Ocean tides, part II: A hydrodynamical interpolation model

Abstract

The strictly mathematical ocean tide model developed in Part I of this paper is modified in order to include realistic hydrodynamical barrier effects of narrow ocean ridges and other large bottom irregularities. This modification begins with a hydrodynamical redefinition of the ocean bathymetry at over 3,000 grid points, increasing simultaneously the depth data range to: 10m ? 7,000m. In a second step a unique hydrodynamical interpolation technique is developed that incorporates into the model over 2,000 empirical tide data collected around the world at continental and island stations. This interpolation is accomplished by a controlled cell‐wise adjustment of the bottom friction coefficient and by allowing a monitored in‐ or out‐flow across the mathematical ocean boundary and so, redefining a more physical shoreline. Extensive computer experiments were conducted to study the characteristics of the novel friction laws and hydrodynamical interpolation methods. The computed M₂‐tide data along with all (specially labeled) empirical constants are tabulated in map form for four typical 30° by 50° ocean areas. It is estimated that the tabulated tidal charts permit a prediction of the M₂‐tide elevation of the ocean surface over the geoidal level with an accuracy of better than 5 cm anywhere in the open ocean and with somewhat less accuracy near rough shorelines. With the forthcoming construction of the lesser S₂, N₂, and K₂; K_1; O₁, P₁, and Q₁; and Mf, Mm, and Ssa tidal constituents, the total tide‐prediction error can be kept below the 10‐cm bound posed by applied researchers of today.