  The applicability of the Parareal parallel-in-time integration scheme for the
solution of a linear, two-dimensional hyperbolic acoustic-advection system,
which is often used as a test case for integration schemes for numerical
weather prediction (NWP), is addressed. Parallel-in-time schemes are a possible
way to increase, on the algorithmic level, the amount of parallelism, a
requirement arising from the rapidly growing number of CPUs in high performance
computer systems. A recently introduced modification of the "parallel implicit
time-integration algorithm" could successfully solve hyperbolic problems
arising in structural dynamics. It has later been cast into the framework of
Parareal. The present paper adapts this modified Parareal and employs it for
the solution of a hyperbolic flow problem, where the initial value problem
solved in parallel arises from the spatial discretization of a partial
differential equation by a finite difference method. It is demonstrated that
the modified Parareal is stable and can produce reasonably accurate solutions
while allowing for a noticeable reduction of the time-to-solution. The
implementation relies on integration schemes already widely used in NWP (RK-3,
partially split forward Euler, forward-backward). It is demonstrated that using
an explicit partially split scheme for the coarse integrator allows to avoid
the use of an implicit scheme while still achieving speedup.
