  We derive boundary conditions and estimates based on the energy and entropy
analysis of systems of the nonlinear shallow water equations in two spatial
dimensions. It is shown that the energy method provides more details, but is
fully consistent with the entropy analysis. The details brought forward by the
nonlinear energy analysis allow us to pinpoint where the difference between the
linear and nonlinear analysis originate. We find that the result from the
linear analysis does not necessarily hold in the nonlinear case. The nonlinear
analysis leads in general to a different minimal number of boundary conditions
compared with the linear analysis. In particular, and contrary to the linear
case, the magnitude of the flow does not influence the number of required
boundary conditions.
