  We propose IMEX HDG-DG schemes for planar and spherical shallow water
systems. Of interest is subcritical flow, where the speed of the gravity wave
is faster than that of nonlinear advection. In order to simulate these flows
efficiently, we split the governing system into a stiff part describing the
gravity wave and a non-stiff part associated with nonlinear advection. The
former is discretized implicitly with the HDG method while an explicit
Runge-Kutta DG discretization is employed for the latter. The proposed IMEX
HDG-DG framework: 1) facilitates high-order solutions both in time and space;
  2) avoids overly small time-step sizes;
  3) requires only one linear system solve per time stage;
  4) relative to DG generates smaller and sparser linear systems while
promoting further parallelism. Numerical results of various test cases
demonstrate that our methods are comparable to explicit Runge-Kutta DG schemes
in terms of accuracy while allowing for much larger time step sizes.
