Open your copy of AR6's Physical Science Basis. Go to Chapter 7.5 on page 992. There the discussion will begin on Equilbrium Climate Sensitivity and Tranient Climate Response (ECS and TCR).
Just a taste to get you going and to show that the topic has been heavily investigated and is not the result of overworked, politically-driven conspiracy to overthrow the planet's governments.
7.5 Estimates of ECS and TCR
Equilibrium climate sensitivity (ECS) and transient climate response
(TCR) are metrics of the global surface air temperature (GSAT)
response to forcing, as defined in Box 7.1. ECS is the magnitude
of the long-term GSAT increase in response to a doubling of
atmospheric CO2 concentration after the planetary energy budget is
balanced, though leaving out feedbacks associated with ice sheets;
whereas the TCR is the magnitude of GSAT increase at year 70 when
CO2 concentration is doubled in a 1% yr –1 increase scenario. Both
are idealized quantities, but can be inferred from paleoclimate or
observational records or estimated directly using climate simulations,
and are strongly correlated with the climate response in realistic
future projections (Sections 4.3.4 and 7.5.7; Grose et al., 2018).
...
7.5.1.1 ECS Estimated Using Process-based
Assessments of Forcing and Feedbacks
The process-based assessment is based on the global energy budget
equation (Box 7.1, Equation 7.1), where the ERF (ΔF) is set equal to
the effective radiative forcing due to a doubling of CO2 concentration
(denoted as ΔF2×CO2) and the climate state reaches a new equilibrium,
that is, Earth’s energy imbalance averages to zero (ΔN = 0). ECS is
calculated as the ratio between the ERF and the net feedback
parameter: ECS = –ΔF2×CO2/α. Estimates of ΔF2×CO2 and α are obtained
separately based on understanding of the key processes that
determine each of these quantities. Specifically, ΔF2×CO2 is estimated
based on instantaneous radiative forcing that can be accurately
obtained using line-by-line calculations, to which uncertainty due
to adjustments are added (Section 7.3.2). The range of α is derived
by aggregating estimates of individual climate feedbacks based not
only on ESMs but also on theory, observations, and high-resolution
process modelling (Section 7.4.2).
The effective radiative forcing of CO2 doubling is assessed to be
ΔF2×CO2 = 3.93 ± 0.47 W m–2 (Section 7.3.2.1), while the net feedback
parameter is assessed to be α = –1.16 ± 0.40 W m–2 °C–1 (Table 7.10),
where the ranges indicate one standard deviation. These values are
slightly different from those directly calculated from ESMs because
more information is used to assess them, as explained above. Assuming
ΔF2×CO2 and α each follow an independent normal distribution, the
uncertainty range of ECS can be obtained by substituting the respective
probability density function into the expression of ECS (red curved bar
in Figure 7.16). Since α is in the denominator, the normal distribution
leads to a long tail in ECS towards high values, indicating the large
effect of uncertainty in α in estimating the likelihood of a high ECS
(Roe and Baker, 2007; Knutti and Hegerl, 2008).
The wide range of the process-based ECS estimate is not due
solely to uncertainty in the estimates of ΔF2×CO2 and α, but is partly
explained by the assumption that ΔF2×CO2 and α are independent in
this approach. In CMIP5 and CMIP6 ensembles, ΔF2×CO2 and α are
negatively correlated when they are calculated using linear regression
in abrupt4xCO2 simulations (r2 = 0.34; Andrews et al., 2012; Webb
et al., 2013; Zelinka et al., 2020). The negative correlation leads to
compensation between the inter-model spreads of these quantities,
thereby reducing the ECS range estimated directly from the models.
If the process-based ECS distribution is reconstructed from probability
distributions of ΔF2×CO2 and α assuming that they are correlated as in
CMIP model ensembles, the range of ECS will be narrower by 14%
(pink curved bar in Figure 7.16). If, however, the covariance between
ΔF2×CO2 and α is not adopted, there is no change in the mean, but the
wide range still applies.
A significant correlation between ΔF2×CO2 and α also occurs when
the two parameters are estimated separately from atmospheric ESM
fixed-SST experiments (Section 7.3.1) or fixed CO2 concentration
experiments (Section 7.4.1; Ringer et al., 2014; Chung and Soden,
2018). Hence the relationship is not expected to be an artefact of
calculating the parameters using linear regression in abrupt4xCO2
simulations. A possible physical cause of the correlation may be
a compensation between the cloud adjustment and the cloud
feedback over the tropical ocean (Ringer et al., 2014; Chung and
Soden, 2018). It has been shown that the change in the hydrological
cycle is a controlling factor for the low-cloud adjustment (Dinh and
Fueglistaler, 2019) and for the low-cloud feedback (Watanabe et al.,
2018), and therefore the responses of these clouds to the direct CO2
radiative forcing and to the surface warming may not be independent.
However, robust physical mechanisms are not yet established,
and furthermore, the process-based assessment of the tropical
low-cloud feedback is only indirectly based on ESMs given that
physical processes which control the low-clouds are not sufficiently
well-simulated in models (Section 7.4.2.4). For these reasons, the
co-dependency between ΔF2×CO2 and α is assessed to have low
confidence and, therefore, the more conservative assumption that
they are independent for the process-based assessment of ECS
is retained.
View attachment 771371
Figure 7.16 | Probability distributions of ERF to CO2 doubling (ΔF2×CO2;
top) and the net climate feedback (α; right), derived from processbased
assessments in Sections 7.3.2 and 7.4.2. Central panel shows the joint
probability density function calculated on a two-dimensional plane of ΔF2×CO2 and
α (red), on which the 90% range shown by an ellipse is imposed to the background
theoretical values of ECS (colour shading). The white dot, and thick and thin curves
inside the ellipse represent the mean, likely and very likely ranges of ECS. An alternative
estimation of the ECS range (pink) is calculated by assuming that ΔF2×CO2 and α have
a covariance. The assumption about the co-dependence between ΔF2×CO2 and α
does not alter the mean estimate of ECS but affects its uncertainty. Further details on
data sources and processing are available in the chapter data table (Table 7.SM.14).
END EXCERPT
There are about 18 more pages of this discussion if you care to look.
IF you don't have a local copy, you can get one (for FREE) at
AR6 Climate Change 2021: The Physical Science Basis — IPCC
I wouldn't mind Frank, Tommy, Todd, jc or even the OP, Bripat9643, addressing the particular points in this section of AR6 dealing with ECS and TCR.