Modeling firn densification through viscosity and microstructures

Abstract

Knowledge of firn densification is important for several applications, such as for ice-sheet surface elevation changes from repeat satellite altimetry methods used to estimate ice-sheet contribution to sea-level rise. Uncertainties in firn-densification rates are among the largest uncertainties for this method mainly because most commonly-used firn-densification models are empirically constructed for estimating the macroscopic behavior of the firn. Currently, no model that is either fully physically-based or is applicable to the entire firn column exists. First, we examine the implicit effective viscosity for models within the Community Firn Model (CFM) under a range of climatic conditions, and find that there exist physically unrealistic discontinuities in viscosity at the transitional density of 550 kg m-3. To generate a continuous viscosity curve, we develop a transition model that gradually transitions processes in zone 1 to those in zone 2 of the firn layer. We use the transition model for estimating depth- density for a range of climates, and we generally see that the transition model shows lower RMSE values compared to the Herron and Langway (1980) model for climatic sites that do not have a regular Clausius-Clapeyron pairing of temperature and accumulation rate, or sites that are influenced by other factors (e.g., horizontal strain, wind). However, the results highlight the limitations of constructing a model empirically. 3 Next, we develop a model that modifies a relationship from previous work to estimate the densification rate through viscosity and the evolution of microstructures. We define microstructural evolution by using micro-CT data from USP50 near South Pole, and run our model for USP50 as well as several other sites. Our results show good agreement; however, more work is necessary to further develop this model, including the collection of more microstructure data. Nevertheless, our research provides a key step towards producing a firn- densification model that estimates firn properties on the microscale and that can potentially be used in a range of climatic conditions and during climate transients.