Most operational numerical weather prediction models update their lateral boundaries via the Davies- Kå llberg relaxation scheme. In this paper an alternative, `transparent boundary conditions' is examined. A hierarchy of transparent boundary conditions is derived for the shallow water equations in one and two dimensions. In order to test the validity of the new boundary condirions the shallow water equations are integrated in a nested environment using real meteorological data. In these tests `characteristic boundary conditions' are seen to emerge as superior to the traditional relaxation boundary conditions.