| In contemporary numerical simulations of the atmosphere, 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.
The most common time-stepping method is the leapfrog scheme combined with the
Robert–Asselin (RA) filter. This method is used in the following atmospheric 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 in these models, it also introduces non-physical damping and
reduces the accuracy.
This presentation proposes a simple modification to the RA filter. The modification has
become known as the RAW filter (Williams 2011). 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 atmospheric
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 (Amezcua, Kalnay & Williams
2011). These improvements are encouraging for the use of the RAW filter in other
models.
References
PD Williams (2011) The RAW filter: An improvement to the Robert–Asselin filter in
semi-implicit integrations. Monthly Weather Review 139(6), pp 1996–2007.
J Amezcua, E Kalnay, and PD Williams (2011) The effects of the RAW filter on the
climatology and forecast skill of the SPEEDY model. Monthly Weather Review 139(2), pp
608-619. |