[Paper Review] Convolution Based Self Attraction and Loading

Anthony Chen, He Wang+2 more|arXiv (Cornell University)|Feb 1, 2026

Geophysics and Gravity Measurements0 citations

TL;DR

The paper introduces a convolution-based approach to Self Attraction and Loading (SAL) for ocean tides, implemented in Modular Ocean Model v6, achieving more accurate tides by reducing Gibbs-related oscillations compared to spherical harmonics.

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.

Motivation & Objective

• Motivate the inclusion of Self Attraction and Loading (SAL) in numerical tide models.
• Develop a convolution-based method as an alternative to spherical harmonics for SAL.
• Demonstrate improved tidal accuracy against satellite-altimetry datasets.
• Integrate the method into Modular Ocean Model, version 6 (MOM6).
• Assess how the new approach mitigates Gibbs phenomenon in coastal regions.

Proposed method

• Formulate SAL as a spherical convolution problem.
• Implement the convolution technique within MOM6.
• Compare convolution-based SAL against traditional spherical harmonic SAL using tidal datasets.
• Evaluate reductions in spurious coastal oscillations (Gibbs phenomenon).
• Quantify improvements in tide accuracy against satellite altimetry data.

Experimental results

Research questions

• RQ1 Does the convolution-based SAL method provide a measurable accuracy improvement for ocean tides over spherical harmonics?
• RQ2 To what extent does the method reduce Gibbs-phenomenon-induced oscillations in coastal regions?
• RQ3 How does SAL with convolution perform when validated against satellite altimetry datasets?
• RQ4 What are the practical implications of integrating convolution SAL into MOM6 for tidal simulations?

Key findings

• Convolution-based SAL reduces spurious oscillations associated with Gibbs phenomenon.
• The approach yields more accurate tides when compared to satellite-altimetry based datasets.
• The method improves SAL representations without relying on spherical harmonics alone.
• Implementation within MOM6 demonstrates feasibility for operational-like tide modeling.
• Coastal region accuracy shows notable improvement due to diminished Gibbs-related artifacts.