Conceptual view of reflection and transmission of a tsunami wave at a step in bathymetry

Recently published data from a WERA phased array radar operating in Chile after the Great Tohuku Earthquake in 2011 show that the tsunami lost a significant amount of energy as it shoaled towards the coast. This experimental result was contrary to that from the linear theory often used to estimate amplitude growth during shoaling. This paper evaluates the reflection of energy from a bathymetric step that might represent the edge of a continental shelf. A geometric wave approach is used to evaluate coefficients of reflection and transmission at the refractive index boundary. It is shown that reflection can explain some, but not all of the difference between linear theory and observations.