Eliminating finite-amplitude non-physical oscillations in the time evolution of adjoint model solutions introduced by the leapfrog time-integration scheme

Abstract

This note provides a detailed theoretical derivation for the removal of non-physical finiteamplitudecomputational oscillations from the solution of the adjoint of a discretized modelusing the leapfrog finite-difference scheme. Numerical results are shown using a 1-dimensionalshallow water equation model.