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Alexander J. Winkler*, Ranga B. Myneni, Alexis Hannart, and Victor Brovkin May 5, 2020 Greening and Browning in Response to the Effects of Rising CO 2 Driver Attribution Using Causal Theory * [email protected]

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  • 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

    * [email protected]

  • 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.

    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

    flip switch

    light bulb

    http://hdl.handle.net/21.11116/0000-0005-9396-B

  • 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

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    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

    http://hdl.handle.net/21.11116/0000-0005-9396-B

  • 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

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    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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