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\begin{document}

\title{Building tangent-linear and adjoint models for data assimilation with
neural networks}



\author[1]{Samuel Edward Hatfield}%
\author[2]{Matthew Chantry}%
\author[1]{Peter Dominik Dueben}%
\author[1]{Philippe Lopez}%
\author[3]{Alan Jon Geer}%
\author[4]{Tim N Palmer}%
\affil[1]{ECMWF}%
\affil[2]{Atmospheric, Oceanic and Planetary Physics, University of Oxford}%
\affil[3]{European Centre for Medium Range Weather Forecasts}%
\affil[4]{Oxford University}%


\vspace{-1em}



  
  \date{June 14, 2024}


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\begin{abstract}
We assess the ability of neural network emulators of physical
parametrization schemes in numerical weather prediction models to aid in
the construction of linearised models required by 4D-Var data
assimilation. Neural networks can be differentiated trivially, and so if
a physical parametrization scheme can be accurately emulated by a neural
network then its tangent-linear and adjoint versions can be obtained
with minimal effort, compared with the standard paradigms of manual or
automatic differentiation of the model code. Here we demonstrate this
idea by emulating the non-orographic gravity wave drag parametrization
scheme in an atmospheric model with a neural network, and deriving its
tangent-linear and adjoint models. We demonstrate that these neural
network-derived tangent-linear and adjoint models not only pass the
standard consistency tests but also can be used successfully to do
4D-Var data assimilation. This technique holds the promise of
significantly easing maintenance of tangent-linear and adjoint codes in
weather forecasting centres, if accurate neural network emulators can be
constructed.%
\end{abstract}%



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