Abstract

The centred-difference time-stepping scheme, known affectionately as the leapfrog scheme, has been used widely in atmosphere and ocean models for over 40 years. However, the numerical dissipation and loss of accuracy associated with the Robert-Asselin filter (which is used to control the computational mode) are becoming unacceptable to some modellers, who are starting to turn to schemes that are less dissipative and more accurate.

This talk will argue that there is still plenty of life left in the leapfrog. I will describe some simple and computationally inexpensive strategies to improve it, including the replacement of the Robert-Asselin filter with the RAW filter. The methods reduce the numerical dissipation and increase the accuracy, whilst retaining the stability of the physical mode and effectively controlling the computational mode. Examples will be shown of recent implementations of these methods in several models, leading to improvements in the simulation skill.