  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 micro-scale 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.
