The oceans remain one of Earth's most enigmatic frontiers, with approximately 75% of the world's oceans still unmapped to modern standards.  To overcome this, interpolation serves as the primary method for creating seamless coverage from incomplete coverage hydrographic data sets and is essential for creating a seamless digital bathymetric model (DBM) compiled from sparse bathymetric datasets and set-line spacing surveys. While methods for quantifying the uncertainty in depth measurements are well-researched, interpolation introduces unqualified depth uncertainties. This study aims to estimate and characterize these uncertainties which are essential to nautical charting, and navigational safety, and important in many other fields.
Organized into two source data scenarios, the research focuses on uncertainties arising from randomly sampled data and set-line surveys. It employs three widely recognized deterministic interpolation methods—Linear, Inverse Distance Weighting (IDW), and Spline— across five testbeds that vary in slope and roughness. The goal is to identify the interpolation method with the lowest uncertainty and unravel the relationships between interpolation uncertainty and three ancillary parameters (distance to the nearest measurement, slope, and roughness) for estimating interpolation uncertainty.

By sampling complete seafloor coverage sonar depth data at different densities and line spacings, the study interpolates across entire testbed areas using the chosen methods. Uncertainty is calculated by comparing interpolated depths against the true depths for independent points.  The resulting uncertainties are analyzed statistically and spatially to assess consistency across interpolation methods and determine the interpolation method that yields the least interpolation uncertainty. Linear regression and machine learning techniques (neural networks and random forest) are used to model the relationship between these uncertainties and ancillary parameters to estimate uncertainty.

Evaluation across the five testbeds, encompassing both random sampling and set-line spacing scenarios, reveals the following: 1) Spline performs better than Linear and IDW in estimating depths from a purely scientific perspective; however, 2) differences among the interpolation methods are not statistically significant and minimal from an operational standpoint; 3) sampling density, line spacing, and spatial scales impact uncertainty; 4) roughness is the most important parameter and distance the least important; 5) relationships between ancillary parameters and uncertainty are weak though statistically significant.

The findings of this work suggest the presence of unaccounted-for factors shaping uncertainty or indicate a strong random component within interpolation uncertainty yet lay a foundational understanding for improving the estimate of uncertainty in DBMs within operational settings. Future research recommendations involve exploring supplementary predictors to enhance the predictive capacity of ancillary parameters. Additionally, innovative approaches such as spectral analysis for uncertainty estimation hold promise in advancing methodologies within this domain.