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\begin{document}

\title{`Simpson's Law' and the Spectral Cancellation of Climate Feedbacks}



\author[1,1]{Nadir Jeevanjee}%
\author[2,2]{Nicholas Lutsko}%
\author[3,3]{Daniel Koll}%
\affil[1]{Geophysical Fluid Dynamics Laboratory}%
\affil[2]{Scripps Institution of Oceanography.}%
\affil[3]{Massachusetts Institute of Technology}%


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  \date{May 24, 2024}


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\begin{abstract}
We spectrally resolve the conventional clear-sky temperature and water
vapor feedbacks in an idealized single-column framework, and show that
the well-known partial compensation of these feedbacks is actually due
to an almost perfect cancellation of the spectral feedbacks at
wavenumbers where H2O is optically thick. This cancellation is a natural
consequence of `Simpson's Law', which says that H2O emission
temperatures do not change with surface warming if RH is fixed. We
provide an explicit formulation and validation of Simpson's Law, and
furthermore show that this spectral cancellation of feedbacks is
naturally incorporated in the alternative RH-based framework proposed by
Held and Shell (2012) and Ingram (2012, 2013), thus bolstering the case
for switching from conventional to RH-based feedbacks. We also find a
negligible RH-based clear-sky lapse rate feedback, suggesting that the
impact of changing lapse rates depends crucially on whether relative or
specific humidity is held fixed%
\end{abstract}%



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