  The Courant-Friedrichs-Lewy (CFL) condition is a well known, necessary
condition for the stability of explicit time-stepping schemes that effectively
places a limit on the size of the largest admittable time-step for a given
problem. We formulate and present a new local time-stepping (LTS) scheme
optimized, in the CFL sense, for the shallow water equations (SWEs). This new
scheme, called FB-LTS, is based on the CFL optimized forward-backward
Runge-Kutta schemes from Lilly et al. (2023). We show that FB-LTS maintains
exact conservation of mass and absolute vorticity when applied to the TRiSK
spatial discretization (Ringler et al., 2010), and provide numerical
experiments showing that it retains the temporal order of the scheme on which
it is based (second order). In terms of computational performance, we show that
when applied to a real-world test case on a highly-variable resolution mesh,
the MPAS-Ocean implementation of FB-LTS is up to 10 times faster than the
classical four-stage, fourth-order Runge-Kutta method (RK4), and 2.3 times
faster than an existing strong stability preserving Runge-Kutta based LTS
scheme (LTS3). Despite this significant increase in efficiency, the solutions
produced by FB-LTS are qualitatively equivalent to those produced by both RK4
and LTS3.
