Barium in seawater: dissolved distribution, relationship to silicon, and barite saturation statedetermined using machine learning

Barium is widely used as a proxy for dissolved silicon and particulate organic carbon fluxes in seawater. However, these proxy applications are limited by insufficient knowledge of the dissolved distribution of Ba ([Ba]). For example, there is significant spatial variability in the barium-silicon relationship, and ocean chemistry may influence sedimentary Ba preservation. To help address these issues, we developed 4095 models for predicting [Ba] using Gaussian process regression machine learning. These models were trained to predict [Ba] from standard oceanographic observations using GEOTRACES data from the Arctic, Atlantic, Pacific, and Southern oceans. Trained models were then validated by comparing predictions against withheld [Ba] data from the Indian Ocean. We find that a model trained using depth, temperature, and salinity, as well as dissolved dioxygen, phosphate, nitrate, and silicate, can accurately predict [Ba] in the Indian Ocean with a mean absolute percentage deviation of 6.0 %. We use this model to simulate [Ba] on a global basis using these same seven predictors in the World Ocean Atlas. The resulting [Ba] distribution constrains the Ba budget of the ocean to 122(+/- 7) x 10(12) mol and reveals oceanographically 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 to barite. We describe a number of possible applications for our model outputs, ranging from use in mechanistic biogeochemical models to paleoproxy calibration. Our approach demonstrates the utility of machine learning in accurately simulating the distributions of tracers in the sea and provides a framework that could be extended to other trace elements. Our model, the data used in training and validation, and global outputs are available in Horner and Mete (2023, 10.26008/1912/bco-dmo.885506.2).