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Articles

1998: Vol. LXXV, No. 2

Mapping the Foot of the Continental Slope with Spline-Smoothed Data Using the Second Derivative in the Gradient Direction

Submitted
June 12, 2015
Published
2015-05-21

Abstract

The United States National Oceanic and Atmospheric Administration’s (NOAA) ET0P05 worldwide digital bathymetric dataset has been in the public domain for some years. Because it is noisy, it has not found much use in oceanography. A bi-cubic spline approach is used to smooth out the noise and represent the data as an explicit mathematical function, thus making it useful in many areas of oceanography. This method requires the data to have a rectangular grid. This report2 gives an effective approach for ET0P05 data’s bi-cubic spline representation and smoothing. It presents a new procedure designed to determine the Foot of the Continental Slope (FCS). This procedure is in accord with The United Nations Law of the Sea (LOS) article 76, section 4.b legal definition of the FCS, which is "the rate of maximum change of the gradient at its base". This explicit mathematical function can also be used to refine the grid. This function can also be differentiated exactly. One may compute from this function, at any point, the second derivative in the normalized gradient direction. The resulting surface is called for brevity "Surface of Directed Gradient" (SDG). The location of the crest of its highest ridge is a good approximation of the FCS. This approach gives an accurate mathematical representation of the LOS Convention’s legal description of the FCS as stated above. The'SDG technique is used to compute the FCS for the U.S. Atlantic coast. The FCS computed by the SDG method is compared to the FCS' computed by the surface of maximum curvature approach that is in general use.