  Two ocean models are considered for geophysical flow simulations: the
multi-layer shallow water equations and the multi-layer primitive equations.
For the former, we investigate the parallel performance of exponential time
differencing (ETD) methods, including exponential Rosenbrock-Euler, ETD2wave,
and B-ETD2wave. For the latter, we take advantage of the splitting of
barotropic and baroclinic modes and propose a new two-level method in which an
ETD method is applied to solve the fast barotropic mode. These methods could
improve the computational efficiency of numerical simulations because ETD
methods allow for much larger time step sizes than traditional explicit
time-stepping techniques that are commonly used in existing computational ocean
models. Several standard benchmark tests for ocean modeling are performed and
comparison of the numerical results demonstrate a great potential of applying
the parallel ETD methods for simulating real-world geophysical flows.
