In this talk we present explicit local time-stepping schemes with second and third order accuracy for the shallow water equations. The system is discretized in space by a C-grid staggering method, namely the TRiSK scheme adopted in MPAS-Ocean, a global ocean model with the capability of resolving multiple resolutions within a single simulation. The time integrations are designed based on the strong stability preserving Runge-Kutta methods, but different time step sizes can be used in different regions of the domain and are only restricted by respective local CFL conditions. The proposed local time-stepping schemes preserve all important properties in the discrete sense, such as exact conservation of the mass and potential vorticity and conservation of the total energy within time-truncation errors. Various numerical examples are tested to illustrate the performance of the proposed algorithms.