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\begin{document}

\title{Revisiting Machine Learning Approaches for Short- and Longwave Radiation
Inference in Weather and Climate Models, Part I: Offline Performance}



\author[1]{Guillaume Bertoli}%
\author[2]{Firat Ozdemir}%
\author[2]{Sebastian Schemm}%
\author[3]{Fernando Perez-Cruz}%
\affil[1]{ETHZ}%
\affil[2]{ETH Zurich}%
\affil[3]{Swiss Data Science Center, ETH Zurich}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\begin{abstract}
As climate modellers prepare their code for kilometre-scale global
global simulations, the computationally demanding radiative transfer
transfer parameterization is a prime candidate for machine learning (ML)
(ML) emulation. Because of the computational demands, many weather
centres centres use a reduced spatial grid and reduced temporal
frequency for radiative radiative transfer calculations in their
forecast models. This strategy is known known to affect forecast
quality, which further motivates the use of ML-based ML-based radiative
transfer parameterizations. This paper contributes to the the discussion
on how to incorporate physical constraints into an ML-based ML-based
radiative parameterization, and how different neural network (NN) (NN)
designs and output normalisation affect prediction performance. A random
random forest (RF) is used as a baseline method, with the European
Centre for for Medium-Range Weather Forecasts (ECMWF) model ecRad, the
operational operational radiation scheme in the Icosahedral
Nonhydrostatic Weather and Climate Climate Model (ICON), used for
training. Surprisingly, the RF is not affected by by the
top-of-atmosphere (TOA) bias found in all NNs tested (e.g., MLP, MLP,
CNN, UNet, RNN) in this and previously published studies. At lower lower
atmospheric levels, the RF can is able to compete with all NNs tested,
but but its memory requirements quickly become prohibitive. For a fixed
memory memory size, most NNs outperform the RF except at TOA. The most
accurate emulator is For the best emulator, we use a recurrent neural
network architecture that which closely imitates imitates the physical
process it emulates. The We additionally normalize the shortwave and
longwave fluxes are normalized to reduce their dependence on from the
solar solar angle and surface temperature respectively. The model are,
furthermore, trained Finally, we train the model with an additional
heating rates penalty in the loss function.function.%
\end{abstract}%



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