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Abstract. The net rate of snow accumulation b is predicted to increase over large areas of the Antarctic 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 palaeo-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 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 increasing surface grain size. We also quantify the circumstances under which porosity advection and grain-size advection balance exactly, which counterintuitively 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.