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We present a spatially and vertically resolved global grid of dissolved barium concentrations ([Ba]) in seawater determined using Gaussian Process Regression machine learning. This model was trained using 4,345 quality-controlled GEOTRACES data from the Arctic, Atlantic, Pacific, and Southern Oceans. Model output was validated by assessing the accuracy of [Ba] simulations in the Indian Ocean, noting that none of the Indian Ocean data were seen by the model during training. We identify a model that can accurate predict [Ba] in the Indian Ocean using seven features: depth, temperature, salinity, as well as dissolved dioxygen, phosphate, nitrate, and silicate concentrations. This model achieves a mean absolute percentage error of 6.0 %, which we assume represents the generalization error. This model was used to simulate [Ba] on a global basis using predictor data from the World Ocean Atlas 2018. The global model of [Ba] is on a 1°x 1° grid with 102 depth levels from 0 to 5,500 m. The dissolved [Ba] output was then used to simulate dissolved Ba* (barium-star), which is the difference between 'observed' and [Ba] predicted from co-located [Si]. Lastly, [Ba] data were combined with temperature, salinity, and pressure data from the World Ocean Atlas to calculate the saturation state of seawater with respect to barite. The model reveals that the volume-weighted mean oceanic [Ba] and and saturation state are 89 nmol/kg and 0.82, respectively. These results imply that the total marine Ba inventory is 122(±7) ×10¹² mol and that the ocean below 1,000 m is at barite equilibrium.
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This content will become publicly available on January 1, 2026
Domain Decomposition for Enhancement of Reduced-Order Models
Decision-support systems for environmental management of coastal areas must account for brine and seawater dynamics. Physics-based models of these phenomena are computationally expensive, which limits their usefulness for decision-making under uncertainty. Data-driven modeling techniques, such as extended dynamic mode decomposition (xDMD), ameliorate these challenges. We demonstrate that xDMD, equipped with a novel domain decomposition component, effectively represents a validated, real-world, coupled nonlinear seawater inundation model. It serves as an efficient surrogate of process-based simulations, capable of accurate reproduction and reconstruction of missing pressure and salinity data in the interpolation regime. It accurately predicts low-rank pressure distributions (repeated dynamics) but struggles to forecast long-term salinity dynamics (cumulative evolution). The addition of domain decomposition improves the robustness and accuracy of xDMD, with the overlapping domain approach outperforming the nonoverlapping one in the projection accuracy. In our experiments, xDMD is 1700 times faster than the process-based model and requires 800 times less storage, while efficiently capturing pressure and salinity dynamics.
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- Award ID(s):
- 2100927
- PAR ID:
- 10618470
- Publisher / Repository:
- Beggel House Inc
- Date Published:
- Journal Name:
- Journal of Machine Learning for Modeling and Computing
- Volume:
- 6
- Issue:
- 3
- ISSN:
- 2689-3967
- Page Range / eLocation ID:
- 19-36
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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