A Comparison of Spatial Interpolation Techniques for Determining Shoaling Rates of the Atlantic Ocean Channel
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The United States of Army Corp of Engineers (USACE) closely monitors the changing depths of navigation channels throughout the U.S. and Western Europe. The main issue with their surveying methodology is that the USACE surveys in linear cross sections, perpendicular to the channel direction. Depending on the channel length and width, these cross sections are spaced 100 - 400 feet apart, which produces large unmapped areas within each cross section of a survey.
Using a variety of spatial interpolation methods, depths of these unmapped areas were produced. The choice of spatial interpolator varied upon which method adequately produced surfaces from large hydrographic survey data sets with the lowest amount of prediction error. The data used for this research consisted of multibeam and singlebeam surveys. These surveys were taken in a systematic manner of linear cross-sections that produced tens of thousands of data points.
Nine interpolation techniques (inverse distance weighting, completely regularized spline, spline with tension, thin plate spline, multiquadratic spline, inverse multiquadratic spline, ordinary kriging, simple kriging, and universal kriging) were compared for their ability to accurately produce bathymetric surfaces of navigation channels. Each interpolation method was tested for effectiveness in determining depths at "unknown" areas. The level of accuracy was tested through validation and cross validation of training and test data sets for a particular hydrographic survey.
By using interpolation, grid surfaces were created at 15, 30, 60, and 90-meter resolution for each survey of the study site, the Atlantic Ocean Channel. These surfaces are used to produce shoaling amounts, which are taken in the form of volumes (yd.3). Because the Atlantic Ocean Channel is a large channel with a small gradual change in depth, a comparison of grid resolution was conducted to determine what difference, if any, exists between the calculated volumes from varying grid resolutions. Also, a comparison of TIN model volume calculations was compared to grid volume estimates.
Volumes are used to determine the amount of shoaling and at what rate shoaling is occurring in a navigation channel. Shoaling in each channel was calculated for the entire channel length. Volumes from varying grid resolutions were produced from the Atlantic Ocean Channel over a seven-year period from 1994-2001.
Using randomly arranged test and training datasets, spline with tension and thin plate spline produced the mean total error when interpolating using singlebeam and multibeam hydrographic data respectively. Thin plate spline and simple kriging produced the lowest mean total error in full cross validation testing of entire singlebeam and multibeam hydrographic datasets respectively.
Volume analysis of varying grid resolution indicates that finer grid resolution provides volume estimates comparable to TIN modeling, the USACE's technique for determining sediment volume estimates. The coarser the resolution, the less similar the volume estimates are in comparison to TIN modeling. All grid resolutions indicate that the Atlantic Ocean Channel is shoaling. Using a plan depth of 53 feet, TIN modeling displayed an annual average increase of 928,985 cubic yards of sediment from 1994 - 2001.
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