Hierarchical Spatial Modeling of Monotone West Antarctic Snow Density Curves
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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 reservoir of fresh water, we develop methods that enable snow density estimation with uncertainty in regions where firn cores have not been drilled. Snow density increases monotonically as a function of depth, except for possible micro-scale variability or measurement error, and it cannot exceed the density of ice. We present two novel models that enable monotone spatial interpolation of snow density and show that spatial monotone spline models offer huge out-of-sample prediction advantages over our more traditional spatial model. We discuss model comparison, model fitting, and prediction for our monotone spatial spline model. Using this model, we extend estimates of snow density beyond the depth of the original core and estimate snow density curves at locations where firn cores have not been drilled. At four illustrative locations, we show how estimated snow density curves can be combined with radar measurements to estimate recent water accumulation.
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