Intrinsic Dimensionality as a Metric for the Impact of Mission Design Parameters. Issue 8 (12th August 2022) - Cawse‐Nicholson, K.; Raiho, A. M.; Thompson, D. R.; Hulley, G. C.; Miller, C. E.; Miner, K. R.; Poulter, B.; Schimel, D.; Schneider, F. D.; Townsend, P. A.; Zareh, S. K.
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. Plain Language Summary: We introduce intrinsic dimensionality (ID) as an objective, quantifiable metric for evaluating space‐based mission design choices. We apply ID to the Surface Biology and Geology mission concept and show that increased ID correlates directly with decreased uncertainties in diverse science and applications products. We explore the challenge of balancing performance for many data products from highly dimensional spectral data. We conclude that ID is a valuable tool for optimizing mission performance and evaluating complex, multi‐dimensional design choices. Key Points: Intrinsic dimensionality (ID) is the size of the signal subspace, or the number of significant principal components in a hyperspectral image ID is an applications‐agnostic metric that can evaluate imaging spectroscopy instrument and mission design Spatial, spectral, temporal resolution, and noise directly impact ID for a wide range of Earth surface scenes