A Lagrange-Laplace Integration Scheme for Weather Prediction and Climate Modelling

A time integration scheme based on semi-Lagrangian advection and Laplace transform adjustment has been implemented in a baroclinic primitive equation model. The semi-Lagrangian scheme makes it possible to use large time steps. However, errors arising from the semi-implicit scheme increase with the time step size. In contrast, the errors using the Laplace transform adjustment remain relatively small for typical time steps used with semi-Lagrangian advection. Numerical experiments confirm the superior performance of the Laplace transform scheme relative to the semiimplicit reference model. The algorithmic complexity of the scheme is comparable to the reference model, making it computationally competitive, and indicating its potential for integrating weather and climate prediction models.