PIMS / AMI Seminar / IGR (Institute for Geophysical Research): Paul Williams

The second-order centered (leapfrog) time-stepping scheme is commonly used in numerical models of weather and climate.  The unstable computational mode is damped by applying a Robert–Asselin filter, which introduces first-order numerical errors.  Despite its poor accuracy, this time-stepping scheme has been used in most weather and climate models for the past 50 years.  In this seminar, I will discuss several simple and computationally inexpensive methods to improve the Robert-Asselin filtered leapfrog scheme.  For example, the RAW filter eliminates the first-order amplitude errors and yields third-order amplitude accuracy.  Other simple modifications yield up to seventh-order amplitude accuracy.  These developments have recently been shown to improve climate models and to significantly increase the skill of medium-range weather forecasts.  The proposed new schemes appear to be attractive alternatives to the filtered leapfrog schemes currently used in many weather and climate models.