Modeling Firn Density through Spatially Varying Smoothed Arrhenius Regression
share
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.
READ FULL TEXT
