Improving piecewise linear snow density models through hierarchical spatial and orthogonal functional smoothing

Abstract

Snow density estimates as a function of depth are used for understanding climate processes, evaluating water accumulation trends in polar regions, and estimating glacier mass balances. The common and interpretable physically derived differential equation models for snow density are piecewise linear as a function of depth (on a transformed scale); thus, they can fail to capture important data features. Moreover, the differential equation parameters show strong spatial autocorrelation. To address these issues, we allow the parameters of the physical model, including random change points over depth, to vary spatially.We also develop a framework for functionally smoothing the physically motivated model. To preserve inference on the interpretable physical model, we project the smoothing function into the physical model's spatially varying null space. The proposed spatially and functionally smoothed snow density model better fits the data while preserving inference on physical parameters. Using this model, we find significant spatial variation in the parameters that govern snow densification.

Outlier accommodation with semiparametric density processes: A study of Antarctic snow density modelling

“…Therefore, the mean density of snow in our model is constrained to be monotonically increasing. Because the estimation of the mean function is not the main goal of the current study, a simple model that imposes constraints similar to those of the model used by (Herron and Langway (1980)) and later modified by (White et al(2020)), while avoiding the complexities of their models, is implemented here.…”

“…The densification of snow due to accumulated overburden pressure is an isolated physical process that can be expressed as a function of depth and various physical constants. Previous researchers have modelled snow density using the thermal physics of densification (Cuffey and Paterson (2010); White et al(2020)), model fitting using exponential functions (Miège et al(2013)), or a combination of the two approaches (Herron and Langway (1980); Hörhold et al(2011)). It is common to adopt a general nonlinear differential equation model for snow density (a special case of Bernoulli's differential equation), …”