Kyra S. Cutler, Mike Cassidy, Jon Blundy

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= 1152). 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 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 characterisation of last-equilibrated P-T-H2O conditions of plagioclase-saturated magmas.