To treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinic-barotropic splitting technique has been widely used for solving the primitive equations for ocean modeling. In this talk, we will discuss several recently developed time stepping algorithms for efficiently simulating such a split dynamics, together with the corresponding temporal truncation error analyses. Two benchmark tests drawn from the "MPAS-Ocean" platform will be presented to illustrate the accuracy and parallel performance of the schemes.