Modeling Firn Density through Spatially Varying Smoothed Arrhenius Regression
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Scientists use firn (compacted snow) density models as a function of depth to understand climate processes, evaluate water accumulation trends, and estimate glacier mass balances. Firn densification is a thermal reaction often modeled in discrete density-dependent stages, each governed by a reaction rate called an Arrhenius constant. Because firn density data are collected at depths rather than times, we infer Arrhenius rate constants from differential equation depth-density models. Arrhenius constants are commonly assumed to be constant over wide regions, but these models can poorly match observed densities, suggesting the need for site-specific models. Our dataset consists of 14,844 density measurements from 57 firn cores drilled at 56 sites in West Antarctica, taken from four research expeditions. For these data, we present a novel physically constrained spatially varying Arrhenius regression model for firn density as a function of depth. Because the Arrhenius regression framework is piecewise linear, we present a smoothed Arrhenius model that allows nonlinear deviations to better fit the data while preserving inference on physical parameters. Lastly, we use a unique hierarchical, heteroscedastic error model that accounts for differences between research expeditions. Using this model, we explore firn densification patterns change over space and compare our model to previous studies.
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