Convolution Based Self Attraction and Loading

TL;DR

The study tackles the accuracy limitations of SAL in ocean tide modeling by replacing the conventional spherical-harmonic SAL with a spherical convolution approach accelerated by CSFMM. The convolution SAL mitigates Gibbs-induced coastal oscillations, yielding smoother SAL gradients and reduced amplitude and phase errors when validated against the TPXO9 tidal atlas, especially at moderate grid resolutions. While high-resolution results show nuanced behavior, the overall improvement in tidal phase accuracy and RMSE demonstrates clear advantages for regional and global tide simulations. The approach also offers favorable strong-scaling properties, enabling integration into larger, multi-layer MOM6 runs and motivating future extensions to regional models and Earth inhomogeneity effects through spatially varying Green's functions.

Abstract

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.

Figures (4)

• Figure 1: SAL acceleration computed from spherical harmonic and convolution based SAL techniques. The accelerations are normalized by dividing the largest magnitude of acceleration.
• Figure 2: As in Fig. \ref{['fig:salaccel']}, but focused on the Northeast Atlantic and North Sea.
• Figure 3: Spherical harmonic spectra of the SAL acceleration, computed from the zonal accelerations in Fig. \ref{['fig:salaccel']} over the ocean grid points. The spectra are normalized to unit norm. The wavelength for a given spherical harmonic degree is $2\pi R_E/n$.
• Figure 4: Strong scaling of the two methods of computing SAL at 0.36 degree nominal grid spacing.