  Severity of warming predicted by climate models depends on their Transient
Climate Response (TCR). Inter-model spread of TCR has persisted at ~100% of its
mean for decades. Existing observational constraints of TCR are based on
observed historical warming to historical forcing and their uncertainty spread
is just as wide, mainly due to forcing uncertainty, and especially that of
aerosols. Contrary, no aerosols are involved in solar-cycle forcing, providing
an independent, tighter, constraint. Here, we define a climate sensitivity
metric: time-dependent response regressed against time-dependent forcing,
allowing phenomena with dissimilar time variations, such as the solar cycle
with 11-year cyclic forcing, to be used to constrain TCR, which has a linear
time-dependent forcing. We find a theoretical linear relationship between the
two. The latest coupled atmosphere-ocean climate models obey the same linear
relationship statistically. The proposed observational constraint on TCR is
about 1/3 as narrow as existing constraints. The central estimate,
2.2$^\circ$C, is at the midpoint of the spread of the latest generation of
climate models, which are more sensitive than those of the previous
generations.
