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Contrasting ecosystem constraints on the seasonal terrestrial CO2 and mean surface air temperature causality projections by the end of the 21st century


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Two centuries of studies have demonstrated the importance of understanding the interaction between the air temperature and carbon dioxide (CO2) emissions, which can impact the climate system and human life in various ways, and across different timescales. While historical interactions have been consistently studied, the nature of future interactions and the impacts of confounding factors still requires more investigation in keeping with the continuous updates of climate projections to the end of the 21st century. The Phase 6 of the Coupled Model Intercomparison Project (CMIP6), like its earlier projects, provides ScenarioMIP multi-model projections to assess the climate under different radiative forcings ranging from a low-end (SSP1-2.6) to a high-end (SSP5-8.5) pathway. In this study, we analyze the localized causal structure of CO2, and near-surface mean air temperature (meanT) interaction for four scenarios from three CMIP6 models using a rigorous multivariate information flow (IF) causality, which can separate the cause from the effect within the interaction (CO2-meanT and meanT-CO2) by measuring the rate of IF between parameters. Firstly, we obtained patterns of the CO2 and meanT causal structures over space and time. We found a contrasting emission-based impact of soil moisture and vegetation (LAI) changes on the meanT-CO2 causal patterns. That is, soil moisture influenced CO2 sink regions in SSP1-2.6 and source regions in SSP58.5, and vice versa found for LAI influences. On the other hand, they similarly function to constrain the future CO2 impact on meanT. These findings are essential for improving long-term predictability where the climate models might be limited.
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Contrasting ecosystem constraints on seasonal terrestrial CO2
and mean surface air temperature causality projections by the
end of the 21st century
Daniel F T Hagan1, Han A J Dolman2,3, Guojie Wang1,, Kenny T C Lim Kam Sian4, Kun Yang5,
Waheed Ullah1and Runping Shen1
1Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters, Nanjing University of Information Science &
Technology, Nanjing 210044, People’s Republic of China
2NIOZ Royal Netherlands Institute for Sea Research, Den Burg 1790 AB, Texel, The Netherlands
3Department of Earth Sciences, Vrije Universiteit Amsterdam, Amsterdam 1081 HV, The Netherlands
4School of Atmospheric Science and Remote Sensing, Wuxi University, Wuxi 214105, People’s Republic of China
5Ministry of Education Key Laboratory for Earth System Modeling and the Department of Earth System Science, Tsinghua University,
Beijing 100084, People’s Republic of China
Author to whom any correspondence should be addressed.
Keywords: CO2–temperature causality, LAI, soil moisture, CMIP6, information flow causality
Supplementary material for this article is available online
Two centuries of studies have demonstrated the importance of understanding the interaction
between air temperature and carbon dioxide (CO2) emissions, which can impact the climate system
and human life in various ways, and across different timescales. While historical interactions have
been consistently studied, the nature of future interactions and the impacts of confounding factors
still require more investigation in keeping with the continuous updates of climate projections to
the end of the 21st century. Phase 6 of the Coupled Model Intercomparison Project (CMIP6), like
its earlier projects, provides ScenarioMIP multi-model projections to assess the climate under
different radiative forcings ranging from a low-end (SSP1–2.6) to a high-end (SSP5–8.5) pathway.
In this study, we analyze the localized causal structure of CO2, and near-surface mean air
temperature (meanT) interaction for four scenarios from three CMIP6 models using a rigorous
multivariate information flow (IF) causality, which can separate the cause from the effect within
the interaction (CO2–meanT and meanT–CO2) by measuring the rate of IF between parameters.
First, we obtain patterns of the CO2and meanT causal structures over space and time. We found a
contrasting emission-based impact of soil moisture (SM) and vegetation (leaf area index (LAI))
changes on the meanT–CO2causal patterns. That is, SM influenced CO2sink regions in SSP1–2.6
and source regions in SSP5–8.5, and vice versa found for LAI influences. On the other hand, they
function similarly to constrain the future CO2impact on meanT. These findings are essential for
improving long-term predictability where climate models might be limited.
1. Introduction
The relationship between near-surface air tem-
perature and carbon dioxide emissions (CO2) has
remained a topic of significant concern and research
for almost two centuries (Arrhenius 1896, Stips et al
2016, Koutsoyiannis and Kundzewicz 2020). Both
observed and modeled increases in temperature have
been noted to impact CO2variability, while increases
in CO2have also been shown to be a pivotal con-
tributor to the warming climate (Lacis et al 2010).
The impacts on various aspects of the ecosystem (van
Nes et al 2015, Deryng et al 2016, Demirhan 2020)
and socio-economic patterns (Deryng et al 2016,
Appiah et al 2018) have been studied from many
perspectives using different approaches. Several stud-
ies have sought to understand the causality within
this interaction using either controlled numerical
© 2022 The Author(s). Published by IOP Publishing Ltd
Environ. Res. Lett. 17 (2022) 124019 D F T Hagan et al
simulations (for instance, Friedlingstein et al
(2001) and Seneviratne et al (2013)) or data-driven
approaches (for instance, Attanasio (2012) and Kout-
soyiannis and Kundzewicz (2020)), both of which
have their strengths and limitations. Based on these
approaches, previous studies have explored the mul-
tiple temporal characteristics of the interaction (Faes
et al 2017) in historical records, ranging from paleo-
climate timescales (Stips et al 2016, Barral et al 2017)
to annual and 6 month timescales (Koutsoyiannis
and Kundzewicz 2020), and even to daily timescales
(Kotz et al 2021). These studies have consistently
shown that climate-carbon feedback is fundamentally
positive. Given the increasing concern regarding the
impact of increased CO2emissions on the climate and
vice versa, assessing how the causal structures would
evolve in the future in a changing climate under vari-
ous warming instances is of utmost importance to
improve the predictability of these impacts where
climate models are limited.
The primary activity of Phase 6 of the Coupled
Model Intercomparison Project (CMIP6)—the Scen-
ario Model Intercomparison Project—has recently
implemented multi-model climate projections based
on different pathways of future emissions and land
use changes (hereafter referred to as CMIP6 emis-
sion scenarios) developed with integrated assessment
models (O’Neill et al 2016). In the past, proceed-
ings from earlier phases of this project have not
only improved our understanding of possible future
climate scenarios but have also served as decision-
making models for characterizing societal risks and
related policies. For instance, Samset et al (2020) used
the CMIP5 datasets to investigate the impact of indi-
vidual climate drivers in mitigating projected global
surface temperature evolution and found that anthro-
pogenic CO2had the most significant potential to
influence it. Furthermore, a more recent study used
the CMIP5 records to show that rising temperatures
could reduce the yields of some major crops (Zhao
et al 2017).
Although there is a tight causal relationship
between temperature and CO2, their impacts on
each other are also influenced by some key para-
meters such as the sea surface temperature in the
ocean (Friedlingstein et al 2001), vegetation (Zhu
et al 2016), soil respiration (Bond-Lamberty and
Thomson 2010) and soil moisture (SM) over land
(Green et al 2019, Humphrey et al 2021). This means
that changes in these parameters could also lead
to changes in the temperature and CO2interac-
tion. These suggest the following: what would be
the changes in the global causal hotspot locations
under the different projection pathways? And how
would changes in key influencing factors modulate
them in the future? Along these lines, this study
attempts to quantify the temperature–CO2causality
based on the CMIP6 projections under four pathways
of socio-economic developments, mitigation of emis-
sions, and pollution control by the end of the 21st
century across the globe from an ensemble of three
climate models since 1979.
Here, we rely on a rigorously formulated inform-
ation flow (IF)-based causality tool that can quantit-
atively evaluate the cause–effect relationship in time
series (Liang 2014). Furthermore, asymmetry in IF
makes it possible to differentiate causal information
from mere correlations that do not have causal suffi-
ciency (Liang 2013). This method has been success-
fully applied to fields such as finance (Liang 2016),
neuroscience (Hristopulos et al 2019), climate science
(Bai et al 2017, Hagan et al 2019, Docquier et al 2022),
and more importantly, historical temperature–CO2
feedback analysis (Stips et al 2016). Here, we invest-
igate the impact of near-surface atmospheric CO2
emissions (CO2) on near-surface mean air temper-
ature (meanT) and vice versa (pixel-wise) under
four degrees of emission pathways ranging from
a sustainable scenario to a business-as-usual scen-
ario chiefly over land. More importantly, we exam-
ine how changes in two important land factors—
vegetation and SM—also contribute to the future
causality between the projected CO2and meanT. This
allows us to analyze regional ecosystem resilience to
changes in the climate-carbon feedback. To capture
the impacts of the two factors on the CO2and meanT
interactions, we focus on the seasonal mean vari-
ations since very long timescales would reduce their
impacts and very short timescales would be signific-
antly impacted by feedbacks over the land. Thus, we
focus on localized short-term impacts.
2. Data and method
2.1. CMIP6 datasets
Historical records (1979–2014) from the CMIP6
framework and four future scenarios (2015–2100) for
pixel-wise meanT from three CMIP6 models (table S1
shows a list of the models used), based on the avail-
ability of all four future scenarios of the model CO2
outputs at the time of the study, are used (O’Neill
et al 2016). Here, we use the near-surface emission-
driven CO2outputs to include the interactive effects
of carbon cycle feedbacks (Friedlingstein et al 2014)
necessary for such causal analyses. The four emission
pathways (or scenarios) in the projections used here
represent four different radiative forcing targets by
the end of the 21st century. The selected scenarios
here, called shared socio-economic pathways (SSPs),
range from SSP1–2.6, the low end of the forcing path-
ways, through the medium (SSP2–4.5 and SSP3–7.0
respectively) to the high-end, SSP5–8.5, which has the
highest emissions among the scenarios. More details
are provided in O’Neill et al (2016). Preprocessing
Environ. Res. Lett. 17 (2022) 124019 D F T Hagan et al
steps for the causality computations are presented
in the supplementary material (text S1). All the res-
ults are based on the ensemble mean of the selected
2.2. Causality formalism
The causal inference technique used here is from
Liang’s IF and causality analysis theory rigorously
derived from first principles (e.g. Liang 2014,2016,
2021) and expressed in terms of sample covariances
(Liang 2014). Given two time series X2(e.g. CO2) and
X1(e.g. meanT), the causality from the former to the
latter proves to be measurable by the time rate of the
flow of information from X2to X1, which is given by
In reality, a third (confounding) variable could
influence the interaction between X2and X1(e.g. leaf
area index (LAI)). Liang (2021) extended the form-
alism (S1) to multivariate settings. For a system of d
number of time series, the IF from X2to X1influenced
by confounding variables in the system is given as:
where Cj,d1 is the sample covariance between Xjand
the derived X1using the Euler forward differencing,
and det Crepresents the determinant of the sample
covariance. It is evident that once d=2, (1) reduces
to (S1). Here, we use the normalized IF of T21|3,4,..,d
taken between 100 and 100 (Liang 2021) which
allows us to fairly compare the IF results for different
degrees of emission scenarios. More details are given
in text S2.
Following Liang (2014), we use the Fisher inform-
ation matrix for significance testing since its inverse
gives a covariance matrix with a given significance
level at a 5% significance level. When T21|3,4,..,dis
significant, X2is considered to be causal to X1.
3. Results and discussion
3.1. Causal structure between CO2and mean air
Figure 1shows the separated cause–effect structure
of the interaction, where the two panels show the
IF from CO2to meanT (CO2–meanT) for both his-
torical and future scenarios. We analyze two projec-
tion periods: 2015–2060 (figures 1(b)–(e)) and 2061–
2100 (figures 1(f)–(i)). Overall, figures 1(a)–(i) show
increasing causal strengths and area coverage along
the equator with the evolution of time and increasing
radiative forcing scenarios. That is, causal strengths
are larger toward the end of the century than at the
beginning in SSP5–8.5. The positive IFs suggest that
changes in CO2increase or amplify meanT anomalies
in these regions. The projections also show weakly
negative IF values in the SSP1–2.6 (figures 1(b) and
(f)) which become stronger over the northern hemi-
sphere (NH). This means the CO2impact on SSP1-
2.6 reverses from amplifying variabilities in meanT
to reducing them by the end of the century due to
reduced CO2emissions that lead to reduced meanT
or milder meanT increases. As we move toward the
higher end of the scenarios in figures 1(f)–(i), CO2
increasingly becomes a source of amplifying meanT
changes. However, regions in the NH appear unaf-
fected. This latter part will be explored further in the
following subsection.
Figure 2demonstrates patterns of sources and
sinks for CO2due to meanT changes in the different
emission pathways and at different century periods.
MeanT by itself cannot be a sink or a source for CO2;
therefore, these results are more representative of how
meanT changes drive sink–source factors of CO2. The
historical results in figure 2(a) show that, generally,
the NH serves mildly as a sink while saturations over
the SH lead to more source regions. The strong posit-
ive signals found in the tropics, specifically over the
Amazon and Congo basins, could be linked to the
impact of land-use change in the region. This has
led to tree-cover loss (due to deforestation, forest
fires and logging), eventually making the region more
sensitive to climate warming (Hansen et al 2013).
Forest loss generally increases surface albedo, eventu-
ally leading to decreased evapotranspiration and LAI
(Li et al 2022). As a result, net warming of the region
increases, and CO2uptake is reduced.
In the projections, the results of the scenarios
show that milder pathways (SSP1–2.6 and SSP2–4.5)
do lead to increased CO2sinks (figures 2(b), (c),
(f) and (g)). However, the sources in SSP2–4.5 are
anomalously amplified briefly (figure 2(c)) before
more sinks appear (figure 2(g)). Friedlingstein et al
(2001) showed that after a continuous increase in
CO2emissions, there would be a point of CO2equi-
librium or stabilization over both the land and the
ocean in the future. Therefore, the change in SSP2–
4.5 could be a reflection of that phenomenon. On
the other hand, SSP1–2.6 quickly converges to sink
scenarios due to reduced emissions (figures 2(b) and
(f)). In the high-end scenarios (SSP3–7.0 and SSP5–
8.5), continuous emissions contribute to substantial
decreases in the sink regions found in the historical
and low-end scenario results, which eventually turn
into source regions. As expected, significant temper-
ature increases lead to subsequent emissions of CO2,
especially over the NH, with the strongest impacts
found in SSP5–8.5 (figures 2(e) and (i)). Over the
SH, we observe that a crucial region like the Amazon
basin, which could otherwise function as a sink, turns
into a source by the end of the century. The negative
IFs found in emission scenarios may be considered
as the resilience of global ecosystems to increasing
Environ. Res. Lett. 17 (2022) 124019 D F T Hagan et al
Figure 1. Causality of CO2on meanT for (a) historical periods and (b)–(i) projections for the first period (b)–(e) of the century
(2015–2060) and (b) second period (f)–(i) of the century (2061–2100). Results are obtained at a 5% significance level. White
regions are statistically insignificant causal areas.
meanT to stabilize CO2emissions, thus modulating
the positive climate-carbon feedback.
Although meanT has been shown to correlate
with CO2in previous studies (Kundzewicz et al 2020),
the patterns in the results seem to suggest the influ-
ence of mediating variables such as vegetation and
SM (Papagiannopoulou et al 2017, Green et al 2019).
Apart from their reported impacts on CO2(Lawrence
et al 2018, Green et al 2019, Chen et al 2021),
both vegetation and SM have also been identified as
essential drivers for meanT changes (Schwingshackl
et al 2017, Hagan et al 2019, Yu et al 2020). In the
remainder of the paper, we explore these two factors’
effects in more detail, especially to explain the poten-
tial reasons for the results obtained.
To assess the reliability of our results, a similarity
analysis (Lo and MacKinlay 1989) is also provided in
figures S1 and S2 to show their agreement within the
models in both periods. Generally, the models seem
to agree in most regions in both periods, which lends
confidence to the results obtained in figures 1and 2.
However, care should be taken when interpreting the
results over regions of strong disagreement as they
may require further verification.
3.2. Constraints of LAI and SM on the CO2–meanT
From the CMIP6 framework, we have chosen LAI
as the indicator for vegetation. Here, to assess the
influence of third variables on the coupling, we use
the normalized multivariate IF causality to estimate
the causalities as shown in figures 3(a1)–(e2) for LAI
and figures 4(a3)–(e4) for SM. Figure 3suggests that
the evolution of meanT over land depends primarily
Environ. Res. Lett. 17 (2022) 124019 D F T Hagan et al
Figure 2. Causality of meanT on CO2for (a) historical periods and (b)–(i) projections for the first period (b)–(e) of the century
(2015–2060) and (b) second period (f)–(i) of the century (2061–2100). Results are obtained at a 5% significance level. White
regions are statistically insignificant causal areas.
on CO2emissions in this interaction. Nonetheless,
there are signs of the influences of LAI and SM. Sim-
ilar to what we observed in figure 1, CO2amplifies
meanT variability more in the higher-end scenarios,
and by the end of the century most strongly near the
equator, especially over the Amazon and the Congo
basins. This could be related to the reported turning
point of the Amazon rainforest where positive feed-
back between vegetation and CO2will break down
at some point in the future due to oversaturation
of the net biospheric uptake of CO2(Friedlingstein
et al 2001) and unfavorable temperatures (Cox et al
2004, Doughty and Goulden 2008). This has been
suggested to already be on the brink even in historical
records (Huang et al 2019). A similar situation may
apply to the Congo basin. In the high-end scenarios
of figures 3(b1)–(e3), significant emissions of CO2
lead to saturations of uptake capacities over these
regions that could have otherwise served as sinks due
to decreased photosynthesis (Green et al 2020).
Figures 3(b) and (c) also show that in the SSP1–
2.6, reductions (negative IFs) in CO2–meanT appear
to be stronger over the NH, although the strength
of these reductions decreases with increasing emis-
sion scenarios. The faint reductions found in the
NH of the high-end scenarios suggest that in the
high-end emissions, LAI and SM continue to func-
tion as constraints on amplifying meanT variabil-
ity over land (figures 3(a1)–(e2)) due to impacts
on CO2and meanT, hence the CO2–meanT coup-
ling. In fact, regions where their constraints are
strongest in the SSP1–2.6 causality are where we
Environ. Res. Lett. 17 (2022) 124019 D F T Hagan et al
Figure 3. Causality of CO2on meanT with impacts due to LAI changes for (a1) historical periods and (b1)–(e2) projections
(other columns) for the (a1)–(e1) first period of the century (2015–2060) and (a2)–(e2) second period of the century
(2061–2100). Results are obtained at a 5% significance level. White regions are not statistically significant causal areas.
(b3)–(e4) are the same as (a1)–(e2), but here the coupling is influenced by changes in SM.
find the weakest or most insignificant IFs in SSP3–
7.0 and SSP5–8.5 CO2–meanT coupling of the lat-
ter part of the century in figures 1(b)–(e) and 3(b2)–
(e2). That is, meanT anomalies would be more
significant in the high-end scenarios if there were
no constraints on the positive climate-carbon feed-
back. This could represent ecosystem resilience to
changes in the carbon-climate feedback that slows
down the impact of CO2on meanT throughout the
3.3. Constraints of LAI and SM on the meanT–CO2
Figures 4(a1)–(e4) explore the influences of LAI and
SM changes on the other side of the separated-
interaction meanT–CO2causality. Figures 4(a1)–
(e2) indicate places where changes in the LAI func-
tion influence meanT–CO2causality. Negative IFs
indicate that LAI contributes to the reductions in
the meanT–CO2causality, and positive IFs indic-
ate regions where LAI contributes to amplifying the
meanT–CO2causality. First, a distinct latitudinal spa-
tial pattern can be observed globally from the his-
torical results and projections. Over the NH, LAI
amplifies the coupling variability, especially over the
Eurasian region, mainly in the low-end scenarios.
This is strongest in SSP1–2.6, which intensifies in the
second half of the projected period (figures (b1) and
(b2)). In figures 4(b1)–(e2), the strong intensification
reduces with increasing emission scenarios. Negative
IFs appear over the high-latitude regions in SSP5-8.5,
although the positive IF regions appear to have moved
into the Mediterranean regions, southern USA and
eastern parts of Brazil, possibly owing to increased
arid conditions, eventually increasing uncertainties
in the meanT–CO2causality there. Over the SH, the
historical results show positive IF due to the influ-
ence of LAI on the causality. However, all the projec-
tions show negative IFs appearing to get stronger with
time and increasing scenarios. This implies that LAI
influences reductions in the variability of the causality
and consequently reductions in CO2variability due to
changes in mean Zhu et al (2016) found that climate
change resulted in greening over high latitudes. This
greening could explain the increases in the negative
IFs since greening would also increase photosynthesis
and eventually increase CO2sinks, as found in the
The impact of SM on the coupling, as shown in
figures 4(c) and (d), appears to have a latitudinal con-
trast with the impact of LAI. While the impact of LAI
on the coupling shows strong positive IF values over
the NH in the low-end SSPs (figures 4(a3)–(e3)), the
impact of SM on the coupling shows positive IF val-
ues over the SH in the first period. The historical res-
ults show that SM tends to reduce the strength of
the meanT–CO2causality over the NH and ampli-
fies it over the SH. In SSP1–2.6, SM changes reduce
the increases in CO2variability due to SM influ-
ences on meanT changes (meanT– CO2|SM) mainly
Environ. Res. Lett. 17 (2022) 124019 D F T Hagan et al
Figure 4. Causality of meanT on CO2influenced by LAI (green-red) changes for (a1) historical periods and (b1)–(e2) projections
(other columns) for the (a1)–(e1) first period of the century (2015–2060) and (a2)–(e2) second period of the century
(2061–2100). Results are obtained at a 5% significance level. White regions are statistically insignificant causal areas. (b3)–(e4) are
the same as (a1)–(e2), but here the coupling is influenced by changes in SM.
in the NH in the first period and extend into the
SH by the end of the second period of the 21st cen-
tury (figures 4(b3) and 4(b4)). This could probably
be because SM serves as a cooling effect on near-
surface air temperature, which changes its impact on
CO2variabilities by increasing photosynthesis. Posit-
ive IFs increase in the NH during the first period with
increasing emission scenarios (figures 4(b3)–(e3)). In
the high-end scenarios, the negative IF values over
the NH change into positive IF values in the second
period of the century. Green et al (2019) suggested
that the carbon sinks due to SM might shift toward
source functions from mid-century leading to CO2
growth in the positive IF regions of figures 4(b3)–(e3)
possibly owing to the impact on photosynthesis. We
find a contrast in these patterns in the SH due to sea-
sonally varying hemispheric conditions which char-
acterize SM (Miralles et al 2012) and vegetation (Wu
et al 2015) interaction with the atmosphere.
3.4. Cross-comparison of the influences of LAI and
SM on the couplings
To highlight what the influences of LAI and SM on
the separated couplings look like, their causalities on
the CO2and meanT couplings are binned over his-
torical LAI and SM climatologies respectively, after
which we plot them against each other for the his-
torical (black), SSP1–2.6 (green), and SSP5–8.5 (red)
for both projection periods (figure 5). Figures 5(a)
and (b) represent the impact on the CO2–meanT
coupling, and figures 5(c) and (d) represent the
impact on the meanT–CO2coupling. The results
demonstrate a positive linear relationship between
them, which intensified in the second century period.
SSP1–2.6 and historical results have very similar
causal strengths in the first period. However, both
factors are observed in the second period to reduce
temperature variability amplification due to changes
in CO2, albeit stronger in SSP1–2.6, shown by the
increases in the negative IF values (figure 5(b)). In
the high-end projection, SSP5–8.5, the CO2–meanT
causality mainly increases. Thus, in the SSP1–2.6,
LAI and SM reduce the coupling strength possibly by
being sinks to CO2, which reduces with increasing
emissions (figures 5(a) and (b)). Overall, the results
in figures 5(a) and (b) suggest that both factors func-
tion similarly to constrain the causality of CO2on
meanT, which was found to be strongest in SSP1–2.6
and make the CO2–meanT in SSP5–8.5 more uncer-
tain with a positive IF rate.
In the meanT–CO2causality, we find an inverse
relationship with how SM and LAI impact the high-
and low-end scenarios of the meanT–CO2causality,
as seen in figures 5(c) and (d). As discussed above and
seen in figures 5(a) and (b), the impacts in figures 5(c)
and (d) also increase from the first to the second
period relative to the historical records. Figure 5(d)
shows that these two factors play significant roles in
modulating the coupling at the end of the century,
whereby SM intensifies the meanT–CO2causality in
Environ. Res. Lett. 17 (2022) 124019 D F T Hagan et al
Figure 5. Cross-comparison of the influences of SM and LAI on the separated causalities within the CO2–meanT interaction for
both the first and second periods. Here only the historical (black), SSP1–2.6 (green) and SSP5–8.5 (red) are shown for the
CO2–meanT (a), (b) and meanT–CO2(c), (d) causalities. y-axes show coupling results with the influence of SM and x-axes show
coupling results with the influence of LAI. The top panels show the results of 2015–2060 and the bottom panels show 2061–2100.
SSP5–8.5 but LAI reduces it in SSP1–2.6. Contrary to
the impact on the CO2–meanT coupling, figures 5(c)
and (d) show that when LAI serves as a sink, SM
serves as a source in the meanT–CO2of SSP5–8.5. The
opposite is seen for SSP1–2.6.
4. Conclusion
In this study, we investigated the causal structure
between near-surface air temperature and CO2using
localized spatial scales (pixel-wise) over short time
scales (seasonal mean variations of monthly anom-
alies where their climatologies are removed) using an
IF causality approach. Additionally, these localized
analyses provided indications of sink–source patterns
in the interaction. The projection period (2016–2100)
was divided into two: the first period 2016–2060 and
the second period 2061–2100 to better understand the
evolution of the causal structures over time.
The results indicate that, as identified in previous
studies, a mutual causality exists within this interac-
tion, although the spatial and temporal characteristics
of the separated causalities are unique. The projection
results for the different pathways, representing scen-
arios of radiative forcing, show that the global CO2
meanT causal relation gets stronger with increasing
emission scenarios, with the strongest found in SSP5–
8.5. Additionally, the areal extent of significant IF
from global CO2to meanT also increases from just
the tropical regions into the high latitudinal regions.
Contrasting latitudinal patterns are observed globally
in the other direction of the interaction, meanT–CO2.
These patterns were found to have both spatial and
temporal changes for the low-end scenarios (SSP1–
2.6, SSP2–4.5) and the high-end scenarios (SSP3–7.0,
SSP5–8.5). CO2sinks mainly dominated SSP1–2.6
and SSP2–4.5 (negative IF), especially in their second
periods where regions that were initially strong posit-
ive IFs (CO2sources) had become weakly positive or
negative IF regions.
On the other hand, SSP3–7.0 and SSP5–8.5 pat-
terns were predominantly strong positive IF values,
especially over the NH. To an appreciable degree,
the spatial pattern over land agrees with the results
obtained in the study by Levy et al (2004), explained
as the impact of land use and land cover change
on CO2variability. This attribution to land cover
change was also noted by Zhu et al (2016). Addi-
tionally, some studies have reported the possible role
of vegetation (here indicated with LAI) and SM on
this interaction because of their sink-source functions
on CO2as well as their impacts on near-surface air
Environ. Res. Lett. 17 (2022) 124019 D F T Hagan et al
temperatures (Zhu et al 2016, Green et al 2019). Thus,
we also assessed the roles of these two parameters on
the projection outcomes.
A detailed study on the impacts of SM and LAI
on the interaction revealed that they impact the separ-
ated causalities (CO2–meanT and meanT–CO2) quite
differently. While both function together to constrain
the CO2–meanT coupling strengths in all the emis-
sion scenarios, they inversely affect the meanT–CO2
coupling strength by the end of the century. This
is due to their changing roles as sources and sinks
for CO2and their modulation of meanT anomalies
to either intensify or cool near-surface temperatures
reported in previous studies (Zscheischler et al 2015,
Schwingshackl et al 2017, Hagan et al 2019). Thus,
both SM and LAI can help us understand the resi-
lience of global ecosystems to changes in the CO2
and meanT interaction within a simplified frame-
work as in this study. However, further studies, like
sensitivity experiments, are required to understand
the mechanisms leading to these results since these so-
called causal tools only assess effects and not mech-
anisms. Furthermore, it may be necessary to assess
how CO2emissions during the COVID-19 pandemic
would impact these results in future studies as already
preliminarily identified by Liu et al (2022). Finally, we
note that although Liang (2018) showed that the caus-
ality formalism could be applied to a highly nonlinear
case to obtain reasonable causal inferences, the res-
ults may not be as precise as expected in some cases
because of the linear assumptions invoked in the for-
mulation of the approach (Liang 2021).
Data availability statement
The data that support the findings of this study are
openly available at the following URL/DOI: https://
This research was funded by the National Natural
Science Foundation of China (Grant No. 41875094)
and the Jiangsu Postdoctoral Research Funding Pro-
gram (Grant No. 2021K302C). We are also extremely
grateful to Pierre Friedlingstein, X San Liang and
the three anonymous reviewers for their very help-
ful suggestions and comments. We acknowledge
the World Climate Research Programme (WCRP)—
Working Group on Coupled Modelling for coordin-
ating and promoting CMIP6. We also appreciate
the different climate modeling groups for producing
and making available their model output, and the
Earth System Grid Federation (ESGF) for archiving
the data and providing access. The multiple fund-
ing agencies supporting CMIP6 and ESGF are also
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