A Schroedinger eigenvalue equation is formulated for shallow water waves on a rotating plane, and this formulation yields zonally propagating waves whose amplitudes attain their maximal values near the equatorward boundary of the domain. The phase speeds of planetary (Rossby) waves in this theory are higher than those of harmonic waves which are obtained when the Coriolis parameter is assumed constant. Numerical simulations of trapped and harmonic Rossby waves by a standard shallow water linear solver validate the analytical results and show that trapped waves dominate the numerical solutions in a wide (including infinitely wide) channel while harmonic waves do so in a narrow channel. Observations of sea surface height anomalies in the Indian Ocean south of Australia made by satellite-borne AVHRR altimeters show that the meridional structure of these anomalies and their westward propagation speeds are accurately approximated by the amplitudes and phase speeds of trapped Rossby waves. Speaker(s): Nathan Paldor (Hebrew University of Jerusalem)