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June 2021 Hierarchical integrated spatial process modeling of monotone West Antarctic snow density curves
Philip A. White, Durban G. Keeler, Summer Rupper
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Ann. Appl. Stat. 15(2): 556-571 (June 2021). DOI: 10.1214/21-AOAS1443


Snow density estimates below the surface, used with airplane-acquired ice-penetrating radar measurements, give a site-specific history of snow water accumulation. Because it is infeasible to drill snow cores across all of Antarctica to measure snow density and because it is critical to understand how climatic changes are affecting the world’s largest freshwater reservoir, we develop methods that enable snow density estimation with uncertainty in regions where snow cores have not been drilled.

In inland West Antarctica, snow density increases monotonically as a function of depth, except for possible microscale variability or measurement error, and it cannot exceed the density of ice. We present a novel class of integrated spatial process models that allow interpolation of monotone snow density curves. For computational feasibility we construct the space-depth process through kernel convolutions of log-Gaussian spatial processes. We discuss model comparison, model fitting and prediction. Using this model, we extend estimates of snow density beyond the depth of the original core and estimate snow density curves where snow cores have not been drilled. Along flight lines with ice-penetrating radar, we use interpolated snow density curves to estimate recent water accumulation and find predominantly decreasing water accumulation over recent decades.

Funding Statement

Summer Rupper acknowledges funding from NASA grant NNX16AJ72G.


We thank the three anonymous reviewers as well as the Editor for their comments that have helped improve the manuscript.


Download Citation

Philip A. White. Durban G. Keeler. Summer Rupper. "Hierarchical integrated spatial process modeling of monotone West Antarctic snow density curves." Ann. Appl. Stat. 15 (2) 556 - 571, June 2021.


Received: 1 August 2020; Revised: 1 January 2021; Published: June 2021
First available in Project Euclid: 12 July 2021

Digital Object Identifier: 10.1214/21-AOAS1443

Rights: Copyright © 2021 Institute of Mathematical Statistics


Vol.15 • No. 2 • June 2021
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