Abstract. Numerical simulations of volcanic processes play a fundamental role in understanding the dynamics of magma storage, ascent and eruption. The recent extraordinary progress in computer performance and improvements in numerical modeling techniques allow simulating multiphase systems in mechanical and thermodynamical disequilibrium. Nonetheless, the growing complexity of these simulations requires the development of flexible computational tools that can easily switch between sub-models and solution techniques. In this work we present MagmaFOAM, a library based on the open source computational fluid dynamics software OpenFOAM, that incorporates models for solving the dynamics of multiphase, multicomponent magmatic systems. Retaining the modular structure of OpenFOAM, MagmaFOAM allows run-time selection of the solution technique depending on the physics of the specific process, and sets a solid framework for in-house and community model development, testing and comparison. MagmaFOAM models thermo-mechanical non-equilibrium phase coupling and phase change, and implements state-of-the-art multiple volatile saturation models and constitutive equations with composition-dependent and space-time local computation of thermodynamic and transport properties. Code testing is performed using different multiphase modeling approches for processes relevant to magmatic systems: Rayleigh-Taylor instability, for buyoancy-driven magmatic processes; multiphase shock tube simulations, propedeutical to conduit dynamics studies; bubble growth and breakage in basaltic melts. Benchmark simulations illustrate the capabilities and potential of MagmaFOAM to account for the variety of non-linear physical and thermodynamical processes characterizing the dynamics of volcanic systems.

Abstract. The model's ability to reproduce the state of the simulated object or particular feature or phenomenon is always a subject of discussion. Multidimensional model quality assessment is usually customized to the specific focus of the study and often to a limited number of locations. In this paper, we propose a method that provides information on the accuracy of the model in general, while all dimensional information for posterior analysis of the specific tasks is retained. The main goal of the method is to perform clustering of the multivariate model errors. The clustering is done using the K-means algorithm of unsupervised machine learning. In addition, the potential application of the K-means clustering of model errors for learning and predicting is shown. The method is tested on the 40-year simulation results of the general circulation model of the Baltic Sea. The model results are evaluated with the measurement data of temperature and salinity from more than one million casts by forming a two-dimensional error space and performing a clustering procedure in it. The optimal number of clusters that consist of four clusters was determined using the Elbow cluster selection criteria and based on the analysis of the different number of error clusters. In this particular model, the error cluster of good quality of the model with a bias of 0.4 °C (std = 0.8 °C) for temperature and 0.6 g kg−1 (std = 0.7 g kg−1) for salinity made up 57 % of all comparison data pairs. The prediction of centroids from a limited number of randomly selected data showed that the obtained centroids gained a stability of at least 100 000 error pairs in the learning dataset.

Abstract. Oceanic dissolved inorganic carbon (TC) is the largest pool of carbon that interacts considerably with the atmosphere on human timescales. Oceanic TC is increasing through uptake of anthropogenic carbon dioxide (CO2), and seawater pH is decreasing as a consequence. Both the exchange of CO2 between ocean and atmosphere and the pH response are governed by a set of parameters that interact through chemical equilibria, collectively known as the marine carbonate system. To investigate these processes, at least two of the marine carbonate system's parameters are typically measured – most commonly, two from TC, total alkalinity (AT), pH, and seawater CO2 fugacity (fCO2; or its partial pressure, pCO2, or its dry-air mole fraction, xCO2) – from which the remaining parameters can be calculated and the equilibrium state of seawater solved. Several software tools exist to carry out these calculations, but no fully functional and rigorously validated tool was previously available for Python, a popular scientific programming language. Here, we present PyCO2SYS, a Python package intended to fill this capability gap. We describe the elements of PyCO2SYS that have been inherited from the existing CO2SYS family of software and explain subsequent adjustments and improvements. For example, PyCO2SYS uses automatic differentiation to solve the marine carbonate system and calculate chemical buffer factors, ensuring that the effect of every solute and reaction is accurately included in all its results. We validate PyCO2SYS with internal consistency tests and comparisons against other software, showing that PyCO2SYS produces results that are either virtually identical or different for known reasons, with the differences negligible for all practical purposes. We discuss new insights that arose during the development process, for example that the marine carbonate system cannot be unambiguously solved from the total alkalinity and carbonate ion parameter pair. Finally, we consider potential future developments to PyCO2SYS and discuss the outlook for this and other software for solving the marine carbonate system. The code for PyCO2SYS is distributed via GitHub ( https://github.com/mvdh7/PyCO2SYS ) under the GNU General Public License v3, archived on Zenodo (Humphreys et al., 2021), and documented online ( https://PyCO2SYS.readthedocs.io ).