Long-wave explicit and Short-wave implicit (LESI) treatment of the barotropic mode to accurately calculate slow modes in ocean models

► Large time steps for efficient calculation of slow modes in an ocean model. ► High-order explicit treatment of the slow modes and the long-wave parts of the fast barotropic mode. ► Only the short-wave part of the fast barotropic mode is calculated implicitly. ► Obviates the need for a fully-converged iterative solution to the elliptic equation for surface elevation.