11institutetext: Department of Earth Sciences, Environment and Georesources,
University of Naples Federico II, Complesso Universitario di Monte S. Angelo,
via Cinthia, 21, 80126 Naples, Italy. Email<EMAIL_ADDRESS>
# CMIP6 GCM ensemble members versus global surface temperatures

Nicola Scafetta

###### Abstract

The Coupled Model Intercomparison Project (phase 6) (CMIP6) global circulation
models (GCMs) predict equilibrium climate sensitivity (ECS) values ranging
between 1.8∘C and 5.7∘C. To narrow this range, we group 38 GCMs into low,
medium and high ECS subgroups and test their accuracy and precision in
hindcasting the mean global surface warming observed from 1980-1990 to
2011-2021 in the ERA5-T2m, HadCRUT5, GISTEMP v4, and NOAAGlobTemp v5 global
surface temperature records. We also compare the GCM hindcasts to the
satellite-based UAH-MSU v6 lower troposphere global temperature record. We use
143 GCM ensemble averaged simulations under four slightly different forcing
conditions, 688 GCM member simulations, and Monte Carlo modeling of the
internal variability of the GCMs under three different model accuracy
requirements. We found that the medium and high-ECS GCMs run too hot up to
over 95% and 97% of cases, respectively. The low ECS GCM group agrees best
with the warming values obtained from the surface temperature records, ranging
between 0.52∘C and 0.58∘C. However, when comparing the observed and GCM
hindcasted warming on land and ocean regions, the surface-based temperature
records appear to exhibit a significant warming bias. Furthermore, if the
satellite-based UAH-MSU-lt record is accurate, actual surface warming from
1980 to 2021 may have been around 0.40∘C (or less), that is up to about 30%
less than what is reported by the surface-based temperature records. The
latter situation implies that even the low-ECS models would have produced
excessive warming from 1980 to 2021. These results suggest that the actual ECS
may be relatively low, i.e. lower than 3∘C or even less than 2∘C if the
1980-2021 global surface temperature records contain spurious warming, as some
alternative studies have already suggested. Therefore, the projected global
climate warming over the next few decades could be moderate and probably not
particularly alarming.

#### Keywords: CMIP6 climate models; temperature records; equilibrium climate
sensitivity; global warming; model validation and testing

#### Cite this paper as: Scafetta, N., 2022. CMIP6 GCM ensemble members versus
global surface temperatures. Climate Dynamics.
https://doi.org/10.1007/s00382-022-06493-w

##  1 Introduction

The Coupled Model Intercomparison Project (phase 6) (CMIP6) collects several
simulations of global climate models (GCM) currently used to interpret past
and future climate changes (Eyring et al., 2016; IPCC, 2021). However, these
GCMs calculate equilibrium climate sensitivity (ECS) values ranging from 1.8∘C
to 5.7∘C (IPCC, 2021). The ECS is the most important climatic parameter as it
measures the long-term increase in air temperature near the surface that
should result from an increase in radiative forcing of approximately 3.8 W/m2,
which corresponds to a doubling of the atmospheric CO2 concentration from 280
ppm (which is defined as the preindustrial level) to 560 ppm. The uncertainty
of the ECS is highly problematic as it indicates that the climate system is
still poorly understood and modeled. Consequently, also the extent of future
climate change is rather uncertain as the impact of anthropogenic CO2
emissions on the climate cannot yet be adequately quantified (cf. Knutti et
al., 2017).

The uncertainty of the ECS stems from the fact that various climate feedback
mechanisms – in particular water vapor and cloud cover – are still too little
known and modeled, as already found sixty years ago by Möller (1963). In the
absence of climate feedback mechanisms, the Stefan-Boltzmann law for
blackbodies predicts that a doubling of the atmospheric CO2 concentration
could cause an increase in global surface temperature of about 1∘C. Therefore,
only strong positive climate feedbacks could significantly increase the ECS
above such a value, but their existence is still debated.

Constraining the ECS value is an urgent task of climatology. In fact, at least
two-thirds of the CMIP6 GCMs could be severely defective. For example, by
grouping models into low ($1.5<ECS\leq 3.0$ ∘C), medium ($3.0<ECS\leq 4.5$ ∘C)
and high ($4.5<ECS\leq 6.0$ ∘C) sensitivity values, if, say, the actual ECS is
less than 3°C, the GCMs with $ECS>3$ ∘C should be ignored. Therefore, it is
very important that detailed evaluations of the models are carried out in
order to determine if, where and how the models should improve both on a
global scale – as proposed, for example, in this work – and on regional
scales, as done in numerous other studies (e.g.: Heo et al., 2014; Seo et al.,
2018, and many others).

Constraining ECS also has important policy implications because the expected
warming for the 21st century depends on the value of the model’s ECS (Grose et
al., 2017; Scafetta, 2022): the higher the ECS, the greater the expected
warming due to GHG emissions. For example, Huntingford et al. (2020) found
that the wide ECS range of CMIP6 GCMs implies that at thermal equilibrium the
global surface temperature could warm up between 1.0∘C and 3.3∘C above the
pre-industrial period (1850-1900) even if anthropocentric emissions cease
today.

Scientists already wondered whether a strong response to greenhouse gases
could be realistic (Voosen, 2019). Indeed, high ECS CMIP6 models have already
been found to perform poorly (e.g.: Ribes et al., 2021; Scafetta, 2022;
Tokarska et al., 2020; Zhu et al., 2020) while the medium and even the low ECS
models are being carefully evaluated.

For example, Nijsse et al. (2020) derived that the most likely ECS interval
should be 1.9-3.4∘C while alternative studies, often empirical based, have
suggested that the actual ECS could be even lower, probably between 1∘C and
2.5∘C (e.g.: Lewis and Curry, 2018; Lindzen and Choi, 2011; Scafetta, 2013;
Stefani, 2021; van Wijngaarden and Happer, 2020). Most GCMs seem to
overestimate the observed surface warming since 1980 (Scafetta, 2021b, 2022)
and also that observed in the global (McKitrick and Christy, 2020) and
tropical troposphere (Mitchell et al., 2020), in particular at its top
(200-300 hPa) where the CMIP6 GCMs predict an unobserved hot spot (McKitrick
and Christy, 2018). A similar situation also occurred with the previous CMIP3
and CMIP5 GCMs (Fu et al., 2011; Scafetta, 2012a, 2013). Actually, as Knutti
et al. (2017) acknowledged, there is a dichotomy between the observed and
modeled ECS as GCMs tend to favor sensitivity values at the top of the
probable range, while several studies based on instrumentally recorded warming
and some from paleoclimate favor values in the lower part of the range.
Therefore, not only the models with high ECS, but also those with medium ECS
should be and are being seriously questioned.

Scafetta (2021a, 2022) showed that the performance of the GCMs improves as
their ECS decreases and, in any case, the low ECS GCMs appear to be the best
performing models. However, even low-ECS GCMs need further evaluation because
biases in some regions (e.g. on land) could be offset by opposite biases in
other regions (e.g. on ocean). Furthermore, serious uncertainties remain in
the solar forcing and in the temperature records themselves (Connolly et al.,
2021; D’Aleo, 2016). These uncertainties question the warming trend reported
by the available climate records and, directly or indirectly, the models
themselves. Finally, climate systems seem to be regulated by various natural
oscillations from the decadal to the millennial scales, which the GCMs are
unable to reproduce, the presence of which would also imply low ECS values,
probably between 1 and 2∘C (Scafetta, 2012a, 2013, 2021c).

Focusing on the performance of the CMIP6 GCMs, Scafetta (2022) proposed that
the probable ECS range could be constrained by statistical investigation to
find which GCM group – low, medium or high ECS – best reproduces the observed
global surface warming between the 1980-1990 and 2011-2021 as reported by
ERA5-T2m (Hersbach et al., 2020; Simmons et al., 2021). The period 1980-2021
was chosen because it is optimally covered by all available climatic
temperature records. Scafetta (2022) analyzed the “average” simulations
provided by the Koninklijk Nederlands Meteorologisch Instituut (KNMI) Climate
Explorer (Oldenborgh, 2020) of 38 CMIP6 GCMs with three shared socioeconomic
pathways (SSP) emission scenarios, which also counted for a partial evaluation
of the internal variability of the models. The low ECS GCM group was found to
be perfectly compatible, at least on a global scale, with the 2011-2021
warming relating to the 1980-1990 period. Conversely, both GCM groups with
medium and high ECS showed too high warming trends.

A possible objection to the analysis proposed in Scafetta (2022) is that
temperature records should be compared with actual members of the CMIP6 GCM
ensemble instead of their ensemble averages because the unforced internal
variability of the models produces different results due to uncertainties in
the initial conditions as well as in the internal parameters of the models.
This problem will be addressed in this paper considering that:

  1. 1.

physical models, including the GCMs, should be accurate and precise (see
Appendix B);

  2. 2.

there are still open issues regarding the reliability of the available global
surface temperature records.

In fact, theoretical models must reproduce observations within a reasonably
small error. In our case, it should be evident that the poor precision of a
GCM cannot be used as a pretext to justify its poor accuracy. For example, a
low-precision model could produce a very wide range of different hindcasts due
to its internal variability. In this situation, even if some of its hindcasts
fit the observations, the result should still be considered unsatisfactory if
the mean of the GCM set diverges too much from the actual data. Similarly, if
an ECS GCM group produces a set of hindcasts that too sparsely encompass the
observations, the ECS values that characterize that group should be considered
unrealistic even though some of the models in the same group might perform
better than others. In general, the accuracy, precision and ECS category of
the GCMs must be evaluated simultaneously.

Furthermore, surface-based temperature records appear to exhibit non-climatic
warming biases due to poorly corrected urban heats or other local surface
phenomena (e.g.: Connolly et al., 2021; D’Aleo, 2016; Scafetta, 2021a). To
account for this problem, the satellite temperature measurements of the lower
troposphere using microwave resonance units (MSU) proposed by the U. of
Alabama Huntsville (UAH-MSU-lt v6) (Spencer et al., 2017) will also be
analyzed.

UAH-MSU-lt is the temperature record that features the lowest global warming
trend (about +0.13 °C/decade) from 1980 to 2021 among all available global
temperature records. According to GCM simulations, the troposphere is expected
to warm up faster than the surface (up to a factor of 3) because greenhouse
gases are expected to warm the atmosphere first (Mitchell et al., 2020).
Consequently, the global warming trend of the troposphere estimated from
satellite measurements should be further reduced to simulate the global
warming trend at the surface. Here, these corrections are ignored and UAH-MSU-
lt is assumed to represent the possible lowest limit for the global warming
trend of the surface. Therefore, comparison with this satellite temperature
record could help assess the presence of non-climatic warming bias in the
surface temperature records, particularly on land where large contaminated
areas appear to exist (cf. Scafetta and Ouyang, 2019; Scafetta, 2021a).

Indeed, preliminary analyzes have shown that the land seems to have warmed too
much and too quickly compared to the ocean (Scafetta, 2021a). Connolly et al.
(2021) used data from rural stations only and showed that the warming of the
Northern Hemisphere’s land surface should be significantly lower than what
reported by the available surface-based temperature records based on both
rural and urban stations. Watts (2022) examined the quality of the U.S.
temperature stations from which official temperature records are obtained and
concluded that approximately 96% of them could not meet the National Oceanic
and Atmospheric Administration (NOAA) requirements for “acceptable placement”
because they could be significantly contaminated by different heat sources. In
general, the surface temperature records and the homogenization algorithms
used to adjust them present several problems that may have exaggerated the
warming. Thus, the integrity of the available global surface temperature
records and, therefore, the ability to correctly determine the global warming
trend of the 20th and 21st century should be questioned as well (Connolly et
al., 2021; D’Aleo, 2016).

There is a different MSU record (Mears and Wentz, 2016), which shows warming
trends that is more compatible with those presented by the surface-based
temperature records. However, this alternative satellite-based record is not
analyzed here because it would overlap the results of the surface-based
temperature records. In any case, adopting it in the present study may not be
optimal because it only covers the latitude range from 70.0∘S to 82.5∘N and
because it appears to perform worse than UAH-MSU-lt that better agrees with
the radiosonde temperature database (Christy et al., 2018).

Here, we significantly expand the analysis presented by Scafetta (2022) by
testing 143 GCM average simulations and all 688 GCM member simulations
available on the KNMI website against four surface-based global temperature
records (ERA5-T2m, HadCRUT5, GISTEMP v4, NOAAGlobTemp v5) and the UAH-MSU-lt
v6 satellite-based record. Since we wish to narrow the ECS range, we again
group the models into three classes corresponding to low, medium and high ECS
values, as proposed in Scafetta (2022). ECS GCM groups that produce
systematically biased trends (e.g. too hot or too cold relative to the
observed temperatures) should be questioned and not used for policy even
though some simulations may appear to reproduce the observations. Finally, we
compare the GCM hindcasts with observed land and ocean warming values to
determine whether the surface-based records could be regionally biased and
whether the ECS should be further constrained towards lower values.

Figure 1: (Left) GCM global surface temperature simulations (colored curves)
and (right) $\pm 1\sigma$ GCM global surface temperature ensembles (yellow
area) versus the ERA5-T2m record (black, 12-month moving average). Figure 2:
GCM global surface temperature ensembles (yellow area, $\pm 1\sigma$) versus
HadCRUT5, GISTEMP v4, NOAAGlobTemp v5, and UAH-MSU-lt v6 temperature records
(black, 12-month moving average).

##  2 Data and methods

We analyze the monthly reanalysis field near-surface air temperature
(ERA5-T2m) record from 1980 to 2021 (Hersbach et al., 2020; Simmons et al.,
2021). We repeat the same analysis using the HadCRUT5 (Morice et al., 2021),
GISTEMP v4 (Lenssen et al., 2019), and NOAAGlobalTemp v5 (Zhang et al., 2019)
global surface temperature records. Some of these records, however, may not
cover the entire surface of the globe from 1980 to 2021. There are other
global surface temperature records such as those proposed by the Japanese
Meteorological Agency (JMA, Ishihara, 2006) and by the Berkeley Earth group
(BE, Rohde and Hausfather, 2020), which will also be discussed briefly. For
completeness, as explained in the Introduction, we add a comparison with the
UAH-MSU-lt v6 temperature measurements (Spencer et al., 2017).

We also analyze all 143 “average” surface air temperature (tas) records and
all 688 ensemble member records from 38 different CMIP6 GCMs downloadable from
KNMI Climate Explorer. These simulations were produced using historical
forcings (1850-2014) further extended up to 2100 with four different SSP
scenarios: SSP1-2.6 (low GHG emissions), SSP2-4.5 (intermediate GHG
emissions), SSP3-7.0 (high GHG emissions ) and SSP5-8.5 (very high greenhouse
gas emissions) (IPCC, 2021). These four scenarios are nearly indistinguishable
until 2021. Thus, from 1850 to 2021 the four simulation sets can be considered
independent assessments of the same models under nearly identical forcing
conditions, which also helps to assess in first approximation the internal
variability of the models.

The 1980-2021 period was chosen to better evaluate the performance of the
CMIP6 GCMs. This period is optimally covered by numerous climatic temperature
records including those based on satellite measurements that are alternative
to those based on land and oceanic measurements that could be affected by
various non-climatic biases, which are difficult to eliminate (D’Aleo, 2016;
Watts, 2022). In fact, going back in time from 1980 to 1850, the temperature
records are affected by ever-larger uncertainties and uncovered areas, which
makes evaluating the CMIP6 models even more difficult. A possible advantage of
the present study is that the previous studies evaluating the performance of
the CMIP6 models attempted to constrain the ECS by comparing GCM simulations
only with surface climate records from 1850 to 2020 (Ribes et al., 2021) or
from 1981 to 2014 (Tokarska et al., 2020), or even using uncertain
paleoclimate records (Zhu et al., 2020) and concluded that only high-ECS
models ($ECS>4.5$ ∘C) could be excluded. However, there are open questions as
to whether cooling adjustments applied to different Earth surface temperature
records from 1850 to 1980 are justified (D’Aleo, 2016) and whether in more
recent periods the global surface climate records are affected by non-climatic
warming biases (Connolly et al., 2021; Scafetta, 2021a). These biases could
have exaggerated the 20th century warming trend and incorrectly provided
support for the medium-ECS GCMs.

The 1980-2021 warming for each record is calculated by evaluating the
2011-2021 average temperature anomaly relative to the 1980-1990 period.
11-year intervals are used to bypass biases due to interannual fluctuations
such as those related to ENSO and the 11-year solar cycle. Then, we apply
standard statistical tests to decide if and how the observed warming values
for each of the temperature records are reproduced by the three ECS GCM
groups.

The ERA5-T2m global surface temperature average warming from 1980-1990 to
2011-2021 is estimated to be:

$\Delta T_{mean}=0.578{{}^{\circ}}C.$ (1)

The other temperature records give: HadCRUT5 (infilled data), $\Delta
T_{mean}=0.581$∘C; GISTEMP v4, $\Delta T_{mean}=0.570$∘C; NOAAGlobalTemp v5,
$\Delta T_{mean}=0.523$∘C. HadCRUT5, GISTEMP, and ERA5-T2m give nearly
identical warmings. We also observe that HadCRUT5 (non-infilled data) gives
$\Delta T_{mean}=0.549$∘C and HadCRUT4 gives $\Delta T_{mean}=0.521$∘C. BE
gives $\Delta T_{mean}=0.591$∘C and JMA gives $\Delta T_{mean}=0.557$∘C, which
do not differ much from the above estimates. Thus, from 1980 to 2021, the
available surface-based global temperature records measure that the global
surface warming from 1980-1990 to 2011-2021 has been between 0.52∘C and
0.59∘C, or approximately between 0.50∘C and 0.60∘C, with an average of 0.56∘C.
In contrast, the satellite-based UAH-MSU-lt v6 temperature record gives
$\Delta T_{mean}=0.402$∘C, suggesting that 2011-2021 actual warming may have
been even less than 0.40∘C because, as explained in the introduction,
according to the GCMs the temperature trend of the troposphere should be
scaled down to make it compatible with the surface warming trend.

For the temperature records, since 1980 the error of the average over an
11-year period can be estimated to be very small, $\bar{\sigma}_{95\%}\approx
0.01$∘C (see Appendix A), which represents about 2% of the warming from
1980-1990 to 2011-2021, and is less than the differences between the various
temperature records.

As explained in the Introduction, the proposed analysis groups the CMIP6 GCMs
into three subsets characterized by low ($1.5<ECS\leq 3.0$∘C), medium
($3.0<ECS\leq 4.5$ ∘C) and high ($4.5<ECS\leq 6.0$ ∘C) sensitivity values.
This choice is based on the following heuristic considerations. In fact, the
IPCC (2013) estimated that the ECS had to have a “likely” range of 1.5 –
4.5∘C. Also Wigley et al. (1997) suggested the same interval although the
best-fit sensitivity was found to be 2.5°C. This range can be heuristically
divided into at least two equal parts: $1.5<ECS\leq 3.0$ ∘C and $3.0<ECS\leq
4.5$ ∘C. In 2013, the CMIP5 GCMs were used. However, the IPCC (2021) adopted
the CMIP6 GCMs that extended the ECS range up to 6∘C so that an equally large
third range, $4.5<ECS\leq 6.0$ ∘C, could be added to the previous two. Zelinka
et al. (2020) explained that the causes of the increased climate sensitivity
in the CMIP6 models were due to stronger positive cloud feedbacks due to
decreased extratropical cloud cover and albedo that, however, might be
questionable.

Therefore, the interval $1.5<ECS\leq 3.0$ ∘C collects the GCMs with ECS values
most consistent with different empirical results, as discussed in the
Introduction; the interval $3.0<ECS\leq 4.5$ ∘C collects the other GCMs that
also the IPCC (2013) would have considered acceptable; finally, the interval
$4.5<ECS\leq 6.0$ ∘C collects the GCMs included in the IPCC (2021) but which
in 2013 the IPCC itself considered to predict an unlikely high ECS.

Figure 3: Average temperature changes (2011-2021 minus 1980-1990) hindcasted by 38 CMIP6 GCMs mean simulations. The blue vertical lines represent the temperature change measured by HadCRUT5, ERA5-T2m, GISTEMP v4, NOAAGlobTemp v5, and UAH-MSU-lt v6 temperature records, respectively, with their 95% confidence interval. The three yellow boxes represent the $\pm 1\sigma$ dispersion of the data referring to the low ($1.5<ECS\leq 3.0$ ∘C), medium ($3.0<ECS\leq 4.5$ ∘C) and high ($4.5<ECS\leq 6.0$ ∘C) ECS GCMs. See Table 1. Figure 4: Temperature change (2011-2021 minus 1980-1990) hindcasted by the full range of model simulations (red dots). The vertical lines represents the global surface warming from 1980-1990 to 2011-2021 reported by HadCRUT5, ERA5-T2m, GISTEMP v4, NOAAGlobTemp v5, and UAH-MSU-lt v6 temperature records, respectively, with their 95% confidence interval. Each of the four panel represents a set of forcing: (a) Hist+SSP1-2.6, (b) Hist+SSP2-4.5, (c) Hist+SSP3-7.0 and (d) Hist+SSP5-8.5. ECS GROUP | GCM | ECS (∘C) | SSP1-2.6 (∘C) | SSP2-4.5 (∘C) | SSP3-7.0 (∘C) | SSP5-8.5 (∘C) |  $mean\pm 1\sigma$ (∘C)
---|---|---|---|---|---|---|---
High ECS | CIESM | 5.67 | 0.67 | 0.75 |  | 0.71 | $0.71\pm 0.04$
CanESM5-CanOE-p2 | 5.62 | 1.15 | 1.17 | 1.17 | 1.16 | $1.16\pm 0.01$
CanESM5-p1 | 5.62 | 1.21 | 1.20 | 1.21 | 1.23 | $1.22\pm 0.01$
CanESM5-p2 | 5.62 | 1.22 | 1.23 | 1.23 | 1.23 | $1.23\pm 0.01$
HadGEM3-GC31-LL-f3 | 5.55 | 1.29 | 1.27 |  | 1.10 | $1.22\pm 0.11$
HadGEM3-GC31-MM-f3 | 5.42 | 0.84 |  |  | 0.87 | $0.85\pm 0.02$
UKESM1-0-LL-f2 | 5.34 | 1.15 | 1.12 | 1.10 | 1.13 | $1.13\pm 0.02$
CESM2 | 5.16 | 0.80 | 0.76 | 0.77 | 0.81 | $0.78\pm 0.02$
CNRM-CM6-1-f2 | 4.83 | 0.68 | 0.66 | 0.66 | 0.69 | $0.67\pm 0.01$
CNRM-ESM2-1-f2 | 4.76 | 0.64 | 0.62 | 0.63 | 0.66 | $0.64\pm 0.02$
CESM2-WACCM | 4.75 | 0.99 | 0.92 | 0.89 | 0.94 | $0.93\pm 0.04$
ACCESS-CM2 | 4.72 | 0.83 | 0.82 | 0.88 | 0.87 | $0.85\pm 0.03$
NESM3 | 4.72 | 0.98 | 0.96 |  | 1.03 | $0.99\pm 0.04$
IPSL-CM6A-LR | 4.56 | 0.76 | 0.77 | 0.76 | 0.77 | $0.77\pm 0.01$
$mean\pm 1\sigma$ |  | $0.94\pm 0.23$ | $0.94\pm 0.23$ | $0.93\pm 0.23$ | $0.94\pm 0.20$ | $0.94\pm 0.23$
Medium ECS | KACE-1-0-G | 4.48 | 0.96 | 0.96 | 0.94 | 0.97 | $0.96\pm 0.01$
EC-Earth3-Veg | 4.31 | 0.86 | 0.87 | 0.84 | 0.88 | $0.86\pm 0.02$
EC-Earth3 | 4.3 | 0.86 | 0.76 | 0.90 | 0.89 | $0.85\pm 0.06$
CNRM-CM6-1-HR-f2 | 4.28 | 0.76 | 0.72 | 0.72 | 0.74 | $0.73\pm 0.02$
GFDL-ESM4 | 3.9 | 0.69 | 0.73 | 0.68 | 0.66 | $0.69\pm 0.03$
ACCESS-ESM1-5 | 3.87 | 0.83 | 0.84 | 0.85 | 0.82 | $0.84\pm 0.01$
MCM-UA-1-0 | 3.65 | 0.87 | 0.83 | 0.80 | 0.91 | $0.85\pm 0.05$
CMCC-CM2-SR5 | 3.52 |  | 0.61 | 0.69 | 0.69 | $0.66\pm 0.04$
AWI-CM-1-1-MR | 3.16 | 0.79 | 0.80 | 0.77 | 0.79 | $0.79\pm 0.01$
MRI-ESM2-0 | 3.15 | 0.75 | 0.71 | 0.64 | 0.80 | $0.73\pm 0.07$
BCC-CSM2-MR | 3.04 | 0.64 | 0.65 | 0.66 | 0.67 | $0.65\pm 0.01$
$mean\pm 1\sigma$ |  | $0.80\pm 0.10$ | $0.77\pm 0.10$ | $0.77\pm 0.10$ | $0.80\pm 0.10$ | $0.79\pm 0.10$
Low ECS | FGOALS-f3-L | 3 | 0.75 | 0.69 | 0.71 | 0.69 | $0.71\pm 0.03$
MPI-ESM1-2-LR | 3 | 0.58 | 0.58 | 0.58 | 0.56 | $0.57\pm 0.01$
MPI-ESM1-2-HR | 2.98 | 0.54 | 0.57 | 0.60 | 0.57 | $0.57\pm 0.02$
FGOALS-g3 | 2.88 | 0.76 | 0.62 | 0.60 | 0.61 | $0.65\pm 0.08$
GISS-E2-1-G-p1 | 2.72 |  |  | 0.71 |  | $0.71$
GISS-E2-1-G-p3 | 2.72 | 0.44 | 0.59 | 0.41 | 0.46 | $0.47\pm 0.08$
MIROC-ES2L-f2 | 2.68 | 0.63 | 0.59 | 0.57 | 0.57 | $0.59\pm 0.03$
MIROC6 | 2.61 | 0.50 | 0.49 | 0.48 | 0.52 | $0.50\pm 0.02$
NorESM2-LM | 2.54 | 0.71 | 0.62 | 0.77 | 0.72 | $0.70\pm 0.06$
NorESM2-MM | 2.5 | 0.75 | 0.78 | 0.68 | 0.72 | $0.73\pm 0.04$
CAMS-CSM1-0 | 2.29 | 0.42 | 0.42 | 0.39 | 0.42 | $0.41\pm 0.02$
INM-CM5-0 | 1.92 | 0.62 | 0.59 | 0.66 | 0.61 | $0.62\pm 0.03$
INM-CM4-8 | 1.83 | 0.56 | 0.54 | 0.54 | 0.60 | $0.56\pm 0.02$
$mean\pm 1\sigma$ |  | $0.61\pm 0.12$ | $0.59\pm 0.09$ | $0.59\pm 0.12$ | $0.59\pm 0.09$ | $0.60\pm 0.12$
Table 1: Warming from 1980-1990 to 2011-2021 for average simulations of 38 GCMs using Historical + SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 forcings. See Figure 3. ECS GROUP |  | SSP1-2.6 | SSP2-4.5 | SSP3-7.0 | SSP5-8.5 | total | %
---|---|---|---|---|---|---|---
| total members | 141 | 172 | 178 | 197 | 688 |
High ECS | $\mathrm{Model>HadCRUT}$ | 86 | 93 | 97 | 93 | 369 | 97%
$\mathrm{Model>ERA5T2m}$ | 86 | 93 | 97 | 93 | 369 | 97%
$\mathrm{Model>GISTEMP}$ | 88 | 93 | 98 | 93 | 372 | 98%
$\mathrm{Model>NOAAGT}$ | 88 | 95 | 100 | 96 | 379 | 99.5%
$\mathrm{Model>UAHMSU}$ | 88 | 96 | 100 | 96 | 380 | 100%
$\mathrm{Model<HadCRUT}$ | 2 | 3 | 3 | 3 | 11 | 3%
$\mathrm{Model<ERA5T2m}$ | 2 | 3 | 3 | 3 | 11 | 3%
$\mathrm{Model<GISTEMP}$ | 0 | 3 | 2 | 3 | 8 | 2%
$\mathrm{Model<NOAAGT}$ | 0 | 1 | 0 | 0 | 1 | 0.5%
$\mathrm{Model<UAHMSU}$ | 0 | 0 | 0 | 0 | 0 | 0%
Medium ECS | $\mathrm{Model>HadCRUT}$ | 25 | 39 | 29 | 26 | 119 | 94%
$\mathrm{Model>ERA5T2m}$ | 25 | 39 | 30 | 26 | 120 | 95%
$\mathrm{Model>GISTEMP}$ | 26 | 39 | 30 | 26 | 121 | 96%
$\mathrm{Model>NOAAGT}$ | 26 | 41 | 32 | 26 | 125 | 99%
$\mathrm{Model>UAHMSU}$ | 26 | 42 | 32 | 26 | 126 | 100%
$\mathrm{Model<HadCRUT}$ | 1 | 3 | 3 | 0 | 7 | 6%
$\mathrm{Model<ERA5T2m}$ | 1 | 3 | 2 | 0 | 6 | 5%
$\mathrm{Model<GISTEMP}$ | 0 | 3 | 2 | 0 | 5 | 4%
$\mathrm{Model<NOAAGT}$ | 0 | 1 | 0 | 0 | 1 | 1%
$\mathrm{Model<UAHMSU}$ | 0 | 0 | 0 | 0 | 0 | 0%
Low ECS | $\mathrm{Model>HadCRUT}$ | 12 | 14 | 25 | 18 | 69 | 38%
$\mathrm{Model>ERA5T2m}$ | 12 | 15 | 26 | 19 | 72 | 40%
$\mathrm{Model>GISTEMP}$ | 13 | 16 | 28 | 24 | 81 | 45%
$\mathrm{Model>NOAAGT}$ | 21 | 26 | 35 | 39 | 121 | 66%
$\mathrm{Model>UAHMSU}$ | 27 | 33 | 43 | 71 | 174 | 96%
$\mathrm{Model<HadCRUT}$ | 15 | 20 | 21 | 57 | 113 | 62%
$\mathrm{Model<ERA5T2m}$ | 15 | 19 | 20 | 56 | 110 | 60%
$\mathrm{Model<GISTEMP}$ | 14 | 18 | 18 | 51 | 101 | 55%
$\mathrm{Model<NOAAGT}$ | 6 | 8 | 11 | 36 | 61 | 34%
$\mathrm{Model<UAHMSU}$ | 0 | 1 | 3 | 4 | 8 | 4%
Table 2: Number of single GCM simulations reporting mean temperature changes
(2011-2021 minus 1980-1990) lower or higher than HadCRUT5, ERA5-T2m, GISTEMP
v4, NOAAGlobTemp v5 and UAH-MSU-lt v6, respectively.

##  3 Analysis of the CMIP6 GCM simulations

Figure 1 shows the GCM simulations (left) and their ensemble $mean\pm 1\sigma$
range (right) grouped according to the three GCM ECS sets with respect to the
ERA5-T2m global surface temperature record (black, moving averages at 12
months). All records are temperature anomalies relative to the period
1980-1990. Figure 2 shows a similar comparison with respect to the HadCRUT,
GISTEMP, NOAAGlobTemp and UAH-MSU-lt temperature records.

Both figures show that as the ECS increases, the global surface warming
predicted by the models also increases. However, only the low-ECS GCM group
can be considered perfectly consistent with the surface-based global
temperature records because it encloses them well within the $\pm 1$$\sigma$
GCM range (yellow area).

Figures 1 and 2 also show that, compared to the satellite record, even the GCM
group with low ECS seems to overestimate the observed warming. In fact, even
for the low ECS GCM group from 2011 to 2021 the UAH-MSU-lt record is not well
enclosed within the $\pm 1\sigma$ model ensemble (yellow) area although a
better agreement is found in the period 2015- 2020. The latter was
characterized by the significant El Niño warming events of 2015-2016 and 2020
(Appendix A, Figure 11). Therefore, the 2015-2020 warming for the period
2000-2014 could also be temporary (Scafetta, 2021c) and not related to the
warming hindcasted by the models because it is clearly due to natural climatic
fluctuations while the average warming produced by the models is due to
anthropogenic forcing. From 2015 to 2022, in fact, a slightly cooling trend is
observed. From 2000 to 2014 the UAH-MSU-lt v6 record also clearly shows the
so-called global warming “hiatus” or “pause” (IPCC, 2013). This decade-long
lack of warming began to seriously question the GCMs, and various statistical
solutions were proposed to circumvent the problem by referring to the
fluctuations of the internal variability of the climate system (e.g. Meehl et
al., 2011). Figures 1 and 2 also show that, at the present, the "pause"
appears missing or attenuated in the latest versions of the surface-based
global temperature records.

###  3.1 Analysis of the GCM average simulations

Scafetta (2022) analyzed the average simulations of 38 GCMs using the
historical + SSP2-4.5, SSP3-7.0, and SSP5-8.5 radiative forcing scenarios up
to June 2021; the warming values for each model were collected in the table
there published. Figure 3 graphically shows the results of the same analysis,
which was updated to the whole year 2021 and also included the SSP1-2.6
simulations, compared to the temperature observations (green vertical lines).
143 average records are analyzed. For each ECS GCM group the statistics
provide (see Table 1):

  * •

High-ECS GCMs (51 records): $\Delta T_{mean}=0.94\pm 0.22$ ∘C;

  * •

Medium-ECS GCMs (43 records): $\Delta T_{mean}=0.79\pm 0.10$ ∘C;

  * •

Low-ECS GCMs (49 records): $\Delta T_{mean}=0.59\pm 0.10$ ∘C.

The result confirms that the GCM group with low ECS is perfectly compatible
with the observed warming (Eq. 1) within the $\pm 1$$\sigma$ range. In
contrast, both GCM groups with medium and high ECS show warming biases.
Moreover, as Scafetta (2022) already observed, Figure 3 also shows that none
of the medium and high ECS models predict an average warming of less than
0.6∘C, which is above the warming reported by all global temperature surface
records. This result suggests that models with $ECS>3$∘C should be questioned
at the 95% confidence level. Thus, by considering only the GCM ensemble
averages for the four SSPs, the real ECS should be equal to or lower than 3∘C.

However, Figure 3 also shows that if the UAH-MSU-LT record better reproduces
the actual 2011-2021 warming, the GCM group with low ECS would also be too hot
because, out of 49 GCM ensemble averages with low ECS, 48 cases (98%) are
warmer than 0.40∘C. The GCM that best agrees with the satellite record is
CAMS-CSM1-0 whose ECS is 2.29∘C.

Figure 5: Boxplots of the CMIP6 ensemble members depicted in Figure 4 for each
CMIP6 GCM; # represents the number of the available simulations for each GCM.
The horizontal blue lines represents the global surface warming from 1980-1990
to 2011-2021 reported by HadCRUT5, ERA5-T2m, GISTEMP v4, NOAAGlobTemp v5, and
UAH-MSU-lt v6 temperature records, respectively. The whiskers extend from each
end of the box for a range up to 1.5 times the interquartile range. Figure 6:
(a, b, c) GCM probability density functions relative to three model precision
requirements: $\sigma=0.05$∘C, $\sigma=0.10$∘C and $\sigma=0.15$∘C, which
approximately correspond to $\sigma_{95\%}=0.10$∘C, $\sigma_{95\%}=0.20$∘C and
$\sigma_{95\%}=0.30$∘C. The green vertical lines represent the global surface
warming from 1980-1990 to 2011-2021 reported by HadCRUT5, ERA5-T2m, GISTEMP
v4, NOAAGlobTemp v5 and UAH-MSU-lt v6 temperature records. (d, e, f) Boxplots
of the the probability density functions depicted in panels a, b, c,
respectively, using double whiskers and boxes indicating the following
probability ranges: 2.5%, 16%, 25%, 50%, 75%, 84% and 97.5%.

###  3.2 Analysis of the full range of the GCM ensemble members

Figure 4 shows in four panels the temperature variations (2011-2021 minus
1980-1990) of the 688 simulations of GCM ensemble members available per
forcing set (Hist+SSP1-2.6, Hist+SSP2-4.5, Hist+SSP3-7.0 and Hist+SSP5-8.5;
red dots) against the five temperature records (vertical lines). The figure
visually confirms that the vast majority of ensemble member simulations
produced by the GCM groups with medium and high ECS run too hot relative to
all five temperature records.

To examine how observed warming values are placed within the distributions of
possible GCM hindcasts for each of the three ECS groups, we count how many
member simulations record temperatures colder or warmer than each of the five
temperature records. Table 2 reports the results.

The analysis confirms that the low-ECS models produce results that well
enclose the 2011-2021 average temperatures obtained using the surface
temperature temperature records, which always fall within the statistical
interval $\pm 1\sigma$ (corresponding to the 16-84% probability interval) of
the distribution of the GCM hindcasts. In contrast, 94-100% and 97-100% of
hindcasts produced by the GCMs with medium and high ECS are warmer than all
five temperature records, respectively. Therefore, also considering the full
range of the available CMIP6 GCM simulations, the GCMs with medium and high
ECS run too hot. Thus, the actual ECS should be equal to or less than 3∘C.

However, 96% of GCM simulations from the low-ECS GCM are warmer and only 4%
cooler than the lower troposphere temperature record. So, once again, we found
that if UAH-MSU-lt better reproduces the actual global warming from 1980-1990
to 2011-2021, the vast majority of the low-ECS GCM ensemble members would also
be found to run too hot.

ECS GROUP |  | high precision | medium precision | low precision
---|---|---|---|---
|  | ( $\sigma_{H}=0.05$∘C) | ( $\sigma_{M}=0.10$∘C) | ( $\sigma_{L}=0.15$∘C)
High ECS | $\mathrm{HadCRUT<Model}$ | 99% | 95% | 92%
$\mathrm{ERA5T2m<Model}$ | 99% | 95% | 92%
$\mathrm{GISTEMP<Model}$ | 99% | 96% | 93%
$\mathrm{NOAAGT<Model}$ | 100% | 98% | 95%
$\mathrm{UAHMSU<Model}$ | 100% | 100% | 99%
$\mathrm{HadCRUT>Model}$ | 1% | 5% | 8%
$\mathrm{ERA5T2m>Model}$ | 1% | 5% | 8%
$\mathrm{GISTEMP>Model}$ | 1% | 4% | 7%
$\mathrm{NOAAGT>Model}$ | 0% | 2% | 5%
$\mathrm{UAHMSU>Model}$ | 0% | 0% | 1%
Medium ECS | $\mathrm{HadCRUT<Model}$ | 98% | 93% | 88%
$\mathrm{ERA5T2m<Model}$ | 98% | 93% | 88%
$\mathrm{GISTEMP<Model}$ | 99% | 94% | 88%
$\mathrm{NOAAGT<Model}$ | 100% | 97% | 93%
$\mathrm{UAHMSU<Model}$ | 100% | 100% | 99%
$\mathrm{HadCRUT>Model}$ | 2% | 7% | 12%
$\mathrm{ERA5T2m>Model}$ | 2% | 7% | 12%
$\mathrm{GISTEMP>Model}$ | 1% | 6% | 12%
$\mathrm{NOAAGT>Model}$ | 0% | 3% | 7%
$\mathrm{UAHMSU>Model}$ | 0% | 0% | 1%
Low ECS | $\mathrm{HadCRUT<Model}$ | 55% | 54% | 53%
$\mathrm{ERA5T2m<Model}$ | 56% | 55% | 53%
$\mathrm{GISTEMP<Model}$ | 59% | 57% | 55%
$\mathrm{NOAAGT<Model}$ | 74% | 69% | 65%
$\mathrm{UAHMSU<Model}$ | 95% | 91% | 85%
$\mathrm{HadCRUT>Model}$ | 45% | 46% | 47%
$\mathrm{ERA5T2m>Model}$ | 44% | 45% | 47%
$\mathrm{GISTEMP>Model}$ | 41% | 43% | 45%
$\mathrm{NOAAGT>Model}$ | 26% | 31% | 35%
$\mathrm{UAHMSU>Model}$ | 5% | 9% | 15%
Table 3: Probability $P_{\Delta T<GCMs}$ and $P_{\Delta T>GCMs}$ that the 2011-2021 warming hindcast from 1980-1990 to 2011-2021 for each ECS GCM ensemble is warmer or colder, respectively, than HadCRUT5, ERA5- T2m, GISTEMP v4, NOAAGlobTemp v5 and UAH-MSU-lt v6, respectively: see Figure 6. | Observations and GCM hindcasts | Modeled Global and Land Warmings
---|---|---
(80∘S:80∘N) | Total (∘C) | Land (∘C) | Ocean (∘C) | ratio | Total (∘C) | Land (∘C) | Ocean (∘C) | average ratio
HadCRUT5 | 0.57 | 0.86 | 0.45 | 1.92 | 0.54 | 0.76 | 0.45 | 1.69
ERA5-T2m | 0.57 | 0.92 | 0.43 | 2.14 | 0.51 | 0.73 | 0.43 | 1.69
GISTEMP | 0.54 | 0.93 | 0.41 | 2.26 | 0.48 | 0.69 | 0.41 | 1.69
NOAAGT | 0.53 | 0.91 | 0.38 | 2.38 | 0.45 | 0.64 | 0.38 | 1.69
MSU-UAH | 0.40 | 0.53 | 0.34 | 1.54 | 0.41 | 0.57 | 0.34 | 1.69
Low ECS GCMs | 0.58$\pm$0.10 | 0.84$\pm$0.18 | 0.48$\pm$0.08 | 1.73$\pm$0.21 |  |  |  |
Medium ECS GCMs | 0.77$\pm$0.10 | 1.07$\pm$0.15 | 0.66$\pm$0.08 | 1.63$\pm$0.13 |  |  |  |
High ECS GCMs | 0.92$\pm$0.21 | 1.31$\pm$0.28 | 0.78$\pm$0.19 | 1.71$\pm$0.22 |  |  |  |
(60∘S:80∘N) | Total (∘C) | Land (∘C) | Ocean (∘C) | ratio | Total (∘C) | Land (∘C) | Ocean (∘C) | average ratio
HadCRUT5 | 0.59 | 0.91 | 0.47 | 1.95 | 0.56 | 0.82 | 0.47 | 1.74
ERA5-T2m | 0.61 | 0.97 | 0.47 | 2.08 | 0.57 | 0.82 | 0.47 | 1.74
GISTEMP | 0.55 | 0.94 | 0.42 | 2.24 | 0.50 | 0.73 | 0.42 | 1.74
NOAAGT | 0.54 | 0.91 | 0.39 | 2.32 | 0.47 | 0.68 | 0.39 | 1.74
MSU-UAH | 0.42 | 0.55 | 0.37 | 1.51 | 0.42 | 0.54 | 0.37 | 1.74
Low ECS GCMs | 0.59$\pm$0.11 | 0.86$\pm$0.19 | 0.49$\pm$0.08 | 1.75$\pm$0.20 |  |  |  |
Medium ECS GCMs | 0.77$\pm$0.11 | 1.10$\pm$0.16 | 0.65$\pm$0.09 | 1.69$\pm$0.14 |  |  |  |
High ECS GCMs | 0.92$\pm$0.21 | 1.34$\pm$0.29 | 0.76$\pm$0.19 | 1.79$\pm$0.24 |  |  |  |
(0∘N:80∘N) | Total (∘C) | Land (∘C) | Ocean (∘C) | ratio | Total (∘C) | Land (∘C) | Ocean (∘C) | average ratio
HadCRUT5 | 0.81 | 1.03 | 0.68 | 1.52 | 0.79 | 0.99 | 0.68 | 1.45
ERA5-T2m | 0.85 | 1.09 | 0.69 | 1.57 | 0.82 | 1.00 | 0.69 | 1.45
GISTEMP | 0.78 | 1.04 | 0.63 | 1.66 | 0.73 | 0.91 | 0.63 | 1.45
NOAAGT | 0.75 | 1.00 | 0.59 | 1.72 | 0.69 | 0.86 | 0.59 | 1.45
MSU-UAH | 0.48 | 0.56 | 0.42 | 1.32 | 0.50 | 0.61 | 0.42 | 1.45
Low ECS GCMs | 0.77$\pm$0.18 | 0.95$\pm$0.23 | 0.66$\pm$0.16 | 1.45$\pm$0.12 |  |  |  |
Medium ECS GCMs | 1.00$\pm$0.17 | 1.21$\pm$0.19 | 0.87$\pm$0.16 | 1.40$\pm$0.09 |  |  |  |
High ECS GCMs | 1.20$\pm$0.32 | 1.47$\pm$0.35 | 1.02$\pm$0.31 | 1.49$\pm$0.28 |  |  |  |
(60∘S:0∘S) | Total (∘C) | Land (∘C) | Ocean (∘C) | ratio | Total (∘C) | Land (∘C) | Ocean (∘C) | average ratio
HadCRUT5 | 0.34 | 0.58 | 0.29 | 1.97 | 0.33 | 0.50 | 0.29 | 1.72
ERA5-T2m | 0.34 | 0.64 | 0.29 | 2.25 | 0.32 | 0.50 | 0.29 | 1.72
GISTEMP | 0.30 | 0.61 | 0.26 | 2.40 | 0.28 | 0.45 | 0.26 | 1.72
NOAAGT | 0.31 | 0.65 | 0.24 | 2.68 | 0.27 | 0.41 | 0.24 | 1.72
MSU-UAH | 0.35 | 0.54 | 0.32 | 1.67 | 0.34 | 0.46 | 0.32 | 1.72
Low ECS GCMs | 0.39$\pm$0.08 | 0.60$\pm$0.13 | 0.35$\pm$0.08 | 1.75$\pm$0.41 |  |  |  |
Medium ECS GCMs | 0.51$\pm$0.08 | 0.76$\pm$0.12 | 0.47$\pm$0.08 | 1.64$\pm$0.29 |  |  |  |
High ECS GCMs | 0.61$\pm$0.13 | 0.96$\pm$0.33 | 0.55$\pm$0.11 | 1.77$\pm$0.54 |  |  |  |
Table 4: Left columns: observed and hindcasted warming over 80∘S:80∘N,
60∘S:80∘N, 0∘N:80∘N, and 60∘S:0∘S latitude ranges from 1980-1990 to 2011-2021
over land+ocean (total), land, and ocean, and land/ocean ratio. The model
estimates use the average GCM simulations. Right columns: global and land
warming calculated assuming correct the ocean warming reported by the
temperature records and the average land/ocean warming ratios hindcasted by
the GCMs.

###  3.3 Statistical modeling of the GCM unforced internal variability

Figure 5 shows the boxplots relating to the simulations shown in Figure 4 for
each model. Again, the GCM group with low ECS is best centered around the
surface-based observations indicated by the horizontal blue lines while the
GCM groups with medium and high ECS exhibit systematic warming bias except for
very few models. However, the dispersion of the boxplots varies greatly among
the GCMs because the models are not physically equivalent to each other and,
furthermore, probably because of the different number of simulations available
for each model.

In fact, the GCMs are represented unevenly in the KNMI collection because the
number of simulations available for each GCM varies from 3 to 100 among the
models: see Figure 5. Therefore, the statistics discussed in Section 3.2 may
be skewed towards models with a larger number of available simulations because
they will weight more in the statistical test reported in Table 3. This
problem could be solved by using a Monte Carlo strategy to simulate the spread
of GCM hindcasts that could be associated with unforced internal variability.
This exercise is proposed below.

It can be assumed that each GCM produces simulations distributed around a mean
$\mu_{m}$ with a given standard deviation $\sigma_{m}$ characterizing its
internal variability. We note that $\sigma_{m}$ should be assumed constant for
all GCM averages because it could be interpreted as a “precision” requirement
for GCMs. Indeed, GCM hindcasts should always agree with observations within
an acceptable statistical uncertainty.

We propose three different options for $\sigma_{m}$ covering approximately the
ranges of the GCM boxplots shown in Figure 5: $\sigma_{H}\approx 0.05$∘C (high
precision), $\sigma_{M}\approx 0.10$∘C (medium precision), and
$\sigma_{L}\approx 0.15$∘C (low precision).

Figure 5 suggests that the high-precision option ($\sigma_{H}\approx 0.05$∘C)
could be satisfied by most GCMs; it requires the model mean to be within $\pm
0.1$∘C (95% confidence interval) of the actual warming value. The 95%
confidence range becomes $\pm 0.2$∘C for the medium-precision requirement
($\sigma_{M}\approx 0.10$∘C) and $\pm 0.3$∘C for the low-precision option
($\sigma_{L}\approx 0.15$∘C).

Appendix B shows that the interval $\pm 0.1$∘C (95% confidence), which
corresponds to the high precision option, $\sigma_{H}\approx 0.05$∘C, should
be the preferred choice for the acceptable uncertainty related to the internal
variability that should be requested for the GCM because it could be derived
from the variability of the temperature records themselves.

Figure 5 also shows that the low-precision option $\sigma_{L}\approx 0.15$∘C
is only consistent with the EC-Earth3 GCM. The usefulness of this model should
be questioned because it hindcasts 2011-2021 global surface warming values
ranging between 0.5∘C to 1.2∘C with an average of 0.82∘C. This means that EC-
Earth3 is both inaccurate and imprecise in hindcasting the global surface
warming from 1980 to 2021.

Figure 6 shows the combined probability density functions (PDF) and the
related boxplots derived from all the GCM means reported in Figure 3 and in
Table 1 with the three precision requirements for the three ECS GCM groups
compared to the warming levels obtained with the adopted five temperature
records. The complementary Gaussian error function was used to evaluate the
relative statistical position of the five actual warming values within each
probability density function.

For each model mean $\mu_{m}$ and precision $\sigma$, the probability $P_{m}$
that the GCM hindcast is larger than the measured warming $\Delta T$ is

$P_{m}=\frac{1}{\sigma\sqrt{2\pi}}\intop_{\Delta
T}^{\infty}e^{-\frac{(t-\mu_{m})}{2\sigma^{2}}^{2}}\,dt=\frac{1}{2}\,\mathrm{erfc}\left(\frac{\Delta
T-\mu_{m}}{\sigma\sqrt{2}}\right).$ (2)

Thus, the mean $P_{\Delta T<GCMs}=\frac{1}{N}\sum_{m=1}^{N}P_{m}$ across all
models for each ECS GCM group gives the probability of obtaining simulations
warmer than the reference temperature value. $P_{\Delta T<GCMs}$ can also be
obtained by integrating the probability density functions shown in Figure
6a-6c from the green line to infinity or by using a Monte Carlo strategy by
generating, for example, 1000 computer values from a Gaussian distribution
with mean $\mu_{m}$ and standard deviation $\sigma$. The relevant statistics
are shown in Table 3.

Figure 6a-6c show that the GCM group with low ECS (blue curves) always
produces predictions well-centered on the observed warming for the four
surface temperature records because their 2011-2021 values always fall within
the $\pm 1\sigma$ statistical interval (which corresponds to the 16%-84%
probability range) of the GCM distributions for the high, medium, and low
precision options, respectively. However, once again, if the actual 1980-2021
warming is given by UAH-MSU-lt, even the GCM group with low ECS seems to be
biased towards too hot values in 95%, 91% and 85% of possible cases,
respectively, for the three precision options (Table 3).

The predictions of the medium (purple) and high (red) ECS GCM groups always
show significant warming biases. Also, particularly for the GCM group with
high ECS, the PDF appears to have two peaks, implying that the GCMs in this
group are physically very different from each other because they produce very
different warming hindcasts that are clustered around 0.8∘C and 1.2∘C; the
warmest PDF peak is mostly due to the CanESM5 GCM.

For the high-precision requirement ($\sigma_{H}=0.05$∘C), these two GCM groups
produce results warmer than the observed values from a minimum of 98% to a
maximum of 100% of their possible output, which is outside the 95% confidence
interval. For the medium precision option ($\sigma_{M}=0.10$∘C), the medium
and high GCM groups produce results warmer than the observed values from a
minimum of 93% to a maximum of 100% of their possible outputs, which is at the
limit of the 95% confidence interval. For the low precision option
($\sigma_{L}=0.15$∘C), the GCM groups with medium and high ECS produce warmer
results than the four surface-based temperature records from 88% to 95% of
cases. Conversely, 99% or more of the theoretical hindcasts of the GCM groups
with high and medium ECS would be warmer than UAH-MSU-lt even for the low
precision option ($\sigma_{L}=0.15$∘C).

The boxplots illustrated in Figures 6d-6f were obtained using the Monte Carlo
strategy proposed above which simulates 1000 randomly distributed outputs for
each of the 143 model averages for each of the three precision options (for a
total of $3\times 143,000$ theoretical hindcasts). The three panels show that
in all cases, with respect to the observed temperature values, the groups with
medium and high ECS are well outside the 68% confidence interval (i.e. the
$\pm 1\sigma$ interval). Furthermore, the GCM groups with medium and high ECS
indicate levels of warming that are respectively 30% and 50% greater than
those actually observed and, consequently, their accuracy is rather low. The
accuracy of the low-ECS GCM group is good compared to the surface-based
temperature records, but it still reports average warming that is about 30%
larger than that reported by the satellite temperature record. The whisker
extension of the boxplot shows that the precision of the low, medium and high
ECS groups varies from modest ($\pm 0.2$∘C) to very poor ($\pm 0.5$∘C) range
from low ECS and high precision GCM group to high and low precision GCM group.

Figure 7: Areal distribution of the warming from 1980-1990 to 2011-2021 for the CMIP6 ensemble average simulation and for the HadCRUT5, ERA5-T2m, GISTEMP v4, NOAAGlobTemp v5, and UAH-MSU-lt v6 temperature records. Figure 8: 2011-2021 warming relative to 1980-1990 of the models over (a) land+ocean, (b) land, (c) ocean areas within the 60∘S:80∘N latitude range for the 143 average model simulations (colored dots) and the five temperature records (colored lines). (d) Ratio between the land and the ocean warming. See Tables 5, 6, and 7. Model | ECS (∘C) | Hist + SSP | Land + Ocean (∘C) | Land (∘C) | Ocean (∘C) | Land/Ocean
---|---|---|---|---|---|---
INM-CM4-8 | 1.83 | SSP1-2.6 | 0.55 | 0.78 | 0.46 | 1.69
INM-CM4-8 | 1.83 | SSP2-4.5 | 0.54 | 0.72 | 0.47 | 1.54
INM-CM4-8 | 1.83 | SSP3-7.0 | 0.52 | 0.72 | 0.45 | 1.62
INM-CM4-8 | 1.83 | SSP5-8.5 | 0.58 | 0.82 | 0.49 | 1.68
INM-CM5-0 | 1.92 | SSP1-2.6 | 0.59 | 0.83 | 0.50 | 1.66
INM-CM5-0 | 1.92 | SSP2-4.5 | 0.56 | 0.82 | 0.46 | 1.76
INM-CM5-0 | 1.92 | SSP3-7.0 | 0.64 | 0.92 | 0.53 | 1.74
INM-CM5-0 | 1.92 | SSP5-8.5 | 0.59 | 0.84 | 0.49 | 1.73
CAMS-CSM1-0 | 2.29 | SSP1-2.6 | 0.43 | 0.57 | 0.38 | 1.50
CAMS-CSM1-0 | 2.29 | SSP2-4.5 | 0.42 | 0.56 | 0.37 | 1.50
CAMS-CSM1-0 | 2.29 | SSP3-7.0 | 0.39 | 0.49 | 0.35 | 1.39
CAMS-CSM1-0 | 2.29 | SSP5-8.5 | 0.42 | 0.55 | 0.37 | 1.49
NorESM2-MM | 2.5 | SSP1-2.6 | 0.77 | 1.16 | 0.62 | 1.86
NorESM2-MM | 2.5 | SSP2-4.5 | 0.80 | 1.20 | 0.64 | 1.87
NorESM2-MM | 2.5 | SSP3-7.0 | 0.71 | 1.11 | 0.55 | 2.03
NorESM2-MM | 2.5 | SSP5-8.5 | 0.74 | 1.18 | 0.57 | 2.06
NorESM2-LM | 2.54 | SSP1-2.6 | 0.74 | 1.21 | 0.56 | 2.17
NorESM2-LM | 2.54 | SSP2-4.5 | 0.64 | 1.04 | 0.48 | 2.15
NorESM2-LM | 2.54 | SSP3-7.0 | 0.79 | 1.31 | 0.59 | 2.23
NorESM2-LM | 2.54 | SSP5-8.5 | 0.74 | 1.23 | 0.55 | 2.24
MIROC6 | 2.61 | SSP1-2.6 | 0.51 | 0.78 | 0.41 | 1.91
MIROC6 | 2.61 | SSP2-4.5 | 0.50 | 0.77 | 0.40 | 1.92
MIROC6 | 2.61 | SSP3-7.0 | 0.49 | 0.75 | 0.39 | 1.92
MIROC6 | 2.61 | SSP5-8.5 | 0.53 | 0.83 | 0.41 | 2.00
MIROC-ES2L-f2 | 2.68 | SSP1-2.6 | 0.65 | 1.00 | 0.51 | 1.98
MIROC-ES2L-f2 | 2.68 | SSP2-4.5 | 0.61 | 0.92 | 0.49 | 1.87
MIROC-ES2L-f2 | 2.68 | SSP3-7.0 | 0.58 | 0.84 | 0.48 | 1.76
MIROC-ES2L-f2 | 2.68 | SSP5-8.5 | 0.58 | 0.87 | 0.48 | 1.82
GISS-E2-1-G-p1 | 2.72 | SSP3-7.0 | 0.70 | 0.98 | 0.60 | 1.63
GISS-E2-1-G-p3 | 2.72 | SSP1-2.6 | 0.45 | 0.66 | 0.37 | 1.79
GISS-E2-1-G-p3 | 2.72 | SSP2-4.5 | 0.60 | 0.86 | 0.50 | 1.72
GISS-E2-1-G-p3 | 2.72 | SSP3-7.0 | 0.40 | 0.58 | 0.33 | 1.74
GISS-E2-1-G-p3 | 2.72 | SSP5-8.5 | 0.46 | 0.67 | 0.37 | 1.80
FGOALS-g3 | 2.88 | SSP1-2.6 | 0.75 | 1.04 | 0.64 | 1.62
FGOALS-g3 | 2.88 | SSP2-4.5 | 0.59 | 0.84 | 0.50 | 1.67
FGOALS-g3 | 2.88 | SSP3-7.0 | 0.58 | 0.84 | 0.47 | 1.77
FGOALS-g3 | 2.88 | SSP5-8.5 | 0.59 | 0.84 | 0.50 | 1.67
MPI-ESM1-2-HR | 2.98 | SSP1-2.6 | 0.53 | 0.71 | 0.46 | 1.55
MPI-ESM1-2-HR | 2.98 | SSP2-4.5 | 0.56 | 0.75 | 0.49 | 1.52
MPI-ESM1-2-HR | 2.98 | SSP3-7.0 | 0.60 | 0.83 | 0.51 | 1.64
MPI-ESM1-2-HR | 2.98 | SSP5-8.5 | 0.56 | 0.71 | 0.50 | 1.41
FGOALS-f3-L | 3 | SSP1-2.6 | 0.75 | 1.08 | 0.62 | 1.75
FGOALS-f3-L | 3 | SSP2-4.5 | 0.67 | 0.92 | 0.57 | 1.60
FGOALS-f3-L | 3 | SSP3-7.0 | 0.71 | 1.02 | 0.59 | 1.72
FGOALS-f3-L | 3 | SSP5-8.5 | 0.69 | 0.95 | 0.59 | 1.61
MPI-ESM1-2-LR | 3 | SSP1-2.6 | 0.58 | 0.81 | 0.49 | 1.65
MPI-ESM1-2-LR | 3 | SSP2-4.5 | 0.58 | 0.81 | 0.50 | 1.63
MPI-ESM1-2-LR | 3 | SSP3-7.0 | 0.58 | 0.81 | 0.49 | 1.66
MPI-ESM1-2-LR | 3 | SSP5-8.5 | 0.56 | 0.78 | 0.47 | 1.64
mean |  |  | 0.59 $\pm$ 0.11 | 0.86$\pm$ 0.19 | 0.49$\pm$ 0.08 | 1.75$\pm$ 0.20
Table 5: Low-ECS GCMs: hindcasted warming from 1980-1990 to 2011-2021 within the 60∘S:80∘N latitude range from 1980-1990 to 2011-2021 over land+ocean (total), land, ocean, and land/ocean ratio. See Figure 8. Model | ECS (∘C) | Hist + SSP | Land + Ocean (∘C) | Land (∘C) | Ocean (∘C) | Land/Ocean
---|---|---|---|---|---|---
BCC-CSM2-MR | 3.04 | SSP1-2.6 | 0.60 | 0.86 | 0.50 | 1.73
BCC-CSM2-MR | 3.04 | SSP2-4.5 | 0.61 | 0.89 | 0.50 | 1.79
BCC-CSM2-MR | 3.04 | SSP3-7.0 | 0.63 | 0.91 | 0.52 | 1.75
BCC-CSM2-MR | 3.04 | SSP5-8.5 | 0.64 | 0.93 | 0.53 | 1.76
MRI-ESM2-0 | 3.15 | SSP1-2.6 | 0.72 | 1.05 | 0.59 | 1.77
MRI-ESM2-0 | 3.15 | SSP2-4.5 | 0.68 | 1.00 | 0.56 | 1.77
MRI-ESM2-0 | 3.15 | SSP3-7.0 | 0.63 | 0.94 | 0.51 | 1.83
MRI-ESM2-0 | 3.15 | SSP5-8.5 | 0.79 | 1.12 | 0.66 | 1.69
AWI-CM-1-1-MR | 3.16 | SSP1-2.6 | 0.77 | 1.09 | 0.65 | 1.69
AWI-CM-1-1-MR | 3.16 | SSP2-4.5 | 0.79 | 1.15 | 0.65 | 1.78
AWI-CM-1-1-MR | 3.16 | SSP3-7.0 | 0.76 | 1.05 | 0.65 | 1.62
AWI-CM-1-1-MR | 3.16 | SSP5-8.5 | 0.77 | 1.11 | 0.64 | 1.73
CMCC-CM2-SR5 | 3.52 | SSP2-4.5 | 0.58 | 0.79 | 0.50 | 1.60
CMCC-CM2-SR5 | 3.52 | SSP3-7.0 | 0.66 | 0.85 | 0.58 | 1.47
CMCC-CM2-SR5 | 3.52 | SSP5-8.5 | 0.66 | 0.90 | 0.57 | 1.59
MCM-UA-1-0 | 3.65 | SSP1-2.6 | 0.86 | 1.07 | 0.78 | 1.36
MCM-UA-1-0 | 3.65 | SSP2-4.5 | 0.82 | 1.03 | 0.74 | 1.40
MCM-UA-1-0 | 3.65 | SSP3-7.0 | 0.78 | 0.92 | 0.73 | 1.27
MCM-UA-1-0 | 3.65 | SSP5-8.5 | 0.90 | 1.07 | 0.83 | 1.29
ACCESS-ESM1-5 | 3.87 | SSP1-2.6 | 0.84 | 1.20 | 0.69 | 1.74
ACCESS-ESM1-5 | 3.87 | SSP2-4.5 | 0.85 | 1.24 | 0.70 | 1.78
ACCESS-ESM1-5 | 3.87 | SSP3-7.0 | 0.86 | 1.27 | 0.70 | 1.82
ACCESS-ESM1-5 | 3.87 | SSP5-8.5 | 0.83 | 1.22 | 0.68 | 1.80
GFDL-ESM4 | 3.9 | SSP1-2.6 | 0.71 | 1.01 | 0.59 | 1.72
GFDL-ESM4 | 3.9 | SSP2-4.5 | 0.73 | 1.06 | 0.60 | 1.77
GFDL-ESM4 | 3.9 | SSP3-7.0 | 0.70 | 1.02 | 0.57 | 1.78
GFDL-ESM4 | 3.9 | SSP5-8.5 | 0.69 | 1.00 | 0.57 | 1.76
CNRM-CM6-1-HR-f2 | 4.28 | SSP1-2.6 | 0.68 | 0.97 | 0.57 | 1.71
CNRM-CM6-1-HR-f2 | 4.28 | SSP2-4.5 | 0.67 | 1.00 | 0.54 | 1.85
CNRM-CM6-1-HR-f2 | 4.28 | SSP3-7.0 | 0.66 | 0.95 | 0.55 | 1.73
CNRM-CM6-1-HR-f2 | 4.28 | SSP5-8.5 | 0.68 | 0.98 | 0.57 | 1.73
EC-Earth3 | 4.3 | SSP1-2.6 | 0.87 | 1.27 | 0.72 | 1.76
EC-Earth3 | 4.3 | SSP2-4.5 | 0.76 | 1.08 | 0.64 | 1.69
EC-Earth3 | 4.3 | SSP3-7.0 | 0.90 | 1.29 | 0.75 | 1.71
EC-Earth3 | 4.3 | SSP5-8.5 | 0.90 | 1.29 | 0.75 | 1.73
EC-Earth3-Veg | 4.31 | SSP1-2.6 | 0.87 | 1.27 | 0.72 | 1.76
EC-Earth3-Veg | 4.31 | SSP2-4.5 | 0.88 | 1.28 | 0.72 | 1.76
EC-Earth3-Veg | 4.31 | SSP3-7.0 | 0.85 | 1.22 | 0.71 | 1.73
EC-Earth3-Veg | 4.31 | SSP5-8.5 | 0.88 | 1.28 | 0.73 | 1.75
KACE-1-0-G | 4.48 | SSP1-2.6 | 0.95 | 1.37 | 0.79 | 1.73
KACE-1-0-G | 4.48 | SSP2-4.5 | 0.96 | 1.36 | 0.80 | 1.69
KACE-1-0-G | 4.48 | SSP3-7.0 | 0.93 | 1.34 | 0.77 | 1.73
KACE-1-0-G | 4.48 | SSP5-8.5 | 0.96 | 1.37 | 0.80 | 1.72
mean |  |  | 0.77 $\pm$ 0.11 | 1.10 $\pm$ 0.16 | 0.65 $\pm$ 0.10 | 1.69 $\pm$ 0.14
Table 6: Medium-ECS GCMs: hindcasted warming from 1980-1990 to 2011-2021 within the 60∘S:80∘N latitude range from 1980-1990 to 2011-2021 over land+ocean (total), land, ocean, and land/ocean ratio. See Figure 8. Model | ECS (∘C) | Hist + SSP | Land + Ocean (∘C) | Land (∘C) | Ocean (∘C) | Land/Ocean
---|---|---|---|---|---|---
IPSL-CM6A-LR | 4.56 | SSP1-2.6 | 0.75 | 1.07 | 0.63 | 1.71
IPSL-CM6A-LR | 4.56 | SSP2-4.5 | 0.75 | 1.07 | 0.63 | 1.70
IPSL-CM6A-LR | 4.56 | SSP3-7.0 | 0.75 | 1.06 | 0.63 | 1.68
IPSL-CM6A-LR | 4.56 | SSP5-8.5 | 0.75 | 1.08 | 0.63 | 1.72
ACCESS-CM2 | 4.72 | SSP1-2.6 | 0.84 | 1.21 | 0.69 | 1.75
ACCESS-CM2 | 4.72 | SSP2-4.5 | 0.83 | 1.20 | 0.69 | 1.74
ACCESS-CM2 | 4.72 | SSP3-7.0 | 0.88 | 1.28 | 0.73 | 1.76
ACCESS-CM2 | 4.72 | SSP5-8.5 | 0.79 | 1.14 | 0.65 | 1.74
NESM3 | 4.72 | SSP1-2.6 | 0.99 | 1.44 | 0.82 | 1.76
NESM3 | 4.72 | SSP2-4.5 | 0.97 | 1.37 | 0.81 | 1.69
NESM3 | 4.72 | SSP5-8.5 | 1.04 | 1.48 | 0.87 | 1.70
CESM2-WACCM | 4.75 | SSP1-2.6 | 0.98 | 1.40 | 0.81 | 1.72
CESM2-WACCM | 4.75 | SSP2-4.5 | 0.90 | 1.32 | 0.74 | 1.78
CESM2-WACCM | 4.75 | SSP3-7.0 | 0.87 | 1.28 | 0.71 | 1.80
CESM2-WACCM | 4.75 | SSP5-8.5 | 0.92 | 1.34 | 0.76 | 1.77
CNRM-ESM2-1-f2 | 4.76 | SSP1-2.6 | 0.63 | 0.93 | 0.51 | 1.82
CNRM-ESM2-1-f2 | 4.76 | SSP2-4.5 | 0.60 | 0.88 | 0.50 | 1.77
CNRM-ESM2-1-f2 | 4.76 | SSP3-7.0 | 0.61 | 0.90 | 0.50 | 1.81
CNRM-ESM2-1-f2 | 4.76 | SSP5-8.5 | 0.64 | 0.94 | 0.52 | 1.81
CNRM-CM6-1-f2 | 4.83 | SSP1-2.6 | 0.66 | 0.92 | 0.55 | 1.67
CNRM-CM6-1-f2 | 4.83 | SSP2-4.5 | 0.63 | 0.88 | 0.54 | 1.62
CNRM-CM6-1-f2 | 4.83 | SSP3-7.0 | 0.65 | 0.91 | 0.54 | 1.68
CNRM-CM6-1-f2 | 4.83 | SSP5-8.5 | 0.66 | 0.93 | 0.56 | 1.66
CESM2 | 5.16 | SSP1-2.6 | 0.78 | 1.15 | 0.64 | 1.82
CESM2 | 5.16 | SSP2-4.5 | 0.74 | 1.11 | 0.60 | 1.87
CESM2 | 5.16 | SSP3-7.0 | 0.75 | 1.13 | 0.61 | 1.86
CESM2 | 5.16 | SSP5-8.5 | 0.79 | 1.17 | 0.65 | 1.79
UKESM1-0-LL-f2 | 5.34 | SSP1-2.6 | 1.12 | 1.56 | 0.94 | 1.66
UKESM1-0-LL-f2 | 5.34 | SSP2-4.5 | 1.10 | 1.53 | 0.93 | 1.65
UKESM1-0-LL-f2 | 5.34 | SSP3-7.0 | 1.06 | 1.48 | 0.90 | 1.64
UKESM1-0-LL-f2 | 5.34 | SSP5-8.5 | 1.10 | 1.55 | 0.93 | 1.67
HadGEM3-GC31-MM-f3 | 5.42 | SSP1-2.6 | 0.81 | 1.23 | 0.64 | 1.91
HadGEM3-GC31-MM-f3 | 5.42 | SSP5-8.5 | 0.86 | 1.25 | 0.71 | 1.76
HadGEM3-GC31-LL-f3 | 5.55 | SSP1-2.6 | 1.21 | 1.71 | 1.01 | 1.70
HadGEM3-GC31-LL-f3 | 5.55 | SSP2-4.5 | 1.20 | 1.69 | 1.01 | 1.68
HadGEM3-GC31-LL-f3 | 5.55 | SSP5-8.5 | 1.07 | 1.53 | 0.89 | 1.72
CanESM5-CanOE-p2 | 5.62 | SSP1-2.6 | 1.20 | 1.72 | 1.00 | 1.72
CanESM5-CanOE-p2 | 5.62 | SSP2-4.5 | 1.19 | 1.72 | 0.99 | 1.73
CanESM5-CanOE-p2 | 5.62 | SSP3-7.0 | 1.20 | 1.73 | 1.00 | 1.74
CanESM5-CanOE-p2 | 5.62 | SSP5-8.5 | 1.22 | 1.76 | 1.01 | 1.74
CanESM5-p1 | 5.62 | SSP1-2.6 | 1.20 | 1.72 | 1.00 | 1.72
CanESM5-p1 | 5.62 | SSP2-4.5 | 1.21 | 1.74 | 1.01 | 1.71
CanESM5-p1 | 5.62 | SSP3-7.0 | 1.22 | 1.74 | 1.01 | 1.72
CanESM5-p1 | 5.62 | SSP5-8.5 | 1.22 | 1.76 | 1.01 | 1.74
CanESM5-p2 | 5.62 | SSP1-2.6 | 1.12 | 1.58 | 0.95 | 1.67
CanESM5-p2 | 5.62 | SSP2-4.5 | 1.14 | 1.63 | 0.96 | 1.70
CanESM5-p2 | 5.62 | SSP3-7.0 | 1.15 | 1.64 | 0.96 | 1.70
CanESM5-p2 | 5.62 | SSP5-8.5 | 1.14 | 1.62 | 0.95 | 1.69
CIESM | 5.67 | SSP1-2.6 | 0.67 | 1.25 | 0.44 | 2.81
CIESM | 5.67 | SSP2-4.5 | 0.73 | 1.33 | 0.51 | 2.62
CIESM | 5.67 | SSP5-8.5 | 0.71 | 1.29 | 0.48 | 2.66
mean |  |  | 0.92 $\pm$ 0.21 | 1.34 $\pm$ 0.29 | 0.76 $\pm$ 0.19 | 1.79 $\pm$ 0.24
Table 7: High-ECS GCMs: hindcasted warming from 1980-1990 to 2011-2021 within
the 60∘S:80∘N latitude range from 1980-1990 to 2011-2021 over land+ocean
(total), land, ocean, and land/ocean ratio. See Figure 8.

##  4 Testing the land versus the ocean warming

Surface-based temperature records imply that the GCM group with low ECS
performs better than those with medium and high ECS, which suggests that the
most likely ECS value should be equal or lower than 3∘C. However, UAH-MSU-lt
implies that even the low-ECS GCMs may perform quite poorly. The observed
discrepancy between the surface and satellite temperature records may be due
to the presence of various non-climatic warming biases in the surface
temperature records (Connolly et al., 2021; D’Aleo, 2016; Scafetta, 2021a;
Watts, 2022). This problem is now being investigated by comparing the GCM
hindcasts against the land and the ocean temperature observations.

Figures 7a-7f show the areal distribution of warming from 1980-1990 to
2011-2021 produced by the CMIP6 GCM ensemble average and by HadCRUT5,
ERA5-T2m, GISTEMP v4, NOAAGlobTemp v5 and UAH-MSU-lt v6. Equivalent maps for
each GCM are found in Scafetta (2021b).

Figure 7b shows that the UAH-MSU-lt v6 temperature record covers the latitude
range 80∘S-80∘N. Figure 7c and 7d show that ERA5-T2m and HadCRUT5 (infilled
data) are global because they adopt interpolations of meteorological models to
extend coverage also in data-scattered regions of the globe such as the poles
and other inhabited areas (large deserts and forests). Figures 7e and 7f show
that the GISTEMP and NOAAGlobTemp records do not cover large areas, in
particular, the polar regions are poorly represented.

Figure 7b is characterized by lighter colors than the other temperature
panels, which means that the UAH-MSU-lt temperature record shows less warming
than the surface-based temperature records almost everywhere. All six
temperature panels in Figure 7 also show that the land area has warmed more
than the ocean region. In any case, Figures 7c-7f show that the surface
temperature records present a greater temperature difference between the land
and the ocean regions. The visual comparison with the CMIP6 ensemble average
simulation (Figure 7a) suggests the same general pattern but, furthermore, the
oceanic area appears slightly warmer than all five temperature records. The
temperature records also show extensive ocean areas where significant cooling
is observed such as around Antarctica, the eastern equatorial Pacific, the
North Atlantic and a few other regions. These cooling regions reveal
interesting dynamic patterns that are not captured by the average simulation
of the CMIP6 ensemble. These patterns are best emphasized in the areal t-test
proposed in Scafetta (2022).

Table 4 reports the warming over 80∘S:80∘N, 60∘S:80∘N, 0∘N:80∘N and 60∘S:0∘S
latitudinal ranges from 1980-1990 to 2011-2021 over land+ocean (total), land,
and ocean. Table 4 also reports the ratios between the land and the ocean
warming levels.

The area 0∘N:80∘N shows that from 1980-1990 to 2011-2021 the surface
temperature records warmed on average by about $0.32\pm 0.05$∘C more than the
satellite-based UAH-MSU-lt record, while the area 80∘S:80∘N the surface-based
records warmed on average by about $0.15\pm 0.02$∘C more than the satellite
record. A similar warming bias on land also appears in the Southern Hemisphere
(60∘S:0∘S) because the surface-based temperate records show ocean warming
averaging $0.05\pm 0.03$ ∘C less than the satellite record while their land
area warmed by $0.08\pm 0.03$ ∘C more.

Figure 8 shows the results for each GCM model (using the 143 GCM average
simulations available for each SSP) for the latitudinal interval 60∘S:80∘N,
which is optimally covered from all temperatures records and includes all
continents except Antarctica. The results are also reported in Tables 5, 6,
and 7 and could be used to evaluate possible anomalous temperature trends on
the continents.

Figure 8a compares the synthetic and observed global warming levels from
1980-1990 and 2011-2021. Figures 8b and 8c show the land and the ocean average
warming levels, respectively. These figures show that the performance of the
models is similar to what we have obtained in the previous sections, i.e. the
GCM group with low ECS performs significantly better than the medium and high
GCM groups, which show warming bias for most of their GCMs.

Figure 8d shows the relationships between average warming on the land and the
ocean areas. The mean land/ocean ratio for the vast majority of the models is
$1.75\pm 0.20$, which is a value placed between the results obtained for the
surface temperature records (ranging from 1.95 to 2.32 ) and that of the
satellite temperature record, which gives 1.51.

The results shown in Figure 8 can be interpreted as follows.

1) Figure 8b shows that the land surface temperature records are on average
0.4∘C warmer than the satellite-based one. On the contrary, Figure 8c shows
that the surface-based ocean temperatures are on average up to a maximum of
0.1∘C warmer than the satellite ones.

2) Therefore, it can be assumed that on the ocean, the satellite-based
temperature record is sufficiently compatible with the surface-based ones. If
so, the large divergence observed on land between surface and satellite
recordings could suggest that the land measurements are significantly
contaminated by non-climatic warming biaes, including those related to
urbanization (cf.: Connolly et al., 2021; D’Aleo, 2016; Scafetta, 2021a;
Watts, 2022).

3) A similar conclusion would also be indirectly supported by the GCM
hindcasts which show that the CMIP6 models are usually unable to correctly
reconstruct the large land/ocean temperature ratio observed in the surface
temperature records. In fact, the models give a land/ocean ratio equal to
$1.75\pm 0.20$, while the surface records give ratios between 1.95 and 2.32.

4) However, as the GCMs attempt to reconstruct the global surface warming of
the surface temperature records even though they cannot adequately explain
their large land/ocean warming ratio, the models could have calibrated
internal parameters to obtain a compromise that attempts to approximate the
global surface warming by simulating a warmer ocean and a cooler land than
observed.

If point 4 above is correct, the reliability of the low-ECS GCMs should also
be questioned. In fact, 8d shows contradictory results regarding the low-ECS
GCMs because some models agree better with the surface-based temperature
records, few others agree better with the satellite temperature record, while
the rest report land/ocean ratios between the two levels, as the vast majority
of the medium and high ECS models does.

We now assume that the GCM’s predicted land/ocean temperature ratio (average
ratio = $1.75\pm 0.20$) corresponds to the actual physical characteristics of
the climate system and that the ocean temperature warming of the surface
records (on average, $0.43\pm 0.03$ ∘C, see Table 4) is sufficiently accurate.
If so, from 1980-1990 to 2011-2021 the earth’s surface within the latitude
interval 60∘S:80∘N should have warmed by $0.75\pm 0.1$∘C instead of the
observed $0.93\pm 0.03$∘C. If the hypothesis is correct, the spurious warming
of the land surface due to uncorrected non-climatic warming biases could be
quantified as approximately +0.2∘C. The proposed correction implies that
global surface warming from 1980-1990 to 2011-2021 could be at least about
0.05∘C ($\sim$10%) lower than what the surface-based records report, which
increases further the warming bias of the medium and high-ECS GCMs observed in
Figures 1-6.

The results depicted in Figure 8 also help to better evaluate the individual
GCMs. For example, Figure 5 suggests that three high-ECS models (CNRM-
CM6-1-f2, CNRM-ESM2-1-f2 and CIESM) produce relatively close warming to what
is reported by the surface-based temperature records. However, Figure 8d
indicates that the same models fail to produce the land/ocean temperature
ratio of the same temperature records showing significantly lower (CNRM) or
higher (CIESM) results than reported. Therefore, it appears that in these GCMs
the biases that occur in some regions are offset by opposite biases that occur
in other regions.

The last four columns of Table 4 report the global (land+ocean) and land
warming calculated assuming that the ocean warming of the temperature records
is correct and that the land/ocean warming ratios hindcasted by the models is
correct as well. The global estimate was calculated from the ocean and the
land ones weighted with their relative area percentages within each
latitudinal range. In particular, we found that for the Northern Hemisphere
(0∘N:80∘N), the land could have warmed about 0.087∘C less than what reported
on average by HadCRUT5, ERA-T2m, and GISTEMP. This bias roughly corresponds to
the different warming estimated in Connolly et al. (2021) for the northern
hemisphere land area by comparing the temperature records reconstructed by
using both urban+rural stations and rural-only stations that should present
significantly mitigated non-climatic warming biases.

In conclusion, the proposed land-ocean comparison suggests that the surface-
based temperature records most likely exhibit non-climatic warming biases and
that the actual global surface warming from 1980-1990 to 2011-2021 may have
been approximately between 0.50∘C and 0.55∘C, which is approximately 10% lower
than what is reported in Section 2. This means that the medium and high-ECS
GCM groups are further confirmed to run too hot and that the low ECS group
performs slightly worse than concluded in Section 3 because the average
warming of its hindcasts from 1980-1990 to 2011-2021 is approximately 0.6∘C
(Table 1). However, if UAH-MSU-lt reproduces the global surface warming more
accurately, the surface-based temperature records would exhibit warming bias
of up to 30% of the reported values, which would indicate that even the low
ECS GCMs run significantly too hot and need to be scaled down by 33% to reduce
their mean warming from 0.6∘C to 0.4∘C, which is the warming reported by the
satellite-based measurements. Indeed, another indirect evidence that the land
surface temperature records could be affected by a significant warming bias is
also given by the divergence observed between instrumental and
dendroclimatological proxy temperature records over the past 50 years, where
the former show a warming trend significantly higher than the latter (Büntgen
et al., 2021; Esper et al., 2018; Scafetta, 2021a).

Figure 9: Low-ECS GCM simulations from 1980 to 2100 using historical + SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios: (a1-a8) original GCM simulations versus HadCRUT5; (b1-b8) GCM simulations reduced by 10% versus NOAAGlobalTemp v5; (c1-c8) GCM simulations reduced by 33% versus UAH-MSU-lt v6. The ordinates represent the temperature anomaly relative to the 1850-1900 average of the correspondent model set. The temperature records are baselined with the GCM simulations in 1980-1990. |  | Hist + SSP1-2.6 | Hist + SSP2-4.5 | Hist + SSP3-7.0 | Hist + SSP5-8.5
---|---|---|---|---|---
|  | (∘C) | (∘C) | (∘C) | (∘C)
Original | 1980-1990 | 0.43 $\pm$ 0.19 | 0.43 $\pm$ 0.21 | 0.45 $\pm$ 0.20 | 0.37 $\pm$ 0.19
2011-2021 | 1.01 $\pm$ 0.20 | 1.01 $\pm$ 0.22 | 1.05 $\pm$ 0.19 | 0.90 $\pm$ 0.21
2040-2060 | 1.52 $\pm$ 0.21 | 1.75 $\pm$ 0.25 | 1.97 $\pm$ 0.21 | 1.98 $\pm$ 0.21
2080-2100 | 1.52 $\pm$ 0.21 | 2.32 $\pm$ 0.25 | 3.28 $\pm$ 0.24 | 3.78 $\pm$ 0.24
RF = 0.90 | 1980-1990 | 0.39 $\pm$ 0.17 | 0.39 $\pm$ 0.19 | 0.41 $\pm$ 0.18 | 0.33 $\pm$ 0.17
2011-2021 | 0.91 $\pm$ 0.18 | 0.91 $\pm$ 0.20 | 0.95 $\pm$ 0.17 | 0.81 $\pm$ 0.19
2040-2060 | 1.37 $\pm$ 0.19 | 1.58 $\pm$ 0.23 | 1.77 $\pm$ 0.19 | 1.78 $\pm$ 0.19
2080-2100 | 1.37 $\pm$ 0.19 | 2.09 $\pm$ 0.23 | 2.95 $\pm$ 0.22 | 3.40 $\pm$ 0.22
RF = 0.67 | 1980-1990 | 0.29 $\pm$ 0.13 | 0.29 $\pm$ 0.14 | 0.30 $\pm$ 0.13 | 0.25 $\pm$ 0.13
2011-2021 | 0.68 $\pm$ 0.13 | 0.68 $\pm$ 0.15 | 0.70 $\pm$ 0.13 | 0.60 $\pm$ 0.14
2040-2060 | 1.02 $\pm$ 0.14 | 1.17 $\pm$ 0.17 | 1.32 $\pm$ 0.14 | 1.33 $\pm$ 0.14
2080-2100 | 1.02 $\pm$ 0.14 | 1.55 $\pm$ 0.17 | 2.20 $\pm$ 0.16 | 2.53 $\pm$ 0.16
Table 8: Low-ECS GCMs: global surface warming in the periods 1980-1990,
2011-2021, 2040-2060, and 2080-2100 using the simulations depicted in Figure
9. Original GCM simulations; (RF = 0.90) GCM simulations reduced by 10%; (RF =
0.67) GCM simulations reduced by 33%. The temperature anomaly is relative to
the 1850-1900 average of the correspondent model set. The temperature records
are baselined with the models simulations in 1980-1990.

##  5 Climate change expectations for the 21st century

Climate impacts several areas of economic and environmental importance and its
changes may require the implementation of various adaptation policies.
However, climate change could also adversely affect some of the Earth’s
climate systems such as in areas of water scarcity, coastal communities,
natural ecosystems and others (IPCC, 2022). It is reasonable to assume that if
climate change is too rapid and too significant, different areas could reach a
point of vulnerability where adaptation will no longer be sufficient to avoid
serious adverse effects. However, adaptation policies are much more affordable
than mitigation ones, so the risks associated with possible future climate
change should not be overestimated.

The IPCC (2021) used the GCM CMIP6 and various scenarios of global
socioeconomic change predicted up to 2100 to produce hypothetical future
stories on climate change for the 21st century. Four SSP scenarios were
studied here: the SSP1-2.6 (low GHG emissions in which CO2 emissions are
reduced to zero around 2075); SSP2-4.5 (intermediate GHG emissions in which
CO2 emissions increase around the current rate until 2050, and then decrease
but not reach net zero by 2100); SSP3-7.0 (high GHG emissions where CO2
emissions double by 2100); and SSP5-8.5 (very high GHG emissions where CO2
emissions triple by 2075).

The IPCC (2022) states that if the global surface temperature rises
significantly above 2∘C over the next few decades compared to the pre-
industrial period (1850-1900), adaptation policies may not be sufficient to
reduce high risks related to climate change. Aggressive climate mitigation
policies should therefore be implemented because the CMIP6 GCMs predict that
the temperature will likely increase between 2°C and 3∘C (compared to
1850-1900) by 2050 if anthropogenic greenhouse gas emissions are not
significantly reduced as soon as possible.

However, in the previous sections we found that only the GCM group with low
ECS, which is also the one predicting less warming, optimally reproduces the
observed warming from 1980-1990 to 2011-2021 reported by the surface-based
global temperature records. Therefore, its scenario forecasts for the 21st
century should be preferred for policy. Furthermore, we also found that global
warming from 1980-1990 to 2011-2021 reported by the surface temperature
records may need to be reduced on average by about 10% assuming that the ocean
warming is correct and that the correct land/ocean temperature ratio is the
one predicted by the models. Finally, if UAH-MSU-lt better reproduces the
actual warming from 1980-1990 to 2011-2021, even the simulations of the low
ECS GCMs would be running too hot and the warming they produce would need to
be reduced by 33% to optimally accommodate the observations. Here, we show and
discuss how the climate could change in the 21st century under the above
assumptions.

Figure 9 shows the simulations produced by the low ECS GCMs from 1980 to 2100
using the historical + SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios in
three conditions: panels a1-a8 show the original GCM simulations versus
HadCRUT5; panels b1-b8 show the GCM simulations reduced by 10% compared to
NOAAGlobalTemp v5; and panels c1-c8 show the GCM simulations reduced by 33%
compared to UAH-MSU-lt v6. The ordinates represent the temperature anomaly
relative to the 1850-1900 average of the corresponding GCM set. The
temperature records are baselined with the model simulations in 1980-1990.
Table 8 reports the global surface warming forecasts produced by the low ECS
GCMs in the periods 1980-1990, 2011-2021, 2040-2060 and 2080-2100 in the same
three conditions.

The analysis shows that the expected warming of the low-ECS GCMs by 2040-2060
is close to 2∘C also for the SSP3-7.0 and SSP5-8.5 scenarios, which Hausfather
and Peters (2020) described as “unlikely” and as “highly unlikely”,
respectively. However, if the surface temperature records contain a warming
bias and, therefore, the GCM simulations need to be scaled down to better
agree with the actual warming, the projected warming for 2040-2060 could be
lower (or even significantly lower if UAH -MSU-lt v6 is correct) than 2∘C also
for the SSP3-7.0 and SSP5-8.5 scenarios.

There is indirect evidence that the surface-based temperature reconstructions
could be affected by non-climatic warming biases. In fact, compared to the
1850-1900 mean, the average warming of 1980-1990 is 0.54∘C for HadCRUT5
(infilled data), 0.48∘C for GISTEMP v4 (using the period 1880-1900) and 0.47∘C
for NOAAGlobalTemp v5 (using the period 1880-1900). However, the low ECS GCMs
give a slightly lower 1980-1990 warming, which is $0.41\pm 0.20$ ∘C by
averaging all GCM simulations although they better hindcast the 1980-2021
warming. In contrast, the medium and high ECS GCMs give $0.48\pm 0.27$ ∘C and
$0.47\pm 0.23$ ∘C, respectively, which better fit the climate records; but
then these same GCMs fail to hindcast the observed warming from 1980 to 2021.

The above findings suggest that climate change will likely be moderate over
the next few decades and that adaptation policies should be sufficient to
manage any adverse effects that may occur.

Furthermore, the warming hindcasted by the low-ECS models from 1850-1900 to
1980-1990 would be lower than $0.41\pm 0.20$ ∘C if the climate simulations
produced by them were to be scaled down. This evidence would suggest that the
more recently applied homogenization adjustments to climate data to attempt to
remove their non-climatic biases may have been inadequate and may have added
or left spurious warming. For example,the continuous homogenization
adjustments made to the surface-based temperature records during the last 10
years may have improperly cooled the raw temperature data of the past for many
land stations (D’Aleo, 2016) and, simultaneously, may have improperly
increased the warming trend from the 1970s to the present, and, in particular,
that of the period 2000-2021 (Connolly et al., 2021; Scafetta, 2021a; Watts,
2022).

In fact, the scientific literature has indicated the period 2000-2014 as a
“hiatus” or “pause” in global warming (IPCC, 2013) because all surface and
satellite climate records available before 2014 (e.g. HadCRUT3, which was
discontinued in 2014, Brohan et al. 2006) showed more than a decade of
relatively little change. Later, however, new versions of the surface
temperature records were published (e.g. HadCRUT4 and later HadCRUT5 non-
infilled and infilled data) and the 2000-2014 “pause” has gradually
disappeared because, from one climate version to the following one, it has
been replaced by an increasingly strong warming trend; e.g. the trend was 0.03
°C/decade for HadCRUT3, 0.08 °C/decade for HadCRUT4, 0.10 °C/decade for
HadCRUT5 non-infilled data, and 0.14 °C/decade for HadCRUT5 infilled data. See
Figure 10 and Table 9. Yet, the 2000-2014 global warming “hiatus” is still
visible in the UAH-MSU-lt v6 record, which shows a 2000-2014 warming trend of
0.012 °C/decade (Figure 2).

Figure 10: HadCRUT3 (1850-2014), HadCRUT4 (1850-2021), HadCRUT5 (non-infilled data, 1850-2021) and HadCRUT5 (filled data, 1850-2021) global surface temperature records relative to the 1850-1900 period. | temperature anomaly (°C, 1850-1900) | trend (°C/year)
---|---|---
| 1960-1980 | 1980-1990 | 1990-2000 | 2000-2010 | 2004-2014 | 2011-2021 | 2000-2014 | 2000-2021
HadCRUT5 (infilled data) | 0.28 | 0.53 | 0.68 | 0.89 | 0.94 | 1.12 | 0.014 | 0.022
HadCRUT5 (non infilled data) | 0.24 | 0.49 | 0.65 | 0.83 | 0.87 | 1.04 | 0.010 | 0.019
HadCRUT4 | 0.25 | 0.42 | 0.59 | 0.78 | 0.81 | 0.95 | 0.008 | 0.016
HadCRUT3 | 0.24 | 0.43 | 0.58 | 0.76 | 0.76 |  | 0.003 |
Table 9: Warming means and trends in various periods for HadCRUT3 (1850-2014),
HadCRUT4 (1850-2021), HadCRUT5 (non-infilled data, 1850-2021) and HadCRUT5
(filled data, 1850-2021) global surface temperature records. See Figure 10.

##  6 Conclusion

Here I tested how well the CMIP6 GCMs – grouped into low, medium and high ECS
subgroups – hindcast the global surface temperature warming from 1980-1990 to
2011-2021 reported by four surface temperature records (ERA5-T2m, HadCRUT5,
GISTEMP v4, and NOAAGlobTemp v5) and by the satellite-based UAH-MSU-lt v6
temperature record. The latter was used as the lowest possible estimate for
the global surface temperature warming during the analyzed period. The
rationale for adding a comparison with the lower troposphere temperature
record is that surface temperatures could be affected by significant non-
climatic warming bias due, for example, to poorly corrected urban heats and
many other factors (Connolly et al., 2021; D’Aleo, 2016; Scafetta, 2021a;
Watts, 2022). For example, indirect evidence for a significant warming bias,
especially over land, may be also provided by the so-called "Divergence
Problem" that is the apparent decoupling between three ring width chronologies
and the rising temperature measurements starting from the 1970s (Büntgen et
al., 2021; Esper et al., 2018; Scafetta, 2021a).

Using the 143 GCM mean simulations available for four different SSPs, all
medium and high ECS models turn out to be warmer than observations. Using the
688 CMIP6 ensemble member simulations available, 94% to 100% of the
simulations produced by GCMs with medium and high ECS hindcasted greater
warming than the five temperature records. In contrast, the low-ECS models are
statistically distributed around the observed warming values obtained from the
four surface-based temperature records. However, if the UAH-MSU-LT record
better represents the actual 2011-2021 warming, even the low-ECS GCM group
would produce on average too hot hindcasts.

I also tested whether the internal variability of the models could produce
results distributed around the observations. Its effect was modeled using
three fixed precision options. Assuming high ($\sigma_{H}\approx 0.05$∘C) and
medium ($\sigma_{M}\approx 0.10$∘C) precision, it was found that 98-100% and
92 -98%, respectively, of all possible outputs from the medium and high ECS
GCMs would be warmer than observations. Only the theoretical results produced
by the low-ECS GCM group optimally agree with the surface-based temperature
records. If the required model accuracy is quite low ($\sigma_{L}\approx 0.15$
∘C), the middle and high GCM simulation groups would agree better with the
data, but this agreement could still be quite unsatisfactory because 87% to
93% (which is still well outside the $\pm 1$$\sigma$ or 68% confidence
interval) of their hindcasts would still be too hot. In any case, the low
precision option should be considered very unsatisfactory because it would
allow the GCMs to deviate too much from the observations. Moreover, such poor
precision would not seem consistent with the natural variability of the data
as argued in Appendix B. Figure 5 suggests that such a low precision could
only occur for EC-Earth3 GCM.

Figures 5 and 6 also show that very few GCMs with medium and high ECS could
produce some simulations consistent with the actual temperature values. In
particular, the two high-ECS CNRM models (Séférian et al., 2019; Voldoire et
al., 2019) appear to perform better than the other models of the same group.
However, as a group, the high-ECS models are physically incompatible with the
low-ECS ones. Indeed, the internal parameters of the GCMs are carefully tuned
to obtain results as acceptable as possible (Hourdin et al., 2017; Mauritsen
et al., 2019). Therefore, the good performance of some isolated cases could
hardly be used to validate the corresponding model since the tuning operations
also risk masking fundamental physical problems and, therefore, the need for
model and/or forcing improvements.

It was found that only the low-ECS GCM group agrees optimally with the
surface-based temperature records because their full hindcast range well
encompasses the actual temperature warming values from 1980-1990 to 2011-2021.
Therefore, since the three ECS chosen ranges should be considered large enough
to be incompatible with each other, the GCM group with low ECS should be
preferred to the other two, implying that the most likely ECS should be equal
to or lower than 3∘C. This result confirms Scafetta (2022). In fact, the
performance of the models seems to increase as the ECS decreases (Scafetta,
2021b).

However, the actual ECS could also be significantly lower than 3∘C if the UAH-
MSU-lt record better represents the 2011-2021 surface warming. In fact, the
satellite record shows that from 1980-1990 and 2011-2021 the global surface
temperature may have warmed by about 0.40∘C, which is about 30% less than
0.58∘C as reported by ERA5-T2m, HadCRUT5, and GISTEMP v4. In this case, even
the GCM group with low ECS would show poor accuracy in reproducing the
temperature data because their average hindcast is about 0.60∘C. This means
that the actual ECS could also be 33% lower than that which characterizes the
low ECS GCM group: that is, it could need to be reduces from 1.8-3.0∘C to
1.2-2.0∘C. This conclusion cannot be ruled out because: (1) the surface
temperature records appear to be severely affected by non-climatic warming
bias (Connolly et al., 2021; D’Aleo, 2016; Scafetta, 2021a; Watts, 2022), as
the direct comparison between land and ocean warming proposed here also seeems
to confirm (Figure 8); (2) because a number of independent studies have
concluded that the ECS could be within such a low range (e.g.: Lewis and
Curry, 2018; Lindzen and Choi, 2011; Scafetta, 2013; Stefani, 2021; van
Wijngaarden and Happer, 2020).

There is a third possibility which would also imply that the actual ECS should
be relatively low. The climate system, in fact, appears to be also modulated
by multidecennial and millennial natural oscillations such as those related to
solar forcings and other astronomical ones, which are not reproduced by the
GCMs (cf.: Scafetta, 2013, 2021c; Wyatt and Curry, 2014). Their presence
implies that the ECS of GCMs should be at least halved (cf.: Loehle and
Scafetta, 2011; Scafetta, 2012a, 2021c) and could vary approximately between
1.0∘C and 2.5∘C, as found by several independent studies (cf.: Lewis and
Curry, 2018; Lindzen and Choi, 2011; Scafetta, 2013; Stefani, 2021; van
Wijngaarden and Happer, 2020). If so, future climate warming and changes will
be moderate and naturally oscillating (Scafetta, 2013, 2021c) and the rate of
global surface warming should likely remain quite low until 2030-2040, when
solar activity is expected to increase again due to its natural multi-decadal
oscillations (Scafetta, 2012b; Scafetta and Bianchini, 2022, and several
others).

In any case, even remaining within the theoretical framework of the CMIP6
GCMs, it should be concluded that only the low ECS GCM group can be considered
sufficiently validated by the global surface warming observed from 1980-1990
to 2011-2021. Therefore, only the 21st century climate projections produced by
the low ECS GCMs should be used for policy. For decades to come, these models
predict more moderate warming than the GCM groups with medium and high ECS do
for similar greenhouse gas emission scenarios. By 2050, projected warming is
expected to be around 2∘C or less even for the worst greenhouse gas emission
scenarios. This moderate warming should not be considered particularly
alarming because the impact and risk assessments related to it are considered
“moderate” assuming even low to no adaptation (IPCC, 2022). Furthermore, as
surface-based temperature records are likely affected by warming biases and
are characterized by natural oscillations that are not reproduced by the CMIP6
models, the global warming expected for the next few decades may be even more
moderate than predicted by the low-ECS GCMs and could easily fall within a
safe temperature range where climate adaptation policies will suffice.
Therefore, aggressive mitigation policies aimed at rapidly and drastically
reducing GHG emissions in order to avoid a too rapid rise in temperature do
not seem justified, also because their costs seem to outweigh any realistic
benefits (cf. Bezdek et al., 2019).

Figure 11: Possible decomposition of the ERA5-T2m global surface temperature
record (blue) into a signal (orange, made of 13 and 5 month moving averages)
and a residual-noise (red) record that could be used to evaluate the error of
the mean.

### Appendix A: Evaluation of the error of the mean for temperature records

Computer simulations are made of pure numbers and their averages over a given
period of time are error free. The uncertainty associated with their unforced
internal variability is a different matter and will be discussed in Appendix
B.

Conversely, the data points of the temperature records are affected by small
statistical errors, which however are not always readily available as is the
case with the ERA5-T2m record. Let’s address the issue.

A generic time series $y_{t}$ with $t=1,...,N$ could be affected by Gaussian
distributed uncertainties $\xi_{t}$ with zero mean and standard deviation
$\sigma_{\xi}$ as

$y_{t}=x_{t}+\xi_{t},$ (3)

where $x_{t}$ is the physical signal of the record. Its mean is

$\bar{y}=\frac{1}{N}\sum_{t=1}^{N}y_{t}\pm\sigma_{\xi}/\sqrt{N},$ (4)

where $\bar{\sigma}=\sigma_{\xi}/\sqrt{N}$ is the error of the mean.

It is important to note that $\sigma_{\xi}$ is the standard error of the
uncertainties $\xi_{t}$, not that of the signal $y_{t}$. For example, the
ERA5-T2m 2011-2021 average (baselined to 1980-1990) is 0.578∘C, which was
obtained by integrating on the globe the temperature variations that occurred
in each cell of the surface grid worldwide. The standard deviation of the same
record is $\sigma_{y,month}=0.20$∘C using the monthly record and
$\sigma_{y,year}=0.18$∘C using the annual record. For random variables, the
error of the mean does not depend on the time resolution of the record, that
is, the monthly and yearly resolved records should give
$\bar{\sigma}_{year}=\bar{\sigma}_{month}$. However, if we apply the equation
$\bar{\sigma}=\sigma_{y}/\sqrt{N}$ from 2011 to 2021, for ERA5-T2m we get
$\bar{\sigma}_{year}=0.054$∘C (using N=11 points) and
$\bar{\sigma}_{month}=0.017$∘C (using N=132 points), respectively. This shows
that from 2011 to 2021 the ERA-T2m record is not composed of random variables
floating around an average value, but contains a physical signal.

It can be assumed that the physical signal of ERA5-T2m is represented by the
moving averages of the data at 13 months, 5 months or 3 months while the
residuals are the noise components that should be used to evaluate
$\sigma_{\xi}$ and $\bar{\sigma}=\sigma_{\xi}/\sqrt{N}$. The three choices
give $\bar{\sigma}=0.01$∘C, $\bar{\sigma}=0.006$∘C, and
$\bar{\sigma}=0.005$∘C, respectively, which suggest that the actual error of
the 2011-2021 mean could be $\bar{\sigma}=0.01$∘C or probably less. The first
two examples of data decomposition are shown in Figure 11.

Alternatively, the statistical uncertainty associated with ERA5-T2m could be
considered compatible with those explicitly provided by the other available
global surface temperature records. In the case of the GISTEMP record, Lenssen
et al. (2019) calculated that the resulting 95% uncertainties are near
$\bar{\sigma}_{95\%,annual}\approx 0.05$ ∘C in the global annual mean for the
last 50 years. HadCRUT5’s global surface temperature record includes its 95%
confidence interval estimate and, from 2011 to 2021, the uncertainties for the
monthly and annual averages are $\bar{\sigma}_{95\%,monthly}\approx 0.05$∘C
and $\bar{\sigma}_{95\%,annual}\approx 0.03$∘C, respectively. Berkeley Earth
land/ocean temperature record estimates $\bar{\sigma}_{95\%,monthly}\approx
0.042$ ∘C, $\bar{\sigma}_{95\%,annual}\approx 0.028$∘C, and
$\bar{\sigma}_{95\%,decadal}\approx 0.022$∘C during the same period. Note that
the error of the mean must decrease as the time scale increases.

Therefore, adopting the equation
$\bar{\sigma}_{95\%}=1.96\times\sigma_{\xi}/\sqrt{N}$, the probable error for
the 2011-2021 mean could be of about 0.01∘C or even smaller. In fact, using
the above estimates, we obtain: $0.05/\sqrt{11}=0.015$∘C,
$0.05/\sqrt{132}=0.0043$∘C, $0.03/\sqrt{11}=0.009$∘C,
$0.042/\sqrt{132}=0.004$∘C, and $0.028/\sqrt{11}=0.008$∘C respectively, the
mean of which is approximately 0.008∘C. Alternatively, the 95% uncertainty
over the period 2011-2021 cannot be greater than about $\pm$0.02∘C, as
explicitly reported by the Berkeley Earth land/ocean temperature record for
the ten-year scale.

Therefore, various methodologies suggest that the uncertainty of the
temperature means in the 11-year period from 2011 to 2021 is very small,
around $\pm 0.01$∘C at 95% confidence and can be safely ignored as done for
example in Scafetta (2022).

Figure 12: Definition of accuracy and precision, and examples of high and low
accuracy and precision cases where the red dots are ensembles of measurements.
Figure 13: 15-year high-pass filter of HadCRUT5, ERA5-T2m, GISTEMP v4,
NOAAGlobTemp v5, and UAH-MSU-lt v6 temperature records.

### Appendix B: Provisional assessment of an acceptable internal variability
of the models

Climate models are unable to accurately simulate temperature records due to
various uncertainties. For example, only by varying the initial conditions
different climatic trajectories are obtained which evolve around an ideal
average with a certain variance.

Each GCM is characterized by its own internal variability. However, in the
main text, we argued that such uncertainty could not be arbitrarily large
because the models must be both accurate and precise. Figure 12 explains the
concepts of “accuracy”, which measures the proximity of the model hindcasts to
the real value, and of “precision”, which indicates the proximity of the same
hindcasts to each other.

An acceptable range for the distribution of hindcasts related to the internal
variability of the models could be assessed by observing that temperature
fluctuations at time scales lower than, for example, 15 years, (which include
the climatic oscillations of the ENSO and those of the 11-year solar cycle)
may not be adequately predicted by the models. From the point of view of the
models, the temperature fluctuations at those time scales could be considered
stochastic and their standard deviation from the mean could represent the
acceptable range that can be associated with the unforced internal variability
of the models (cf. Knight et al., 2009).

Figure 13 shows the 15-year high-pass filter curves of HadCRUT5, ERA5-T2m,
GISTEMP v4, NOAAGlobTemp v5, and UAH-MSU-lt v6 temperature records from 1980
to 2021. Using the standard deviation $\sigma$ for each record, the error of
the mean on 11-year intervals (e.g. from 2011 to 2021) at the 95% confidence
is $\bar{\sigma}_{95\%}=1.96\times\sigma/\sqrt{11}$, that is:
$\bar{\sigma}_{95\%}=0.080$∘C for HadCRUT5; $\bar{\sigma}_{95\%}=0.094$∘C for
ERA5-T2m; $\bar{\sigma}_{95\%}=0.079$∘C for GISTEMP v4;
$\bar{\sigma}_{95\%}=0.075$∘C for GISTEMP v4; and
$\bar{\sigma}_{95\%}=0.104$∘C for UAH-MSU-lt v6.

Based on the above assumptions, over an 11-year period, the uncertainty of the
2011-2021 warming compared to 1980-1990 could be estimated at approximately
$\pm 0.1$∘C at the 95% confidence, which corresponds to the high precision
option ($\sigma_{H}=0.05$∘C) discussed in Section 3.

The high precision option should not be interpreted as the actual dispersion
produced by each GCM, which varies greatly from model to model, but only as
the acceptable uncertainty that a CGM should exhibit in reproducing the
warming from 1980-1990 to 2011-2021. In our case, a $\pm 0.1$∘C error would
imply a $\pm 0.17\%$ of the actual warming from 1980 to 2021, which can be
considered a reasonable error.

### Conflict of Interest

The author declares no conflict of interest.

### Data Availability Statement

All data used in the manuscript can be downloaded from KNMI Climate Explorer
or from the original websites:

  * •

KNMI Climate Explorer, https://climexp.knmi.nl/start.cgi

  * •

ERA5-T2m, https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-
era5-single-levels-monthly-means

  * •

GISTEMP v4, https://data.giss.nasa.gov/gistemp,
https://data.giss.nasa.gov/gistemp/graphs_v4/

  * •

HadCRUT5, https://www.metoffice.gov.uk/hadobs/hadcrut5/

  * •

HadCRUT4, https://www.metoffice.gov.uk/hadobs/hadcrut4/

  * •

HadCRUT3, https://www.metoffice.gov.uk/hadobs/hadcrut3/

  * •

NOAAGlobTemp v5, https://www.eea.europa.eu/data-and-maps/data/external/noaa-
global-temperature-v5

  * •

Berkeley Earth land/ocean temperature, http://berkeleyearth.org/archive/land-
and-ocean-data/

  * •

Japanese Meteorological Agency,
https://ds.data.jma.go.jp/tcc/tcc/products/gwp/temp/ann_wld.html

  * •

UAH-MSU-lt v6, https://www.nsstc.uah.edu/data/msu/v6.0/tlt/uahncdc_lt_6.0.txt

  * •

CMIP6 GCMs, http://climexp.knmi.nl/selectfield_cmip6.cgi?id=someone@somewhere.

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