Intrinsic Dimensionality as a Metric for the Impact of Mission Design Parameters

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 ratio. 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 ID 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. ID is simple to compute, providing a single quantitative standard to evaluate combinations of design parameters, irrespective of higher‐level algorithms, products, applications, or disciplines.

Designing an Observing System to Study the Surface Biology and Geology (SBG) of the Earth in the 2020s

“…While not explicitly called out in the Decadal Survey, these are necessary prerequisites for all Earth surface studies. Intermediate and derived products will be decided later in mission formulation but will draw from the deep literature review of available algorithms (Cawse‐Nicholson et al., 2021) and an end‐to‐end uncertainty assessment using the frameworks develops during this architecture study (Cawse‐Nicholson et al., 2022; Raiho et al., in press).…”

Spectral dimensionality of imaging spectroscopy data over diverse landscapes and spatial resolutions

“…There were several methods for estimating dimensionality in the literature with similar conceptualizations. 22,24,25,28,29 We adopted the automatic noise estimation approach by Thompson et al 22 to investigate the intrinsic spectral dimensionalities of aforementioned 400-hectare subimages. This aims to determine the number of principle components corresponding with spatially coherent structures in the scene.…”

“…Most imaging spectroscopy investigations focus on surface features rather than atmospheric effects, so it is also important to understand the variability in surface reflectance alone. Cawse-Nicholson et al 28 investigated the responses of image intrinsic dimensionality to spatial, spectral, and temporal resolutions, as well as signal-to-noise ratio. They concluded that intrinsic dimensionality would generally decrease at coarser spatial resolutions.…”

Simulating Global Dynamic Surface Reflectances for Imaging Spectroscopy Spaceborne Missions: LPJ‐PROSAIL

“…E2E simulators quantify instrument, retrieval, and algorithmic uncertainties and the propagation of these uncertainties under various workflows. For example, the Hypertrace workflow was developed for SBG to assess science value trades and algorithm performance (Cawse‐Nicholson et al., 2022; Raiho et al., 2022). Three dimensional radiative transfer models (RTMs), such as the Digital Imaging and Remote Sensing Image Generation (DIRSIG, Lentilucci & Brown, 2003; Schott et al., 1999) and Discrete Anisotropic Radiative Transfer (DART, Gastellu‐Etchegorry et al., 2015), can also inform E2E as they provide a controlled simulation environment whereby surface leaving reflectances are modeled via detailed 3‐dimensional representation of objects and the scattering, absorption and transmission of light (Goodenough & Brown, 2012).…”