#### Title

UM Firn Densification Model

#### Presentation Type

Poster

#### Faculty Mentor’s Full Name

Jesse Johnson

#### Faculty Mentor’s Department

Computer Science

#### Abstract

In regions where ice sheets are increasing in mass, there is a 50-200 m layer of old snow called firn which does not melt in the summer months. The density of firn tracks the transformation of snow into glacial ice at approximately 917 kg m^-3. The process of firn densification is important in at least two ways: 1) it can be a dominant component in the observed rate of change of the surface elevation, and 2) storage of liquid water in the lower density firn layer is now considered a critical component in the mass balance of ice sheets. If the rate of change of surface elevation can be equated with the rate of change in the mass of the ice sheet, we would have an excellent means of monitoring ice sheet mass balance. However, knowledge of firn densification rates is needed to make the inference of mass rate of change from volume rate of change.

Several firn models have been created for areas without melt. Herron and Langway [1980] developed a firn densification model based on Arrhenius-type equations with variable rate constants, and found that the densification rate increased suddenly around 550 kg m^-3. Zwally and Li [2002] expanded upon this model and found an alternate temperature-dependent value for the rate constant. Arthern et al. [2010] developed yet another set of equations based on their in situ measurements of Antarctic snow compaction, while Ligtenberg et al. [2011] modified the Arthern parametrization to better fit areas with a higher average annual temperature.

We have reformulated these models with the finite-element software package FEniCS and integrated them with an enthalpy-formulation proposed by Aschwanden et al. [2012]. This integration allows us to account for the melting and subsequent re-freezing of firn layers into ice lenses.

UM Firn Densification Model

UC Ballroom

In regions where ice sheets are increasing in mass, there is a 50-200 m layer of old snow called firn which does not melt in the summer months. The density of firn tracks the transformation of snow into glacial ice at approximately 917 kg m^-3. The process of firn densification is important in at least two ways: 1) it can be a dominant component in the observed rate of change of the surface elevation, and 2) storage of liquid water in the lower density firn layer is now considered a critical component in the mass balance of ice sheets. If the rate of change of surface elevation can be equated with the rate of change in the mass of the ice sheet, we would have an excellent means of monitoring ice sheet mass balance. However, knowledge of firn densification rates is needed to make the inference of mass rate of change from volume rate of change.

Several firn models have been created for areas without melt. Herron and Langway [1980] developed a firn densification model based on Arrhenius-type equations with variable rate constants, and found that the densification rate increased suddenly around 550 kg m^-3. Zwally and Li [2002] expanded upon this model and found an alternate temperature-dependent value for the rate constant. Arthern et al. [2010] developed yet another set of equations based on their in situ measurements of Antarctic snow compaction, while Ligtenberg et al. [2011] modified the Arthern parametrization to better fit areas with a higher average annual temperature.

We have reformulated these models with the finite-element software package FEniCS and integrated them with an enthalpy-formulation proposed by Aschwanden et al. [2012]. This integration allows us to account for the melting and subsequent re-freezing of firn layers into ice lenses.