Plagioclase‐Saturated Melt Hygrothermobarometry and Plagioclase‐Melt Equilibria Using Machine Learning

Compositions of plagioclase‐melt pairs are commonly used to constrain temperatures (T), dissolved water contents (H2O) and pressures (P) of pre‐eruptive magma storage and transport. However, previous plagioclase‐based thermometers, hygrometers, and barometers can have significant errors, leading to imprecise reconstructions of conditions during plagioclase growth. Here, we explore whether we can refine existing plagioclase‐based hygrothermobarometers with either plagioclase‐melt or melt‐only chemistry (±T/H₂O), calibrated using random forest machine learning on experimental petrology data (n = 1,152). We find that both the plagioclase‐melt and melt‐only models return similar cross‐validation root‐mean‐square errors (RMSEs), as the melt holds most of the P‐T‐H₂O information rather than the plagioclase. T/H₂O‐dependent melt models have test set RMSEs of 25°C, 0.70 wt.% and 76 MPa for temperature, H2O content and pressure, respectively, while T/H₂O‐independent models have RMSEs of 38°C, 0.97 wt.% and 91 MPa. The melt thermometer and hygrometer are applicable to a wide range of plagioclase‐bearing melts at temperatures between 664 and 1355°C, and with H₂O concentrations up to 11.2 wt.%, while the melt barometer is suitable for pressures of ≤500 MPa. An updated plagioclase‐melt equilibrium model has also been calibrated, allowing the equilibrium anorthite content to be predicted with an error of 5.8 mol%. The new P‐T‐H₂O‐An models were applied to matrix glasses and melt inclusions from the 1980 Mount St Helens (USA) and 2014–2015 Holuhraun (Iceland) eruptions, corroborating previous independent estimates and observations. Models are available at https://github.com/kyra‐cutler/Plag‐saturated‐melt‐P‐T‐H2O‐An, enabling assessment of plagioclase‐melt equilibrium and characterization of last‐equilibrated P‐T‐H₂O conditions of plagioclase‐saturated magmas.