Distribution-Free, Variable Resolution Depth Estimation with Composite Uncertainty

Recent algorithms for processing hydrographic data have treated the problem of achievable resolution by constructing grids of fixed resolution, a composite grid of variable resolution, recursive sub-division in a quad-tree, or by relying on a comprehensive TIN of the original points. These algorithms all impose some artificial structure on the data to allow for efficient computation, however, which this paper attempts to address. A scheme is outlined which provides a robust estimate of depth and associated uncertainty that makes as few assumptions as possible. Using a non-uniform spectral analysis, it estimates the spatial scales at which the data are consistent so it can estimate within the Nyquist limit for the underlying surface. Kernel density techniques estimate the most likely depth, and density partitioning estimates the observational and modeling uncertainty. After correcting for potential biases the uncertainty is augmented using a modified Hare-Godin-Mayer system integration uncertainty and a sound speed profile variability due to Beaudoin et al. The result is a robust, distributionfree, continuously variable-resolution estimate of depth with an associated uncertainty. This algorithm is illustrated by estimating the depth (and uncertainty) of Challenger Deep, and the paper then provides some perspectives on efficiency, extensibility and adaptability of this algorithm in the hydrographic context.