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

=== 7.4.1 Methodology of the Feedback Assessment ===

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The global surface temperature changes of the climate system are generally analysed with the classical forcing–feedback framework as described in Box 7.1 (Equation 7.1). In this equation α is the net feedback parameter (W m <sup>–2</sup> °C <sup>–1</sup> ). As surface temperature changes in response to the TOA energy imbalance, many other climate variables also change, thus affecting the radiative flux at the TOA. The aggregate feedback parameter can then be decomposed into an approximate sum of terms α = Σ x α x , where ''x'' is a vector representing variables that have a direct effect on the net TOA radiative flux ''N'' and

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Following the conventional definition, the physical climate feedbacks are here decomposed into terms associated with a vertically uniform temperature change (Planck response, P), changes in the water-vapour plus temperature lapse-rate (WV+LR), surface albedo (A) and clouds (C). The water-vapour plus temperature lapse rate feedback is further decomposed using two different approaches, one based on changes in specific humidity, the other on changes in relative humidity. Biogeochemical feedbacks arise due to changes in aerosols and atmospheric chemical composition in response to changes in surface temperature, and [[#Gregory--2009|Gregory et al. (2009)]] and [[#Raes--2010|Raes et al. (2010)]] show that they can be analysed using the same framework as for the physical climate feedbacks (Sections 5.4 and 6.4.5). Similarly, feedbacks associated with biogeophysical and ice-sheet changes can also be incorporated.

In global climate models, the feedback parameters α x in global warming conditions are often estimated as the mean differences in the radiative fluxes between atmosphere-only simulations in which the change in SST is prescribed ( [[#Cess--1990|Cess et al., 1990]] ), or as the regression slope of change in radiation flux against change in GSAT using atmosphere–ocean coupled simulations with abrupt CO <sub>2</sub> changes ( ''abrupt 4xCO2'' ) for 150 years (Box 7.1; [[#Gregory--2004|Gregory et al., 2004]] ; [[#Andrews--2012|Andrews et al., 2012]] ; [[#Caldwell--2016|Caldwell et al., 2016]] ). Neither method is perfect, but both are useful and yield consistent results ( [[#Ringer--2014|Ringer et al., 2014]] ). In the regression method, the radiative effects of land warming are excluded from the ERF due to doubling of CO <sub>2</sub> [[#7.3.2|Section 7.3.2]] ), which may overestimate feedback values by about 15%. At the same time, the feedback calculated using the regression over years 1–150 ignores its state-dependence on multi-centennial time scales ( [[#7.4.3|Section 7.4.3]] ), probably giving an underestimate of α by about 10% ( [[#Rugenstein--2019|Rugenstein et al., 2019]] ). These effects are both small and approximately cancel each other in the ensemble mean, justifying the use of regression over 150 years as an approximation to feedbacks in ESMs.

The change of the TOA radiative flux ''n'' as a function of the change of a climate variable ''x'' (such as water vapour) is commonly computed using the ‘radiative kernel’ method ( [[#Soden--2008|Soden et al., 2008]] ). In this method, the kernel ∂ ''N'' ''/'' ∂ ''x'' is evaluated by perturbing ''x'' within a radiation code. Then multiplying the kernel by d ''x/'' d ''T'' inferred from observations, meteorological analysis or GCMs produces a value of α x ''.''

Feedback parameters from lines of evidence other than global models are estimated in various ways. For example, observational data combined with GCM simulations could produce an emergent constraint on a particular feedback ( [[#Hall--2006|Hall and Qu, 2006]] ; [[#Klein--2015|Klein and Hall, 2015]] ), or the observed interannual fluctuations in the global mean TOA radiation and the surface air temperature, to which the linear regression analysis is applied, could generate a direct estimate of the climate feedback, assuming that the feedback associated with internal climate variability at short time scales can be a surrogate of the feedback to CO <sub>2</sub> -induced warming ( [[#Dessler--2013|Dessler, 2013]] ; [[#Loeb--2016|Loeb et al., 2016]] ). The assumption is not trivial, but can be justified given that the climate feedbacks are fast enough to occur at the interannual time scale. Indeed, a broad agreement has been obtained in estimates of individual physical climate feedbacks based on interannual variability and longer climate change time scales in GCMs ( [[#Zhou--2015|Zhou et al., 2015]] ; [[#Colman--2017|Colman and Hanson, 2017]] ). This means that the climate feedbacks estimated from the observed interannual fluctuations are representative of the longer-term feedbacks (decades to centuries). Care must be taken for these observational estimates because they can be sensitive to details of the calculation such as data sets and periods used ( [[#Dessler--2013|Dessler, 2013]] ; [[#Proistosescu--2018|Proistosescu et al., 2018]] ). In particular, there would be a dependence of physical feedbacks on the surface warming pattern at the interannual time scale due, for example, to El Niño–Southern Oscillation. However, this effect both amplifies and suppresses the feedback when data include the positive and negative phases of the interannual fluctuation, and therefore the net bias will be small.

In summary, the classical forcing–feedback framework has been extended to include biogeophysical and non-CO <sub>2</sub> biogeochemical feedbacks in addition to the physical feedbacks. It has also been used to analyse seasonal and interannual-to-decadal climate variations in observations and ESMs, in addition to long-term climate changes as seen in ''abrupt 4xCO2'' experiments. These developments allow an assessment of the feedbacks based on a larger variety of lines of evidence compared to AR5.

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