Multiscale Topology of the Spectroscopic Mixing Space: Impervious Substrates

Characterization of topology and dimensionality of spectral feature spaces provides insight into information content. The objective of this study is to characterize topology and spectral dimensionality of spectral mixing spaces representing a diversity of built environments in urban areas worldwide using both spaceborne and airborne imaging spectroscopy. Comparing complementary types of dimensionality reduction to render high dimensional spectral mixing spaces allows for characterization of both spectral dimensionality and mixing space topology. Using a diverse collection of 30 decameter-resolution urban core subscenes imaged by the EMIT spaceborne imaging spectrometer and 5 sub-decameter-resolution urban gradient flight lines imaged by the AVIRIS-NG airborne imaging spectrometer, we conduct such characterizations. Global scale topology of low order principal component-derived mixing spaces resembles the Substrate, Vegetation, Dark (SVD) triangular topology of globally diverse composite mixing spaces found in numerous earlier studies - but these spaces are also characterized by multiple (2-3) distinct substrate endmembers and a wide variety of less common spectra corresponding to synthetic anthropogenic materials. Local scale topology from 2D and 3D UMAP manifold embeddings reveals the presence of multiple spectrally distinct impervious substrate mixing continua corresponding to geographically distinct built environments.