Geostatistical interpolation methods to create robust bathymetric surfaces across the USACE dredging portfolio

The United States Corps of Engineers (USACE) maintains over 30,000 km (25,000 mi) of coastal and inland waterways to ensure safe navigation for commercial, recreational, and military traffic. The USACE leverages hydrographic surveying with SONAR echosounders to generate bathymetric surfaces used to identify where and how much material needs removal for channel maintenance. Bathymetric survey data is archived within the USACE eHydro database. However, since these hydrographic survey operations are contracted externally, the data retained have discrepancies impacting end-use cases (e.g., single-beam vs. dual-beam echosounders, survey density, projection system). For operational use in hydrologic and hydrographic applications, SONAR data must be reprocessed into a standard raster data format. Since small errors in bathymetric surface estimation can translate to economically impactful sediment volumes, robust surface generation and uncertainty quantification is crucial.

The USACE currently uses Triangulated Irregular Networks (TIN) as the default surface generation algorithm; this deterministic method has limited capability to capture spatial correlation structure in SONAR data. This study compares bathymetric surfaces created with TIN, Nearest Neighbor (NEAN), and Natural Neighbor (NATN) interpolation and two robust geostatistical interpolation methods—isotropic Ordinary Kriging (OK), and isotropic Regression Kriging (RK) based on spline trend residuals, with a goal of creating an automatic SONAR-to-bathymetric surface data processing pipeline.

The analysis uses 100 independent SONAR surveys collected from across the USACE civil works districts representing diverse spatial extents, sampling densities, and channel morphologies. 10-foot spatial resolution bathymetric surfaces are generated using each of the five interpolation methods for each SONAR dataset. To ensure reproducible kriging models for OK and RK approaches, multiple empirical semivariogram shape functions were fit using a weighted least squares solution with final shape function selection based on maximum Coefficient of Determination. A 5-fold cross-validation using Root Mean Squared Error (RMSE) selects the optimal spline trend surface for RK.

Once bathymetric surfaces are generated, a 10-fold cross-validation scheme for each SONAR dataset compares the five interpolation methods. Normalized Median Absolute Deviation (NMAD) and RMSE assess each method’s accuracy across all surveys. Across the 100 surveys, the OK approach proved best, yielding a 39.1% and 54.6% decrease in RMSE and NMAD, respectively, compared to TIN. The RK approach produced 8.1% decrease in RMSE and 31.4% decrease in NMAD compared to TIN. Conversely, neighbor-based approaches produced worse bathymetric surfaces with a 15.0% increase in RMSE and 5.2% increase in NMAD for the NEAN approach, and an 11.1% increase in RMSE and 11.3% increase in NMAD for the NATN approach.

The preliminary results of the study indicate the importance of accounting for spatial autocorrelation between points in generating accurate bathymetric surface estimates with unbiased uncertainty. Simple deterministic interpolation (TIN) cannot reliably account for complex topography that manifests from dredging and tidal response. However, methods modeling semivariance across the dataset (OK and RK) can account for spatial structure to better model seabed morphologies. In practice, employing geostatistical methods to generate accurate bathymetric surfaces could improve coastal morphological modeling and dredge planning.