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\begin{document}

\title{ClimAG-Krigger: A New (Paleo)Climatology-Oriented Toolbox for
Anisotropic Global Kriging Interpolation}



\author[1]{Nicolas Cosentino}%
\author[2]{Fabrice Lambert}%
\author[2]{Natalia Opazo}%
\author[3]{Axel Osses}%
\author[1]{Elwin van 't Wout}%
\affil[1]{Pontificia Universidad Católica de Chile}%
\affil[2]{Pontifical Catholic University of Chile}%
\affil[3]{Universidad de Chile}%


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  \date{June 07, 2024}


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\begin{abstract}
Data-model comparisons are common when addressing (paleo)climate
questions. Many applications require deriving continuous surface fields
of scalar variables from a set of irregularly distributed data points,
typically for model validation against data or data-derived model input
as initial or boundary conditions. While various interpolation
techniques and interfaces exist, few can simultaneously: (1) interpolate
across local to global spatial scales, (2) perform anisotropic
interpolation using the spatial structure derived from the data instead
of an assumed one, and (3) explicitly derive uncertainty in the
interpolated fields due to both data density and measurement error. We
present a standalone interpolation toolbox including a graphical user
interface (GUI), which is aimed at the general earth science community.
It uses a kriging algorithm whose distance metric is the geodesic on an
oblate spheroid, be it the WGS-84 reference ellipsoid for applications
on the surface of the Earth, or an equivalent ellipsoid with varying
radii for interpolation on vertical levels above the surface. While
kriging algorithms exist that perform interpolation on such
non-Euclidean distances, they do not provide a check for conditionally
negative semi-definiteness (CNSD) of the variogram matrix, which is a
requisite for the kriging method. Since mathematical theory of kriging
on spheroids or ellipsoids has not yet provided a set of authorized
variance-distance functions, we incorporated a numerical check for CNSD
condition for each data realization and variance-distance modeling
scheme. The GUI will allow the user a high degree of customization.
Preliminary results are promising, with robust results for isotropic
interpolation. The derivation of CNSD variogram matrices for anisotropic
interpolation remains the major challenge of the project. When
completed, ClimAG-Krigger will provide the community with an
easy-to-use, robust tool for anisotropic global kriging that will be
specifically tailored for (paleo)climate applications.%
\end{abstract}%



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