Accuracy of Interpolated Bathymetric Digital Elevation Models

Digital elevation models (DEMs) are the framework for the modeling of numerous coastal processes including tsunami propagation and inundation, storm-surge, and sea-level-rise. The National Oceanic and Atmospheric Administration (NOAA) National Geophysical Data Center (NGDC) develops integrated bathymetric-topographic DEMs across coastal zones to support tsunami propagation and inundation modeling efforts. The development of integrated bathymetric-topographic DEMs requires extreme interpolation across large distances between sparse bathymetric measurements in order for the model to retain the resolution of dense coastal topographic data, particularly lidar. This study examines the accuracy of three common interpolation methods used to develop bathymetric DEMs of Kachemak Bay, Alaska: inverse distance weighting (IDW), spline, and triangular irregular network (TIN). The goal of the study is to examine the relationship between interpolation deviations from measured depths and sample density, distance to the nearest depth measurement, and terrain characteristics. A split-sample method was used to determine that the accuracy of the three evaluated interpolation methods decreases in areas of high surface curvature, at greater distances from the nearest measurement, and at smaller sampling densities. Furthermore, spline is the most accurate interpolation method at all sampling densities. Predictive equations of interpolation uncertainty derived from the quantification of interpolation deviations in relationship to sample density and distance to the nearest depth measurement were developed. These predictive equations of the uncertainty in DEMs introduced by interpolation methods can aid mitigation efforts for coastal communities prone to tsunamis, storm-surge, and other coastal hazards, by improving the understanding of the propagation of uncertainty into the modeling of such coastal processes that rely on integrated bathymetric-topographic DEMs