Three algorithms for the computation of tidal loading and their numerical accuracy

Abstract

The efficiency and numerical accuracy of three algorithms to compute tidal loading are reviewed. The interest extends to vertical deformations and the self-attraction and loading effect caused by ocean tides. Load calculations require evaluation of convolution integrals over the sphere. In order to assess the numerical accuracy of a load calculation procedure we recall that there exists an almost exact point-wise integration method. This recipe is suitable for computations at individual stations; unfortunately the algorithm is rather expensive for evaluations on a global grid. The other two algorithms are fast implementations of this procedure; the first relies on the use of spherical harmonics and multiplication in the spectral domain of ocean tide spherical harmonic coefficients by Green’s function coefficients that appear in a series of zonal Legendre functions. An alternative is a new method that only relies on rotational symmetry on the sphere. The performance of both field methods deteriorates near coastal boundaries where the average error is about 3 mm, while some energy radiates outward into nearby coastal seas and continents. In rare extreme cases there are localized errors reaching 10 mm. The conclusion is that the accurate load and SAL tides in coastal areas should be computed with a point-wise method rather than a field method, that the FFT method is compatible to the spherical harmonics method, and that all field methods are capable of tidal dissipation errors in coastal seas as large as 100 mWatt/m2 whereas open ocean dissipation errors are typically a factor of 100 smaller.