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\begin{document}

\title{Technical Report - Methods: Automated Discovery of Functional
Relationships in Earth Systems Data}



\author[1]{Robert Reinecke}%
\author[2]{Francesca Pianosi}%
\author[3]{Thorsten Wagener}%
\affil[1]{University Mainz}%
\affil[2]{University of Bristol}%
\affil[3]{University of Potsdam}%


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  \date{June 17, 2024}


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\begin{abstract}
Functional relationships capture how variables co-vary across specific
spatial or temporal\\
domains. However, these relationships often take complex forms beyond
linear, and they may\\
only hold for sub-sets of the domain. More problematically, it is often
a priori unknown how\\
such sub-domains are defined. Here we present a new method called SONAR
(diScovery Of\\
fuNctionaAl Relationships) that enables the automated discovery of
functional relationships in\\
large datasets. SONAR operates on existing unstructured data and is
designed to be an\\
explorative tool for large datasets where manual search for functional
relationships would be\\
impossible. We test the method on groundwater recharge outputs of
several global hydrological\\
models to explore its usefulness and limitations. Further, we compare
SONAR to the established\\
CART (Classification and Regression Trees) and CIT (Conditional
Inference Trees) methods.\\
SONAR results in smaller trees with functional relationships in the leaf
nodes instead of specific\\
classes or numbers. SONAR provides a robust and automated method for the
exploration of\\
functional relationships.%
\end{abstract}%



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