We introduce a new approach, based on machine learning, to estimate pre‐eruptive temperatures and storage depths using clinopyroxene‐melt pairs and clinopyroxene‐only chemistry. The model is calibrated for magmas of a wide compositional range, it complements existing models, and it can be applied independently of tectonic setting. Additionally, it allows the identification of the main chemical exchange mechanisms occurring in response to pressure and temperature variations on the base of experimental data without a priori assumptions. After the validation process, performances are assessed with test data never used during the training phase. We estimate the uncertainty using the root‐mean‐square error (RMSE) and the coefficient of determination (R²). The application of the best performing algorithm (trained in the range 0–40 kbar and 952–1882 K) to clinopyroxene‐melt pairs from primitive to extremely differentiated magmas of both subalkaline and alkaline systems returns a RMSE on the order of 2.6 kbar and 40 K for pressure and temperature, respectively. We additionally present a melt‐ and temperature‐independent clinopyroxene barometer in the range 0–40 kbar, characterized by a RMSE of the order of 3 kbar. Tested for tholeiitic compositions in the range 0–10 kbar, the melt‐ and temperature‐independent clinopyroxene barometer has a RMSE of 1.7 kbar. We finally apply the proposed approach to clinopyroxenes from Iceland, providing new, independent, insights about pre‐eruptive storage depths of Icelandic volcanoes. The general applicability of this model will promote the comparison between the architecture of plumbing systems across tectonic settings and facilitate the comparison between petrologic and geophysical studies.

Thermobarometry is a fundamental tool to quantitatively interrogate magma plumbing systems and broaden our appreciation of volcanic processes. Developments in random forest‐based machine learning lend themselves to a data‐driven approach to clinopyroxene thermobarometry, allowing users to access large experimental data sets that can be tailored to individual applications in Earth Sciences. We present a methodological assessment of random forest thermobarometry using the R freeware package extraTrees. We investigate the model performance, the effect of hyperparameter tuning, and assess different methods for calculating uncertainties. Deviating from the default hyperparameters used in the extraTrees package results in little difference in overall model performance (<0.2 kbar and <3°C difference in standard error estimate, SEE). However, accuracy is greatly affected by how the final value from the distribution of trees in the random forest is selected (mean, median, or mode). Using the mean value leads to higher residuals between experimental and predicted P and T, whereas using median values produces smaller residuals. Additionally, this work provides two scripts for users to apply the methodology to natural data sets. The first script permits modification and filtering of the model calibration data set. The second script contains premade models, where users can rapidly input their data to recover PT estimates (SEE clinopyroxene‐only model: 3.2 kbar, 72.5°C and liquid‐clinopyroxene model: 2.7 kbar, 44.9°C). Additionally, the scripts allow the user to estimate the uncertainty for each analysis, which in some cases is significantly smaller than the reported SEE. These scripts are open source and can be accessed at https://github.com/corinjorgenson/RandomForest-cpx-thermobarometer.

We present Thermobar, a new open-source Python3 package for calculating pressures, temperatures, and melt compositions from mineral and mineral-melt equilibrium. Thermobar allows users to perform calculations with >100 popular parametrizations involving liquid, olivine-liquid, olivine-spinel, pyroxene only, pyroxene-liquid, two pyroxene, feldspar-liquid, two feldspar, amphibole only, amphibole-liquid, and garnet equilibria. Thermobar is the first open-source tool which can match up all possible pairs of phases from a given region, and apply various equilibrium tests to identify pairs from which to calculate pressures and temperatures (e.g. pyroxene-liquid, two pyroxene, feldspar-liquid, two feldspar, amphibole-liquid). Thermobar also contains functions allowing users to propagate analytical errors using Monte-Carlo methods, convert pressures to depths using different crustal density profiles, plot mineral classification and mineral-melt equilibrium diagrams, calculate liquid viscosities, and convert between oxygen fugacity values, buffer positions and Fe speciation in a silicate melt. Thermobar can be downloaded using pip and extensive documentation is available at https://thermobar.readthedocs.io/.