Toward Quantifying Interpolation Uncertainty in Set-Line Spacing Hydrographic Surveys

The oceans remain one of Earth’s last great unknowns, with about 74% still unmapped to modern standards. Consequently, interpolation is employed to create seamless digital bathymetric models (DBMs) from incomplete hydrographic datasets, but this introduces unquantified depth uncertainties. This study aims to estimate and characterize uncertainties arising from set-line spacing hydrographic surveys, which are important for nautical charting, navigational safety, and many other applications. By sampling four distinct complete-coverage testbeds in United States waters that vary in slope and roughness at different line spacings, this study interpolates across entire testbed areas using Spline, Inverse Distance Weighting, and Linear interpolation. Uncertainty is calculated by comparing interpolated depths against the source depths for independent points. The resulting interpolation uncertainties are evaluated from both scientific and operational perspectives. Linear regression and machine learning techniques, specifically artificial neural networks and random forest, are used to model the relationship between these uncertainties and three ancillary predictors (distance to the nearest known measurement, slope, and roughness) for interpolation uncertainty quantification. The results show operational equivalence among the three interpolators, how line spacing and morphology impact uncertainty, and the statistical significance of the examined uncertainty predictors. However, the relationships between the combined ancillary predictors and interpolation uncertainty are weak. These findings suggest the potential presence of unaccounted-for factors influencing uncertainty yet provide a foundational understanding for improving uncertainty estimates in DBMs within operational settings.