Reconstructing thermal properties of firn at Summit, Greenland from a temperature profile

Thermodynamic properties of firn are important factors when considering energy balance and temperature-dependent physical processes in the near-surface of glaciers. Of particular interest is thermal diffusivity, which can take a range of values and which governs both the temperature gradient and its evolution through time. Given that temperature is a well-established driver of firn densification, a better understanding of heat transfer will permit greater accuracy in the compaction models essential for interpreting inter-annual and seasonal ice surface elevation changes detected by airborne and satellite altimetry. Due to its dependence on microstructure, diffusivity can vary significantly by location. Rather than directly measuring diffusivity or one of its proxies (e.g. density, hardness, shear strength), this study inverts the heat equation to reconstruct diffusivity values. This is a less logistically-intensive approach which circumvents many of the challenges associated with imperfect proxies and snow metamorphism during measurement. Hourly records (May 2004 - July 2008) from 8 thermistors placed in the top 10 m at Summit, Greenland provide temperature values for Summit's firn, which is broadly representative of firn across the ice sheet's dry snow zone. In this study, we use both physical analysis and a finite-difference numerical model to determine a diffusivity magnitude and gradient; we find that diffusivity of Summit firn falls in the lower end of the range expected from local density and temperature conditions alone (i.e. 15 - 36 m^2/a for firn at -30C). Further, we assess the utility of our modeling approach, explore the validity of assuming bulk conductive heat transfer when modeling temperature changes in non-homogeneous firn, and investigate the implications of a low-end diffusivity value for surface compaction modeling in Greenland.