MAPPING THE FOOT OF THE CONTINENTAL-SLOPE WITH SPLINE-SMOOTHED DATA USING THE 2ND DERIVATIVE IN THE GRADIENT DIRECTION

The United States National Oceanic and Atmospheric Administration's (N OAA) ETOPO5 worldwide digital bathymetric dataset has been in the publ ic domain for some years. Because it is noisy, it has not found much u se in oceanography. A bi-cubic spline approach is used to smooth out t he noise and represent the data as an explicit mathematical function, thus making it useful in many areas of oceanography. This method requi res the data to have a rectangular grid. This report(2) gives an effec tive approach for ETOPO5 data's bi-cubic spline representation and smo othing. It presents a new procedure designed to determine the Foot of the Continental Slope (FCS). This procedure is in accord with The Unit ed Nations Law of the Sea (LOS) article 76, section 4.b legal definiti on of the FCS, which is ''the rate of maximum change of the gradient a t 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 i n the normalized gradient direction. The resulting surface is called f or brevity ''Surface of Directed Gradient'' (SDG). The location of the crest of its highest ridge is a good approximation of the FCS. This a pproach gives an accurate mathematical representation of the LOS Conve ntion's legal description of the FCS as stated above. The SDG techniqu e is used to compute the FCS for the U.S. Atlantic coast. The FCS comp uted by the SDG method is compared to the FCS-computed by the surface of maximum curvature approach that is in general use.