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\begin{document}

\title{Spectrally Resolved Longwave Surface Emissivity Reduces Atmospheric
Heating Biases}



\author[1]{Lili Manzo}%
\author[1]{Charles Sutton Zender}%
\author[1]{Juan P Tolento}%
\author[2]{Chloe A. Whicker}%
\affil[1]{University of California, Irvine}%
\affil[2]{University  of Michigan}%


\vspace{-1em}



  
  \date{June 14, 2024}


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\begin{abstract}
Many Earth system models (ESMs) approximate surface emissivity as a
constant. This broadband approximation reduces computational burden, yet
biases longwave (LW) atmospheric fluxes and heating by neglecting the
spectral structure of surface emissivity and atmospheric absorption.
These biases are largest over surfaces with strongly varying emissivity
and minimal atmospheric opacity (e.g., due to water vapor and clouds).
Our study focuses on liquid water, ice, and snow surfaces. We use LW
spectral emissivity \selectlanguage{greek}ε\selectlanguage{english}(\selectlanguage{greek}λ\selectlanguage{english}) calculated via the Fresnel equations and
validated against a dataset of spectral surface emissivity. We
flux-weight and bin \selectlanguage{greek}ε\selectlanguage{english}(\selectlanguage{greek}λ\selectlanguage{english}) into 16 spectral bands accepted by an offline
single-column atmospheric radiative transfer model (RRTMG\_LW) commonly
used in ESMs (including E3SM and CESM). We quantify flux and heating
biases introduced by broadband emissivity assumptions in comparison with
the 16-band spectrally resolved case for three different surface types,
three standard atmospheric profiles, and for the key drivers surface
temperature, cloud water path, and atmospheric water vapor. In addition,
we devise and test novel greybody and semi-spectral methods of
representing \selectlanguage{greek}ε\selectlanguage{english}(\selectlanguage{greek}λ\selectlanguage{english}) with the goal of reducing biases while preserving
computational efficiency. We find that typical broadband assumptions
artificially cool Earth's surface, thereby stabilizing the lower
troposphere. LW upwelling flux is overestimated by 4.5
W/m\textsuperscript{2} (\textasciitilde{}1.4\%) at the bottom of a
mid-latitude winter atmosphere over an ice surface, and by 3.3
W/m\textsuperscript{2} (\textasciitilde{}1.4\%) at the top of
atmosphere. Lastly, we find that a semi-spectral approach (five bands
instead of 16) reduces biases by up to 99\% relative to the broadband
approximation.%
\end{abstract}%



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