81GHGs (Vial et al. 2013 ; Zelinka et al. 2013 ; Zhou et al. 2015 ).^25 Furthermore, GCMs
that represent clouds in such a way that they act as a strong positive feedback tend to
have larger values of ECS (Vial et al. 2013 ). It is quite challenging to define cloud
feedback from observations because the effect of clouds on ΔRF of climate depends
on cloud height, cloud thickness, and radiative effects in two distinct spectral regions.^26
To truly discern cloud feedback, the effect of anthropogenic tropospheric aerosols on
clouds should be quantified and removed (Peng et al. 2016 ). The ephemeral nature of
clouds requires either a long observing time to discern a signal from an inherently
noisy process or the use of seasonal changes to deduce a relation between forcing and
response (Dessler 2010 ). Nonetheless, evidence has emerged that cloud feedback in
the actual atmosphere is indeed positive (Weaver et al. 2015 ; Zhou et al. 2015 ; Norris
et al. 2016 ). However, the uncertainty in the empirical determination of cloud feed-
back is quite large (Dessler 2010 ; Zhou et al. 2015 ). Furthermore, the vast majority of
satellite-based studies of cloud feedback that compare to GCM output make no
attempt to quantify the effect of aerosols on clouds, which is problematic given the
change in the release of aerosol precursors that has occurred in the past three decades
(Smith and Bond 2014 ) combined with varied representation of the effect of aerosols
on clouds within GCMs (Schmidt et al. 2014 ). There are major efforts underway to
evaluate and improve the representation of clouds within GCMs (Webb et al. 2016 ).
Based on the considerable existing uncertainty in the empirical determination of cloud
feedback and the wide range of GCM representations of this process, cloud feedback
within GCMs is the leading candidate for explaining why most of the GCM-based
values of AAWR exceed the empirical determination of AAWR.
Next, our determination of AAWR is compared to estimates published by other
groups. All studies considered here examined the time period 1979–2010. Our best
estimate (and range) for AAWR found using the CRU ΔT dataset is 0.107 (0.080,
0.143) °C/decade. Foster and Rahmstorf ( 2011 ) (hereafter, FR2011) reported a value
for AAWR of 0.170 °C/decade based on analysis of an earlier version of the CRU ΔT
record.^27 They used multiple linear regression to remove the influence of ENSO,
volcanoes, and total solar irradiance on observed ΔT and then examined the differ-
ence between observed ΔT and the contribution from these three exogenous factors,
termed the residual, to quantify ΔT. The FR2011 estimate of AAWR exceeds the
upper limit of our analysis shown in Fig. 2.12 and lies closer to median GCM-based
value of 0.218 °C/decade found upon our analysis of the CMIP5 archive.
The difference between our best estimate for AAWR (0.107 °C/decade) and the
value reported by FR2011 (0.170 °C/decade), both for ΔT from CRU, is due to the two
approaches used to quantify the human influence on global warming. We have applied
(^25) Figure 7.10 of IPCC ( 2013 ) provides a concise summary of the representation of cloud feedback
within GCMs.
(^26) Proper determination of ΔRF due to clouds requires analysis of the impact of clouds on reflectiv-
ity and absorption of solar radiation, commonly called the cloud short wavelength (SW) effect in
the literature, as well as the impact of clouds on the trapping of infrared radiation (or heat) emitted
by Earth’s surface, commonly called the long wavelength (LW) effect.
(^27) FR2011 also reported slightly higher values of AAWR, 0.171 and 0.175 °C/decade, upon use of
ΔT from GISS and NCEI, respectively.
2.3 Attributable Anthropogenic Warming Rate