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\begin{document}

\title{Sparse, Empirically Optimized Quadrature for Radiative Calculations}



\author[1]{Paulina Czarnecki}%
\author[1]{Robert Pincus}%
\author[1]{Lorenzo M Polvani}%
\affil[1]{Columbia University}%


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  \date{May 08, 2024}


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\begin{abstract}
Broadband (spectrally-integrated) radiation calculations are dominated
by the expense of spectral integration, and many applications require
fast parameterizations for computing radiative flux. Here we describe a
novel approach using a linear weighted sum of monochromatic calculations
at a small set of optimally-chosen frequencies. The
empirically-optimized quadrature method is used to compute atmospheric
boundary fluxes, net flux profiles throughout the atmosphere, heating
rate profiles, and top-of-the-atmosphere forcing by CO2. We evaluate the
method against two modern correlated k-distributions and find that we
can achieve comparable errors with 32 spectral points. We also examine
the effect of minimizing different cost functions, and find that in
order to accurately represent heating rates and CO2 forcing, these
quantities must be included in the cost function.%
\end{abstract}%



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