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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. 

Biogeochemical processes are often spatially discrete (hot spots) and temporally isolated (hot moments) due to variability in controlling factors like hydrologic fluxes, lithological characteristics, bio-geomorphic features, and external forcing. Although these hot spots and hot moments (HSHMs) account for a high percentage of carbon, nitrogen and nutrient cycling within the Critical Zone, the ability to identify and incorporate them into reactive transport models remains a significant challenge. This chapter provides an overview of the hot spots hot moments (HSHMs) concepts, where past work has largely focused on carbon and nitrogen dynamics within riverine systems. This work is summarized in the context of process-based and data-driven modeling approaches, including a brief description of recent research that casts a wider net to incorporate Hg, Fe and other Critical Zone elements, and focuses on interdisciplinary approaches and concepts. The broader goal of this chapter is to provide an overview of the gaps in our current understanding of HSHMs, and the opportunities therein, while specifically focusing on the underlying parameters and processes leading to their prognostic and diagnostic representation in reactive transport models.