Exploring Ancillary Parameters for Quantifying Interpolation Uncertainty in Digital Bathymetric Models

The oceans remain one of Earth's most enigmatic frontiers, with approximately 75% of the world's oceans still unmapped. To create a seamless digital bathymetric model (DBM) from sparse bathymetric datasets, interpolation is employed, but this introduces uncertainties of unknown nature. This study aims to estimate and characterize these uncertainties, which is important in many fields, particularly nautical charting, and navigational safety. Complete seafloor coverage sonar depth data for five testbeds that varied in slope and roughness are sampled at a range of densities (1% to 50%) and interpolated across an entire area using Spline, Inverse Distance Weighting (IDW), and Linear interpolation. The resulting uncertainties are evaluated from both scientific and operational perspectives. Employing linear regression and machine learning techniques, the relationships between these uncertainties and ancillary parameters (distance to the nearest measurement, seabed roughness, and slope) are examined for quantifying and characterizing the interpolation uncertainty. Results indicate insignificant operational differences among the three interpolators in depth estimation, as well as the statistical significance of the examined uncertainty predictors. Additionally, findings suggest the potential presence of unaccounted-for factors shaping uncertainty, yet this work lays a foundational understanding for improving the estimate of uncertainty in DBMs.