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\begin{document}

\title{Intrinsic Dimensionality as a Metric for the Impact of Mission Design
Parameters}



\author[1]{Kerry Cawse-Nicholson}%
\author[2]{Ann Raiho}%
\author[1]{David Ray Thompson}%
\author[1]{Glynn Hulley}%
\author[3]{Charles E. Miller}%
\author[3]{Kimberley Miner}%
\author[4]{Benjamin Poulter}%
\author[3]{David Schimel}%
\author[5]{Fabian Schneider}%
\author[6]{Philip A Townsend}%
\author[1]{Shannon-Kian Zareh}%
\affil[1]{Jet Propulsion Laboratory, California Institute of Technology}%
\affil[2]{NASA Goddard Space Flight Center}%
\affil[3]{Jet Propulsion Laboratory}%
\affil[4]{NASA}%
\affil[5]{California Institue of Technology}%
\affil[6]{University of Wisconsin-Madison}%


\vspace{-1em}



  
  \date{May 24, 2024}


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\begin{abstract}
High-resolution space-based spectral imaging of the Earth's surface
delivers critical information for monitoring changes in the Earth system
as well as resource management and utilization. Orbiting spectrometers
are built according to multiple design parameters, including ground
sampling distance (GSD), spectral resolution, temporal resolution, and
signal-to-noise. The different applications drive divergent instrument
designs, so optimization for wide-reaching missions is complex. The
Surface Biology and Geology component of NASA's Earth System Observatory
addresses science questions and meets applications needs across diverse
fields, including terrestrial and aquatic ecosystems, natural disasters,
and the cryosphere. The algorithms required to generate the geophysical
variables from the observed spectral imagery each have their own
inherent dependencies and sensitivities, and weighting these objectively
is challenging. Here, we introduce intrinsic dimensionality (ID), a
measure of information content, as an applications-agnostic, data-driven
metric to quantify performance sensitivity to various design parameters.
ID is computed through the analysis of the eigenvalues of the image
covariance matrix, and can be thought of as the number of significant
principal components. This metric is extremely powerful for quantifying
the information content in high-dimensional data, such as spectrally
resolved radiances and their changes over space and time. We find that
the intrinsic dimensionality decreases for coarser GSD, decreased
spectral resolution and range, less frequent acquisitions, and lower
signal-to-noise levels. This decrease in information content has
implications for all derived products. Intrinsic dimensionality is
simple to compute, providing a single quantitative standard to evaluate
combinations of design parameters, irrespective of higher-level
algorithms, products, applications, or disciplines.%
\end{abstract}%



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\textbf{Hosted file}

\verb`essoar.10510874.1.docx`  available at \url{https://authorea.com/users/532018/articles/597796-intrinsic-dimensionality-as-a-metric-for-the-impact-of-mission-design-parameters}

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