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  1. 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 = ∞). 
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  2. Abstract

    Subglacial lakes are bodies of water that form at the base of ice sheets and glaciers. Ice‐surface elevation above these lakes responds to water volume changes, providing one of few ways to monitor subglacial hydrological systems. Here, we use numerical models to compare surface elevation‐derived estimates of subglacial‐lake length, water‐volume change, and highstand or lowstand timing with their true values. Because ice flow influences the surface expression of lake‐volume change, the correspondence between these estimates and their true values depends strongly on ice thickness, volume‐change rate, and basal drag coefficient. For many realistic combinations of these factors, viscous relaxation of the ice‐sheet surface can render lake volume‐changes unobservable with altimetry. Our results highlight the need for new estimation methods that account for the effects of ice flow, as well as improvements to current resolution limitations that render some events unobservable with altimetry.

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