A Simple Method for Improving the Time-Stepping Accuracy of Weather and Climate Models

In contemporary numerical simulations of the atmosphere and ocean, evidence suggests that time-stepping errors may be a significant component of total model error, on both weather and climate time-scales. This presentation will review the available evidence, and will then suggest a simple but effective method for substantially improving the time-stepping numerics at no extra computational expense.

A common time-stepping method in atmosphere and ocean models is the leapfrog scheme combined with the Robert–Asselin (RA) filter. This method is used in the following models (and many more): ECHAM, MAECHAM, MM5, CAM, MESO-NH, HIRLAM, KMCM, LIMA, SPEEDY, IGCM, PUMA, COSMO, FSU-GSM, FSU-NRSM, NCEP-GFS, NCEP-RSM, NSEAM, NOGAPS, RAMS, and CCSR/NIES-AGCM. Although the RA filter controls the time-splitting instability, it also introduces non-physical damping and reduces the accuracy.

This presentation proposes a simple modification to the RA filter, which has become known as the RAW filter. When used in conjunction with the leapfrog scheme, the RAW filter eliminates the non-physical damping and increases the amplitude accuracy by two orders, yielding third-order accuracy. (The phase accuracy remains second-order.) The RAW filter can easily be incorporated into existing models, typically via the insertion of just a single line of code. Better simulations are obtained at no extra computational expense.

Results will be shown from recent implementations of the RAW filter in various models, including SPEEDY and COSMO. For example, in SPEEDY, the skill of weather forecasts is found to be significantly improved. In particular, in tropical surface pressure predictions, five-day forecasts made using the RAW filter have approximately the same skill as four-day forecasts made using the RA filter. These improvements are encouraging for the use of the RAW filter in other atmosphere and ocean models.