Editing IPCC:AR6/WGI/Chapter-7 (section)

=== 7.3.1 Methodologies and Representation in Models: Overview of Adjustments ===

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As introduced in Box 7.1, AR5 ( [[#Boucher--2013|Boucher et al., 2013]] ; [[#Myhre--2013b|Myhre et al., 2013b]] ) recommended ERF as a more useful measure of the climate effects of a physical driver than the stratospheric-temperature-adjusted radiative forcing (SARF) adopted in earlier assessments. The AR5 assessed that the ratios of surface temperature change to forcing resulting from perturbations of different forcing agents were more similar between species using ERF than SARF. ERF extended the SARF concept to account for not only adjustments to stratospheric temperatures, but also responses in the troposphere and effects on clouds and atmospheric circulation, referred to as ‘adjustments’. For more details see Box 7.1. Since circulation can be affected, these responses are not confined to the locality of the initial perturbation (unlike the traditional stratospheric-temperature adjustment).

This chapter defines ‘adjustments’ as those changes caused by the forcing agent that are independent of changes in surface temperature, rather than defining a specific time scale. The AR5 used the term ‘rapid adjustment’, but in this assessment the definition is based on the independence from surface temperature rather than the rapidity. The definition of ERF in Box 7.1 aims to create a clean separation between forcing (energy budget changes that are not mediated by surface temperature) and feedbacks (energy budget changes that are mediated by surface temperature). This means that changes in land or ocean surface temperature patterns (for instance as identified by [[#Rugenstein--2016b|Rugenstein et al., 2016b]] ) are not included as adjustments. As in previous assessments ( [[#Forster--2007|Forster et al., 2007]] ; [[#Myhre--2013b|Myhre et al., 2013b]] ) ERFs can be attributed simply to changes in the forcing agent itself or attributed to components of emitted gases (Figure 6.12). Because ERFs can include chemical and biospheric responses to emitted gases, they can be attributed to precursor gases, even if those gases do not have a direct radiative effect themselves. Similar chemical and biospheric responses to forcing agents can also be included in the ERF in addition to their direct effects.

Instantaneous radiative forcing (IRF) is defined here as the change in the net TOA radiative flux following a perturbation, excluding any adjustments. SARF is defined here as the change in the net radiative flux at TOA following a perturbation including the response to stratospheric temperature adjustments. These differ from AR5 where these quantities were defined at the tropopause ( [[#Myhre--2013b|Myhre et al., 2013b]] ). The net IRF values will be different using the TOA definition. The net SARF values will be the same as with the tropopause definition, but will have a different partitioning between the longwave and shortwave. Defining all quantities at the TOA enables consistency in breaking down the ERF into its component parts.

The assessment of ERFs in AR5 was preliminary because ERFs were only available for a few forcing agents, so for many forcing agents the Report made the assumption that ERF and SARF were equivalent. This section discusses the body of work published since AR5. This work has computed ERFs across many more forcing agents and models; closely examined the methods of computation; quantified the processes involved in causing adjustments; and examined how well ERFs predict the ultimate temperature response. This work is assessed to have led to a much-improved understanding and increased confidence in the quantification of radiative forcing across the Report. These same techniques allow for an evaluation of radiative forcing within Earth system models (ESMs) as a key test of their ability to represent both historical and future temperature changes (Sections 3.3.1 and 4.3.4).

The ERF for a particular forcing agent is the sum of the IRF and the contribution from the adjustments, so in principle this could be constructed bottom-up by calculating the IRF and adding in the adjustment contributions one-by-one or together. However, there is no simple way to derive the global tropospheric adjustment terms or adjustments related to circulation changes without using a comprehensive climate model (e.g., CMIP5 or CMIP6). There have been two main modelling approaches used to approximate the ERF definition in Box 7.1. The first approach is to use the assumed linearity (Box 7.1, Equation 7.1) to regress the net change in the TOA radiation budget (Δ ''N'' ) against change in global mean surface temperature (Δ ''T'' ) following a step change in the forcing agent (Box 7.1, Figure 1; [[#Gregory--2004|Gregory et al., 2004]] ). The ERF (Δ ''F'' ) is then derived from Δ ''N'' when Δ ''T'' = 0. Regression-based estimates of ERF depend on the temporal resolution of the data used ( [[#Modak--2016|Modak et al., 2016]] , 2018). For the first few months of a simulation both surface temperature change and stratospheric-temperature adjustment occur at the same time, leading to misattribution of the stratospheric-temperature adjustment to the surface temperature feedback. Patterns of sea surface temperature (SST) change also affect estimates of the forcing obtained by regression methods ( [[#Andrews--2015|Andrews et al., 2015]] ). At multi-decadal time scales the curvature of the relationship between net TOA radiation and surface temperature can also lead to biases in the ERF estimated from the regression method ( [[#7.4|Section 7.4]] ; [[#Armour--2013|Armour et al., 2013]] ; [[#Andrews--2015|Andrews et al., 2015]] ; [[#Knutti--2017|Knutti et al., 2017]] ). The second modelling approach to estimate ERF is to set the Δ ''T'' term in Box 7.1 (Box 7.1, Equation 7.1) to zero. It is technically difficult to constrain land surface temperatures in ESMs ( [[#Shine--2003|Shine et al., 2003]] ; [[#Ackerley--2016|Ackerley and Dommenget, 2016]] ; [[#Andrews--2021|Andrews et al., 2021]] ), so most studies reduce the Δ ''T'' term by prescribing the SSTs and sea ice concentrations in a pair of ‘fixed-SST’ (fSST) simulations with and without the change in forcing agent ( [[#Hansen--2005b|Hansen et al., 2005b]] ). An approximation to ERF (Δ ''F'' <sub>fsst</sub> ) is then given by the difference in Δ ''N'' <sub>fsst 4</sub> between the simulations. The fSST method has less noise due to internal variability than the regression method. Nevertheless a 30-year fSST integration or 10 × 20-year regression ensemble needs to be conducted in order to reduce the 5–95% confidence range to 0.1 W m <sup>–2</sup> ( [[#Forster--2016|Forster et al., 2016]] ).Neither the regression or fSST methods are practical for quantifying the ERF of agents with forcing magnitudes of the order of 0.1 W m <sup>–2</sup> or smaller. The internal variability in the fSST method can be further constrained by nudging winds towards a prescribed climatology ( [[#Kooperman--2012|Kooperman et al., 2012]] ). This allows the determination of the ERF of forcing agents with smaller magnitudes but excludes adjustments associated with circulation responses ( [[#Schmidt--2018|Schmidt et al., 2018]] ). There are insufficient studies to assess whether these circulation adjustments are significant.

Since the near-surface temperature change over land, Δ ''T'' <sub>land</sub> , is not constrained in the fSST method, this response needs to be removed for consistency with the ( [[#7.1|Section 7.1]] definition. These changes in the near-surface temperature will also induce further responses in the tropospheric temperature and water vapour that should also be removed to conform with the physical definition of ERF. The radiative response to Δ ''T'' <sub>land</sub> can be estimated through radiative transfer modelling in which a kernel, ''k'' , representing the change in net TOA radiative flux per unit of change in near-surface temperature change over land (or an approximation using land surface temperature), is precomputed ( [[#Smith--2018b|Smith et al., 2018b]] , 2020b; [[#Richardson--2019|Richardson et al., 2019]] ; [[#Tang--2019|Tang et al., 2019]] ). Thus ERF ≈ Δ ''F'' <sub>fsst</sub> – ''k'' Δ ''T'' <sub>land</sub> . Since ''k'' is negative this means that Δ ''F'' <sub>fsst</sub> underestimates the ERF. For 2×CO <sub>2</sub> , this underestimate is around 0.2 W m <sup>–2</sup> ( [[#Smith--2018b|Smith et al., 2018b]] , 2020b). There have been estimates of the corrections due to tropospheric temperature and water vapour ( [[#Tang--2019|Tang et al., 2019]] ; [[#Smith--2020b|Smith et al., 2020b]] ) showing additional radiative responses of comparable magnitude to those directly from Δ ''T'' <sub>land</sub> . An alternative to computing the response terms directly is to use the feedback parameter, α ( [[#Hansen--2005b|Hansen et al., 2005b]] ; [[#Sherwood--2015|Sherwood et al., 2015]] ; [[#Tang--2019|Tang et al., 2019]] ). This gives approximately double the correction compared to the kernel approach ( [[#Tang--2019|Tang et al., 2019]] ). The response to land surface temperature change varies with location and even for GSAT change ''k'' is not expected to be the same as α [[#7.4|Section 7.4]] ). One study where land surface temperatures are constrained in a model ( [[#Andrews--2021|Andrews et al., 2021]] ) finds this constraint adds +1.0 W m <sup>–2</sup> to Δ ''F'' <sub>fsst</sub> for 4×CO <sub>2</sub> , thus confirming the need for a correction in calculations where this constraint is not applied. For this assessment the correction is conservatively based only on the direct radiative response kernel to Δ ''T'' <sub>land</sub> as this has a strong theoretical basis to support it. While there is currently insufficient corroborating evidence to recommend including tropospheric temperature and water-vapour corrections in this assessment, it is noted that the science is progressing rapidly on this topic.

TOA radiative flux changes due to the individual adjustments can be calculated by perturbing the meteorological fields in a climate model’s radiative transfer scheme (partial radiative perturbation approach) ( [[#Colman--2015|Colman, 2015]] ; [[#Mülmenstädt--2019|Mülmenstädt et al., 2019]] ) or by using precomputed radiative kernels of sensitivities of the TOA radiation fluxes to changes in these fields (as done for near-surface temperature change above; [[#Vial--2013|Vial et al., 2013]] ; [[#Zelinka--2014|Zelinka et al., 2014]] ; [[#Zhang--2014|Zhang and Huang, 2014]] ; [[#Smith--2018b|Smith et al., 2018b]] , 2020b). The radiative kernel approach is easier to implement through post-processing of output from multiple ESMs, whereas it is recognized that the partial radiation perturbation approach gives a more accurate estimate of the adjustments within the setup of a single model and its own radiative transfer code. There is little difference between using a radiative kernel from the same or a different model when calculating the adjustment terms, except for stratospheric temperature adjustments where it is important to have sufficient vertical resolution in the stratosphere in the model used to derive the kernel ( [[#Smith--2018b|Smith et al., 2018b]] , 2020a).

For comparison with offline radiative transfer calculations the SARFs can be approximated by removing the adjustment terms (apart from stratospheric temperature) from the ERFs using radiative kernels to quantify the adjustment for each meteorological variable. Kernel analysis by [[#Chung--2015|Chung and Soden (2015)]] suggested a large spread in CO <sub>2</sub> SARF across climate models, but their analysis was based on regressing variables in a coupled-ocean experiment rather than using a fSST approach which leads to a large spread due to natural variability ( [[#Forster--2016|Forster et al., 2016]] ). Adjustments computed from radiative kernels are shown for seven different climate drivers (using a fSST approach) in Figure 7.4. Table 7.2 shows the estimates of SARF, Δ ''F'' <sub>fsst</sub> and ERF (corrected for land surface temperature change) for 2×CO <sub>2</sub> from the nine climate models analysed in [[#Smith--2018b|Smith et al. (2018b)]] . The SARF shows a smaller spread over previous studies ( [[#Pincus--2016|Pincus et al., 2016]] ; [[#Soden--2018|Soden et al., 2018]] ) and most estimates are within 10% of the multi-model mean and the assessment of 2×CO <sub>2</sub> SARF in ( [[#7.3.2|Section 7.3.2]] (3.75 W m <sup>–2</sup> ). It is not possible from these studies to determine how much of this reduction in spread is due to convergence in the model radiation schemes or the meteorological conditions of the model base states; nevertheless the level of agreement in this and earlier intercomparisons gives ''medium confidence'' in the ability of ESMs to represent radiative forcing from CO <sub>2</sub> . The 4×CO <sub>2</sub> CMIP6 fSST experiments ( [[#Smith--2020b|Smith et al., 2020b]] ) in Table 7.2 include ESMs with varying levels of complexity in aerosols and reactive gas chemistry. The CMIP6 experimental setup allows for further climate effects of CO <sub>2</sub> (including on aerosols and ozone) depending on model complexity. The chemical effects are adjustments to CO <sub>2</sub> but are not separable from the SARF in the diagnosis in Table 7.2. In these particular models, this leads to higher SARF than when only CO <sub>2</sub> varies, however there are insufficient studies to make a formal assessment of composition adjustments to CO <sub>2</sub> .

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[[File:71c76ec9643e9fe81cead6cedb433f25 IPCC_AR6_WGI_Figure_7_4.png]]

'''Figure 7.4''' '''|''' '''Radiative adjustments at top of atmosphere for seven different climate drivers as a proportion of forcing.''' Tropospheric temperature (orange), stratospheric temperature (yellow), water vapour (blue), surface albedo (green), clouds (grey) and the total adjustment (black) is shown. For the greenhouse gases (carbon dioxide, methane, nitrous oxide and CFC-12) the adjustments are expressed as a percentage of stratospheric-temperature-adjusted radiative forcing (SARF), whereas for aerosol, solar and volcanic forcing they are expressed as a percentage of instantaneous radiative forcing (IRF). Land surface temperature response (outline red bar) is shown, but included in the definition of forcing. Data from [[#Smith--2018b|Smith et al. (2018b)]] for carbon dioxide and methane; [[#Smith--2018b|Smith et al. (2018b)]] and [[#Gray--2009|Gray et al. (2009)]] for solar; [[#Hodnebrog--2020b|Hodnebrog et al. (2020b)]] for nitrous oxide and CFC-12; [[#Smith--2020b|Smith et al. (2020b)]] for aerosol, and [[#Marshall--2020|Marshall et al. (2020)]] for volcanic. Further details on data sources and processing are available in the chapter data table (Table 7.SM.14).

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'''Table 7.2''' '''|''' '''SARF, Δ''' ''F'' <sub>fsst</sub> ''', and ERF diagnosed from Earth system models for fixed-SST (fSST) CO''' <sub>2</sub> '''experiments.''' 2×CO <sub>2</sub> data taken from fixed atmospheric composition experiments ( [[#Smith--2018b|Smith et al., 2018b]] ). 4×CO <sub>2</sub> data taken from CMIP6 experiments with interactive aerosols (and interactive gas phase chemistry in some; [[#Smith--2020b|Smith et al., 2020b]] ). The radiative forcings from the 4×CO <sub>2</sub> experiments are scaled by 0.476 for comparison with 2×CO <sub>2</sub> ( [[#Meinshausen--2020|Meinshausen et al., 2020]] ). SARF is approximated by removing the (non-stratospheric-temperature) adjustment terms from the ERF. In [[#Smith--2018b|Smith et al. (2018b)]] , separation of temperature adjustments into tropospheric and stratospheric contributions is approximate based on a fixed tropopause of 100 hPa at the equator, varying linearly in latitude to 300 hPa at the poles. In [[#Smith--2020b|Smith et al. (2020b)]] , this separation is based on the model-diagnosed tropopause. ERF is approximated by removing the response to land surface temperature change from Δ ''F'' <sub>fsst</sub> . The confidence range is based on the inter-model standard deviation.

{| class="wikitable"
|-
| 2×CO <sub>2</sub> Experiments

( [[#Smith--2018b|Smith et al., 2018b]] )

| Stratospheric- temperature-adjusted Radiative Forcing (SARF, W m <sup>–2</sup> )

| Δ ''F'' <sub>fsst</sub> (W m <sup>–2</sup> )

| Effective Radiative Forcing (ERF, W m <sup>–2</sup> )

|-
| HadGEM2-ES

| 3.45

| 3.37

| 3.58

|-
| NorESM1

| 3.67

| 3.50

| 3.70

|-
| GISS-E2-R

| 3.98

| 4.06

| 4.27

|-
| CanESM2

| 3.68

| 3.57

| 3.77

|-
| MIROC-SPRINTARS

| 3.89

| 3.62

| 3.82

|-
| NCAR-CESM1-CAM5

| 3.89

| 4.08

| 4.39

|-
| HadGEM3

| 3.48

| 3.64

| 3.90

|-
| IPSL-CM5A

| 3.50

| 3.39

| 3.61

|-
| MPI-ESM

| 4.27

| 4.14

| 4.38

|-
| NCAR-CESM1-CAM4

| 3.50

| 3.62

| 3.86

|-
| Multi-model mean and 5–95% confidence range

| 3.73 ± 0.44

| 3.70 ± 0.44

| 3.93 ± 0.48

|-
|
|-
| 0.476 × 4×CO <sub>2</sub> Experiments

( [[#Smith--2020b|Smith et al., 2020b]] )

| Stratospheric- temperature-adjusted Radiative Forcing (SARF, W m <sup>–2</sup> )

| Δ ''F'' <sub>fsst</sub> (W m <sup>–2</sup> )

| Effective Radiative Forcing (ERF, W m <sup>–2</sup> )

|-
| ACCESS-CM2

| 3.56

| 3.78

| 3.98

|-
| CanESM5

| 3.67

| 3.62

| 3.82

|-
| CESM2

| 3.56

| 4.24

| 4.48

|-
| CNRM-CM6-1

| 3.99

| 3.81

| 4.01

|-
| CNRM-ESM2-1

| 3.99

| 3.77

| 3.94

|-
| EC-Earth3

|
| 3.85

| 4.04

|-
| GFDL-CM4

| 3.65

| 3.92

| 4.10

|-
| GFDL-ESM4

| 3.27

| 3.68

| 3.85

|-
| GISS-E2-1-G

| 3.78

| 3.50

| 3.69

|-
| HadGEM3-GC31-LL

| 3.61

| 3.85

| 4.07

|-
| IPSL-CM6A-LR

| 3.84

| 3.81

| 4.05

|-
| MIROC6

| 3.63

| 3.48

| 3.69

|-
| MPI-ESM1-2-LR

| 3.74

| 3.97

| 4.20

|-
| MRI-ESM2-0

| 3.76

| 3.64

| 3.80

|-
| NorESM2-LM

| 3.58

| 3.88

| 4.10

|-
| NorESM2-MM

| 3.62

| 3.99

| 4.22

|-
| UKESM1-0-LL

| 3.49

| 3.78

| 4.01

|-
| Multi-model mean and 5–95% confidence range

| 3.67 ± 0.29

| 3.80 ± 0.30

| 4.00 ± 0.32

|}

ERFs have been found to yield more consistent values of GSAT change per unit forcing than SARF, that is, α shows less variation across different forcing agents ( [[#Rotstayn--2001|Rotstayn and Penner, 2001]] ; [[#Shine--2003|Shine et al., 2003]] ; [[#Hansen--2005b|Hansen et al., 2005b]] ; [[#Marvel--2016|Marvel et al., 2016]] ; [[#Richardson--2019|Richardson et al., 2019]] ). Having a consistent relationship between forcing and response is advantageous when making climate projections using simple models (Cross-Chapter Box 7.1) or emissions metrics ( [[#7.6|Section 7.6]] ). The definition of ERF used in this assessment, which excludes the radiative response to land surface temperature changes, brings The α values into closer agreement than when SARF is used ( [[#Richardson--2019|Richardson et al., 2019]] ), although for individual models there are still variations, particularly for more geographically localized forcing agents. However, even for ERF, studies find that α is not identical across all forcing agents ( [[#Shindell--2014|Shindell, 2014]] ; [[#Shindell--2015|Shindell et al., 2015]] ; [[#Modak--2018|Modak et al., 2018]] ; [[#Modak--2019|Modak and Bala, 2019]] ; [[#Richardson--2019|Richardson et al., 2019]] ). [[#7.4.4|Section 7.4.4]] discusses the effect of different SST response patterns on α . Analysis of the climate feedbacks ( [[#Kang--2014|Kang and Xie, 2014]] ; [[#Gregory--2016|Gregory et al., 2016]] , 2020; [[#Marvel--2016|Marvel et al., 2016]] ; [[#Duan--2018|Duan et al., 2018]] ; [[#Persad--2018|Persad and Caldeira, 2018]] ; [[#Stuecker--2018|Stuecker et al., 2018]] ; [[#Krishnamohan--2019|Krishnamohan et al., 2019]] ) suggests a weaker feedback (i.e., less-negative α ) and hence larger sensitivity for forcing of the higher latitudes (particularly the Northern Hemisphere). Nonetheless, as none of these variations are robust across models, the ratio of 1/ α from non-CO <sub>2</sub> forcing agents (with approximately global distributions) to that from doubling CO <sub>2</sub> is within 10% of unity.

In summary, this Report adopts an estimate of ERF based on the change in TOA radiative fluxes in the absence of GSAT changes. This allows for a theoretically cleaner separation between forcing and feedbacks in terms of factors respectively unrelated and related to GSAT change (Box 7.1). ERF can be computed from prescribed SST and sea ice experiments after removing the TOA energy budget change associated with the land surface temperature response. In this assessment this is removed using a kernel accounting only for the direct radiative effect of the land surface temperature response. To compare these results with sophisticated high spectral resolution radiative transfer models the individual tropospheric adjustment terms can be removed to leave the SARF. SARFs for 2×CO <sub>2</sub> calculated by ESMs from this method agree within 10% with the more sophisticated models. The new studies highlighted above suggest that physical feedback parameters computed within this framework have less variation across forcing agents. There is ''high confidence'' that an α based on ERF as defined here varies by less (less than variation 10% across a range of forcing agents with global distributions), than α based on SARF. For geographically localized forcing agents there are fewer studies and less agreement between them, resulting in ''low confidence'' that ERF is a suitable estimator of the resulting global mean near-surface temperature response ''.''

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