Abstract
An empirical model for the densification of dry snow has been calibrated using strain-rate data from Pine Island Glacier basin, Antarctica. The model provides for a smooth transition between Stage 1 and Stage 2 densification, and leads to an analytical expression for density as a function of depth. It introduces two new parameters with a simple physical basis: transition density ρ T and a scaling factor, M, which controls the extent of the transition zone. The standard (Herron and Langway) parameterization is used for strain rates away from the transition zone. Calibration, though tentative, produces best parameter values of ρ T = 580 kg m − 3 and M = 7 for the region. Using these values, the transition model produces better simulations of snow profiles from Pine Island Glacier basin than the well-established Herron and Langway and Ligtenberg models, both of which postulate abrupt transition. Simulation of density profiles from other sites using M = 7 produces the best values of ρ T = 550 kg m − 3 for a high accumulation site and 530 kg m − 3 for a low accumulation site, suggesting that transition density may vary with climatic conditions. The variation of bubble close-off depth and depth-integrated porosity with mean annual accumulation predicted by the transition model is similar to that predicted by the Simonsen model tuned for Greenland.
Highlights
In the accumulation areas of ice sheets, ice caps, and glaciers, snow is deposited on the surface and, with time, becomes denser until it turns into ice
The variation of bubble close-off depth and depth-integrated porosity with mean annual accumulation predicted by the transition model is similar to that predicted by the Simonsen model tuned for Greenland
A simple model that removes the abrupt transition between Stage 1 and Stage 2 densification can be constructed using an activation function for c centered around transition density ρ T, which is likely to be close to 550 kg m−3
Summary
In the accumulation areas of ice sheets, ice caps, and glaciers, snow is deposited on the surface and, with time, becomes denser until it turns into ice. A better approach to empirical modelling of dry-snow densification might be to accept that strain rate is dependent on a more complex function of density than that proposed by Robin. This would allow a gradual change in densification rate with depth, as the relative importance of grain-boundary sliding, grain growth, and sintering changes. The Robin hypothesis states that c(ρ0 ) is a constant and the dependence of strain rate on density is described solely by the function (ρi − ρ0 )/ρ0 Hidden within this formulation is an assumption that overburden stress σ, which increases with water-equivalent depth, is offset by a corresponding increase in snow strength because of some other factor that increases with depth, such as time since deposition τ. We call c the density-corrected strain rate whether or not it it is constant
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