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

Abstract

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 semi-implicit 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.