Convolution Based Self Attraction and Loading

Self Attraction and Loading (SAL), which includes the deformation of the solid Earth under the load of the ocean tide and the self-gravitation of the so-deformed Earth as well as of the ocean tides themselves, is an important term to include in numerical models of the ocean tides. Computing SAL is a challenging problem that is usually tackled using spherical harmonics. The spherical harmonic approach has several drawbacks which limit its accuracy. In this work, we propose an alternative technique based on a spherical convolution. We implement the convolution technique in the Modular Ocean Model, version 6, and demonstrate that it allows for more accurate tides when measured against tidal datasets based upon satellite altimetry. The convolution based SAL reduces the error by reducing spurious oscillations associated with the Gibbs phenomenon. These oscillations are large in coastal regions under the traditional spherical harmonic approach.