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\begin{document}

\title{Emulating present and future simulations of melt rates at the base of
Antarctic ice shelves with neural networks}



\author[1]{Clara Burgard}%
\author[2]{Nicolas C Jourdain}%
\author[3]{Pierre Mathiot}%
\author[4]{Robin Smith}%
\author[5]{Rieke Schäfer}%
\author[3]{Justine Caillet}%
\author[6]{Tobias S. Finn}%
\author[1]{J. Emmanuel Johnson}%
\affil[1]{Univ. Grenoble Alpes/CNRS/IRD/G-INP/INRAe, Institut des Geosciences de l'Environnement}%
\affil[2]{French National Centre for Scientific Research (CNRS)}%
\affil[3]{Univ. Grenoble Alpes/CNRS/IRD/G-INP, Institut des Geosciences de l'Environnement}%
\affil[4]{University  of  Reading,}%
\affil[5]{Physikalisch-Technische Bundesanstalt}%
\affil[6]{CEREA, École des Ponts and EDF R\&D}%


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  \date{June 14, 2024}


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\begin{abstract}
Melt rates at the base of Antarctic ice shelves are needed to drive
projections of the Antarctic ice sheet mass loss. Current basal melt
parameterisations struggle to link open ocean properties to ice-shelf
basal melt rates for the range of current sub-shelf cavity geometries
around Antarctica. We present a novel parameterisation based on deep
learning. With a simple feedforward neural network, or multilayer
perceptron, acting on each grid cell separately, we emulate the behavior
of circum-Antarctic cavity-resolving ocean simulations. We explore
different neural network sizes and find that, in all cases containing at
least one hidden layer, this kind of emulator produces reasonable basal
melt rates for our training ensemble, closer to the reference simulation
than traditional parameterisations. For testing, we use an independent
ensemble of simulations that was produced with the same ocean model but
with different model parameters, different cavity geometries and
different forcing. In this challenging test, traditional and neural
network parameterisations yield similar results on present conditions.
In much warmer conditions than the training ensemble, both traditional
parameterisations and neural networks struggle, but the neural networks
tend to produce basal melt rates closer to the reference than a majority
of traditional parameterisations. These neural networks are therefore
suitable for century-scale Antarctic ice-sheet projections.%
\end{abstract}%



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