight
temporary increase in airborne fraction of the RCP 6.0 scenario from 2040–2070 that can be seen in
Figure 10. Future greenhouse gas concentrations up to 2100 under "Business-As-Usual" conditions,
compared to the RCP scenarios, for (a) CO2; (b) CH4; and (c) N2O. Concentrations for CH4 and N2O in
“CO2 equivalents” are shown on the right-hand side vertical axes for comparison. The horizontal axes
correspond to years.
With regards to CH4, our projected CH4 concentrations are higher than all of the RCP scenarios
except RCP 8.5—see Figure 9b. RCP 8.5 projects a rapid acceleration in atmospheric CH4 beginning
over the coming decades, which is not predicted under BAU growth.
Meanwhile, our BAU projections for N2O imply a growth rate that is higher than all of the RCP
scenarios, even though our projected emissions in Figure 5d implied a projection intermediate
between the two middle RCP scenarios (RCP 4.5 and 6.0). This is due to the relatively low airborne
fraction for N2O projected by the RCP scenarios for the 21st century.
4. How Do We Define “Pre-Industrial” Global Temperatures?
4.1. How Much of the Recent Global Warming is Human-Caused vs. Natural?
Several widely cited papers have argued that 90%–95% (or more) of scientists agree on global
warming and climate change, e.g., Doran and Zimmerman (2009) ; Cook et al. (2013) ;
Stenhouse et al. (2013) ; Verheggen et al. (2014) . Separately, the IPCC 5th Assessment
Energies 2020, 13, 1365 25 of 53
Report has stated that, “warming of the climate system is unequivocal”, and that, “it is extremely likely
that human influence has been the dominant cause of the observed warming since the mid-20th century.” .
For this reason, many readers may be wondering at the title of this subsection. With that in mind, let
us briefly dissect what exactly was found by the studies just mentioned.
There have indeed been many surveys of the scientific community that have confirmed that
90%–95% (or more) of scientists agree that it is probably warmer today than during the late-19th
century and/or that the climate is changing. However, as we have written elsewhere, the climate is
always changing, and global temperatures have changed on timescales varying from decades and
centuries, e.g., Soon et al. (2003) [150,151]; Soon et al. (2015) , to millennia, e.g., Carter and
Gammon (2004) , to millions of years, e.g., Carter (2010) . Therefore, agreeing that the
climate has changed and/or that there has been long-term global warming since the late-19th century
does not in itself say anything about whether this is natural, human-caused, or a mixture of both.
That said, it is often implied that these surveys have also shown that 90%-95% (or more) of scientists
agree that this climate change and global warming is human-caused. However, a close inspection of
the survey results reveals that this is not true.
For instance, Doran and Zimmerman (2009)  sent a survey to over 10,000 Earth scientists
and received more than 3000 responses. Of the 3146 respondents, 90% answered “risen” to the
question, “When compared with pre-1800s levels, do you think that mean global temperatures have generally
risen, fallen, or remained relatively constant?”, i.e., they agreed that there has been global warming since
“pre-1800s”. However, the question they were asked on the causes of this warming was remarkably
ambiguous: “Do you think human activity is a significant contributing factor in changing mean global
temperatures?”. While 82% of the respondents answered, “yes”, Doran and Zimmerman neglected to
ask them what percentage they considered to be “a significant contributing factor”. In our experience,
among the general public, “significant” is synonymous with “large” or “substantial”, but among the
scientific community, it generally means, “not insignificant”, i.e., more than, e.g., 5%. In other words,
many of the respondents may still have felt that the recent global warming was mostly natural (or
perhaps a mixture of human and natural factors).
On the other hand, Cook et al. (2013)  purported to be a survey of the scientific literature
rather than the scientific community. The authors examined more than 10,000 abstracts from papers
that matched the search phrases of either “global climate change” or “global warming”. In total, 2/3
of the papers apparently expressed no position on the causes of global warming. Of the remaining
abstracts, only 2.1% of the abstracts explicitly disputed that global warming was mostly human-
caused and only 0.9% explicitly stated uncertainty over the causes of global warming. Therefore, they
concluded that 97% of published scientific articles agreed that global warming is human-caused.
However, as one of us has pointed out in Legates et al. (2015) , Cook et al. had neglected to
mention that only 8% of the 11,944 abstracts had actually made any explicit claim on the causes of
global warming. It is true that, of this 8%, very few abstracts explicitly disputed the claim that recent
global warming was mostly human-caused (3%). However, similarly, very few abstracts explicitly
endorsed the claim (6%). The vast majority (91%) of the abstracts that made an explicit claim on the
causes of global warming merely implied that human activity was a factor, i.e., they did not state
whether global warming was mostly human-caused or mostly natural.
Verheggen et al. (2014)’s survey of nearly 2000 climate scientists  was a bit more nuanced.
However, a close inspection of the survey results reveals that only 38% of the respondents believed
that recent global warming was entirely human-caused, and only 27% believed that it was mostly
human-caused. Meanwhile 12% of respondents believed that it was mostly or entirely natural, 12%
believed it was a mixture of both and 10% did not know. Meanwhile Stenhouse et al. (2013)’s survey
of nearly 2000 meteorologists  revealed that 52% believed that it was mostly or entirely human-
caused, but that 15% believed it was mostly natural or a mixture of both, and 21% were unsure. The
rest were not convinced that global warming would increase in the future.
In other words, there are actually several different perspectives among the scientific community
as to the causes of recent global warming:
Energies 2020, 13, 1365 26 of 53
• Paradigm 1. Recent global warming was mostly or entirely human-caused, and future
climate change is going to be increasingly dominated by human-caused global warming
• Paradigm 2. Recent global warming was a mixture of human and natural causes. This means
that the current climate models are probably underestimating the role of natural factors in
the recent warming and are therefore probably overestimating the magnitude of human-
caused global warming that we should expect.
• Paradigm 3. Recent global warming was mostly or entirely natural, and not human-caused.
This implies that there is something fundamentally wrong with the computer models, and
their projections of future human-caused global warming should be treated with skepticism.
This has important implications for our assessment of how much human-caused global warming
we shoul d expec t under BAU. So, it is important to understand why there could be such disagreement
among the scientific community on this fundamental point. To get an idea of why, in Figure 11, we
consider two competing perspectives. The left-hand side, i.e., Figure 11a–f, illustrates a common take
on the “mostly human-caused” paradigm as argued by the IPCC 5th Assessment Report . The
right-hand side, i.e., Figure 11g–l, summarizes the counter-arguments made by some of us in Soon et
al. (2015)  and presents a perspective from the “mostly natural” paradigm. For a detailed
discussion of each perspective, we refer readers to Chapter 10 of the IPCC 5th Assessment Report
 and Soon et al. (2015) , respectively. However, in brief, the key differences are as follows:
• The IPCC argued that automated statistical homogenization techniques, such as Menne and
Williams (2009) , are able to remove any non-climatic biases, such as the growth of
urban heat islands, and therefore use as many stations as possible to estimate global
temperature trends—regardless of whether they have been affected by urbanization bias or
not. Soon et al. argued that those automated homogenization techniques are inadequate for
that purpose, and therefore estimated global temperature trends using only rural (or mostly
• The IPCC argued that solar variability has been very low since the 19th century, and that
solar activity has been, if anything, declining since the mid-20th century. Therefore, they
only considered solar variability estimates that fit that narrative, e.g., Wang et al. (2005) 
or Krivova et al. (2010) . Soon et al. argued that all of the plausible estimates of solar
variability in the literature should be considered, and they identified one which implied
quite a substantial role for the Sun in global temperature changes since at least 1881, i.e.,
Scafetta and Willson (2014)’s updated version  of Hoyt and Schatten (1993) —see
also Scafetta et al. (2019) .
• The IPCC were therefore unable to explain any of the post-1950s global temperature trends
in terms of natural factors and concluded that human-caused factors (chiefly increasing
greenhouse gas concentrations) were needed to explain the warming since then. They
therefore concluded that recent global warming was mostly (or entirely) human caused. On
the other hand, Soon et al. were able to explain almost all of the temperature trends since
1881 in terms of changes in solar output. They therefore concluded that recent global
warming was probably mostly (or entirely) natural.
Energies 2020, 13, 1365 27 of 53
Figure 11. Example of two narratives from the competing (a–f) “recent global warming is mostly
human-caused” and (g–l) “recent global warming is mostly natural” paradigms. See text for a detailed
discussion. The horizontal axes correspond to years.
Energies 2020, 13, 1365 28 of 53
4.2. When Exactly Was “Pre-industrial”?
The UNFCCC-organized 2015 Paris Agreement declared an international agreement to, “(hold)
the increase in the global average temperature to well below 2 °C above pre-industrial levels and (pursue)
efforts to limit the temperature increase to 1.5 °C above pre-industrial levels” . However, while this
initially sounds like a very specific and definite agreement, a careful parsing of the wording reveals
a remarkable degree of ambiguity about what exactly the agreement is agreeing to.
Implicit in the above agreement is the “recent global warming is mostly human-caused”
paradigm described in Section 4.1. Pielke Jr. (2005)  has noted that the UNFCCC explicitly
defines “climate change” as being entirely human-caused, and so it is therefore not surprising that
their agreement does not consider the possibility that much (or even all) of this warming is natural.
However, even if we ignore the ongoing debate over how much of the warming since the late-19th
century is human-caused vs. natural, and assume for the sake of argument that the “mostly human-
caused” argument is correct, what exactly is meant by “pre-industrial levels” [22,162,163]?
As noted by Hawkins et al. (2017) , “in the absence of a formal definition for preindustrial, the
IPCC AR5 made a pragmatic choice to reference global temperatures to the mean of 1850-1900 when assessing
the time at which particular temperature levels would be crossed”. This decision seems to have been because
several of the standard instrumentally based global temperature time series used by the IPCC began
in 1850 or 1880. In the penultimate draft of the report, this period was apparently explicitly referred
to as “preindustrial”, but during the ensuing governmental approval session, this reference was
Therefore, although the IPCC AR5 reports seem to have been considered during the drafting of
the Paris Agreement, it is unclear which baseline was meant. Hawkins et al. (2017) argue that 1720–
1800 would make a more suitable baseline for “pre-industrial” global average temperatures than
1850–1900, while Lüning and Vahrenholt (2017)  argue that 1940–1970 is the most suitable
baseline. The choice of baseline is quite significant since paleoclimate reconstructions suggest that
global average temperatures have varied substantially over the last millennium and earlier, e.g., refs.
[164–170]. In particular, it seems that coincidentally the 18th and 19th centuries corresponded to a
relatively cool period known as the “Little Ice Age”. On this basis, Akasofu (2010) argued that much
of the warming since the 19th century corresponded to a natural “recovery from the Little Ice Age”
. This would imply that using an 18th or 19th century baseline for “pre-industrial” would be too
cold. By comparing the instrumental time series to various paleoclimate reconstructions, Lüning and
Vahrenholt (2017)  argue that the 1940–1970 period was closer to the long-term global
temperature average of the last few millennia. However, clearly, 1940–1970 is long after the start of
the actual Industrial Revolution. Hawkins et al. (2017) argue that “pre-industrial” should be defined
much earlier, e.g., 1720–1800 . On the other hand, if the context of the baseline is to indicate a
period before human activity had a significant influence on the climate, then some researchers have
argued that humans were already significantly influencing the climate before the Industrial
Revolution. E.g., Koch et al., 2019  argue that depopulation from the disease epidemics in the
Americas initiated by the arrival of Europeans in 1492 indirectly led to a substantial reforestation of
the Americas, and that this might have caused a significant global cooling. On this basis, they argue
that “the Great Dying of the Indigenous Peoples of the Americas resulted in a human-driven global impact on
the Earth Systems in the two centuries prior to the Industrial Revolution” . Ruddiman et al., 2016,
argue that human influence on global average temperatures began even earlier—with the
development of agriculture thousands of years ago .
At any rate, the question of which temperature baseline defines “pre-industrial levels” depends
on how the global average temperature has varied over the last millennium or so. This turns out to
be yet another topic of ongoing debate in the scientific literature. Up until the mid-1990s, it was
generally accepted that before the Little Ice Age, sometime around 1000–1200, there was a Medieval
Warm Period when global average temperatures were at least as warm as present, if not warmer.
However, in the late-1990s, a series of paleoclimate reconstructions were published which implied
that global average temperatures had been fairly constant for at least the last thousand years up until
the end of the 19th century before rising sharply, e.g., . In particular, the main figure of a highly
Energies 2020, 13, 1365 29 of 53
cited paper, Mann et al., (1999)  was dubbed “the hockey stick graph” because its estimate of
Northern Hemisphere temperatures since 1000 AD apparently looked similar to an ice hockey stick
lying on the ground with the “blade” sticking up in the air. This graph featured prominently in the
IPCC’s 3rd Assessment Report (2001) , and appeared to confirm the claim of that report that global
average temperature changes are currently dominated by human activities, and that the 20th century
global warming was unprecedented in at least 1000 years. However, the striking claims of Mann et
al. (1999) have been very controversial and contentious both in the scientific literature and in the
wider public sphere. One important unanswered puzzle is the blending of proxy temperatures with
instrumental thermometer data in the 20th century, which seems to have been a major component of
the apparent “blade”, as cautioned by Soon et al. (2004) . Readers interested in a detailed
discussion of the debate might find the books by Montford (2010)  and Mann (2013)  useful
for seeing two opposing perspectives. Each of us has also written extensively on this debate
elsewhere, e.g., [113,150,151,177–179].
At any rate, within the scientific literature, the debate over both the Mann et al. (1999) “hockey
stick” study (e.g., [150,151,177,180–189]) and the broader question of how the Medieval Warm Period
and the Little Ice Age compare to the Current Warm Period (e.g., [165–168,170,190–196]) has been
quite lively and contentious. This has been accentuated by the implications for the wider public
debate over climate policy.
As an example of the contentious nature of this topic, in 2003, one of us (WS) co-authored two
studies which disputed the claims of Mann et al. (1999), i.e., Soon and Baliunas (2003)  and Soon
et al. (2003a) . In response, Mann et al. (2003a)  criticized both of these studies. Although
Soon et al. (2003b)  countered the criticism of Mann et al. (2003a) (see also Mann et al. (2003b)’s
reply ), this coincided with considerable political pressure being placed on von Storch, the
editor-in-chief of the journal that Soon and Baliunas (2003) had been published in. Although the
founding editor of the journal defended the publication of the article , von Storch still chose to
resign as editor-in-chief. However, ironically, the following year, von Storch also co-authored an
article criticizing the Mann et al. (1999) study, i.e., von Storch et al. (2004) , which itself led to
more debate with a group including one of the authors (Amman) of Mann et al. (2003a; 2003b), i.e.,
Wahl et al. (2006)  and von Storch et al. (2006) .
For readers who are interested in learning more about these debates and various other similar
controversies that have arisen from the debate over this controversial topic, we recommend reading
Connolly and Connolly (2014) . However, it should already be apparent that this is another topic
that includes several competing scientific paradigms. We can get an idea of these paradigms by
considering Figure 12. Essentially, there appear to be four main paradigms when it comes to current
views on how the Current Warm Period compares to the Little Ice Age and Medieval Warm Period:
• Paradigm 1. Until the end of the 19th century, global average temperatures were fairly
constant, with if anything a gradual long-term cooling. This is consistent with the post-19th
century warming being entirely human caused. An example of a reconstruction that fits this
paradigm is the Mann et al. (1999)  reconstruction in Figure 12a.
• Paradigm 2. There was a Medieval Warm Period around 11th/12th centuries (or possibly a
bit earlier), and the 18th/19th centuries were relatively cold (the Little Ice Age), but the
Current Warm Period is warmer than the Medieval Warm Period was. This is consistent
with much of the post-19th century warming being human caused, but also allows the
possibility that some of it could be natural in origin (similar to the Medieval Warm Period).
An example of a reconstruction that fits this paradigm is the D’Arrigo et al. (2006) 
reconstruction in Figure 12b.
• Paradigm 3. There was a Medieval Warm Period around 11th/12th centuries (or possibly a
bit earlier) and the 18th/19th centuries were relatively cold (the Little Ice Age), and the
Medieval Warm Period was at least as warm as the Current Warm Period was. This is
consistent with much of the post-19th century warming being natural in origin (similar to
the Medieval Warm Period). An example of a reconstruction that fits this paradigm is the
Moberg et al. (2005)  reconstruction in Figure 12c.
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• Paradigm 4. There are still too many inconsistencies between the various reconstructions
and uncertainties and poorly justified assumptions associated with many of the underlying
proxy series for us to establish how the globally representative averaged temperature
changes during the current period compared to those over the last millennium or longer.
Some of these problems and uncertainties have been described by, e.g., [178,183–185,190–
Figure 12. Examples of some of the different paleoclimate reconstructions for Northern Hemisphere
temperature trends since 1000. (a) Mann et al. (1999) ; (b) D’Arrigo et al. (2006) ; (c) Moberg
et al. (2005) . The time series were downloaded from NOAA NCEI’s Paleoclimatology public
data repository, https://www.ncdc.noaa.gov/data-access/paleoclimatology-data (Accessed: January
2020). Highlighted dates correspond to different proposed baseline periods for the “pre-industrial”
era, as discussed in the text. The horizontal axes correspond to years.
The debate over the relative warmth of the Medieval Warm Period, Little Ice Age and Current
Warm Period has continued, and appears to be ongoing. For instance, while the PAGES-2K (2019)
reconstruction  appears to support Paradigm 1 or 2, the Ljungqvist (2010)  reconstruction
appears to support Paradigm 3. Meanwhile Shi et al. (2013)  provide three different
reconstructions all using the same data but different methods for processing the data. Each of the
Energies 2020, 13, 1365 31 of 53
three Shi et al. (2013) reconstructions appears to support a different one of the first three paradigms.
Some might argue that this in itself supports Paradigm 4.
Another issue that should be noted is that we did not include any thermometer-based time series
in Figure 12. Many groups have chosen to superimpose the instrumental record on top of the proxy-
based series, e.g., refs. [164–170]. As noted by e.g., Soon et al. (2004)  and Ljungqvist (2010) ,
because the proxy-based series tend to show less variability than the direct instrumental record, this
has the visual effect of artificially making the Current Warm Period seem warmer than it would
At any rate, it should be apparent that there are many plausible baseline periods for defining
“pre-industrial temperatures”, but because climate change was also occurring during the pre-
industrial era, you could end up with different answers depending on whether you chose a relatively
cool period or a relatively warm period. However, we suggest that the underlying motivation behind
the Paris Agreement was not to define any particular pre-industrial period as having a supposedly
ideal global temperature. Rather, to us, the motivation seems to have been to attempt to minimize the
magnitude of future human-caused global warming that was specifically due to increasing greenhouse
With this in mind, we argue that a better metric to use for defining “pre-industrial levels” is to
assume the Paris Agreement is only referring to changes in global temperature that are due to human-
caused global warming from increasing greenhouse gases above pre-industrial levels. Therefore, for
our analysis, we will calculate the estimated human-caused global warming up to 2100 under BAU
in terms of the increases in greenhouse gases relative to “pre-industrial levels”. We will define “pre-
industrial levels” as that implied by the Antarctic ice cores, although we remind the reader of the
controversies over the reliability of these estimates, which we discussed in Section 3.
5. How “Sensitive” Is the Global Average Temperature to Changes in Greenhouse Gas
If we assume that the changes in atmospheric greenhouse gas concentrations up to 2100 under
Business-As-Usual conditions are indeed as proposed in Section 3.5, that still does not tell us how
much Anthropogenic Global Warming this would cause. In order to establish this, we need to know
what the “climate sensitivity” is, i.e., how much human-caused global warming is generated by an
increase in greenhouse gases (typically defined in terms of a doubling of CO2). Unfortunately, there
is as of yet still no consensus on what the actual “climate sensitivity” is, e.g., see Knutti et al. (2017)
for a list of several hundred estimates .
5.1. Climate Sensitivity Paradigms
Part of the reason for the ongoing debate over the “climate sensitivity” is that nobody has been
able to directly measure it. Although it has been well established experimentally that: (i) each of the
greenhouse gases is infrared-active, e.g., Tyndall (1861) ; (ii) the presence of greenhouse gases in
the Earth’s atmosphere alters the shape of the outgoing infrared spectrum of the Earth, e.g., Harries
et al. (2001) ; and (iii) globally-averaged surface temperatures have on average increased since
the late-19th century, e.g., see the discussion in Section 4, there have (as yet!) been no experimental
measurements that have directly demonstrated and quantified the proposed increase in atmospheric
temperatures specifically from increasing greenhouse gases. We urge readers to note the nuance in
this statement—as we will discuss in this section, there have indeed been many computer model-
based, theoretical, or semi-empirical studies that have attempted to quantify the influence of
increasing greenhouse gases on atmospheric temperature (and particularly surface temperatures).
However, none of these studies have been able to directly demonstrate and quantify experimentally
the proposed increase in atmospheric temperatures from an increase in atmospheric greenhouse gas
In other words, it has not been directly established experimentally how “sensitive” the global
average temperature is to changes in greenhouse gas concentrations. Instead, attempts have either
been indirect by fitting the changes in greenhouse gas concentrations to global temperature trends
Energies 2020, 13, 1365 32 of 53
(e.g., refs. [37,152,202–205]), computer model-based (e.g., refs. [2,8,10,206]), or relying on theoretical
and/or semi-empirical models or assumptions (e.g., refs. [207–209]). We stress that this does not
invalidate the attempts, but it means that the estimates that are obtained often depend heavily on the
theoretical assumptions explicit (or implicit) in the approach taken. As in previous sections, we have
identified several distinct paradigms within the literature on this topic, and each of them appear to
involve different assumptions (implicit or explicit):
• Paradigm 1: “Global warming is mostly or entirely human-caused”. Changes in greenhouse
gas concentrations are the primary driver of global temperature change, especially in recent
decades, and the long-term warming since the late-19th century is mostly (if not entirely)
due to human-caused greenhouse gas emissions. Within this paradigm, there is generally
less interest in trying to understand the causes of recent climate change, and instead the
focus is largely on quantifying future climate change from increasing greenhouse gas
concentrations, e.g., Andronova and Schlesinger (2001) ; Hegerl et al. (2006) ;
Chylek et al. (2007) ; Aldrin et al. (2012) ; Ring et al. (2012) ; Lewis (2013) ;
Shindell (2014) ; Skeie et al. (2014) ; Lovejoy (2014) ; Monckton et al. (2015a)
; Bates (2016) ; Marvel et al. (2016) ; Lewis and Curry (2018) ; Shurer et
al. (2018) .
• Paradigm 2: “Global warming is a mixture of human-caused and natural factors”. It is
assumed that human-caused greenhouse gas emissions are a significant driver of recent
global temperature change (as in Paradigm 1), but that natural climate change has probably
also been a significant driver. Within this paradigm, satisfactorily establishing the relative
roles of natural and human-caused factors in recent climate change is a primary focus since
this strongly influences both our understanding of recent climate change and our
expectations for future climate change. For instance, if 50% of the warming since the late-
19th century was due to natural climate change, then this suggests that the future warming
from increasing greenhouse gases would probably only be at most half of what might be
expected if 100% of the warming was due to greenhouse gases, e.g., Idso (1998) ; Loehle
and Scafetta (2011) ; Ziskin and Shaviv (2012) ; Loehle (2014) ; Spencer and
Braswell (2014) ; van der Werf and Dolman (2014) ; Wyatt and Curry (2014) ;
Lim et al. (2014) ; Harde (2017) ; Christy and McNider (2017) ; McKitrick and
Christy (2018) .
• Paradigm 3: “Global warming is mostly or entirely natural”. Greenhouse gases are not
necessarily a major driver of global temperature change, and most (or all) of the warming
since the late-19th century is due to the same natural climatic changes that have occurring
since long before the Industrial Revolution. Within this paradigm, there is generally less
interest in describing future climate change (which is typically assumed to be comparable to
the climate changes experienced over the last few millennia). Instead, the primary focus
tends to be on better quantifying the magnitudes and causes of past climate changes, e.g.,
Carter and Gammon (2004) ; Svensmark (2007) ; Eschenbach (2010); Loehle and
Singer (2010) ; Carter (2010) ; Shaviv et al. (2014) ; Lüning and Vahrenholt
(2015) ; Soon et al. (2015); Svensmark et al. (2016) ; Lüning and Vahrenholt (2016)
; Kravtsov et al. (2018) .
Within Paradigm 1, there are actually several competing philosophies and approaches that
largely boil down to the fundamental question of whether or not the results from computer model
simulations of potential future climate change are more relevant than observations of recent climate
change. Within Paradigms 2 and 3, the fact that this question is debated can seem largely
incomprehensible as it is usually assumed that empirical observations automatically take precedence
over computer model results (the four of us can vouch for this since most of our climate change
research has been based on either Paradigm 2 or 3 and it has been difficult for us to appreciate the
unquestioned credibility afforded to computer model results by many in the scientific community).
This is even the case for some working within Paradigm 1, e.g., Schwartz (2008) . However,
within Paradigm 1, the debate is considered non-trivial, e.g., see the debate over the Schwartz (2007)
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 study between Knutti et al. (2008)  and Schwartz (2008) , or that over Monckton et al.
(2015a)  between Richardson et al. (2015)  and Monckton et al. (2015b) .
Given that Paradigm 1 assumes that greenhouse gas concentrations are the primary driver of
climate change and is largely concerned with estimating future climate change if carbon dioxide
doubles or trebles (along with other increasing greenhouse gases), the recent climate changes that
have been experienced up to present are considered to be just the beginning of increasingly
substantial human-caused global warming. As a result, many researchers within this paradigm,
argue that the computer model projections of future global warming under substantially increased
greenhouse gas concentrations provide more insight into future global warming than the
experimental observations up to present, e.g., refs. [8,206,238,239]. That is, in terms of understanding
the climate changes to be expected from increasing CO2, the computer model projections are
considering concentrations twice, four times, or more that of pre-industrial CO2, while the historical
observations still only cover a period where CO2 has still only increased by less than 45% relative to
the pre-industrial concentrations implied by the Antarctic ice cores. Moreover, because the computer
model simulations can provide continuous and complete values for every aspect of the model’s
climate system, the time series and results that can be extracted from the model simulations are very
tidy, comprehensive, and precise, while experimental measurements of the real climate system are
often based on an incomplete sampling network, and may be affected by various non-climatic biases
and instrument errors .
On the other hand, other researchers argue that the computer model projections are only
describing climate change in a computer model world. They argue that if you want to understand
how the climate changes in the real world, you will get more realistic answers if you base them on
actual experimental observations .
Meanwhile, many researchers argue that running a typical Global Climate Model simulation
with the latest code requires a large computational expense (a typical run can take a few weeks or
even months to complete for a climate modelling group even using high-end supercomputers).
Furthermore, the simulations arguably report far more information than is necessary for most
studies. As a result, a lot of climate sensitivity studies are based on relatively simple analytical models
or theoretical frameworks that do not require the computational expense of a full Global Climate
With this in mind, it can be helpful to divide Paradigm 1 into three sub-paradigms:
• Paradigm 1a: For estimating the future climate change that would occur if CO2 doubles or
quadruples, the latest simulations from the most up-to-date Global Climate Models are
probably more reliable than extrapolating from historical observations, e.g., Knutti et al.
(2008) ; Shindell (2014) ; Marvel et al. (2016) ; Gregory and Andrews (2016)
; Rohrschneider et al. (2019) ; Forster et al. (2020) .
• Paradigm 1b: The use of relatively simple analytical models or theoretical frameworks
(preferably coupled to historical observations) offers a quicker and more flexible method for
estimating future climate changes, e.g., Aldrin et al. (2012) ; Lewis (2013) ; Geoffroy
et al. (2013) ; Skeie et al. (2014) ; Monckton et al. (2015a) ; Bates (2016) ;
Lewis and Curry (2018) .
• Paradigm 1c: The most realistic (or, at least, the most compelling) estimates of climate
sensitivity are probably ones that are derived from historical observations, although the
calculations often require making theoretical assumptions that can be subjective, e.g.,
Andronova and Schlesinger (2001) ; Edwards et al. (2007) ; Chylek et al. (2007)
; Schwartz (2007) ; (2008) ; Ring et al. (2012) ; Lovejoy (2014) .
5.2. Different Climate Sensitivity Definitions and Estimates
The computational power of the first climate model simulations in the 1960s, 1970s, and 1980s
was very limited compared to today. As a result, most of the early attempts to model the effects that
increasing CO2 would have on the climate tended to focus on idealized hypothetical scenarios where
the atmospheric CO2 concentration was doubled relative to the concentration of the time. Modelers
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would run these “2 × CO2” simulations until the climate system in the model world had equilibrated.
This climate system was then compared with the results from a similar model world where the
atmospheric CO2 was the same as present (i.e., “1 × CO2”), e.g., Manabe and Wetherald (1975) . The
difference between the globally averaged temperatures of the two simulations came to be known as
the “Equilibrium Climate Sensitivity” (ECS).
In a well-cited National Research Council report in 1979 , led by Jule Charney (and hence
commonly referred to as “the Charney report”), the results of such ECS simulations from several
computer modelling groups were used to conclude that a doubling of atmospheric CO2 would
probably lead to 1.5–4.5 °C of human-caused global warming. Schlesinger (1986) noted that although
the simulations from these “general circulation models” did indeed imply a similar range of climate
sensitivity estimates (1.3–4.2 °C, taken from seven separate studies), alternative approaches led to
different ranges . He found three different studies that used “surface energy balance models”, but
implied the climate sensitivity was anywhere in the range 0.24–9.6 °C. He also found estimates from
17 studies using “radiative-convective models”, and these implied that the range was 0.48–4.20 °C.
Nonetheless, van der Sluijs et al. (1998) noted that, “in international assessments of the climate
issue, the consensus-estimate of 1.5 to 4.5 °C for climate sensitivity has remained unchanged for two
decades” . More recently, Knutti et al. (2017) confirmed that, still, “the consensus on the ‘likely’
range for climate sensitivity of 1.5 to 4.5 °C today is the same as given by Jule Charney in 1979” .
We will return to this question later, but for now we note that the most recent IPCC 5th Assessment
Report (2013) also argued that the “likely” value for the Equilibrium Climate Sensitivity was probably
in the range 1.5–4.5 °C .
At any rate, by the mid-1980s, it was already apparent that the long-term global warming since
1880 was at least half of what would have been expected from the ECS values, given the increase in
atmospheric CO2 that had already occurred. However, Schlesinger (1986) argued that this did not
mean the climate models were wrong. Instead, he argued that the problem was that the ECS values
were for equilibrium conditions and that, “the actual response of the climate system lags the equilibrium
response because of the thermal inertia of the ocean” . Bryan et al. (1982) had referred to this apparent
lag as being the “Transient Climate Response to increasing atmospheric carbon dioxide” , and the term
Transient Climate Response (TCR) is now generally used to refer to the climate sensitivity that would
be observed as carbon dioxide gradually doubles over a multidecadal period (typically defined as a
1%/annum increase over 70 years).
Computational power has improved dramatically over the decades, and since the 2000s, it has
become increasingly standard for climate modelling groups to carry out Transient Climate Response
simulations where CO2 gradually increases over time as well as the original “2 × CO2” Equilibrium
Climate Sensitivity simulations (and more recently, “4 × CO2” simulations ), e.g., refs.
[217,244,250–256]. The climate sensitivity estimates implied by the Transient Climate Response
simulations are typically a good bit lower than those from the Equilibrium Climate Sensitivity
simulations. That is, the expected human-caused global warming for a doubling of CO2 is typically a
good bit lower for the TCR estimates than the ECS estimates, e.g., Forster et al. (2013) estimate the
ECS to be in the range 1.90–4.54 °C with a most-likely value of 3.22 °C, while they estimate the TCR
to be in the range 1.19–2.45 °C with a most-likely value of 1.82 °C .
Within Paradigm 1, it is now generally accepted that the reason why the climate sensitivities
implied by the TCR simulations is lower than that from the ECS simulations is that proposed by
Bryan et al. (1982)  and Schlesinger (1986) . That is, in the computer model world, some of the
extra “greenhouse heating” from increasing greenhouse gas concentrations is temporarily absorbed
by the oceans, but because the model oceans have a large heat capacity and relatively slow circulation
rates, this can take decades or even centuries of time (in model “years”) before the climate system has
fully equilibrated, see, e.g., Gregory and Mitchell (1997) ; Raper et al. (2002) ; Gregory et al.
(2004) ; Hansen et al. (2005) ; Dufresne and Bony (2008) ; Winton et al. (2009) ;
Held et al. (2010) ; Geoffroy et al. (2013) ; Gregory et al. (2015) . According to this
theory, even if CO2 concentrations stop increasing once they have doubled, the human-caused global
warming will continue to rise over time until the oceans have equilibrated. At that point, the expected
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warming will be that of the ECS rather than the initial TCR. However, the models also predict that
this could potentially take centuries, meaning that the lower TCR estimates are the ones that are most
relevant for the coming century. Hope (2015) has even argued that finding out a more accurate value
for the TCR has a “$10 trillion value” . Hansen et al. (2005) argue that the exact length of this
proposed “lag” should increase with ECS, e.g., they argue that for an ECS of ~1 °C, the lag could be
as short as a decade, but for an ECS of ~4 °C or greater, the lag could be a century or longer .
On the other hand, while these arguments carry a lot of weight within Paradigm 1a, many
researchers from outside that paradigm are unimpressed by claims that we should base our policies
solely on computer model predictions of how the climate would hypothetically change over multiple
centuries into the future. Partly for that reason, a lot of researchers have tried to estimate the true
climate sensitivity to greenhouse gases guided by observations of how the climate has changed
already. As discussed in the previous section, different researchers have attempted this from within
Some of those working from within Paradigm 1b or 1c have obtained similar estimates to those
of the climate models, e.g., Otto et al. (2013) estimated the ECS is in the range 1.2–3.9 °C and that the
TCR is in the range 0.9–2.0 °C . However, others find that the climate sensitivity is significantly
smaller for both TCR and ECS, e.g., Lewis and Curry (2018) estimate the ECS is 1.05–2.45 °C and the
TCR is 0.9–1.7 °C ; while Bates (2016)  estimates the ECS at 0.85-1.30°C and Lindzen and
Choi (2011)  estimate it at 0.5–1.3°C.
Many of the estimates based on Paradigm 2, i.e., assuming that some of the warming since the
19th century may have been natural, suggest climate sensitivities that are even lower still, e.g., Idso
(1998) calculated a maximum climate sensitivity (equivalent to either ECS or TCR) of 0.4 °C, while
Zisking and Shaviv (2012) calculated a climate sensitivity range that is equivalent to an ECS of 0.69–
We have found very few studies working from within Paradigm 3 that provide a climate
sensitivity value. This seems to be because if you are finding (or assuming) that the global warming
since the late 19th century is mostly or entirely natural (and therefore not a result of increasing CO2),
then there is less motivation for estimating these values. However, as part of our analysis in Soon et
al. (2015)  (which we summarized in Section 4.1), we argued that—after accounting for
urbanization bias, and using the updated Hoyt and Schatten (1993) [231,232] estimate for solar
variability—the residuals left implied a maximum climate sensitivity of 0.44 °C for a doubling of CO2.
Although we did not define it there in terms of ECS or TCR, in this case, this would probably be most
equivalent to an upper bound for TCR. However, as discussed in Section 4.1, even adding this small
role for CO2 did not substantially improve the fit to the observed temperature trends from 1881–2014,
i.e., it suggested that the climate sensitivity to greenhouse gases was very small or even zero .
At any rate, for the purposes of the final stage of our analysis, regardless of whether we use the
TCR or ECS estimates, what value should we assume for the climate sensitivity? The IPCC 5th
Assessment Report (2013)’s “likely” estimate for the TCR climate sensitivity is in the range 1.0 °C–2.5
°C. They consider it “extremely unlikely” to be higher than 3.0 °C. They argue that the ECS, “is likely
in the range 1.5°C to 4.5°C (high confidence), extremely unlikely less than 1°C (high confidence), and very
unlikely greater than 6°C (medium confidence)” . However, as can be seen from the list of estimates
in Table 5, there is a wide range of estimates for both the ECS and TCR, and several of these estimates
include values that are outside the IPCC’s range. This is actually only a partial sample of the various
estimates available in the literature. For a more complete list, Knutti et al. (2017)  provide a
summary of hundreds of estimates for both TCR and ECS.
Table 5. Various different estimates of the climate sensitivity, i.e., expected human-caused global
warming from a doubling of atmospheric CO2, in terms of either Equilibrium Climate Sensitivity
(ECS) or Transient Climate Response (TCR). The estimates are in no way meant as comprehensive
(see Knutti et al. 2018  for a summary of several hundred estimates in the literature), but are
rather an illustrative sample of typical values in the literature, with examples taken from each of the
paradigms described in the text. The values accompanied by a † correspond to the most-likely, mean,
or median value if provided by the study.
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Study Paradigm ECS (or Equivalent) TCR (or Equivalent)
“Charney Report” (1979)  1 1.5–4.5 °C -
Schlesinger (1986)  1 0.24–9.6 °C -
IPCC AR1 (1990)  1 1.5–4.5 °C -
IPCC AR2 (1995)  1 1.5–4.5 °C -
IPCC AR3 (2001)  1 1.5–4.5 °C 1.1–3.1 °C
IPCC AR4 (2007)  1 2.0–4.5 °C 1.0–3.0 °C
IPCC AR5 (2013)  1 1.5–4.5 °C 1.0–2.5 °C
Gregory and Andrews (2008)  1a - 1.3–2.3 °C
Vial et al. (2013)  1a 1.9–4.4 °C -
Forster et al. (2013)  1a 1.90–4.54 °C (†3.22 °C) 1.19–2.45 °C (†1.82 °C)
Shindell (2014)  1a - >1.3 °C
Marvel et al. (2016)  1a ~3.0 °C ~1.8 °C
Zelinka et al. (2020)  1a 1.8–5.6 °C -
Lindzen & Choi (2011)  1b 0.5–1.3 °C (†0.7 °C) -
Aldrin et al. (2012)  1b 0.7–4.3°C (†2 °C) -
Otto et al. (2013)  1b 1.2–3.9 °C (†2.0 °C) 0.9–2.0 °C (†1.3 °C)
Skeie et al. (2014)  1b 0.9–3.2 °C (†1.8 °C) 0.79–2.2 °C (†1.4 °C)
Monckton et al. (2015a)  1b 0.8–1.3 °C (†1.05 °C) 0.8–1.3 °C (†1.05 °C)
Bates (2016)  1b 0.85–1.30 °C (†1.05 °C) -
Lewis and Grünwald (2018)  1b 1.1–4.05 °C (†1.87 °C) -
Lewis and Curry (2018)  1b 1.05–2.45 °C (†1.50 °C) 0.9–1.7°C (†1.20 °C)
Schurer et al. (2018)  1b - 1.2–2.4 °C (†1.7 °C)
Andronova and Schlesinger (2001)  1c 1.0–9.3 °C -
Lea (2004)  1c 4.4–5.6 °C -
Hegerl et al. (2006)  1c 1.6–6.2 °C (†2.5 °C) -
Chylek et al. (2007)  1c 1.1–1.8 °C -
Schwartz (2007)  1c 0.6–1.6 °C (†1.1 °C) -
Schwartz (2008)  1c 0.9–2.9 °C (†1.9 °C) -
Ring et al. (2012)  1c 1.45–2.01 °C (†1.6 °C) -
Masters (2014)  1c 1.2–5.1 °C (†2.0 °C) -
Lovejoy (2014)  1c 2.5–3.66 °C (†3.08 °C) -
Idso (1998)  2 <0.4 °C <0.4 °C
Loehle and Scafetta (2011)  2 <1–1.5°C <1–1.5 °C
Ziskin and Shaviv (2012)  2 0.69–1.26 °C (†0.93 °C) -
van der Werf and Dolman (2014)  2 - 1.0–3.3 °C (†1.6 °C)
Spencer and Braswell (2014)  2 1.3–2.2 °C -
Loehle (2014)  2 1.75–2.23 °C (†1.99 °C) 0.96–1.23 °C (†1.09 °C)
Specht et al. (2016)  2 0.4 °C -
Harde (2017)  2 0.7 °C -
Christy and McNider (2017)  2 - 0.84–1.36°C (†1.10 °C)
Soon et al. (2015)  3 - <0.44 °C
Given that the 2015 Paris Agreement has set an international, but voluntary, target of keeping
human-caused global warming below 2 °C, it should be apparent that establishing whether the actual
values are at the high end or at the low end of the IPCC’s ranges (or outside their ranges) has huge
implications for what exactly the Paris Agreement has agreed to. More specifically for this study, in
order to estimate how much human-caused global warming we should expect for our projected BAU
increases in atmospheric greenhouse gas concentrations, we need to establish what the actual climate
sensitivity is. However, as can be seen from Table 4, there are many different estimates of both the
TCR and ECS published in the literature.
Therefore, rather than considering just one value for the climate sensitivity, for the rest of our
analysis, we will consider a range of six different values for TCR: 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 °C This
covers the IPCC’s current “likely” range of 1.0–2.5 °C, but also considers a lower value of 0.5°C,
recognizing that several recent studies have argued that the TCR could be less than 1.0 °C, e.g., refs.
[152,207,208,215,216,219,221,227] as well as a higher value of 3.0°C. Similarly, we consider a range of
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six different values for ECS (1, 2, 3, 4, 5, and 6 °C), which encompasses the IPCC’s current “likely”
range of 1.5–4.5 °C, but also considers the possibility that the ECS might be lower than 1.5 °C, e.g.,
refs. [202,207–209,211,212,215,216,218–220,222,226,236,237,260,263,265,266] or that it might be higher
than 4.5 °C, e.g., refs. [202,210,262,264,265]. We also stress that if Soon et al. (2015) are correct, then
the TCR is less than 0.44 °C , i.e., less than the lowest value of 0.5 °C that we will consider in this
analysis. In that case, the expected human-caused global warming under BAU will be even smaller.
5.3. Converting Projected Greenhouse Gas Concentrations into Projected Human-Caused Global Warming
for Different Transient Climate Response and Equilibrium Climate Sensitivity Estimates
Both the TCR and ECS metrics are typically defined in terms of a doubling of atmospheric CO2
concentrations. However, our BAU projections of future greenhouse gas concentrations from Section
3.5 describe annual changes. Therefore, we need to come up with a suitable approach to translating
a metric in terms of a doubling to the expected annual changes. Moreover, as discussed in the
previous section, according to Paradigm 1, the equilibration time required for the ECS values to be
reached is in the order of centuries, e.g., refs. [244,250–253,255–258]. Hence, since our projections only
cover the ~80-year period up to the end of the 21st century, we will need to convert the ECS values
into estimates of the shorter term warming that would have occurred up to 2100. Finally, since we
are also considering the potential contributions of CH4 and N2O, we will need to translate these CO2-
defined metrics into metrics that are also relevant for CH4 and N2O.
Let us consider the final problem first. Myhre et al. (1998)  and others (e.g., refs. [10,268–
271]) argue that the expected relationship between increasing concentrations and global temperatures
should be different for CO2, CH4, and N2O, since they each have different infrared activities as well
as different calculated atmospheric lifespans. Therefore, in order to convert an increase in
concentration of a non-CO2 greenhouse gas into a CO2-equivalent concentration change, it has
become standard practice to multiply the concentration change by a metric called the “Global
Warming Potential” (GWP). The value of this calculated metric depends on the timescale being
considered, and the IPCC reports offer different estimates for timescales of 20 years and 100 years.
Since the timescale we are considering (up to 2100) is ~80 years, we use the 100-year GWP figures
from Table 8.7 of the IPCC Working Group 1’s 5th Assessment Report , as described in Section
3.5. We then sum the combined greenhouse gas concentrations for each year in CO2-equivalent
concentrations, i.e., we sum the time series plotted in Figure 10a–c into one time series.
In order to describe the modelled global temperature response to an increase in greenhouse gas
concentrations predicted by climate models, it has become standard practice to describe the modelled
relationships in terms of a metric called the “Radiative Forcing” (RF). This is a calculated metric with
units of W m−2, and so can be easily compared with measured changes in incoming solar irradiance,
for instance. Calculated values of the RF associated with a change in atmospheric CO2 are so prevalent
within the literature that some readers might initially have assumed that these values are somehow
experimentally derived. Therefore, we stress that the RF of CO2 is a calculated metric. Some widely
cited values are calculated from radiative transfer models, e.g., Shi (1992) ; Myhre et al. (1998)
; Byrne and Goldblatt (2014) ; Etminan et al. (2016) . However, the RF for a given Global
Climate Model can be also be inferred from the computer model output, e.g., Forster et al. (2013)
At any rate, the RF of CO2 is typically assumed to increase logarithmically with concentration
according to the following equation taken from Myhre et al. (1998) :
∆𝐹 = 𝛼 ln
where ΔF is the change in RF (in W m−2), C is the new concentration, C0 is the reference concentration
(in our case, the pre-industrial concentrations implied by the Antarctic ice core estimates), and α is a
constant. The value of α varies from study to study, e.g., in the IPCC’s 1st Assessment Report (1990)
, it was assumed that α = 6.3, but following Myhre et al. (1998) , more recent reports have
assumed that α = 5.35. This implies an RF of ΔF = 3.71 W m−2 for a doubling of atmospheric CO2.
However, the exact value varies from study to study, e.g., Forster et al. (2013)  found that the RF
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for a doubling of CO2 for each of the CMIP5 Global Climate Models covered the range 2.59–4.31 W
m−2. For this paper, we will assume that the value of ΔF = 3.71 W m−2 used in the IPCC’s 5th
Assessment Report  applies. However, for comparison, in the Supplementary Materials, we will
include the equivalent results using the upper and lower values from Forster et al. (2013) .
Gregory and Mitchell (1997)  argued that this increase in radiative forcing can be related to
the temperature response, ΔT, for a well-equilibrated system via the following equation:
∆𝑇 = ∆
where λ is a constant “climate response factor”, sometimes called the “feedback” factor, meaning that
for a doubling of CO2, ΔT in Equation (2) would correspond to the ECS. Meanwhile, for the Transient
Climate Response, the transient temperature response is reduced by a term to account for the
proposed lag due to ocean heat uptake, which is expressed as follows:
∆𝑇 = ∆
where κ is also treated as a constant which is known as the “ocean heat uptake efficiency”. (Note:
Gregory and Mitchell (1997) actually used a different label of Q for ΔF).
This relatively simple framework for relating the Transient Climate Response and Equilibrium
Climate System has become quite popular, and many studies have included estimates of κ, e.g., refs.
[252,255,258,261]. For example, Dufresne and Bony (2008) calculated that κ varied from a 0.53 to 0.92
W m−2 K
−1 with a mean of 0.69 W m−2 K
−1 across 12 of the CMIP3 Global Climate Models .
However, implicit in this framework is the paradox that the κ “constant” is not actually a constant,
but that it must tend towards zero as the oceans equilibrate, i.e., Equations (2) and (3) must equal
each other under equilibrium conditions.
As a result, several researchers have attempted to develop more sophisticated analytical
approaches to overcome the eventual breakdown of this simple approximation, e.g., the Held et al.
(2010)  and Geoffroy et al. (2012)  “two-layer models”. Geoffroy et al. (2012) found that their
two-layer model is able to replicate the transient and equilibrium temperature responses of the
CMIP5 Global Climate Models with a fairly high accuracy .
Rohrschneider et al. (2019) compared the results from this two-layer model—and also “two-
region models” similar to those used by Bates (2016) —to those of the complete Global Climate
Models. They found that the two-layer models did indeed provide a good approximation of the
Global Climate Models (and that in terms of globally averaged results they were equivalent to the
two-region models), but they recommended that the Global Climate Models were more reliable for
detailed studies .
Gregory et al. (2015)  also carried out a detailed comparison of the two-layer model
approach to the equivalent results from CMIP5 Global Climate Models. They also compared the
results of the Gregory and Mitchell (1997)  framework of Equations (2) and (3) described above,
which they call the “zero-layer model”. They found that the two-layer model was a much better
approximation of the CMIP5 model results than the zero-layer model when considering long
timescales of several centuries at high CO2 concentrations. Specifically, they found that in the CMIP5
models, the implied value of κ gradually decreased from a range of 0.73 ± 0.11 W m−2 K−1 to 0.54 ±
0.11 W m−2 K−1 after 120–140 years, during which CO2 quadrupled.
Therefore, if we were to extend our BAU projections to, e.g., the middle of the 22nd century,
then we would probably need to use a more sophisticated approach than the zero-layer model.
However, since we are only extending our projections ~80 years, i.e., to 2100, and greenhouse gas
concentrations are only projected to have slightly more than doubled by then (see Figure 10), we
argue that the zero-layer model is a reasonable approximation for estimating the transient
temperature response to increasing greenhouse gas concentrations over the next ~80 years for a given
With this in mind, we will take the following approach to converting the projected BAU
greenhouse gas increases into the expected human-caused global warming for a given climate
Energies 2020, 13, 1365 39 of 53
For the TCR values, we will assume that λ and κ are both constant, and that the increase in
temperature, ΔT, for a given year is therefore proportional to the increase in ΔF (Equation (3)). The
TCR value corresponds to the ΔT when C = 2 × C0 in Equation (1). Therefore, the expected ΔT for a
given year is related to the concentration of greenhouse gases in that year (in CO2-equivalent), C, by:
∆𝑇 = TCR × ln
The calculations are a little more complex for a given ECS value. If we want to calculate the
transient temperature response for a given year, we need to use Equation (3). However, the ECS only
tells us what the expected temperature response would be for Equation (2), i.e., when κ = 0.
Our first step is to decide on a suitable value of κ. As mentioned above, Gregory et al. (2015)
 calculated the mean value of κ for the CMIP5 models after a doubling of CO2 was 0.73 W m−2
K−1. Therefore, for our analysis in this paper, we will assume that κ = 0.73 W m−2 K−1. However, in the
Supplementary Materials, we also provide equivalent analyses using either the highest or lowest
values for a doubling of CO2 of the CMIP5 models from Gregory et al. (2015)’s Table 1.
We then need to decide on a value for λ. We do this by assuming ΔF = 3.71 W m−2 for a doubling
of CO2, i.e., the value used by Myhre et al. (1998)  and also the IPCC 5th Assessment Report .
However, in the Supplementary Materials, we also provide equivalent analyses using the highest and
lowest estimates of ΔF calculated by Forster et al. (2013)  for the CMIP5 models, i.e., 2.59 and
4.31 W m−2. We can then calculate the corresponding value of λ for each of our ECS values by
rearranging Equation (2):
∆ ×, (5)
where ΔT(×2CO2) is the ECS value. We then use Equation (3) to calculate ΔT for each year by
calculating ΔF for that year by plugging the corresponding concentration, C into Equation (1).
6. How Much Human-Caused Global Warming Should We Expect with Business-As-Usual
(BAU) Climate Policies?
Figure 13a shows the results of our analysis for a TCR of 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 °C, while
Figure 13b shows the results for an ECS of 1, 2, 3, 4, 5, and 6 °C. One point which might initially seem
surprising is that the results are already different for the historic period, 1980–2019. That is, the
magnitude of “human-caused global warming”, which is presumed to have already occurred over
the historic period, increases with the value of the higher climate sensitivity which is assumed. Some
readers may wonder at why there should be uncertainty over this given that we have reasonable
estimates of the global warming which occurred over this period. However, as discussed in Section
4.1, the magnitude of “global warming” over a given period does not automatically tell us the
magnitude of “human-caused global warming” from increasing greenhouse gases. Some (or even all)
of the observed global warming may have been due to natural factors and/or other non-greenhouse
gas-related factors. On the other hand, there may have been additional “global cooling” factors—
either natural (e.g., decreases in solar activity) or human-caused (e.g., increases in aerosols)—that led
to a reduction in human-caused global warming. That is, the amount of human-caused global
warming that should have already occurred might be less than or greater than the amount of observed
global warming. Indeed, this is a major part of the reason why there is still such uncertainty over the
actual climate sensitivity to greenhouse gases.
At any rate, for us, probably the most striking result is the sheer range of possible values by the
end of our BAU projections in 2100. This is quite problematic given that recently international climate
policies have been framed within the context of limiting the magnitude of future human-caused
global warming to within a specific value. In particular, the 2015 Paris Agreement involved a
voluntary international agreement for, “holding the increase in the global average temperature to well below
2 °C above pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5 °C above pre-
industrial levels” . More recently, in 2018, the IPCC issued an intermediate Special Report entitled,
“Global Warming of 1.5°C. An IPCC Special Report on the impacts of global warming of 1.5°C above pre-
industrial levels and related global greenhouse gas emission pathways, in the context of strengthening the global
Energies 2020, 13, 1365 40 of 53
response to the threat of climate change, sustainable development, and efforts to eradicate poverty.” . For
readers who are more interested in future human-caused global warming relative to present, in the
Supplementary Materials we provide an equivalent figure using 2018 greenhouse gas concentrations
as the starting baseline.
We will not get into the debate here which we referred to in the introduction, e.g., refs. [21–26],
over whether those specific targets of 1.5 and 2.0 °C are useful. Although, we do note that Lang and
Gregory (2019)  have calculated that, “3.0 °C of global warming from 2000 would increase global
economic growth”, and Dayaratna et al. (2020)  have recently argued that some recent research
suggests that increasing CO2 could be a net positive, “at least through the mid-twenty-first century”. See
also NIPCC (2019) . Rather, we will explicitly assume here that these targets of keeping human-
caused global warming well below 2.0 °C and ideally below 1.5 °C are indeed worthy. With than in
mind, what implications do the results in Figure 13 have for these targets?
Figure 13. Projected human-caused global warming (from CO2, CH4, and N2O greenhouse gases) up
to 2100 under Business-As-Usual conditions for various estimates of (a) the Transient Climate
Response and (b) Equilibrium Climate Sensitivity. For comparison, the 2.0 and 1.5 °C targets
described under the Paris Agreement (2015)  are shown. The horizontal axes correspond to years.
If the ECS is 5 °C or higher, or the TCR is 2.5 °C or higher, then under Business-As-Usual, we are
projected to have broken the 1.5°C target by 2026–2028, and the 2 °C target by 2045–2053. On the
other hand, if the ECS is 2 °C, we are not projected to break the 1.5 °C target until 2069–2082, and we
are not projected to break the 2 °C target until the 22nd century. Similarly, if the TCR is 1.5 °C, then
Energies 2020, 13, 1365 41 of 53
we are not projected to break the 1.5 °C target until 2065–2077, and we would probably not break the
2 °C target until the 22nd century (or 2095 at the earliest). Meanwhile, if the ECS or TCR is 1 °C or
less, then we are not projected to break either of the two targets in the 21st century under BAU.
In other words, the urgency (or otherwise) of the Paris Agreement depends critically on what
the actual value of the climate sensitivity is. According to the IPCC’s 5th Assessment Report, the ECS
is “likely” to be any value in the range 1.5–4.5 °C and the TCR is “likely” to be any value in the range
1.0–2.5 °C . That is, the results of the latest IPCC Assessment Report still do not tell us whether
the Paris Agreement is trying to solve a problem for the next few decades or the 22nd century.
Moreover, as can be seen from Table 4, several studies have suggested that the climate sensitivity
may be either higher or lower than the IPCC’s “likely” ranges. For instance, Zelinka et al. (2020) have
noted that several of the latest CMIP6 Global Climate Models imply an ECS that is greater than 4.5
°C. On the other hand, Lindzen and Choi (2011) argue that the ECS is in the range 0.5–1.3 °C, with a
most likely value of 0.7 °C , and both Monckton et al. (2015a)  and Bates (2016)  argue
that the ECS is in the range 0.8–1.3 °C, with a most likely value of 1.05°C. All of these estimates are
below the IPCC’s “likely” range. Meanwhile, some of us have argued in Soon et al. (2015) that the
TCR is less than 0.44 °C, and that it is possible to explain all of the observed warming since at least
1881 in terms of natural climate change .
Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1, Figure S1: Effects
on projected future greenhouse gas concentrations (from CO2, CH4 and N2O greenhouse gases) up to 2100
of using the implied projected airborne fractions of the IPCC RCP scenarios (as used for IPCC AR5)
compared to using the fixed, empirically-derived estimates as in the paper, Figure S2: Effects of changing
the ocean heat uptake efficiency constant, κ, on projected human-caused global warming (from CO2, CH4
and N2O greenhouse gases) up to 2100 under Business-As-Usual conditions for various estimates of
Equilibrium Climate Sensitivity. For comparison the 2.0 °C and 1.5 °C targets described under the Paris
Agreement (2015) are shown; Figure S3: Effects of changing the estimated Radiative Forcing for a doubling
of CO2, F (×2 CO2), on projected human-caused global warming (from CO2, CH4 and N2O greenhouse gases)
up to 2100 under Business-As-Usual conditions for various estimates of Equilibrium Climate Sensitivity.
For comparison the 2.0 °C and 1.5 °C targets described under the Paris Agreement (2015) are shown. Figure
S4: As for Figure 13 in the main article, except only projecting future warming (relative to 2018 values).
Projected human-caused global warming (from CO2, CH4 and N2O greenhouse gases) up to 2100 under
Business-As-Usual conditions for various estimates of (a) Transient Climate Response and (b) Equilibrium
Climate Sensitivity. The horizontal axes correspond to years.
Author Contributions: Sadly, R.M.C. died unexpectedly during the preparation of an earlier 2016 version
of this article, however his family encouraged us to continue the article without him. Although W.S. was
not involved with the 2016 version, he has contributed substantially to the current version.
Conceptualization, R.M.C., R.C. and M.C.; methodology, R.M.C. (for the 2016 version), R.C., M.C. and W.S.;
writing—original draft preparation, R.M.C. (for the 2016 version), R.C., M.C. and W.S.; writing—review
and editing, R.C., M.C. and W.S. All authors have read and agreed to the published version of the
Funding: Two of us (RC and WS) received financial support from the Center for Environmental Research and
Earth Sciences (CERES), http://ceres-science.com/, while carrying out the research for this paper. The aim of
CERES is to promote open-minded and independent scientific inquiry. For this reason, donors to CERES are
strictly required not to attempt to influence either the research directions or the findings of CERES.
Acknowledgments: As mentioned above, our co-author, Robert “Bob” M. Carter, passed away during the
preparation of an earlier version of this article. His calm, measured, yet passionate love of science and his good
sense of humour were inspiring, and he is deeply missed by his friends and colleagues. We would like to thank
Bob’s family for encouraging us to finish the article without him. After the 2016 version was submitted for peer
review, two reviewers provided several critical comments which prompted us to take a much more
comprehensive approach than in the original version as well as to substantially rewrite and revise much of the
paper. We would like to thank the two reviewers of that early manuscript for these comments, as well as the
editor and four reviewers of this revised manuscript whose collective feedback substantially improved our
analysis and manuscript.
Energies 2020, 13, 1365 42 of 53
Conflicts of Interest: The authors declare no conflict of interest.
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