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Publication Date
1 April 2023

Faster Self-Attraction and Loading for Variable Resolution Ocean Models

Modeling tides across global and coastal scales is up to 4x faster with scalable self-attraction and loading computations.
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A variable resolution mesh for computing tides with 45-km cells in the open ocean and 5-km cells near the coast and steep bottom topography. (Image by Steven Brus | Argonne National Laboratory)

Ocean tides are important processes that have a variety of interactions with the global climate. Tidal motion creates mass anomalies that affect the Earth’s gravitational field and, in turn, influence tidal dynamics. This effect is referred to as self-attraction and loading (SAL) and is an important process in global-scale tidal modeling. Computing this effect can be a bottleneck in current ocean models. Researchers developed a new technique to more efficiently compute SAL effects. The technique directly computes the SAL terms in parallel on the same mesh used to calculate other dynamical processes in the model. This approach is much faster and more accurate compared to the sequential, interpolation-based strategies conventionally used in Earth system models.


The newly developed technique can increase the efficiency of tidal simulations by up to 4x compared to existing methods. It achieves a higher rate of error convergence for variable resolution meshes because it does not require interpolation to a structured mesh-like existing methodologies. With this technique, the computation time of the SAL terms decreases more effectively in proportion to increasing processor counts, allowing it to be used efficiently within large-scale climate simulations.


An advantage of variable-resolution ocean models is their ability to refine the model’s accuracy in specific target regions. This is particularly important for accurately simulating tides, which become more energetic in shallow coastal regions. However, coastal tidal dynamics also depend on the of the accuracy global tidal signal. SAL effects are particularly important for global tides because they describe how water mass anomalies caused by tidal waves affect the Earth’s gravity and deform the Earth’s crust. The ability to efficiently model this process is essential to capturing the effects of tides as they evolve with climate change.

Typically, efficient calculation of SAL effects requires a structured mesh and existing computational libraries, which are not well-suited for the massively parallel computing required for climate simulations. A newly developed approach avoids these limitations by computing the SAL terms directly on the unstructured mesh and exploits the same strategy used to parallelize the rest of the model’s computations. Researchers showed that by eliminating interpolation to structured meshes, their new method achieves improved error convergence and better performance on parallel computing systems than existing methodologies.

Point of Contact
Darren Engwirda
Argonne National Laboratory
Funding Program Area(s)
Scalable self attraction and loading calculations for unstructured ocean tide models
Brus, Steven R., Kristin N. Barton, Nairita Pal, Andrew F. Roberts, Darren Engwirda, Mark R. Petersen, Brian K. Arbic, Damrongsak Wirasaet, Joannes J. Westerink, and Michael Schindelegger. 2023. “Scalable Self Attraction And Loading Calculations For Unstructured Ocean Tide Models”. Ocean Modelling 182. Elsevier BV: 102160. doi:10.1016/j.ocemod.2023.102160.