Adaptive, variable resolution grids for bathymetric applications using a quadtree approach

Abstract

The spatial sampling often used to process and represent bathymetric data are of fixed grid resolution where the least depth value is stored in each grid cell. This results in Digital Elevation Models (DEMs) that are used to depict the underlying features of the seafloor. With the discretion of the user, the resulting DEMs used may either be of coarse resolution or a very fine resolution surface which provides as many details as possible. However, depending on the resolution of the data collected and the variability of the seafloor, the arbitrary user defined grid resolution is not the best option. Hence we address the problem of finding an optimal grid resolution for representing and processing the bathymetric data for the application of bathymetric risk assessment whilst maintaining computational efficiency. Here we adopt the quadtree decomposition approach. In addition, the research suggests the optimal criteria and standard deviation threshold, σ t h {\sigma -{th}} values for this particular application. These suggestions are still flexible and can be optimized for this application depending on the end user requirements. Previous studies have focused only on the splitting criteria or the constrained criteria to ensure that there is homogeneous accuracy over the entire dataset. However, an investigation into the threshold selection for the standard deviation, σ t h {\sigma -{th}} which describes the variability in the dataset is one of the most important splitting criterion, that is still lacking. Also, a new approach to store the depths in the grid in a time ordered approach for each epoch is shown. By optimizing the criteria for the quadtree decomposition and time series algorithm, the approaches shown in this paper provide the adaptive, accurate DEM which makes optimal use of the available bathymetric data for the Netherlands Continental Shelf (NCS) as the study area. This data preparation step forms the basis for developing a probabilistic approach to assigning hydrographic resurvey frequencies in the NCS.