Assessment of a Finite Volume Discretization of the Horizontal Pressure Gradient Force Beneath Sloping Ice Shelves

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Abstract The accurate computation of pressure gradients in ocean models is essential for simulating ocean and climate processes. Inaccurate computation can result in spurious velocities on the order of real ocean flows, particularly in quiescent ice shelf cavities. We introduce improvements to a finite volume discretization of the pressure gradient force, required with a sloped ocean surface boundary beneath ice shelves and when model layers intersect with ice shelves and bathymetry. We demonstrate the sensitivity of pressure gradient force calculations to choices of sub‐grid cell pressure, density and geopotential distributions. Our method results in a marked improvement in the simulation of pressure gradient forces in idealized ice shelf cavities, with spurious velocities reduced to order m or smaller in quiet, linear stratification test cases. These velocities are substantially smaller than the magnitude of real ocean flows beneath ice shelf cavities, providing confidence in their simulated flows. Though we provide methods to reduce spontaneous motion from very thin ocean layers subject to numerical errors, these methods could be further improved, as could the small spurious flows that remain with nonlinear stratification.

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