greening and browning in response to the effects of rising co2 - … · 2020. 5. 2. · alexander...
TRANSCRIPT
-
Alexander J. Winkler*, Ranga B. Myneni, Alexis Hannart, and Victor Brovkin
May 5, 2020
Greening and Browning in Response to the Effects of Rising CO2Driver Attribution Using Causal Theory
-
Winkler, 2020 DOI: 10.17617/2.3190373
What is driving the observed changes in natural vegetation?
�2
• Human dominated land surface is greening due to land management (Chen et al., 2019).
• Rising CO2 as driver of changes in natural vegetation is debated:
– CO2 fertilization explain 70% of the global greening trend (Zhu et al., 2016).
– However, no significant increase in leaf area under elevated CO2 in field studies (e.g. Norby et al. 2003).
• A rigorous regional attribution at biome-level of what is behind the observed changes is currently lacking.
Our approach:
• Analyze multi-decadal satellite observations of natural vegetation
• Disentangle the effects of CO2 in idealized model simulations
• Apply Causal Theory for driver attribution on biome scale*
* here only tropical forests and northern ecosystems are shown
http://hdl.handle.net/21.11116/0000-0005-9396-B
-
Winkler, 2020 DOI: 10.17617/2.3190373
How Rising CO2 Affects Plant Productivity
�3
Radiative effect (RE): Climatic changesPhysiological effect (PE): CO2 fertilization
1. Stimulation of carbon fixation
radiation (cloudiness)
precipitationtemperature
2. Enhancement of water-use efficiency
↓H2O
↑CO2
RuBisCO enzyme
↑CO2O2
↑Carbon assimilationPhotorespiration
Stomata
Plant productivity can be affected either way:
↑ Increase due to e.g. warming or increased rainfall ↓ Decline due to e.g. drying or disturbances
http://hdl.handle.net/21.11116/0000-0005-9396-B
-
Winkler, 2020 DOI: 10.17617/2.3190373
Observed Patterns of Greening and Browning
• CO2 increased by 65 ppm throughout the satellite era (1982 to 2017).
• Satellite observations of leaf area index (LAI, leaf area per unit ground area).
• 54% of Earth’s natural vegetation exhibit significant* trends:
- Greening: 40%
- Browning: 14%
�4
AVHRR LAI3g
* Mann-Kendall test ( p < 0.1 )
http://hdl.handle.net/21.11116/0000-0005-9396-B
-
Winkler, 2020 DOI: 10.17617/2.3190373
Driver Attribution Using Causal Theory
�5
Probability of Necessary Causation
Probability of Sufficient Causation
Probability of Necessary and Sufficient Causation
EG
results,andstreamliningthecommunicationofcausal
claims—inparticularwhenitcomestothequantification
ofuncertainty,thatis,oftheprobabilitythatagiven
forcinghascausedagivenobservedphenomenon.
Here,weadaptsomeformaldefinitionsofcausality
andprobabilityofcausationtothecontextofclimate
changeattribution.Then,wedetailtechnicalimple-
mentationunderstandardassumptionsusedinD&A.
Themethodisfinallyillustratedonthewarmingob-
servedoverthetwentiethcentury.
2.Causalcounterfactualtheory
Whileanoverviewofcausaltheorycannotberepeated
here,itisnecessaryforclarityandself-containednessto
highlightitskeyideasandmostrelevantconceptsforthe
presentdiscussion.
Letusfirstrecalltheso-calledcounterfactualdefini-
tionofcausalitybyquotingtheeighteenth-century
ScottishphilosopherDavidHume:‘‘Wemaydefinea
causetobeanobjectfollowedbyanother,where,ifthe
firstobjecthadnotbeen,thesecondneverhadexisted.’’
Inotherwords,aneventE(Estandsforeffect)iscaused
byaneventC(Cstandsforcause)ifandonlyifEwould
notoccurwereitnotforC.Notethatthewordeventis
usedhereinitsgeneral,mathematicalsenseofasubset
ofasamplespaceV.Accordingtothisdefinition,evi-
dencingcausalityrequiresacounterfactualapproachby
whichoneinquireswhetherornottheeventEwould
haveoccurredinahypotheticalworld,termedcoun-
terfactual,inwhichtheeventCwouldnothaveoc-
curred.Thefundamentalapproachofcausalitythatis
impliedbythisdefinitionisstillentirelyrelevantin
thestandardcausaltheory.Itmayalsoarguablybe
connectedtotheguidanceprinciplesoftheconventional
climatechangeattributionframeworkandtotheopti-
malfingerprintingmodels,inaqualitativemanner.The
mainvirtueofthestandardcausalitytheoryofPearl
consistsinourviewinformalizingpreciselytheabove
qualitativedefinition,thusallowingforsoundquantita-
tivedevelopments.Aprominentfeatureofthistheory
consistsinfirstrecognizingthatcausationcorresponds
toratherdifferentsituationsandthatthreedistinct
facetsofcausalityshouldbedistinguished:(i)necessary
causation,wheretheoccurrenceofErequiresthatofC
butmayalsorequireotherfactors;(ii)sufficientcausa-
tion,wheretheoccurrenceofCdrivesthatofEbutmay
notberequiredforEtooccur;and(iii)necessaryand
sufficientcausation,where(i)and(ii)bothhold.The
fundamentaldistinctionbetweenthesethreefacetscan
bevisualizedbyusingthesimpleillustrationshownin
Fig.1.
Whilethecounterfactualdefinitionaswellasthe
threefacetsofcausalitydescribedabovemaybeun-
derstoodatfirstinafullydeterministicsense,perhaps
themainstrengthofPearl’sformalizationistopropose
anextensionofthesedefinitionsunderaprobabilistic
setting.Theprobabilitiesofcausationaretherebyde-
finedasfollow:
PS(C/
E)5PhEjdo(C),C,Ei,
(3a)
PN(C/
E)5PhEjdo(C),C,Ei,
(3b)
PNS(C/
E)5PhEjdo(C),Ejdo(C)i,
(3c)
whereCandEarethecomplementariesofCandE,and
wherethenotationdo(.)meansthataninterventionis
appliedtothesystemundercausalinvestigation.For
instancePS,theprobabilityofsufficientcausation,reads
fromtheabovethattheprobabilitythatEoccurswhen
Cisinterventionallyforcedtooccur,conditionalonthe
factthatneitherCnorEwasoccurringinthefirstplace.
ConverselyPN,theprobabilityofnecessarycausation,is
definedastheprobabilitythatEwouldnotoccurwhenC
isinterventionallyforcedtonotoccur,conditionalon
thefactthatbothCandEwereoccurringinthefirst
place.Whileweomitheretheformaldefinitionofthe
interventiondo(.)forbrevity,thelattercanbeunder-
stoodmerelyasexperimentation:applyingthesedefi-
nitionsthusrequirestheabilitytoexperiment.Real
experimentation,whetherinsituorinvivo,isoftenac-
cessibleinmanyfieldsbutitisnotinclimateresearchfor
obviousreasons.Inthiscase,onecanthusonlyrelyon
numericalinsilicoexperimentation:theimplicationsof
thisconstraintarediscussedfurther.
Whiletheprobabilitiesofcausationarenoteasily
computableingeneral,theirexpressionfortunately
FIG.1.Thethreefacetsofcausality.(a)BulbEcanneverbelit
unlessswitchC1ison,yetactivatingC1doesnotalwaysresultin
lightingEasthisalsorequiresturningonC2:turningonC1isthus
anecessarycauseofElighting,butnotasufficientone.(b)Eislit
anytimeC1isturnedon,yetifC1isturnedoffEmaystillbelitby
activatingC2:turningonC1isthusasufficientcauseofElighting,
butnotanecessaryone.(c)TurningonC1alwayslightsE,andE
maynotbelightedunlessC1ison:turningonC1isthusanecessary
andsufficientcauseofElighting.
15JULY2018
HANNART
AND
NAVEAU
5509
C1
C2CPE
CRE
EG
results,andstreamliningthecommunicationofcausal
claims—inparticularwhenitcomestothequantification
ofuncertainty,thatis,oftheprobabilitythatagiven
forcinghascausedagivenobservedphenomenon.
Here,weadaptsomeformaldefinitionsofcausality
andprobabilityofcausationtothecontextofclimate
changeattribution.Then,wedetailtechnicalimple-
mentationunderstandardassumptionsusedinD&A.
Themethodisfinallyillustratedonthewarmingob-
servedoverthetwentiethcentury.
2.Causalcounterfactualtheory
Whileanoverviewofcausaltheorycannotberepeated
here,itisnecessaryforclarityandself-containednessto
highlightitskeyideasandmostrelevantconceptsforthe
presentdiscussion.
Letusfirstrecalltheso-calledcounterfactualdefini-
tionofcausalitybyquotingtheeighteenth-century
ScottishphilosopherDavidHume:‘‘Wemaydefinea
causetobeanobjectfollowedbyanother,where,ifthe
firstobjecthadnotbeen,thesecondneverhadexisted.’’
Inotherwords,aneventE(Estandsforeffect)iscaused
byaneventC(Cstandsforcause)ifandonlyifEwould
notoccurwereitnotforC.Notethatthewordeventis
usedhereinitsgeneral,mathematicalsenseofasubset
ofasamplespaceV.Accordingtothisdefinition,evi-
dencingcausalityrequiresacounterfactualapproachby
whichoneinquireswhetherornottheeventEwould
haveoccurredinahypotheticalworld,termedcoun-
terfactual,inwhichtheeventCwouldnothaveoc-
curred.Thefundamentalapproachofcausalitythatis
impliedbythisdefinitionisstillentirelyrelevantin
thestandardcausaltheory.Itmayalsoarguablybe
connectedtotheguidanceprinciplesoftheconventional
climatechangeattributionframeworkandtotheopti-
malfingerprintingmodels,inaqualitativemanner.The
mainvirtueofthestandardcausalitytheoryofPearl
consistsinourviewinformalizingpreciselytheabove
qualitativedefinition,thusallowingforsoundquantita-
tivedevelopments.Aprominentfeatureofthistheory
consistsinfirstrecognizingthatcausationcorresponds
toratherdifferentsituationsandthatthreedistinct
facetsofcausalityshouldbedistinguished:(i)necessary
causation,wheretheoccurrenceofErequiresthatofC
butmayalsorequireotherfactors;(ii)sufficientcausa-
tion,wheretheoccurrenceofCdrivesthatofEbutmay
notberequiredforEtooccur;and(iii)necessaryand
sufficientcausation,where(i)and(ii)bothhold.The
fundamentaldistinctionbetweenthesethreefacetscan
bevisualizedbyusingthesimpleillustrationshownin
Fig.1.
Whilethecounterfactualdefinitionaswellasthe
threefacetsofcausalitydescribedabovemaybeun-
derstoodatfirstinafullydeterministicsense,perhaps
themainstrengthofPearl’sformalizationistopropose
anextensionofthesedefinitionsunderaprobabilistic
setting.Theprobabilitiesofcausationaretherebyde-
finedasfollow:
PS(C/
E)5PhEjdo(C),C,Ei,
(3a)
PN(C/
E)5PhEjdo(C),C,Ei,
(3b)
PNS(C/
E)5PhEjdo(C),Ejdo(C)i,
(3c)
whereCandEarethecomplementariesofCandE,and
wherethenotationdo(.)meansthataninterventionis
appliedtothesystemundercausalinvestigation.For
instancePS,theprobabilityofsufficientcausation,reads
fromtheabovethattheprobabilitythatEoccurswhen
Cisinterventionallyforcedtooccur,conditionalonthe
factthatneitherCnorEwasoccurringinthefirstplace.
ConverselyPN,theprobabilityofnecessarycausation,is
definedastheprobabilitythatEwouldnotoccurwhenC
isinterventionallyforcedtonotoccur,conditionalon
thefactthatbothCandEwereoccurringinthefirst
place.Whileweomitheretheformaldefinitionofthe
interventiondo(.)forbrevity,thelattercanbeunder-
stoodmerelyasexperimentation:applyingthesedefi-
nitionsthusrequirestheabilitytoexperiment.Real
experimentation,whetherinsituorinvivo,isoftenac-
cessibleinmanyfieldsbutitisnotinclimateresearchfor
obviousreasons.Inthiscase,onecanthusonlyrelyon
numericalinsilicoexperimentation:theimplicationsof
thisconstraintarediscussedfurther.
Whiletheprobabilitiesofcausationarenoteasily
computableingeneral,theirexpressionfortunately
FIG.1.Thethreefacetsofcausality.(a)BulbEcanneverbelit
unlessswitchC1ison,yetactivatingC1doesnotalwaysresultin
lightingEasthisalsorequiresturningonC2:turningonC1isthus
anecessarycauseofElighting,butnotasufficientone.(b)Eislit
anytimeC1isturnedon,yetifC1isturnedoffEmaystillbelitby
activatingC2:turningonC1isthusasufficientcauseofElighting,
butnotanecessaryone.(c)TurningonC1alwayslightsE,andE
maynotbelightedunlessC1ison:turningonC1isthusanecessary
andsufficientcauseofElighting.
15JULY2018
HANNART
AND
NAVEAU
5509
results,andstreamliningthecommunicationofcausal
claims—inparticularwhenitcomestothequantification
ofuncertainty,thatis,oftheprobabilitythatagiven
forcinghascausedagivenobservedphenomenon.
Here,weadaptsomeformaldefinitionsofcausality
andprobabilityofcausationtothecontextofclimate
changeattribution.Then,wedetailtechnicalimple-
mentationunderstandardassumptionsusedinD&A.
Themethodisfinallyillustratedonthewarmingob-
servedoverthetwentiethcentury.
2.Causalcounterfactualtheory
Whileanoverviewofcausaltheorycannotberepeated
here,itisnecessaryforclarityandself-containednessto
highlightitskeyideasandmostrelevantconceptsforthe
presentdiscussion.
Letusfirstrecalltheso-calledcounterfactualdefini-
tionofcausalitybyquotingtheeighteenth-century
ScottishphilosopherDavidHume:‘‘Wemaydefinea
causetobeanobjectfollowedbyanother,where,ifthe
firstobjecthadnotbeen,thesecondneverhadexisted.’’
Inotherwords,aneventE(Estandsforeffect)iscaused
byaneventC(Cstandsforcause)ifandonlyifEwould
notoccurwereitnotforC.Notethatthewordeventis
usedhereinitsgeneral,mathematicalsenseofasubset
ofasamplespaceV.Accordingtothisdefinition,evi-
dencingcausalityrequiresacounterfactualapproachby
whichoneinquireswhetherornottheeventEwould
haveoccurredinahypotheticalworld,termedcoun-
terfactual,inwhichtheeventCwouldnothaveoc-
curred.Thefundamentalapproachofcausalitythatis
impliedbythisdefinitionisstillentirelyrelevantin
thestandardcausaltheory.Itmayalsoarguablybe
connectedtotheguidanceprinciplesoftheconventional
climatechangeattributionframeworkandtotheopti-
malfingerprintingmodels,inaqualitativemanner.The
mainvirtueofthestandardcausalitytheoryofPearl
consistsinourviewinformalizingpreciselytheabove
qualitativedefinition,thusallowingforsoundquantita-
tivedevelopments.Aprominentfeatureofthistheory
consistsinfirstrecognizingthatcausationcorresponds
toratherdifferentsituationsandthatthreedistinct
facetsofcausalityshouldbedistinguished:(i)necessary
causation,wheretheoccurrenceofErequiresthatofC
butmayalsorequireotherfactors;(ii)sufficientcausa-
tion,wheretheoccurrenceofCdrivesthatofEbutmay
notberequiredforEtooccur;and(iii)necessaryand
sufficientcausation,where(i)and(ii)bothhold.The
fundamentaldistinctionbetweenthesethreefacetscan
bevisualizedbyusingthesimpleillustrationshownin
Fig.1.
Whilethecounterfactualdefinitionaswellasthe
threefacetsofcausalitydescribedabovemaybeun-
derstoodatfirstinafullydeterministicsense,perhaps
themainstrengthofPearl’sformalizationistopropose
anextensionofthesedefinitionsunderaprobabilistic
setting.Theprobabilitiesofcausationaretherebyde-
finedasfollow:
PS(C/
E)5PhEjdo(C),C,Ei,
(3a)
PN(C/
E)5PhEjdo(C),C,Ei,
(3b)
PNS(C/
E)5PhEjdo(C),Ejdo(C)i,
(3c)
whereCandEarethecomplementariesofCandE,and
wherethenotationdo(.)meansthataninterventionis
appliedtothesystemundercausalinvestigation.For
instancePS,theprobabilityofsufficientcausation,reads
fromtheabovethattheprobabilitythatEoccurswhen
Cisinterventionallyforcedtooccur,conditionalonthe
factthatneitherCnorEwasoccurringinthefirstplace.
ConverselyPN,theprobabilityofnecessarycausation,is
definedastheprobabilitythatEwouldnotoccurwhenC
isinterventionallyforcedtonotoccur,conditionalon
thefactthatbothCandEwereoccurringinthefirst
place.Whileweomitheretheformaldefinitionofthe
interventiondo(.)forbrevity,thelattercanbeunder-
stoodmerelyasexperimentation:applyingthesedefi-
nitionsthusrequirestheabilitytoexperiment.Real
experimentation,whetherinsituorinvivo,isoftenac-
cessibleinmanyfieldsbutitisnotinclimateresearchfor
obviousreasons.Inthiscase,onecanthusonlyrelyon
numericalinsilicoexperimentation:theimplicationsof
thisconstraintarediscussedfurther.
Whiletheprobabilitiesofcausationarenoteasily
computableingeneral,theirexpressionfortunately
FIG.1.Thethreefacetsofcausality.(a)BulbEcanneverbelit
unlessswitchC1ison,yetactivatingC1doesnotalwaysresultin
lightingEasthisalsorequiresturningonC2:turningonC1isthus
anecessarycauseofElighting,butnotasufficientone.(b)Eislit
anytimeC1isturnedon,yetifC1isturnedoffEmaystillbelitby
activatingC2:turningonC1isthusasufficientcauseofElighting,
butnotanecessaryone.(c)TurningonC1alwayslightsE,andE
maynotbelightedunlessC1ison:turningonC1isthusanecessary
andsufficientcauseofElighting.
15JULY2018
HANNART
AND
NAVEAU
5509
CRE
CPE
What is the probability that a given forcing has caused a long-term change in the system?
Event E: occurrence of long-term change in the system, e.g. greening (EG)
Cause C: presence of given forcing, e.g. radiative (CRE) or physiological (CPE) effect of CO2
References: Pearl, 2009 Hannart & Naveau, 2018
PNS
EG
results,andstreamliningthecommunicationofcausal
claims—inparticularwhenitcomestothequantification
ofuncertainty,thatis,oftheprobabilitythatagiven
forcinghascausedagivenobservedphenomenon.
Here,weadaptsomeformaldefinitionsofcausality
andprobabilityofcausationtothecontextofclimate
changeattribution.Then,wedetailtechnicalimple-
mentationunderstandardassumptionsusedinD&A.
Themethodisfinallyillustratedonthewarmingob-
servedoverthetwentiethcentury.
2.Causalcounterfactualtheory
Whileanoverviewofcausaltheorycannotberepeated
here,itisnecessaryforclarityandself-containednessto
highlightitskeyideasandmostrelevantconceptsforthe
presentdiscussion.
Letusfirstrecalltheso-calledcounterfactualdefini-
tionofcausalitybyquotingtheeighteenth-century
ScottishphilosopherDavidHume:‘‘Wemaydefinea
causetobeanobjectfollowedbyanother,where,ifthe
firstobjecthadnotbeen,thesecondneverhadexisted.’’
Inotherwords,aneventE(Estandsforeffect)iscaused
byaneventC(Cstandsforcause)ifandonlyifEwould
notoccurwereitnotforC.Notethatthewordeventis
usedhereinitsgeneral,mathematicalsenseofasubset
ofasamplespaceV.Accordingtothisdefinition,evi-
dencingcausalityrequiresacounterfactualapproachby
whichoneinquireswhetherornottheeventEwould
haveoccurredinahypotheticalworld,termedcoun-
terfactual,inwhichtheeventCwouldnothaveoc-
curred.Thefundamentalapproachofcausalitythatis
impliedbythisdefinitionisstillentirelyrelevantin
thestandardcausaltheory.Itmayalsoarguablybe
connectedtotheguidanceprinciplesoftheconventional
climatechangeattributionframeworkandtotheopti-
malfingerprintingmodels,inaqualitativemanner.The
mainvirtueofthestandardcausalitytheoryofPearl
consistsinourviewinformalizingpreciselytheabove
qualitativedefinition,thusallowingforsoundquantita-
tivedevelopments.Aprominentfeatureofthistheory
consistsinfirstrecognizingthatcausationcorresponds
toratherdifferentsituationsandthatthreedistinct
facetsofcausalityshouldbedistinguished:(i)necessary
causation,wheretheoccurrenceofErequiresthatofC
butmayalsorequireotherfactors;(ii)sufficientcausa-
tion,wheretheoccurrenceofCdrivesthatofEbutmay
notberequiredforEtooccur;and(iii)necessaryand
sufficientcausation,where(i)and(ii)bothhold.The
fundamentaldistinctionbetweenthesethreefacetscan
bevisualizedbyusingthesimpleillustrationshownin
Fig.1.
Whilethecounterfactualdefinitionaswellasthe
threefacetsofcausalitydescribedabovemaybeun-
derstoodatfirstinafullydeterministicsense,perhaps
themainstrengthofPearl’sformalizationistopropose
anextensionofthesedefinitionsunderaprobabilistic
setting.Theprobabilitiesofcausationaretherebyde-
finedasfollow:
PS(C/
E)5PhEjdo(C),C,Ei,
(3a)
PN(C/
E)5PhEjdo(C),C,Ei,
(3b)
PNS(C/
E)5PhEjdo(C),Ejdo(C)i,
(3c)
whereCandEarethecomplementariesofCandE,and
wherethenotationdo(.)meansthataninterventionis
appliedtothesystemundercausalinvestigation.For
instancePS,theprobabilityofsufficientcausation,reads
fromtheabovethattheprobabilitythatEoccurswhen
Cisinterventionallyforcedtooccur,conditionalonthe
factthatneitherCnorEwasoccurringinthefirstplace.
ConverselyPN,theprobabilityofnecessarycausation,is
definedastheprobabilitythatEwouldnotoccurwhenC
isinterventionallyforcedtonotoccur,conditionalon
thefactthatbothCandEwereoccurringinthefirst
place.Whileweomitheretheformaldefinitionofthe
interventiondo(.)forbrevity,thelattercanbeunder-
stoodmerelyasexperimentation:applyingthesedefi-
nitionsthusrequirestheabilitytoexperiment.Real
experimentation,whetherinsituorinvivo,isoftenac-
cessibleinmanyfieldsbutitisnotinclimateresearchfor
obviousreasons.Inthiscase,onecanthusonlyrelyon
numericalinsilicoexperimentation:theimplicationsof
thisconstraintarediscussedfurther.
Whiletheprobabilitiesofcausationarenoteasily
computableingeneral,theirexpressionfortunately
FIG.1.Thethreefacetsofcausality.(a)BulbEcanneverbelit
unlessswitchC1ison,yetactivatingC1doesnotalwaysresultin
lightingEasthisalsorequiresturningonC2:turningonC1isthus
anecessarycauseofElighting,butnotasufficientone.(b)Eislit
anytimeC1isturnedon,yetifC1isturnedoffEmaystillbelitby
activatingC2:turningonC1isthusasufficientcauseofElighting,
butnotanecessaryone.(c)TurningonC1alwayslightsE,andE
maynotbelightedunlessC1ison:turningonC1isthusanecessary
andsufficientcauseofElighting.
15JULY2018
HANNART
AND
NAVEAU
5509
CRE CPE
High PNS reflects evidence for the existence of a causal relationship.
results,andstreamliningthecommunicationofcausal
claims—inparticularwhenitcomestothequantification
ofuncertainty,thatis,oftheprobabilitythatagiven
forcinghascausedagivenobservedphenomenon.
Here,weadaptsomeformaldefinitionsofcausality
andprobabilityofcausationtothecontextofclimate
changeattribution.Then,wedetailtechnicalimple-
mentationunderstandardassumptionsusedinD&A.
Themethodisfinallyillustratedonthewarmingob-
servedoverthetwentiethcentury.
2.Causalcounterfactualtheory
Whileanoverviewofcausaltheorycannotberepeated
here,itisnecessaryforclarityandself-containednessto
highlightitskeyideasandmostrelevantconceptsforthe
presentdiscussion.
Letusfirstrecalltheso-calledcounterfactualdefini-
tionofcausalitybyquotingtheeighteenth-century
ScottishphilosopherDavidHume:‘‘Wemaydefinea
causetobeanobjectfollowedbyanother,where,ifthe
firstobjecthadnotbeen,thesecondneverhadexisted.’’
Inotherwords,aneventE(Estandsforeffect)iscaused
byaneventC(Cstandsforcause)ifandonlyifEwould
notoccurwereitnotforC.Notethatthewordeventis
usedhereinitsgeneral,mathematicalsenseofasubset
ofasamplespaceV.Accordingtothisdefinition,evi-
dencingcausalityrequiresacounterfactualapproachby
whichoneinquireswhetherornottheeventEwould
haveoccurredinahypotheticalworld,termedcoun-
terfactual,inwhichtheeventCwouldnothaveoc-
curred.Thefundamentalapproachofcausalitythatis
impliedbythisdefinitionisstillentirelyrelevantin
thestandardcausaltheory.Itmayalsoarguablybe
connectedtotheguidanceprinciplesoftheconventional
climatechangeattributionframeworkandtotheopti-
malfingerprintingmodels,inaqualitativemanner.The
mainvirtueofthestandardcausalitytheoryofPearl
consistsinourviewinformalizingpreciselytheabove
qualitativedefinition,thusallowingforsoundquantita-
tivedevelopments.Aprominentfeatureofthistheory
consistsinfirstrecognizingthatcausationcorresponds
toratherdifferentsituationsandthatthreedistinct
facetsofcausalityshouldbedistinguished:(i)necessary
causation,wheretheoccurrenceofErequiresthatofC
butmayalsorequireotherfactors;(ii)sufficientcausa-
tion,wheretheoccurrenceofCdrivesthatofEbutmay
notberequiredforEtooccur;and(iii)necessaryand
sufficientcausation,where(i)and(ii)bothhold.The
fundamentaldistinctionbetweenthesethreefacetscan
bevisualizedbyusingthesimpleillustrationshownin
Fig.1.
Whilethecounterfactualdefinitionaswellasthe
threefacetsofcausalitydescribedabovemaybeun-
derstoodatfirstinafullydeterministicsense,perhaps
themainstrengthofPearl’sformalizationistopropose
anextensionofthesedefinitionsunderaprobabilistic
setting.Theprobabilitiesofcausationaretherebyde-
finedasfollow:
PS(C/
E)5PhEjdo(C),C,Ei,
(3a)
PN(C/
E)5PhEjdo(C),C,Ei,
(3b)
PNS(C/
E)5PhEjdo(C),Ejdo(C)i,
(3c)
whereCandEarethecomplementariesofCandE,and
wherethenotationdo(.)meansthataninterventionis
appliedtothesystemundercausalinvestigation.For
instancePS,theprobabilityofsufficientcausation,reads
fromtheabovethattheprobabilitythatEoccurswhen
Cisinterventionallyforcedtooccur,conditionalonthe
factthatneitherCnorEwasoccurringinthefirstplace.
ConverselyPN,theprobabilityofnecessarycausation,is
definedastheprobabilitythatEwouldnotoccurwhenC
isinterventionallyforcedtonotoccur,conditionalon
thefactthatbothCandEwereoccurringinthefirst
place.Whileweomitheretheformaldefinitionofthe
interventiondo(.)forbrevity,thelattercanbeunder-
stoodmerelyasexperimentation:applyingthesedefi-
nitionsthusrequirestheabilitytoexperiment.Real
experimentation,whetherinsituorinvivo,isoftenac-
cessibleinmanyfieldsbutitisnotinclimateresearchfor
obviousreasons.Inthiscase,onecanthusonlyrelyon
numericalinsilicoexperimentation:theimplicationsof
thisconstraintarediscussedfurther.
Whiletheprobabilitiesofcausationarenoteasily
computableingeneral,theirexpressionfortunately
FIG.1.Thethreefacetsofcausality.(a)BulbEcanneverbelit
unlessswitchC1ison,yetactivatingC1doesnotalwaysresultin
lightingEasthisalsorequiresturningonC2:turningonC1isthus
anecessarycauseofElighting,butnotasufficientone.(b)Eislit
anytimeC1isturnedon,yetifC1isturnedoffEmaystillbelitby
activatingC2:turningonC1isthusasufficientcauseofElighting,
butnotanecessaryone.(c)TurningonC1alwayslightsE,andE
maynotbelightedunlessC1ison:turningonC1isthusanecessary
andsufficientcauseofElighting.
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results,andstreamliningthecommunicationofcausal
claims—inparticularwhenitcomestothequantification
ofuncertainty,thatis,oftheprobabilitythatagiven
forcinghascausedagivenobservedphenomenon.
Here,weadaptsomeformaldefinitionsofcausality
andprobabilityofcausationtothecontextofclimate
changeattribution.Then,wedetailtechnicalimple-
mentationunderstandardassumptionsusedinD&A.
Themethodisfinallyillustratedonthewarmingob-
servedoverthetwentiethcentury.
2.Causalcounterfactualtheory
Whileanoverviewofcausaltheorycannotberepeated
here,itisnecessaryforclarityandself-containednessto
highlightitskeyideasandmostrelevantconceptsforthe
presentdiscussion.
Letusfirstrecalltheso-calledcounterfactualdefini-
tionofcausalitybyquotingtheeighteenth-century
ScottishphilosopherDavidHume:‘‘Wemaydefinea
causetobeanobjectfollowedbyanother,where,ifthe
firstobjecthadnotbeen,thesecondneverhadexisted.’’
Inotherwords,aneventE(Estandsforeffect)iscaused
byaneventC(Cstandsforcause)ifandonlyifEwould
notoccurwereitnotforC.Notethatthewordeventis
usedhereinitsgeneral,mathematicalsenseofasubset
ofasamplespaceV.Accordingtothisdefinition,evi-
dencingcausalityrequiresacounterfactualapproachby
whichoneinquireswhetherornottheeventEwould
haveoccurredinahypotheticalworld,termedcoun-
terfactual,inwhichtheeventCwouldnothaveoc-
curred.Thefundamentalapproachofcausalitythatis
impliedbythisdefinitionisstillentirelyrelevantin
thestandardcausaltheory.Itmayalsoarguablybe
connectedtotheguidanceprinciplesoftheconventional
climatechangeattributionframeworkandtotheopti-
malfingerprintingmodels,inaqualitativemanner.The
mainvirtueofthestandardcausalitytheoryofPearl
consistsinourviewinformalizingpreciselytheabove
qualitativedefinition,thusallowingforsoundquantita-
tivedevelopments.Aprominentfeatureofthistheory
consistsinfirstrecognizingthatcausationcorresponds
toratherdifferentsituationsandthatthreedistinct
facetsofcausalityshouldbedistinguished:(i)necessary
causation,wheretheoccurrenceofErequiresthatofC
butmayalsorequireotherfactors;(ii)sufficientcausa-
tion,wheretheoccurrenceofCdrivesthatofEbutmay
notberequiredforEtooccur;and(iii)necessaryand
sufficientcausation,where(i)and(ii)bothhold.The
fundamentaldistinctionbetweenthesethreefacetscan
bevisualizedbyusingthesimpleillustrationshownin
Fig.1.
Whilethecounterfactualdefinitionaswellasthe
threefacetsofcausalitydescribedabovemaybeun-
derstoodatfirstinafullydeterministicsense,perhaps
themainstrengthofPearl’sformalizationistopropose
anextensionofthesedefinitionsunderaprobabilistic
setting.Theprobabilitiesofcausationaretherebyde-
finedasfollow:
PS(C/
E)5PhEjdo(C),C,Ei,
(3a)
PN(C/
E)5PhEjdo(C),C,Ei,
(3b)
PNS(C/
E)5PhEjdo(C),Ejdo(C)i,
(3c)
whereCandEarethecomplementariesofCandE,and
wherethenotationdo(.)meansthataninterventionis
appliedtothesystemundercausalinvestigation.For
instancePS,theprobabilityofsufficientcausation,reads
fromtheabovethattheprobabilitythatEoccurswhen
Cisinterventionallyforcedtooccur,conditionalonthe
factthatneitherCnorEwasoccurringinthefirstplace.
ConverselyPN,theprobabilityofnecessarycausation,is
definedastheprobabilitythatEwouldnotoccurwhenC
isinterventionallyforcedtonotoccur,conditionalon
thefactthatbothCandEwereoccurringinthefirst
place.Whileweomitheretheformaldefinitionofthe
interventiondo(.)forbrevity,thelattercanbeunder-
stoodmerelyasexperimentation:applyingthesedefi-
nitionsthusrequirestheabilitytoexperiment.Real
experimentation,whetherinsituorinvivo,isoftenac-
cessibleinmanyfieldsbutitisnotinclimateresearchfor
obviousreasons.Inthiscase,onecanthusonlyrelyon
numericalinsilicoexperimentation:theimplicationsof
thisconstraintarediscussedfurther.
Whiletheprobabilitiesofcausationarenoteasily
computableingeneral,theirexpressionfortunately
FIG.1.Thethreefacetsofcausality.(a)BulbEcanneverbelit
unlessswitchC1ison,yetactivatingC1doesnotalwaysresultin
lightingEasthisalsorequiresturningonC2:turningonC1isthus
anecessarycauseofElighting,butnotasufficientone.(b)Eislit
anytimeC1isturnedon,yetifC1isturnedoffEmaystillbelitby
activatingC2:turningonC1isthusasufficientcauseofElighting,
butnotanecessaryone.(c)TurningonC1alwayslightsE,andE
maynotbelightedunlessC1ison:turningonC1isthusanecessary
andsufficientcauseofElighting.
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flip switch
light bulb
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-
Winkler, 2020 DOI: 10.17617/2.3190373
�6
Overview of experiments:
1. Control run at preindustrial conditions
2. Historical simulation with all forcings
All historical forcings except the
3. physiological effect of CO2 (No PE)
4. radiative effect of CO2 (No RE)
5. combined effect of CO2 (No CO2)
Multi-Model Ensemble: TRENDYv7
• Stand-alone land surface models
• Driven with observed climate 1900-2017
• Ensemble of 13 different models
Model SimulationsSingle Model Ensemble: MPI-ESM1.2
• Fully-coupled Earth system model
• Historical simulations 1850-2013
• Ensemble of 6 realizations
http://hdl.handle.net/21.11116/0000-0005-9396-B
-
Winkler, 2020 DOI: 10.17617/2.3190373
Radiative Effect is Dominant Driver in the North
�7
PNS MPI-ESM TRENDYv7Combined 99 % 99 %
Physiological 98 % 61 %
Radiative 86 % 87 %
PNS MPI-ESM TRENDYv7Combined 98 % 99 %
Physiological 59 % 47 %
Radiative 84 % 99 %
TundraBoreal Forests1985 1990 1995 2000 2005 2010 2015Time, yr
1.00
1.05
1.10
1.15
1.20
1.25
Ann
ualav
erag
eLA
I,m
2m
�2
a
Positive ⇤ (40%)
Negative ⇤ (19%)
Total signal
1985 1990 1995 2000 2005 2010 2015Time, yr
0
2
4
6
8
10
12
14
16
Rel
ativ
ech
ange
inLA
I,%
b
MPI-ESM (r=0.36, p=0.029)
TRENDYv7 (r=0.5, p=0.0018)
OBS
OBS IV
0.0
0.5
1.0
1.5
2.0
2.5
Rel
ativ
etr
end
inLA
I,%
deca
de�
1
c
ALL No PE No RE No CO2
1982–2017
MPI-ESM TRENDYv7
PE RE Both0.0
0.2
0.4
0.6
0.8
1.0
PN
S
d1982–2017
MPI-ESM
TRENDYv7
OBS IV
0.0
0.5
1.0
1.5
2.0
2.5
Rel
ativ
etr
end
inLA
I,%
deca
de�
1
e
ALL No PE No RE No CO2
2000–2017
MPI-ESM TRENDYv7
PE RE Both0.0
0.2
0.4
0.6
0.8
1.0
PN
S
f2000–2017
MPI-ESM
TRENDYv7
Rela
tive
trend
in L
AI, %
dec
ade-
1
OBS IV* ALL No PE No RE No CO2
Rela
tive
trend
in L
AI, %
dec
ade-
1
1985 1990 1995 2000 2005 2010 2015Time, yr
0.40
0.45
0.50
0.55
0.60
0.65
0.70
Ann
ualav
erag
eLA
I,m
2m
�2
a
Positive ⇤ (41%)
Negative ⇤ (14%)
Total signal
1985 1990 1995 2000 2005 2010 2015Time, yr
0
5
10
15
20
Rel
ativ
ech
ange
inLA
I,%
b
MPI-ESM (r=0.35, p=0.036)
TRENDYv7 (r=0.55, p=0.0005)
OBS
OBS IV
0
1
2
3
4
Rel
ativ
etr
end
inLA
I,%
deca
de�
1
c
ALL No PE No RE No CO2
1982–2017
MPI-ESM TRENDYv7
PE RE Both0.0
0.2
0.4
0.6
0.8
1.0
PN
S
d1982–2017
MPI-ESM
TRENDYv7
OBS IV
0
1
2
3
4
Rel
ativ
etr
end
inLA
I,%
deca
de�
1
e
ALL No PE No RE No CO2
2000–2017
MPI-ESM TRENDYv7
PE RE Both0.0
0.2
0.4
0.6
0.8
1.0
PN
S
f2000–2017
MPI-ESM
TRENDYv7
OBS IV* ALL No PE No RE No CO2
* Internal Variability
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Winkler, 2020 DOI: 10.17617/2.3190373
Tropical Forests are Browning with Rising CO2
�8
• No attribution possible due to high uncertainty.
• Models show compensatory effects of rising CO2.
• Observed trend switches sign in recent decades.
1982
-201
7
1985 1990 1995 2000 2005 2010 2015Time, yr
3.60
3.80
4.00
4.20
4.40
Ann
ualav
erag
eLA
I,m
2m
�2
a
Positive ⇤ (28%)
Negative ⇤ (16%)
Total signal
1985 1990 1995 2000 2005 2010 2015Time, yr
0
2
4
6
8
10
12
Rel
ativ
ech
ange
inLA
I,%
b
MPI-ESM (r=-0.06, p=0.73)
TRENDYv7 (r=0.18, p=0.28)
OBS
OBS IV
�2.0
�1.5
�1.0
�0.5
0.0
0.5
1.0
1.5
Rel
ativ
etr
end
inLA
I,%
deca
de�
1
c
ALL No PE No RE No CO2
1982–2017
MPI-ESM TRENDYv7
PE RE Both0.0
0.2
0.4
0.6
0.8
1.0
PN
S
d1982–2017
MPI-ESM
TRENDYv7
OBS IV
�2.0
�1.5
�1.0
�0.5
0.0
0.5
1.0
1.5
Rel
ativ
etr
end
inLA
I,%
deca
de�
1
e
ALL No PE No RE No CO2
2000–2017
MPI-ESM TRENDYv7
PE RE Both0.0
0.2
0.4
0.6
0.8
1.0
PN
S
f2000–2017
MPI-ESM
TRENDYv7
OBS IV ALL No PE No RE No CO2
Rela
tive
trend
in L
AI, %
dec
ade-
1Re
lativ
e tre
nd in
LAI
, % d
ecad
e-1
2000
-201
7
1985 1990 1995 2000 2005 2010 2015Time, yr
3.60
3.80
4.00
4.20
4.40
Ann
ualav
erag
eLA
I,m
2m
�2
a
Positive ⇤ (28%)
Negative ⇤ (16%)
Total signal
1985 1990 1995 2000 2005 2010 2015Time, yr
0
2
4
6
8
10
12
Rel
ativ
ech
ange
inLA
I,%
b
MPI-ESM (r=-0.06, p=0.73)
TRENDYv7 (r=0.18, p=0.28)
OBS
OBS IV
�2.0
�1.5
�1.0
�0.5
0.0
0.5
1.0
1.5
Rel
ativ
etr
end
inLA
I,%
deca
de�
1
c
ALL No PE No RE No CO2
1982–2017
MPI-ESM TRENDYv7
PE RE Both0.0
0.2
0.4
0.6
0.8
1.0
PN
S
d1982–2017
MPI-ESM
TRENDYv7
OBS IV
�2.0
�1.5
�1.0
�0.5
0.0
0.5
1.0
1.5
Rel
ativ
etr
end
inLA
I,%
deca
de�
1
e
ALL No PE No RE No CO2
2000–2017
MPI-ESM TRENDYv7
PE RE Both0.0
0.2
0.4
0.6
0.8
1.0
PN
S
f2000–2017
MPI-ESM
TRENDYv7
OBS IV ALL No PE No RE No CO2
http://hdl.handle.net/21.11116/0000-0005-9396-B
-
Winkler, 2020 DOI: 10.17617/2.3190373
Conclusions
�9
• Northern ecosystems are mainly greening due to the radiative effect of CO2.
• Tropical forests enter browning phase which is not captured by models.
•☞ Rising CO2 drives divergent responses of the natural vegetation: Persistent leaf area loss in tropical forests and gain in northern ecosystems.
• This development indicates the respective contributions of these ecosystems to the recent terrestrial carbon sink.
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