Reply to “Basal buoyancy and fast-moving glaciers: in defense of analytic force balance” by C. J. van der Veen (2016)

Abstract. Two approaches to ice-sheet modeling are available. Analytical modeling is the traditional approach (Van der Veen, 2016). It solves the force (momentum), mass, and energy balances to obtain three-dimensional solutions over time, beginning with the Navier–Stokes equations for the force balance. Geometrical modeling employs simple geometry to solve the force and mass balance in one dimension along ice flow (Hughes, 2012a). It is useful primarily to provide the first-order physical basis of ice-sheet modeling for students with little background in mathematics. The geometric approach uses changes in ice-bed coupling along flow to calculate changes in ice elevation and thickness, using a floating fraction ϕ along a flow line or flow band, where ϕ = 0 for sheet flow, 0 < ϕ < 1 for stream flow, and ϕ = 1 for shelf flow. An attempt is made to reconcile the two approaches.