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Storm surge modeling of Hurricane Sandy around Delaware Bay is used to demonstrate variable-resolution ocean time-stepping methods • Local time-stepping schemes are up to 35% faster, and produce solutions of comparable quality to higher-order globally-uniform schemes

Variable-resolution climate models have become increasingly popular in the past decade (e.g., Skamarock et al., 2012;Danilov et al., 2017;Korn, 2017), as they offer the ability to create high-resolution regions within global domains, with fine control over the extent and transitions in grid-cell size. It is well known that the size of the largest time-step that can be used by an explicit time-stepping scheme is bounded above by the size of the smallest cell in the mesh according to the Courant-Friedrichs-Lewy (CFL) condition. This restriction is of particular interest on meshes where the cell size varies greatly. To optimize the computational cost of running a model on a variable-resolution mesh, one would like to select a small time-step on regions of high resolution (regions defined by small cells), and a large time-step on regions of low resolution (defined by large cells). For simplicity, variable-resolution climate model components typically use global time-stepping schemes, where a uniform time-step is used on the entire computational domain. As a result, one is forced to use a small time-step that is restricted by the CFL condition influenced by the smallest cell in the mesh even on large cells that would admit a larger time-step in the absence of smaller cells. This approach results in unnecessary computational cost

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