Hierarchical integrated spatial process modeling of monotone West Antarctic snow density curves

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 cores across all Antarctica measure and because critical understand how climatic changes are affecting world's largest freshwater reservoir, we develop methods that enable estimation uncertainty in regions where have not been drilled. In inland West Antarctica, increases monotonically as function depth, except for possible micro-scale variability or measurement error, cannot exceed ice. We present novel class integrated spatial process models allow interpolation monotone curves. For computational feasibility, construct space-depth through kernel convolutions log-Gaussian processes. discuss model comparison, fitting, prediction. Using this model, extend beyond depth original core estimate curves Along flight lines radar, use interpolated recent accumulation find predominantly decreasing over decades.