Grain-size evolution controls the accumulation dependence of modeled firn thickness

Abstract. The net rate of snow accumulation b is predicted to increase over large areas of the Antarctica and Greenland ice sheets as the climate warms. Models disagree on how this will affect the thickness of the firn layer – the relatively low-density upper layer of the ice sheets that influences altimetric observations of ice-sheet mass change and paleo-climate reconstructions from ice cores. Here we examine how b influences firn compaction and porosity in a simplified model that accounts for mass conservation, dry firn compaction, grain size evolution, and the impact of grain size on firn compaction. Treating b as a boundary condition and employing an Eulerian reference frame helps to untangle the factors controlling the b-dependence of firn thickness. We present numerical simulations using the model as well as simplified steady-state approximations to the full model, to demonstrate how the downward advection of porosity and of grain size are both affected by b, but have opposing impacts on firn thickness. The net result is that firn thickness increases with b and that the strength of this dependence increases with the surface grain size. We also quantify the circumstances under which porosity- and grain-size-advection balance exactly, which counter-intuitively renders steady-state firn thickness independent of b. These findings are qualitatively independent of the stress-dependence of firn compaction and whether the thickness of the ice-sheet is increasing, decreasing, or steady. They do depend on the grain-size dependence of firn compaction. Firn models usually ignore grain-size evolution, but we highlight the complex effect it can have on firn thickness when included in a simplified model. This work motivates future efforts to better observationally constrain the rheological effect of grain size in firn.