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

This note provides a detailed theoretical derivation for the removal of non‐physical finite‐amplitude computational oscillations from the solution of the adjoint of a discretized model using the leapfrog finite‐difference scheme. Numerical results are shown using a 1‐dimensional shallow water equation model.