# Anthropogenic contributions to slow warming over 1998-2012

Xuanming Su1,∗, Hideo Shiogama2, Katsumasa Tanaka2,3,
Kaoru Tachiiri4, Tomohiro Hajima4, Michio Watanabe4,
Michio Kawamiya4, Kiyoshi Takahashi1 & Tokuta Yokohata2
1Social Systems Division, National Institute for Environmental
Studies(NIES), Tsukuba, Japan
2Earth System Division, National Institute for Environmental
Studies (NIES), Tsukuba, Japan
3Laboratoire des Sciences du Climat et de l’Environnement
(LSCE), IPSL, CEA/CNRS/UVSQ, Université Paris-Saclay,
Gif-sur-Yvette, France
4Research Institute for Global Change/Research Centre for
Environmental Modelling and Application, Japan Agency for
Marine-Earth Science and Technology (JAMSTEC),
Yokohama, Japan
∗To whom correspondence should be addressed; E-mail<EMAIL_ADDRESS>
> The observed global mean surface temperature increase from 1998 to 2012 was
> slower than that since 1951. The relative contributions of all relevant
> factors including climate forcers, however, have not been comprehensively
> analyzed. Using a reduced-complexity climate model and an observationally
> constrained statistical model, we find that La Niña cooling and a descending
> solar cycle contributed approximately 50% and 26% of the total warming
> slowdown during 1998-2012 compared to 1951-2012. Furthermore, reduced ozone-
> depleting substances and methane accounted for roughly a quarter of the
> total warming slowdown, which can be explained by changes in atmospheric
> concentrations. We identify that human factors played an important role in
> slowing global warming during 1998-2012, shedding light on the evidence for
> controlling global warming by reducing greenhouse gas emissions.

## Introduction

Observations implied a slow warming (SW) in global mean temperature change
($\Delta T$) from 1998 to 2012 compared to the warming from 1951 to 2012,
despite the rapid growth in greenhouse gas (GHG) emissions during the same
period (?). The warming difference of decadal trends (DDT), that is, the
decadal trend of 1998-2012 minus that of 1951-2012, indicated a negative
trend. Newer temperature records with updated sea surface temperature (SST)
datasets and the infilling of missing data in places such as the Arctic showed
greater positive trends, implying that the slowing was not as severe as
previously thought (?). For example, the latest Met Office Hadley
Centre/Climatic Research Unit global surface temperature anomalies, version 5
(HadCRUT5), used by default in this study, showed an apparently less negative
DDT (-0.011 ∘C/decade) compared to the older version of HadCRUT4.6 (-0.055
∘C/decade). Such a slowing trend may differ among independent observations
(fig. S1). Nonetheless, there is no doubt that SW does exist (?). The Sixth
Assessment Report (AR6) of the Intergovernmental Panel on Climate Change
(IPCC) referred to this phenomenon as a temporary event (?), primarily due to
internal variability (?, ?, ?, ?, ?, ?) and natural forcings such as volcanic
and solar irradiance (?, ?, ?, ?, ?, ?, ?). The strengths of internal
variability or natural forcings, however, are uncertain (?, ?, ?, ?).
Reductions in methane and ozone-depleting substances (ODS) (?, ?) or
stratospheric water vapour (?) may also have contributed, but their respective
impacts have not been explicitly calculated. Furthermore, SW cannot be
described by a single factor; rather, it necessitates an integrated influence
combining multiple components, such as internal variability, forcing changes,
ocean heat uptake, and insufficient observational coverage (?, ?, ?, ?, ?).
Quantifications of relative contributions from these individual components are
important to interpret the causes of SW.

Physical climate models may insufficiently capture the internal variability or
underestimate the response of solar irradiance (?), resulting in a higher-
than-observed $\Delta T$ during the SW period (?). Statistical models, on the
other hand, can capture $\Delta T$ variations but strongly depend on the
chosen predictors and their time lags and usually use the whole anthropogenic
influence as an input (?, ?, ?), hindering further attributions at the
emission level. A systematic and reliable assessment of the individual
contributing factors to SW has not been conducted to our knowledge. Here, we
combined a reduced-complexity model (RCM) used to quantify the $\Delta T$
trends caused by individual climate forcers with a statistical regression
model to reconcile the causes with the observed $\Delta T$.

## Results

### Method summary

To attribute anthropogenic and natural $\Delta T$, first, we applied a
normalized marginal approach (?, ?, ?) to an RCM, the Simple Climate Model for
Optimization version 3.3 (SCM4OPT v3.3) (?, ?, ?, ?), to quantify the $\Delta
T$ trends for respective climate forcers (see materials and methods). Second,
we used a regression statistical model (?, ?, ?) to decode the impacts of
anthropogenic and natural factors. This was a twofold approach: the regression
can correct the biases in the magnitude of the simulated $\Delta T$, while the
relative contributions of external forcing factors and internal variability to
the observed $\Delta T$ are resolved. To avoid overfitting, we tested a group
of statistical models with different predictors and chose the one with the
lowest Bayesian information criterion (BIC) (table S1). The monthly observed
$\Delta T$ was then modeled as a multiple regression of anthropogenic factors,
natural forcings, El Niño and Southern Oscillation (ENSO), and residuals
allowing for errors in simulations and observations (see materials and
methods). As a result, we decomposed the observed $\Delta T$ into $\Delta T$
caused by each anthropogenic factor, such as CO2, CH4, N2O, ODS, other
fluorinated gases, aerosols and pollutants, and land use albedo, as well as
each natural factor, such as volcanic eruptions, solar irradiance, and ENSO
(Fig. 1). There was a high correlation (r = 0.94, 1951-2018) between the
modeled $\Delta T$ (total sum of individual factors) and the observed $\Delta
T$, indicating that most of the perturbation in the observed $\Delta T$ was
captured in our study.

Figure 1: Anthropogenic and natural $\Delta T$. (A) Anthropogenic $\Delta T$.
The thick red solid line and error bars indicate total anthropogenic $\Delta
T$. (B) $\Delta T$ caused by natural forcings. The thick purple solid line and
range represent the total $\Delta T$ induced by natural forcings. Color
ribbons in (A and B) show $\Delta T$ caused by individual factors. (C) $\Delta
T$ caused by ENSO. (D) HadCRUT5 and the total summed $\Delta T$. Pearson’s
correlation between the total sum and HadCRUT5 is shown in (D). The error bar
in (A) and ranges in (B to D) are the one-sigma produced by the ensemble of
statistical regressions. See materials and methods for further information on
estimating uncertainty. The SW era from 1998 to 2012 is shaded in light gray.

### Methane stabilization and ODS mitigation help slow global warming

Fig. 2A-L shows $\Delta T$ attributions by source, the total sum of all
sources, and the observed $\Delta T$ HadCRUT5 to aid comparison. Gradients
indicated by the thin solid and solid with extended dashed lines represent
$\Delta T$ linear trends from 1951 to 2012 and from 1998 to 2012,
respectively. Accordingly, to the left of the junction, if the dashed line is
above the solid line, it implies that the growth rate is slowing, and vice
versa. Methane, ODS, solar irradiance, and ENSO negatively contributed to
$\Delta T$ during 1998-2012 compared to 1951-2012. The emission attributions
of $\Delta T$ agree mostly with the AR6 forcing-based estimate (?) (fig. S2),
except for halogenated $\Delta T$, which is approximately twice as high as
AR6. This is because our method generated a smaller negative ozone effective
radiative forcing ($\Delta F$) (-0.05 Wm-2 out of total ozone forcing 0.26
Wm-2, 1850-2019), which was induced by halogenated gases (cf. -0.16 Wm-2 out
of 0.47 Wm-2, 1750-2019 (?), used in AR6) (see fig. S3 for the attribution of
ozone effective $\Delta F$). Consequently, a smaller $\Delta T$ was mitigated
by ozone, and halogenated $\Delta T$ was positively larger in our results.

Based on the attributed $\Delta T$, we computed the decadal trend (fig. S4)
and DDT (Fig. 2M) for each source. Note that DDT was also affected by the
referred historical period; selecting a smaller period of 1960-2012 would
highlight such a slowdown more clearly because $\Delta T$ increased more
rapidly throughout 1960-2012 (fig. S1). However, we examined 1951-2012 for a
general case.

ENSO contributed the most to the SW, with a DDT of -0.063$\pm$0.002 ∘C/decade,
followed by solar irradiance (-0.033$\pm$0.002 ∘C/decade). Anthropogenic ODS
(-0.016$\pm$0.007 ∘C/decade) and methane (-0.014$\pm$0.008 ∘C/decade) also
contributed to the SW. Specifically, ENSO and solar variations diminished
warming directly with a negative decadal trend, while ODS and methane
emissions simply exhibited a smaller decadal trend during 1998-2012 compared
to that of 1951-2012. Other sources, including CO2, N2O, other fluorinated
gases, aerosols and pollutants, land albedo, and volcanic activity, showed
positive DDT, meaning that they increased faster between 1998 and 2012 than
they did between 1951 and 2012. It is worth noting that the $\Delta T$ of
total GHG emissions increased steadily (DDT 0.012$\pm$0.015 ∘C/decade),
masking the slowdown of ODS and methane $\Delta T$ (fig. S5), which is likely
why previous research missed them. In addition, aerosols and pollutants and
land albedo (see fig. S6 for the forcing trends) contributed to negative
warming and declined over 1951-2012. However, during the SW period, their
downward tendencies slowed and contributed to a positive DDT (see fig. S7).

Figure 2: Anthropogenic and natural $\Delta T$ by source and their DDT between
1998-2012 and 1951-2012. (A to J) $\Delta T$ and uncertainty ranges caused by
individual anthropogenic and natural factors. (K and L) The total sum and
HadCRUT5 and their uncertainty ranges. Thin solid and solid with extended
dashed lines denote linear trends from 1951 to 2012 and 1998 to 2012,
respectively. (M) DDT derived from (A to L). The mean is displayed on top of
the bar, and the error bar is the one-sigma produced by the ensemble of
statistical regressions.

The slowdown of methane $\Delta T$ can be explained by the associated
atmospheric concentrations ($\Delta C$). Growths in methane $\Delta C$ is
reported to have slowed from the 1980s and to have stabilized between 1999 and
2006 (?, ?, ?, ?, ?, ?), owing in part to reductions in emissions from oil-gas
exploitation and enteric fermentation in Europe and Russia (?). As shown in
Fig. 3A, the DDT of methane $\Delta C$ simulated by SCM4OPT v3.3 presented a
negative value of -52.4 ppb/decade, indicating that growths in methane $\Delta
C$ slowed significantly during the SW period, which partly explains the
slowdown of methane $\Delta T$ at the same time. Our results do not reflect
methane emissions from natural sources, which accounted for approximately 39%
of overall methane emissions in the recent decade (ref. (?), top-down estimate
for 2008–2017). Furthermore, methane emissions from ultraemitters in the oil
and gas industry, accounting for up to 12% of global methane emissions from
oil and gas production and transmission (?), were not included in our
calculations. Hence, the actual methane $\Delta C$ (for instance, DDT of CMIP6
$\Delta C$ -88.6 ppb/decade) may have contributed a more negative DDT in
methane $\Delta T$.

ODS manifested consistent DDT between the simulated $\Delta C$ (-224.9 CFC-12
equivalent ppt/decade) and the observed $\Delta C$ (CMIP6 -212.5 CFC-12
equivalent ppt/decade) (Fig. 3B) because they are well documented (?, ?, ?);
hence, $\Delta C$ can be well captured by the model. ODS have been effectively
mitigated under the Montreal Protocol since the late 1980s (?), resulting in a
stabilized mixing ratio in the atmosphere. Such a tendency can also be used to
interpret the negative DDT of ODS $\Delta T$. The $\Delta C$ of other GHGs
including CO2, N2O and other fluorinated gases, however, continued to rise,
accelerating $\Delta T$ rather than slowing it during the SW era (fig. S8).

The emission-based attribution takes chemical-physical changes in the
atmosphere into account. Methane $\Delta T$, for example, includes $\Delta T$
produced by atmospheric methane $\Delta C$, stratospheric water vapour from
methane oxidation, the feedback on tropospheric ozone and on sinks of
halogenated gases, and CO2 from oxidized methane. Concerning ODS $\Delta T$,
their contributions contain $\Delta T$ caused by ODS $\Delta C$ and its
feedback on stratospheric ozone and on methane sinks (Fig. 3B). A minor
difference might exist between the $\Delta T$ resulting from $\Delta C$ and
the associated emissions, but their major trends are consistent (Fig. 3, fig.
S8). Therefore, the slowdown of ODS and methane $\Delta T$ during the SW can
be robustly explained by their slowing trends in atmospheric $\Delta C$. It is
important to note that the slowing trends for both $\Delta C$ and $\Delta T$
induced by ODS and methane occurred earlier than 1998-2012, which also
contributed to the SW.

Figure 3: Rate of change of methane and ODS $\Delta C$ and the induced $\Delta
T$. (A) Methane and (B) ODS. The SCM4OPT v3.3 uncertainties in (A and B) are
the one-sigma of the Monte Carlo simulation with $n=1000$. $\Delta T$
uncertainty ranges in (A and B) are the one-sigma produced by the ensemble of
statistical regressions. In (B), the ODS components for each source differ
(table S2). Uncertainty is not considered in ODS $\Delta C$ because it is an
equivalent value combining a collection of compounds of ODS (?). CMIP6 (?) and
SCM4OPT v3.3 contain data for the entire evaluation period. Mean values from
1951 to 2012 and 1998 to 2012 are illustrated by thin horizontal solid and
dashed lines, respectively. The SW era from 1998 to 2012 is shaded in light
gray.

### Contributions of natural forcing factors and ENSO

As shown in Fig. 4A, our natural forcing $\Delta T$ is in line with results
from previous RCMs (?) as well as more complex Earth system models (ESMs) (?)
(for GHGs and aerosols and pollutants, see figs. S5&S9). Fig. 4B depicts
volcanic $\Delta F$ and $\Delta T$. Although volcanic $\Delta F$ had a
negative DDT (-0.045 Wm-2/decade), recovery from the cooling caused by large
volcanic activities in the 20th century caused a long-term negative trend
(-0.012 ∘C/decade, 1951-2012), whereas weak volcanic activity in the 1998-2012
period caused a small positive trend (0.019 ∘C/decade, 1998-2012), resulting
in a positive DDT. In the case of solar irradiance (Fig. 4C), the decadal
trends for both $\Delta F$ and $\Delta T$ became slower during 1998-2012
compared to 1951-2012. Thus, we can pin at least some of the cooling on the
descending solar cycle. Regarding volcanic aerosols, in contrast to earlier
studies (?, ?, ?), which could balance out up to 30% of anthropogenic $\Delta
T$ (?), our results suggest that volcanic forcing is not responsible for the
SW. Our result also implies a relatively large contribution from the
descending solar cycle, similar to Lean (2018) (?), which mitigated
approximately 36% of anthropogenic $\Delta T$ from 2001 to 2011. However, Lean
(2018) also showed a small 8% cut in anthropogenic $\Delta T$ from volcanic
aerosols at the same time, possibly due to the use of stratospheric aerosol
optical depth (AOD) to estimate volcanic $\Delta T$ in her study, which is a
proxy of volcanic aerosol $\Delta F$. The volcanic $\Delta F$ actually
presented a relatively small negative decadal trend (-0.046 Wm-2/decade, blue
thin dashed line in Fig. 4B) from 1998-2012, which could produce the small
volcanic cooling effect reported by Lean (2018).

ENSO was a major contributor to the SW, which was mainly led by strong La Niña
cooling immediately after El Niño warming prior to 1998 (?, ?) (Fig. 4D).
Because of its seasonality, ENSO contributed to SW in the form of an annual
pulse signal (figs. S10-S13), whereas the descending solar cycle, ODS, and
methane had a relatively continuous and stable influence on SW. Our result is
consistent with that of Lean (2018), which signifies the largest contribution
from ENSO, with a cooling decadal trend of -0.086 ∘C/decade from 2001-2011
(cf. -0.065 ∘C/decade from 1998-2012 in this study, see fig. S4).

Figure 4: $\Delta T$ due to natural forces. (A) Natural forcing $\Delta T$
from OSCAR v3.1 (?) and CMIP6 Earth System Models (ESMs) (?) (ensemble mean
for each ESM, table S3), as well as this study. OSCAR v3.1 uncertainty denotes
the one-sigma obtained from Monte Carlo simulations with n = 1000. (B and C)
$\Delta F$ and $\Delta T$ for volcanic eruptions and solar irradiance. In (B
and C), thin solid and solid with extended dashed lines represent linear
trends for the years 1951-2012 and 1998-2012, respectively. Three large
volcanic eruptions are indicated in (B). (D) $\Delta T$ rate of change caused
by ENSO (see fig. S10 for the ENSO $\Delta T$ trend). Gray dashed lines in (D)
depict $\Delta T$ rates of changes estimated by using other ENSO indices shown
in figs. S11-S13. Thick horizontal lines represent the mean values for the
specified periods. The $\Delta T$ ranges of this study in (A to D) are the
one-sigma produced by the ensemble of statistical regressions. The SW era from
1998 to 2012 is shaded in light gray.

## Discussion and conclusions

The total sum of the DDT of individual factors converged on the observation
(Fig. 2M), explaining almost all of the $\Delta T$ slowdown during the SW
period. The use of different independent observations (figs. S14-S16) or ENSO
indices (figs. S17-S19) gave similar results, implying that our analysis is
quantitatively robust. The uncertainties may result from the autocorrelation
of chosen predictors and cross-correlation among the predictors, as well as
observational errors or inaccurate depictions of the real processes (?). The
correlation between simulated $\Delta T$ and observed $\Delta T$ here is
higher than Lean’s (2018) statistical method (r= 0.91 for space-based model
during 1979–2017), most likely due to the full consideration of all available
factors, which were derived from a physical RCM. This is also due to the use
of the latest temperature record, while the older version may overmeasure the
SW, resulting in larger residuals and lower goodness-of-fit (lower R-squared
values) in the regression (fig. S20, table S4). Therefore, our causal
explanation of the SW is sound.

Combining a physical RCM and an observationally constrained statistical model,
we comprehensively evaluated the relative contributions to the SW from
1998-2012. Using DDT, we captured not only the direct cooling contributions
but also the slowing trends of $\Delta T$ in the SW caused by anthropogenic
and natural factors. Our results show that carbon dioxide, aerosols and
pollutants and erupting volcanoes significantly accelerated global $\Delta T$
during the SW period compared to 1951-2012, whereas La Niña cooling and a
descending solar cycle strongly offset the increased $\Delta T$, accounting
for approximately 50% and 26% of the total warming slowdown during 1998-2012
compared to 1951-2012. In particular, we identified that the reduced
anthropogenic ODS and methane emissions also contributed approximately 13% and
11% of the total warming slowdown, which can be explained by the recorded
atmospheric $\Delta C$. Various factors superimposed on the timeline slowed
$\Delta T$ between 1998 and 2012, while the beginning and end of a single
source did not necessarily match the SW period. The contribution of
anthropogenic ODS and methane was comparable in scale to La Niña cooling and
the descending solar cycle, as well as the overall downward trend exhibited by
the temperature records (Fig. 2M), all of which can be detected with
instruments, either directly or indirectly. Thus, our findings provide
practical evidence for preventing global warming by reducing GHG emissions.

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## Acknowledgments

The computational resources were provided by the National Institute for
Environmental Studies (NIES), Japan. Funding: This work was supported by the
Decarbonized and Sustainable Society Research Program at the National
Institute for Environmental Studies, Japan, and the Program for the advanced
studies of climate change projection (SENTAN, Grant Number JPMXD0722681344)
from the Ministry of Education, Culture, Sports, Science and Technology
(MEXT), Japan. K. Tanaka benefited from state assistance managed by the
National Research Agency in France under the Programme d’Investissements
d’Avenir under the reference ANR-19-MPGA-0008. Author contributions: X.S.
designed the study, performed the simulations, produced all figures, and led
the writing with contributions from all authors. H.S. provided insights to
create the statistical model. Competing interests: The authors declare no
competing interests. Data and materials availability: The data used in this
analysis can be accessed online (last access for all, 22 May 2023): Coupled
Model Intercomparison Project 6 (CMIP6) (https://esgf-
node.llnl.gov/projects/cmip6/); Community Emissions Data System (CEDS)
(https://esgf-node.llnl.gov/search/input4mips/); Emission Database for Global
Atmospheric Research (EDGAR) v7.0 (Global Greenhouse Gas Emissions)
(https://edgar.jrc.ec.europa.eu/dataset_ghg70); EDGAR v6.1 (Global Air
Pollutant Emissions) (https://edgar.jrc.ec.europa.eu/dataset_ap61); Coupled
Model Intercomparison Project Phase 6 (CMIP6) emissions from the Integrated
Assessment Modeling Consortium (IAMC) (https://esgf-
node.llnl.gov/search/input4mips/); The Atmospheric Chemistry and Climate Model
Intercomparison Project (ACCMIP) (?) (https://tntcat.iiasa.ac.at/RcpDb);
Carbon emissions from land use and land-cover change (?, ?)
(http://www.globalcarbonatlas.org/en/CO2-emissions); Historical landcover
change and wood harvest CO2 emissions from the Max Planck Institute for
Meteorology (MPI-M) (https://www.mpimet.mpg.de/en/science/the-land-in-the-
earth-system/working-groups/climate-biogeosphere-interaction/landuse-change-
emission-data/); Land-use change emissions from ref (?) (https://cdiac.ess-
dive.lbl.gov/ftp/Smith_Rothwell_Land-Use_Change_Emissions/); Land-Use
Harmonization (LUH2) (https://luh.umd.edu/); Historical greenhouse gas
concentrations for climate modelling (CMIP6)
(https://doi.org/10.5194/gmd-10-2057-2017); National Oceanic & Atmospheric
Administration Carbon Cycle Greenhouse Gases (atmospheric concentrations of
CO2, CH4 and N2O) (https://gml.noaa.gov/ccgg/); The NOAA Ozone Depleting Gas
Index (https://gml.noaa.gov/odgi/); Advanced Global Atmospheric Gases
Experiment (AGAGE) (https://agage.mit.edu/data/agage-data); The Global Carbon
Project (GCP) (?) (https://www.globalcarbonproject.org); Global Methane Budget
(https://www.globalcarbonproject.org/methanebudget/); Hadley Centre/Climatic
Research Unit Temperature (HadCRUT) v5.0
(https://www.metoffice.gov.uk/hadobs/hadcrut5/); Berkeley Earth (Global
Temperature Data) (https://berkeleyearth.org/data/); NOAAGlobalTemp v5.1
(https://www.ncei.noaa.gov/products/land-based-station/noaa-global-temp); GISS
Surface Temperature Analysis (GISTEMP v4)
(https://data.giss.nasa.gov/gistemp/); NOAA MEI (?)
(https://psl.noaa.gov/enso/mei.old/mei.html); MEI from NCEP-NCAR
(https://www.webberweather.com/multivariate-enso-index.html); Cold Tongue
Index (CTI) (https://github.com/ToddMitchellGH/Cold-Tongue-Index); “BEST” ENSO
Index (?) (https://psl.noaa.gov/people/cathy.smith/best/). The code for
reproducing the study will be deposited in the permanent repository Zenodo.

## Supplementary Materials for

Anthropogenic contributions to slow warming over 1998-2012

Xuanming Su et al.

Corresponding author: Xuanming Su<EMAIL_ADDRESS>
Materials and Methods
Figs. S1 to S22
Tables S1 to S4
References (56-64)

## Materials and Methods

###  $\Delta T$ simulations

We used an RCM - SCM4OPT v3.3 (?, ?, ?, ?) to simulate global $\Delta T$
trends resulting from anthropogenic factors (such as CO2, CH4, N2O,
halogenated gases (16 ODS and 23 other fluorinated gases), carbon monoxide
(CO), nitrogen oxide (NOx), volatile organic compounds (VOCs), sulfate (SOx),
black carbon (BC), organic carbon (OC), and land albedo) and natural forcings
(such as volcanic and solar irradiance). SCM4OPT v3.3 was created by updating
an older version, SCM4OPT v3.2 (?). We present a new parameterization for CH4
forcing (?). The methane $\Delta T$ trend in this study was estimated using a
hybrid of the new Etminan parameterization and a traditional technique as in
AR5 (?), and the associated processes and parameters were used in the Monte
Carlo simulation as below. The former showed a 25% higher CH4 forcing than the
latter (1750–2011), resulting in a lower DDT level of -0.015$\pm$0.008
∘C/decade (cf. -0.012$\pm$0.007 ∘C/decade using AR5’s method) in the final
attribution (figs. S21-S22).

A normalized marginal method (?, ?, ?, ?) was applied to SCM4OPT v3.3 for
$\Delta T$ quantifications of climate forcers. $\Delta T$ trends induced by
nonemission factors such as natural forcings including volcanoes and solar
irradiance, as well as human factors such as land albedo resulting from land-
use change, were quantified using a residual method: (1) one historical
emulation with all emissions and nonemission factors as input; (2) one
“exclusive” experiment for estimating land-use albedo $\Delta T$ trends with
constant preindustrial land cover levels, and two “exclusive” experiments for
estimating natural forcing $\Delta T$ trends by deleting volcanic or solar
forcings from historical emulations. We compared $\Delta T$ obtained from
historical and “exclusive” experiments, and the differences between the two
experiments were $\Delta T$ trends caused by these nonemission factors. For
the remaining $\Delta T$, the normalized marginal method was used to quantify
the emission-induced $\Delta T$ trends (?). We assumed that the ratio of a
species’ ($e$) $\Delta T$ to overall $\Delta T$, defined as $\alpha^{t}_{e}$,
is proportional to the marginal effect of $e$ divided by the total marginal
effect. To estimate $\alpha^{t}_{e}$, two simulations were carried out for
each species: (1) one historical simulation as above and the resulting $\Delta
T$ denoted as $\Delta T_{all}$; and (2) another identical simulation except
emission $e$ reduced by a fraction of $\epsilon$ = 0.001 to calculate the
$\Delta T$ termed as $\Delta T_{e,\epsilon}$. Therefore, the relative
contribution $\alpha^{t}_{e}$ can be obtained:

$\alpha^{t}_{e}=\frac{\Delta T_{all}-\Delta
T_{e,\epsilon}}{\sum_{e\prime}{\left(\Delta T_{all}-\Delta
T_{e\prime,\epsilon}\right)}}$ (S1)

$\Delta T_{e}$ resulting from emission $e$ can be calculated as follows:

$\Delta T_{e}={\Delta T_{all}}\cdot\alpha^{t}_{e}$ (S2)

After calculating $\Delta T$ induced by emissions and nonemission factors, we
classified the resulting $\Delta T$ as CO2, CH4, N2O, ODS, other fluorinated
gases, aerosols and pollutants, land albedo, volcanoes, and solar irradiance,
considering their inherent characteristics and rates of change since the
preindustrial revolution.

To estimate $\Delta T$ trends induced by GHGs $\Delta C$ (Fig. 3, fig. S8), we
again used the above normalized marginal method for the forcing-driven mode of
SCM4OPT v3.3. We calculated the associated $\Delta F$ from $\Delta C$ and
applied $\epsilon$ = 0.001 to $\Delta F$ to obtain the trend of $\Delta
C$-induced $\Delta T$. The same $\beta_{GHG}$ (as below) was multiplied to
estimate the final $\Delta T$ induced by the GHG $\Delta C$.

It is worth noting that the numbers of ODS or other fluorinated gases used in
this study differ from the compiled data or observations (table S2). For
example, a few ODS gases (such as CFC-13, CH2Cl2 and CHCl3) and other
fluorinated gases (such as SO2F2, C7F16, C8F18 and C2Cl4) were not included in
our simulation due to data availability. However, the warming effects from
these gases are relatively small, and our results retained almost the same
total equivalent $\Delta C$ trends as the observations (Fig. 3, fig. S8).
Therefore, our conclusions are unaffected.

### Statistical model

ENSO has larger influences on the global $\Delta T$ than other internal
variabilities (?, ?, ?, ?). We used ENSO to reflect the main changes due to
internal variability. SCM4OPT v3.3 does not replicate ENSO. We employed a
statistical model to correct the biases in the magnitude of the simulated
$\Delta T$, and distinguish ENSO influences from the observed $\Delta T$ (?,
?, ?). We hypothesized that the observed $\Delta T$ consists of $\Delta T$
induced by anthropogenic GHG emissions, other anthropogenic factors such as
aerosols and pollutants and land albedo, natural forcings, and ENSO.
Accordingly, the observed $\Delta T$ is defined as a multiple regression among
the time series of these elements plus a residual component allowing for
errors resulting from simulations and observations:

$\begin{split}\Delta T_{obs}(t)&=\beta_{GHG}(\Delta T_{CO_{2}}(t)+\Delta
T_{CH_{4}}(t)+\Delta T_{N_{2}O}(t)+\Delta T_{ODS}(t)+\Delta T_{oFGS}(t))\\\
&+\beta_{non-GHG}(\Delta T_{aero}(t)+\Delta T_{lcc}(t))\\\
&+\beta_{nat}(\Delta T_{volc}(t)+\Delta T_{solar}(t))\\\
&+\beta^{1}_{MEI}MEI(t-\tau_{1})+\beta^{2}_{MEI}MEI(t-\tau_{2})+\beta^{3}_{MEI}MEI(t-\tau_{3})\\\
&+Resi(t)\\\ &+T_{0}\end{split}$ (S3)

where $\Delta T_{obs}(t)$ is the observed $\Delta T$. $\Delta T_{CO_{2}}(t)$,
$\Delta T_{CH_{4}}(t)$, $\Delta T_{N_{2}O}(t)$, $\Delta T_{ODS}(t)$, $\Delta
T_{oFGS}(t)$, $\Delta T_{aero}(t)$, $\Delta T_{lcc}(t)$, $\Delta T_{volc}(t)$
and $\Delta T_{solar}(t)$ indicate the simulated $\Delta T$ caused by CO2,
CH4, N2O, ODS, other fluorinated gases, aerosols and pollutants, land albedo,
volcanoes and solar irradiance, respectively. $\beta_{GHG}$, $\beta_{non-GHG}$
and $\beta_{nat}$ are fitted coefficients for the associated factors. $MEI(t)$
indicates the monthly multivariate ENSO index (MEI) taken from existing
literature (?). Before applying the MEI, we eliminated the linear trend from
it. $\beta^{i}_{MEI}$ and $\tau_{i}$ ($i=1,2,3$) represent the fitted
coefficients and the delayed months for the MEI, respectively, which were
selected to maximize the variance explained (table S4). $Resi(t)$ and $T_{0}$
are the residuals and intercept, respectively. The time series of the $\Delta
T$ trends estimated from SCM4OPT v3.3 are bimonthly data, which we linearly
interpolated into monthly values before employing in the statistical model.
Multiple regression was applied to data from 1951 to 2018. The fitted
coefficients, $R^{2}$ values and correlation coefficients are shown in table
S4.

### Uncertainties

This study considered uncertainties in historical emissions, climate model
uncertainties, and uncertainties found in various observation records. First,
three emission datasets, i.e., the Community Emissions Data System (CEDS) (?),
Emission Database for Global Atmospheric Research (EDGAR) v7.0_GHG 1970-2021
and EDGAR v6.1_AP 1970-2018 (?, ?), and ACCMIP (?), were used to represent
uncertainties resulting from estimates of historical emissions. We compiled
and processed the data in the same way as ref. (?). When a certain species was
not available, we used equivalent emission data from a separate dataset. These
emissions were used to generate the atmospheric $\Delta C$ and the associated
$\Delta F$, and then to estimate the global $\Delta T$. Second, we performed a
Monte Carlo simulation with $n=1000$ (see table S4 in the forcing study (?)
for the parameter sets) for the climate system to calculate the climate model
uncertainties. Third, we carried out regressions for individual temperature
records or the representative record HadCRUT5 with different ENSO indices,
considering that ENSO effects and residuals are somewhat sensitive to the
temperature records and ENSO indices. The statistical regression was also
performed using the Monte Carlo method with $n=1000$. For example, the
observed value was randomly chosen from the available dataset ensemble (for
HadCRUT5 $n=200$), while the predictor variables were randomly selected from
the ensemble of SCM4OPTv3.3 simulations.

To estimate the uncertainty of aerosols presented in fig. S2, we summed the
aerosols’ $\Delta T$ from AR6, namely, NOx, VOC, SO2, OC, BC and NH3. Their
uncertainties were propagated by assuming that the individual $\Delta T$
values are independent variables that are normally distributed. Thus, their
sum was also normally distributed. For example, from $X\sim
N(\mu_{X},\sigma_{X}^{2})$ and $Y\sim N(\mu_{Y},\sigma_{Y}^{2})$, we obtained
the uncertainty of $Z=X+Y$: $Z\sim
N(\mu_{X}+\mu_{Y},\sigma_{X}^{2}+\sigma_{Y}^{2})$. A similar estimation was
used in the AR6 calculation (https://github.com/sarambl/AR6_CH6_RCMIPFIGS).

## Supplementary Figures

Figure S1: Observed $\Delta T$. Linear trends across the selected periods are
represented by solid and solid with extended dashed lines. $\Delta T$ of
GISTEMPv4 is relative to 1880-1900 since there are no data available before
1880. Differences of decadal trends (DDT) are shown in the upper part of the
panel for each temperature record. The SW era from 1998 to 2012 is shaded in
light gray. Figure S2: Attributions of $\Delta T$ in this study vs. AR6. The
AR6 attribution was extracted from Figure SPM.2. Error bars in both this study
and AR6 are one-sigma uncertainties. Note that Figure SPM.2 shows very likely
ranges (5th-95th percentiles). We estimated the one-sigma uncertainty based on
the AR6 calculation (https://github.com/sarambl/AR6_CH6_RCMIPFIGS) (see
materials and methods). Figure S3: Attribution of ozone effective $\Delta F$
in this study compared to AR6. The effective $\Delta F$ for AR6 was extracted
from https://github.com/sarambl/AR6_CH6_RCMIPFIGS. This study’s evaluation
period is 1850-2019, while AR6’s evaluation period is 1750-2019. The effective
$\Delta F$ for this study includes effects from both stratospheric and
tropospheric ozone. This study’s uncertainty ranges represent the one-sigma of
the Monte Carlo simulation with n = 1000; however, the AR6 uncertainty ranges
are not included due to data availability.  Figure S4: Decadal $\Delta T$
trends. The decadal $\Delta T$ trends are shown for the periods of 1998-2012
(red) and 1951-2012 (green). The histogram in (A to K) represents the
distribution produced by the ensemble of statistical regressions, while the
histogram in (L) shows the 200 realizations of the HadCRUT5 ensemble. The
ensemble means are represented by vertical dashed lines over the selected
periods. The ENSO is derived from HadCRUT5. Figure S5: $\Delta T$ caused by
GHG emissions. See Fig. 4 for the uncertainties of this study and OSCAR v3.1
(?). The SW era from 1998 to 2012 is shaded in light gray. Note that the hist-
GHG simulation does not account for stratospheric and tropospheric ozone. See
table S3 for the investigated CMIP6 ESMs (?). Figure S6: (Effective) $\Delta
F$ by anthropogenic surface albedo change. IPCC AR6 (?) and SCM4OPT v3.3 are
effective $\Delta F$, whereas OSCARv3.1 (?) is $\Delta F$ due to data
availability. Figure S7: $\Delta T$ rate of change. Color horizontal solid and
dashed lines represent mean values from 1951 to 2012 and from 1998 to 2012,
respectively. Black horizontal solid and dashed lines represent the linear
temperature trends from 1951 to 2012 and 1998 to 2012, respectively (Fig. 2 (A
to L)). See Fig. 2 for the uncertainty description. HadCRUT5 was used to
calculate the ENSO. Figure S8: Observed and simulated atmospheric $\Delta C$
and the induced $\Delta T$. See Fig. 3 for the uncertainty description. The
components of ODS and other fluorinated gases for each source in (D and E)
differ (table S2). Uncertainties are not considered in the $\Delta C$ of ODS
and other fluorinated gases because they are equivalent values combining a
collection of compounds (?). The SW era from 1998 to 2012 is shaded in light
gray. Figure S9: Aerosol and pollutant-induced $\Delta T$. See Fig. 4 for the
uncertainty description. The thin solid and solid with extended dashed lines
represent linear trends for the years 1951-2012 and 1998-2012, respectively.
The SW era from 1998 to 2012 is shaded in light gray. See table S3 for the
investigated CMIP6 ESMs (?). Figure S10: $\Delta T$ caused by ENSO. (A)
$\Delta T$ trend caused by ENSO. Linear trends across the selected periods are
represented by solid and solid with extended dashed lines. (B) Rate of change
of ENSO $\Delta T$. Thick horizontal lines represent the mean values for the
specified periods. The MEI uses the NOAA MEI (?)
(https://psl.noaa.gov/enso/mei.old/mei.html), which is the default MEI in this
study. The ENSO is derived from HadCRUT5. The SW era from 1998 to 2012 is
shaded in light gray. Figure S11: $\Delta T$ caused by ENSO. The same as in
fig. S10, except that ENSO is estimated by using the MEI from NCEP-NCAR
(https://www.webberweather.com/multivariate-enso-index.html). Figure S12:
$\Delta T$ caused by ENSO. The same as in fig. S10, except that ENSO is
estimated by using the cold tongue index (CTI)
(https://github.com/ToddMitchellGH/Cold-Tongue-Index). Figure S13: $\Delta T$
caused by ENSO. The same as in fig. S10, except that ENSO is estimated by
using the “BEST” ENSO Index (?)
(https://psl.noaa.gov/people/cathy.smith/best/). Figure S14: Anthropogenic and
natural $\Delta T$ by source and their DDT between 1998-2012 and 1951-2012.
The same as in Fig. 2, except that the temperature record uses Berkeley Earth.
Figure S15: Anthropogenic and natural $\Delta T$ by source and their DDT
between 1998-2012 and 1951-2012. The same as in Fig. 2, except that the
temperature record uses GISTEMPv4. Figure S16: Anthropogenic and natural
$\Delta T$ by source and their DDT between 1998-2012 and 1951-2012. The same
as in Fig. 2, except that the temperature record uses GlobalTemp v5.1. Figure
S17: Anthropogenic and natural $\Delta T$ by source and their DDT between
1998-2012 and 1951-2012. The same as in Fig. 2, except that ENSO is estimated
by using the MEI from NCEP-NCAR (https://www.webberweather.com/multivariate-
enso-index.html). Figure S18: Anthropogenic and natural $\Delta T$ by source
and their DDT between 1998-2012 and 1951-2012. The same as in Fig. 2, except
that ENSO is estimated by using the cold tongue index (CTI)
(https://github.com/ToddMitchellGH/Cold-Tongue-Index). Figure S19:
Anthropogenic and natural $\Delta T$ by source and their DDT between 1998-2012
and 1951-2012. The same as in Fig. 2, except that ENSO is estimated by using
the “BEST” ENSO Index (?) (https://psl.noaa.gov/people/cathy.smith/best/).
Figure S20: Anthropogenic and natural $\Delta T$ by source and their DDT
between 1998-2012 and 1951-2012. The same as in Fig. 2, except that the
temperature record uses HadCRUT4.6. Figure S21: Anthropogenic and natural
$\Delta T$ by source and their DDT between 1998-2012 and 1951-2012. The same
as in Fig. 2, except that the methane forcing is parameterized using the
Etminan method (?). Figure S22: Anthropogenic and natural $\Delta T$ by source
and their DDT between 1998-2012 and 1951-2012. The same as in Fig. 2, except
that the methane forcing is parameterized using the usual IPCC method (?).

## Supplementary Tables

Table S1: Test of statistical models using the Bayesian Information Criterion (BIC) Index |  Regression among variables |  BIC |  Remark
---|---|---|---
1 |  GHGs, Non-GHGs, natural, MEI |  -1216.766 |  Used in this study
2 |  Total sum, MEI |  -1180.292 |
3 |  Anthropogenic, natural, MEI |  -1205.087 |
4 |  GHGs, aerosols, land albedo, natural, MEI |  -1211.329 |  Negative coefficient occurs in land albedo, invalid
5 |  GHGs, Non-GHGs, volcanic, solar, MEI |  -1216.033 |
6 |  CO2, CH4, N2O, ODS, other fluorinated, aerosols, land albedo, natural, MEI |  -1206.71 |  Negative coefficients occur in CH4, N2O, other fluorinated and land albedo, invalid
7 |  CO2, CH4, N2O, ODS, other fluorinated, aerosols, land albedo, volcanic, sola, MEI |  -1225.454 |  Negative coefficients occur in CH4, N2O and land albedo, invalid
Table S2: List of halogenated compounds used in this study and observational records Compounds |  This study |  CMIP6 |  NOAA |  AGAGE_md (*) |  AGAGE_ms (†)
---|---|---|---|---|---
Ozone-Depleting Substances (ODS)
CFC-11 |  $\surd$ |  $\surd$ |  $\surd$ |  $\surd$ |
CFC-12 |  $\surd$ |  $\surd$ |  $\surd$ |  $\surd$ |
CFC-13 |  |  |  |  |  $\surd$
CFC-113 |  $\surd$ |  $\surd$ |  $\surd$ |  $\surd$ |  $\surd$
CFC-114 |  $\surd$ |  $\surd$ |  |  |  $\surd$
CFC-115 |  $\surd$ |  $\surd$ |  |  |  $\surd$
HCFC-22 |  $\surd$ |  $\surd$ |  $\surd$ |  |  $\surd$
HCFC-141b |  $\surd$ |  $\surd$ |  $\surd$ |  |  $\surd$
HCFC-142b |  $\surd$ |  $\surd$ |  $\surd$ |  |  $\surd$
CH3CCl3 |  $\surd$ |  $\surd$ |  $\surd$ |  $\surd$ |  $\surd$
CCl4 |  $\surd$ |  $\surd$ |  $\surd$ |  $\surd$ |
CH3Cl |  $\surd$ |  $\surd$ |  |  |  $\surd$
CH2Cl2 |  |  $\surd$ |  |  |  $\surd$
CHCl3 |  |  $\surd$ |  |  $\surd$ |  $\surd$
CH3Br |  $\surd$ |  $\surd$ |  $\surd$ |  |  $\surd$
Halon-1211 |  $\surd$ |  $\surd$ |  $\surd$ |  |  $\surd$
Halon-1202 |  $\surd$ |  |  |  |
Halon-1301 |  $\surd$ |  $\surd$ |  $\surd$ |  |  $\surd$
Halon-2402 |  $\surd$ |  $\surd$ |  $\surd$ |  |  $\surd$
Other fluorinated gases
HFC-134 |  $\surd$ |  |  |  |
HFC-134a |  $\surd$ |  $\surd$ |  $\surd$ |  |  $\surd$
HFC-23 |  $\surd$ |  $\surd$ |  |  |  $\surd$
HFC-32 |  $\surd$ |  $\surd$ |  $\surd$ |  |  $\surd$
HFC-125 |  $\surd$ |  $\surd$ |  $\surd$ |  |  $\surd$
HFC-143 |  $\surd$ |  |  |  |
HFC-143a |  $\surd$ |  $\surd$ |  $\surd$ |  |  $\surd$
HFC-152a |  $\surd$ |  $\surd$ |  $\surd$ |  |  $\surd$
HFC-227ea |  $\surd$ |  $\surd$ |  $\surd$ |  |  $\surd$
HFC-236fa |  $\surd$ |  $\surd$ |  |  |  $\surd$
HFC-245fa |  $\surd$ |  $\surd$ |  |  |  $\surd$
HFC-365mfc |  $\surd$ |  $\surd$ |  $\surd$ |  |  $\surd$
HFC-41 |  $\surd$ |  |  |  |
HFC-43-10mee |  $\surd$ |  $\surd$ |  |  |  $\surd$
NF3 |  $\surd$ |  $\surd$ |  |  |  $\surd$
SF6 |  $\surd$ |  $\surd$ |  |  |  $\surd$
SO2F2 |  |  $\surd$ |  |  |  $\surd$
CF4 |  $\surd$ |  $\surd$ |  |  |  $\surd$
C2F6 |  $\surd$ |  $\surd$ |  |  |  $\surd$
C3F8 |  $\surd$ |  $\surd$ |  |  |  $\surd$
C4F10 |  $\surd$ |  $\surd$ |  |  |
C5F12 |  $\surd$ |  $\surd$ |  |  |
C6F14 |  $\surd$ |  $\surd$ |  |  |
C7F16 |  |  $\surd$ |  |  |
C8F18 |  |  $\surd$ |  |  |
c-C4F8 |  $\surd$ |  $\surd$ |  |  |
C2Cl4 |  |  |  |  |  $\surd$
* AGAGE_md: AGAGE GC-MD data
(https://agage2.eas.gatech.edu/data_archive/global_mean/global_mean_md.txt)
† AGAGE_ms: AGAGE GCMS-Medusa data
(https://agage2.eas.gatech.edu/data_archive/global_mean/global_mean_ms.txt)
Table S3: The investigated CMIP6 ESMs and ensemble sizes Index |  Model |  hist-GHG |  hist-aer |  hist-nat
---|---|---|---|---
1 |  ACCESS-CM2 |  3 |  3 |  3
2 |  ACCESS-ESM1-5 |  3 |  3 |  3
3 |  BCC-CSM2-MR |  3 |  3 |  3
4 |  CanESM5 |  50 |  30 |  50
5 |  CESM2 |  3 |  2 |  3
6 |  CNRM-CM6-1 |  10 |  10 |  10
7 |  FGOALS-g3 |  3 |  3 |  3
8 |  GFDL-CM4 |  0 |  0 |  3
9 |  GFDL-ESM4 |  1 |  1 |  3
10 |  GISS-E2-1-G |  10 |  15 |  20
11 |  HadGEM3-GC31-LL |  5 |  5 |  10
12 |  IPSL-CM6A-LR |  10 |  10 |  10
13 |  MIROC6 |  3 |  10 |  50
14 |  MRI-ESM2-0 |  5 |  5 |  5
15 |  NorESM2-LM |  3 |  3 |  3
Table S4: Fitted coefficients for the statistical model Corresponding figures and estimates |  Berkeley Earth |  GISTEMPv4 |  GlobalTemp v5.1 |  HadCRUT5 (mainly used) |  HadCRUT4.6
---|---|---|---|---|---
In Figs. |  figs. S2, S14 |  figs. S2, S15 |  figs. S2, S16 |  Figs. 1, 2, 3, 4
figs. S2, S4, S5, S7, S8, S9, S10 |  fig. S20
$\beta_{GHG}$ |  1.28$\pm$0.20 |  1.16$\pm$0.15 |  1.13$\pm$0.14 |  1.31$\pm$0.22 |  1.08$\pm$0.22
$\beta_{non-GHG}$ |  1.83$\pm$0.70 |  1.30$\pm$0.48 |  1.26$\pm$ 0.48 |  2.07$\pm$0.81 |  1.57$\pm$0.84
$\beta_{nat}$ |  1.51$\pm$0.19 |  1.52$\pm$0.19 |  1.51$\pm$0.19 |  1.56$\pm$0.21 |  1.32$\pm$0.32
$\beta^{1}_{MEI}$ |  0.048$\pm$0.001 |  0.017$\pm$0.001 |  0.039$\pm$0.001 |  0.057$\pm$0.002 |  0.062$\pm$0.001
$\beta^{2}_{MEI}$ |  0.016$\pm$0.000 |  0.017$\pm$0.001 |  0.000$\pm$0.000 |  0.006$\pm$0.002 |  0.028$\pm$0.002
$\beta^{3}_{MEI}$ |  0.043$\pm$0.001 |  0.038$\pm$0.000 |  0.039$\pm$0.000 |  0.041$\pm$0.002 |  0.025$\pm$0.002
$\tau_{1}$ |  0 |  2 |  2 |  0 |  0
$\tau_{2}$ |  1 |  2 |  3 |  6 |  7
$\tau_{3}$ |  9 |  3 |  4 |  8 |  10
Mean $R^{2}$ |  0.87 |  0.87 |  0.88 |  0.88 |  0.86
Mean correl. between ENSO & residuals |  2.8E-17 |  6.8E-18 |  8.7E-17 |  3.2E-17 |  1.5E-17
Mean correl. between estimate & observation |  0.93 |  0.93 |  0.94 |  0.94 |  0.93
Table: Fitted coefficients for the statistical model (continued) Corresponding figures and estimates |  HadCRUT5 w/ NCEP index |  HadCRUT5 w/ CTI |  HadCRUT5 w/ BEST index |  HadCRUT5 w/ Etminan forcing |  HadCRUT5 w/ AR5 forcing
---|---|---|---|---|---
In Figs. |  figs. S2, S11, S17 |  figs. S2, S12, S18 |  figs. S2, S13, S19 |  figs. S2, S21 |  figs. S2, S22
$\beta_{GHG}$ |  1.17$\pm$0.17 |  1.16$\pm$0.19 |  1.25$\pm$0.19 |  1.36$\pm$0.23 |  1.25$\pm$ 0.20
$\beta_{non-GHG}$ |  1.42$\pm$0.69 |  1.40$\pm$0.70 |  1.82$\pm$0.73 |  2.18$\pm$0.82 |  1.96$\pm$ 0.80
$\beta_{nat}$ |  0.84$\pm$0.30 |  0.91$\pm$0.34 |  1.66$\pm$0.22 |  1.64$\pm$0.21 |  1.49$\pm$0.18
$\beta^{1}_{MEI}$ |  0.035$\pm$0.002 |  0.068$\pm$0.003 |  0.054$\pm$0.002 |  0.057$\pm$0.002 |  0.057$\pm$0.002
$\beta^{2}_{MEI}$ |  0.016$\pm$0.002 |  0.032$\pm$0.003 |  0.029$\pm$0.002 |  0.006$\pm$0.002 |  0.006$\pm$0.002
$\beta^{3}_{MEI}$ |  0.021$\pm$0.002 |  0.035$\pm$0.003 |  0.018$\pm$0.002 |  0.040$\pm$0.002 |  0.041$\pm$ 0.003
$\tau_{1}$ |  6 |  3 |  0 |  0 |  0
$\tau_{2}$ |  7 |  8 |  8 |  6 |  6
$\tau_{3}$ |  8 |  11 |  10 |  8 |  8
Mean $R^{2}$ |  0.87 |  0.84 |  0.86 |  0.88 |  0.88
Mean correl. between ENSO & residuals |  1.3E-17 |  -8.7E-18 |  -6.2E-18 |  6.7E-18 |  8.5E-18
Mean correl. between estimate & observation |  0.93 |  0.92 |  0.92 |  0.94 |  0.94


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