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; K1; 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.