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In this paper, we examine the accuracy of manifold coordinate representations as a reduced representation of a hyperspectral imagery (HSI) lookup table (LUT) for bathymetry retrieval. We also explore on a more limited basis the potential for using these coordinates for modeling other in water properties. Manifold coordinates are chosen because they are a data-driven intrinsic set of coordinates, which naturally parameterize nonlinearities that are present in HSI of water scenes. The approach is based on the extraction of a reduced dimensionality representation in manifold coordinates of a sufficiently large representative set of HSI. The manifold coordinates are derived from a scalable version of the isometric mapping algorithm. In the present and in our earlier works, these coordinates were used to establish an interpolating LUT for bathymetric retrieval by associating the representative data with ground truth data, in this case from a Light Detection and Ranging (LIDAR) estimate in the representative area. While not the focus of the present paper, the compression of LUTs could also be applied, in principle, to LUTs generated by forward radiative transfer models, and some preliminary work in this regard confirms the potential utility for this application. In this paper, we analyze the approach using data acquired by the Portable Hyperspectral Imager for Low-Light Spectroscopy (PHILLS) hyperspectral camera over the Indian River Lagoon, Florida, in 2004. Within a few months of the PHILLS overflights, Scanning Hydrographic Operational Airborne LIDAR Survey LIDAR data were obtained for a portion of this study area, principally covering the beach zone and, in some instances, portions of contiguous river channels. Results demonstrate that significant compression of the LUTs is possible with little loss in retrieval accuracy.