Spatial Interpolation of Tidal Data Using a Multiple-Order Harmonic Equation for Unstructured Grids

Lei Shi, Kurt W. Hess, Edward P. Myers

1Coast Survey Development Laboratory, NOAA, Silver Spring, USA 2Chesapeake Research Consortium, Edgewater, USA.
1Coast Survey Development Laboratory, NOAA, Silver Spring, USA 2Earth Resources Technology, Laurel, USA.
Coast Survey Development Laboratory, NOAA, Silver Spring, USA.

DOI: 10.4236/ijg.2013.410140                

Abstract

A general spatial interpolation method for tidal properties has been developed by solving a partial differential equation with a combination of different orders of harmonic operators using a mixed finite element method. Numerically, the equation is solved implicitly without iteration on an unstructured triangular mesh grid. The paper demonstrates the performance of the method for tidal property fields with different characteristics, boundary complexity, number of input data points, and data point distribution. The method has been successfully applied under several different tidal environments, including an idealized distribution in a square basin, coamplitude and cophase lines in the Taylor semi-infiite rotating channel, and tide coamplitude and cophase lines in the Bohai Sea and Chesapeake Bay. Compared to Laplace’s equation that NOAA/NOS currently uses for interpolation in hydrographic and oceanographic applications, the multiple-order harmonic equation method eliminates the problem of singularities at data points, and produces interpolation results with better accuracy and precision.

Keywords

Tides; Tidal Data; Approximation; Harmonic Functions; Finite Element Method; Spatial Interpolation; Taylor Basin; Bohai Sea; Chesapeake Bay

Conflicts of Interest

The authors declare no conflicts of interest.

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