Editing IPCC:AR6/WGI/Chapter-5 (section)

==== 5.4.5.5 Linear Feedback Analysis ====

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To diagnose the causes of the varying time-evolution of carbon sinks, the traditional linear feedback approach is adopted ( [[#Friedlingstein--2003|Friedlingstein et al., 2003]] ), as used previously to analyse C <sup>4</sup> MIP ( [[#Friedlingstein--2006|Friedlingstein et al., 2006]] ) and CMIP5 models ( [[#Arora--2013|Arora et al., 2013]] ). Changes in land carbon storage ( ''Δ'' ''C'' <sub>L</sub> ) and changes in ocean carbon storage ( Δ ''C'' <sub>o</sub> ) are decomposed into contributions arising from warming ( ''Δ'' ''T'' ) and increases in CO <sub>2</sub> ( Δ ''CO'' 2 ):

[[File:fd37bf72ee47cd82827d75d6c0fa6132 IPCC_AR6_WGI_Formula_Chapter_5_5455_1.jpg]]

where ''β'' <sub>L</sub> ( β <sub>o</sub> ) and γ <sub>L</sub> ( γ <sub>o</sub> ) are coefficients that represent the sensitivity of land (ocean) carbon storage to changes in CO <sub>2</sub> and global mean temperature respectively. This feedback formalism is one of several that have been proposed for analysing climate–carbon cycle feedbacks ( [[#Lade--2018|Lade et al., 2018]] ).

This quasi-equilibrium framework is scenario dependent because of the time scales associated with land and ocean carbon uptake, as discussed in AR5 (WGI, Box 6.4). However, it is retained here for traceability with AR5. This approach has been used to define a number of emergent constraints on carbon cycle feedbacks ( [[#5.4.6|Section 5.4.6]] ) and to reconstruct the transient climate response to cumulative CO <sub>2</sub> emissions (TCRE) ( [[#Jones--2020|Jones and Friedlingstein, 2020]] ), as in [[#5.5|Section 5.5]] . To minimize the confounding effect of the scenario dependence, β and γ values are diagnosed from idealized runs in which a 1% per year increase in atmospheric CO <sub>2</sub> concentration is prescribed, as for AR5 (WGI, Box 6.4; [[#Arora--2013|Arora et al., 2013]] ). Values of β are calculated from ‘biogeochemical’ runs in which the prescribed CO <sub>2</sub> increases do not affect climate, and these are then used to isolate γ values in fully coupled runs where both climate and CO <sub>2</sub> change ( [[#Friedlingstein--2003|Friedlingstein et al., 2003]] ).

Table 5.5 shows the global land and global ocean values of β and γ for each of the CMIP6 ESMs ( [[#Arora--2020|Arora et al., 2020]] ). The last two rows show the ensemble means and standard deviation across the ensemble for CMIP6 and CMIP5. In both ensembles, the largest uncertainties are in the sensitivity of land carbon storage to CO <sub>2</sub> ( β <sub>L</sub> ) and the sensitivity of land carbon storage to temperature ( γ <sub>L</sub> ). The more widespread modelling of nitrogen limitations in CMIP6 was expected to lead to reductions in both of these feedback parameters. There is some evidence for that, with ensemble mean γ <sub>L</sub> moving from –58 ± 38 GtC K <sup>–1</sup> to –33 ± 33 GtC K <sup>–1</sup> . Between CMIP5 and CMIP6, there are also reductions in ensemble mean β <sub>o</sub> (0.82 to 0.77 GtC ppm <sup>–1</sup> ), β <sub>L</sub> (0.93 to 0.89 GtC ppm <sup>–1</sup> ) and γ <sub>o</sub> (–17.3 to –16.9 GtC K <sup>–1</sup> ), but these are progressively less significant compared to the model spread in each case.

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'''Table 5.5 |''' '''Diagnosed global feedback parameters for CMIP6 ESMs based on 1% per year runs to 4×CO''' <sub>2</sub> (Arora et al., 2020). The last two rows show the mean and standard deviation across the CMIP6 and CMIP5 models, respectively.

{| class="wikitable"
|-
!
! colspan="2"| '''Land F''' '''eedback Factors'''

! colspan="2"| '''Ocean F''' '''eedback Factors'''

|-
! '''Model Name'''

! β '''L''' '''(PgC ppm''' –1 ''')'''

! γ '''L''' '''(PgC K''' –1 ''')'''

! β '''o''' '''(PgC p_uo c;hnjppm''' –1 ''')'''

! γ '''o''' '''(PgC K''' –1 ''')'''

|-
| ACCESS-ESM1.5

| 0.37

| –21.1

| 0.90

| –23.8

|-
| CanESM5

| 1.28

| 16.0

| 0.77

| –14.7

|-
| CESM2

| 0.90

| –21.6

| 0.71

| –10.9

|-
| CNRM-ESM2-1

| 1.36

| –83.1

| 0.70

| –9.4

|-
| IPSL-CM6A-LR

| 0.62

| –8.7

| 0.76

| –13.0

|-
| MIROC-ES2L

| 1.12

| –69.6

| 0.73

| –22.3

|-
| MPI-ESM1.2-LR

| 0.71

| –5.2

| 0.77

| –20.1

|-
| NOAA-GFDL-ESM4

| 0.93

| –80.1

| 0.84

| –21.7

|-
| NorESM2-LM

| 0.85

| –21.0

| 0.78

| –19.6

|-
| UKESM1-0-LL

| 0.75

| –38.4

| 0.75

| –14.1

|-
| '''CMIP6 Model Mean'''

| '''0.89''' ± '''0.30'''

| '''–33.3''' ± '''33.8'''

| '''0.77''' ± '''0.06'''

| '''–16.9''' ± '''5.1'''

|-
| '''CMIP5 Model Mean'''

| '''0.93''' ± '''0.49'''

| '''–57.9''' ± '''38.2'''

| '''0.82''' ± '''0.07'''

| '''–17.3''' ± '''3.8'''

|}

In these idealized 1% per year CO <sub>2</sub> runs, the CMIP6 models show reasonable agreement on the patterns of carbon uptake and also on the separate impacts of CO <sub>2</sub> increase and climate change (Figure 5.27). For the ensemble mean, increasing atmospheric CO <sub>2</sub> increases carbon uptake by the oceans, especially in the Southern Ocean and the North Atlantic Ocean, and on the land, especially in tropical and boreal forests ( β '','' Figure 5.27a). Climate change further enhances land carbon storage in the boreal zone, but has a compensating negative impact on the carbon sink in tropical and subtropical lands, and in the North Atlantic Ocean ( γ '','' Figure 5.27b). Overall, the ensemble mean of the CMIP6 ESMs model indicates increasing carbon storage with CO <sub>2</sub> in almost all locations (Figure 5.27c).

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[[File:01a1dba8ed4789b745ddb11da3734ff4 IPCC_AR6_WGI_Figure_5_27.png]]

'''Figure 5.27 |''' '''Maps of carbon-concentration and carbon–climate feedback terms, as well as net carbon changes under the idealized 1% per year carbon dioxide (CO''' <sub>2</sub> ''') scenario, as evaluated from CMIP6 Earth system models (ESMs)''' . Shown are the model means from nine CMIP6 ESMs. Uncertainty is represented using the simple approach (see Cross-Chapter Box Atlas.1 for more information): No overlay indicates regions with high model agreement, where ≥80% of models agree with the ensemble mean on the sign of change; diagonal lines indicate regions with low model agreement, where &lt;80% of models agree with the ensemble mean on the sign of change. Also shown are zonal-mean latitude profiles of land (green) and ocean (blue) feedbacks. On the land, the zonal mean feedback for the mean of the ensemble of models that include nitrogen is shown as dashed lines, and for carbon-only models as dash-dotted lines, and the carbon–climate feedback from one permafrost-carbon enabled ESM is shown as a dotted line. Carbon changes are calculated as the difference between carbon stocks at different times on land and for the ocean as the time integral of atmosphere–ocean CO <sub>2</sub> flux anomalies relative to the pre-industrial. The denominator for gamma here is the global mean surface air temperature. Further details on data sources and processing are available in the chapter data table (Table 5.SM.6).

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