Earth and Atmospheric Sciences, Department of


Date of this Version



Elkins, L. J., & Spiegelman, M. (2021). pyUserCalc: A revised Jupyter notebook calculator for uranium-series disequilibria in basalts. Earth and Space Science, 8, e2020EA001619. https://doi. org/10.1029/2020EA001619


Open access.


Meaningful analysis of uranium-series isotopic disequilibria in basaltic lavas relies on the use of complex forward numerical models like dynamic melting (McKenzie, 1985, 821x(85)90001-9) and equilibrium porous flow (Spiegelman & Elliott, 1993, 821x(93)90155-3). Historically, such models have either been solved analytically for simplified scenarios, such as constant melting rate or constant solid/melt trace element partitioning throughout the melting process, or have relied on incremental or numerical calculators with limited power to solve problems and/or restricted availability. The most public numerical solution to reactive porous flow, UserCalc (Spiegelman, 2000, https:// was maintained on a private institutional server for nearly two decades, but that approach has been unsustainable in light of modern security concerns. Here, we present a more long-lasting solution to the problems of availability, model sophistication and flexibility, and long-term access in the form of a cloud-hosted, publicly available Jupyter notebook. Similar to UserCalc, the new notebook calculates U-series disequilibria during time-dependent, equilibrium partial melting in a one-dimensional porous flow regime where mass is conserved. In addition, we also provide a new disequilibrium transport model which has the same melt transport model as UserCalc, but approximates rate-limited diffusive exchange of nuclides between solid and melt using linear kinetics. The degree of disequilibrium during transport is controlled by a Damköhler number, allowing the full spectrum of equilibration models from complete fractional melting (Da = 0 ) to equilibrium transport (Da = ∞).