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Abstract Early studies revealed relationships between barium (Ba), particulate organic carbon and silicate, suggesting applications for Ba as a paleoproductivity tracer and as a tracer of modern ocean circulation.But, what controls the distribution of barium (Ba) in the oceans?Here, we investigated the Arctic Ocean Ba cycle through a one‐of‐a‐kind data set containing dissolved (dBa), particulate (pBa), and stable isotope Ba ratio (δ¹³⁸Ba) data from four Arctic GEOTRACES expeditions conducted in 2015. We hypothesized that margins would be a substantial source of Ba to the Arctic Ocean water column. The dBa, pBa, and δ¹³⁸Ba distributions all suggest significant modification of inflowing Pacific seawater over the shelves, and the dBa mass balance implies that ∼50% of the dBa inventory (upper 500 m of the Arctic water column) was supplied by nonconservative inputs. Calculated areal dBa fluxes are up to 10 μmol m⁻² day⁻¹on the margin, which is comparable to fluxes described in other regions. Applying this approach to dBa data from the 1994 Arctic Ocean Survey yields similar results. The Canadian Arctic Archipelago did not appear to have a similar margin source; rather, the dBa distribution in this section is consistent with mixing of Arctic Ocean‐derived waters and Baffin Bay‐derived waters. Although we lack enough information to identify the specifics of the shelf sediment Ba source, we suspect that a sedimentary remineralization and terrigenous sources (e.g., submarine groundwater discharge or fluvial particles) are contributors. 

Abstract. Barium is widely used as a proxy for dissolved silicon and particulateorganic carbon fluxes in seawater. However, these proxy applications arelimited by insufficient knowledge of the dissolved distribution of Ba([Ba]). For example, there is significant spatial variability in thebarium–silicon relationship, and ocean chemistry may influence sedimentaryBa preservation. To help address these issues, we developed 4095 models forpredicting [Ba] using Gaussian process regression machine learning. Thesemodels were trained to predict [Ba] from standard oceanographic observationsusing GEOTRACES data from the Arctic, Atlantic, Pacific, and Southernoceans. Trained models were then validated by comparing predictions againstwithheld [Ba] data from the Indian Ocean. We find that a model trained usingdepth, temperature, and salinity, as well as dissolved dioxygen, phosphate,nitrate, and silicate, can accurately predict [Ba] in the Indian Ocean with amean absolute percentage deviation of 6.0 %. We use this model tosimulate [Ba] on a global basis using these same seven predictors in theWorld Ocean Atlas. The resulting [Ba] distribution constrains the Ba budgetof the ocean to 122(±7) × 1012 mol and revealsoceanographically consistent variability in the barium–silicon relationship. We then calculate the saturation state of seawater with respect to barite. This calculation reveals systematic spatial and vertical variations in marine barite saturation and shows that the ocean below 1000 m is at equilibrium with respect tobarite. We describe a number of possible applications for our model outputs, ranging from use in mechanistic biogeochemical models to paleoproxy calibration. Ourapproach demonstrates the utility of machine learning in accurately simulatingthe distributions of tracers in the sea and provides a framework that couldbe extended to other trace elements. Our model, the data used in training and validation, and global outputs are available in Horner and Mete (2023, https://doi.org/10.26008/1912/bco-dmo.885506.2).