Modeling Firn Density through Spatially Varying Smoothed Arrhenius Regression

by   Philip White, et al.

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.



There are no comments yet.


page 32

page 33

page 35

page 36

page 37

page 38


Hierarchical Spatial Modeling of Monotone West Antarctic Snow Density Curves

Snow density estimates below the surface, used with airplane-acquired ic...

Stochastic modeling of non-linear adsorption with Gaussian kernel density estimators

Adsorption is a relevant process in many fields, such as product manufac...

Parameter and density estimation from real-world traffic data: A kinetic compartmental approach

The main motivation of this work is to assess the validity of a LWR traf...

On the simultaneous recovery of the conductivity and the nonlinear reaction term in a parabolic equation

This paper considers the inverse problem of recovering both the unknown,...

Cutting out the Middle-Man: Training and Evaluating Energy-Based Models without Sampling

We present a new method for evaluating and training unnormalized density...

Spatial statistics and stochastic partial differential equations: a mechanistic viewpoint

The Stochastic Partial Differential Equation (SPDE) approach, now common...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.