Numerical weather prediction (NWP) requires an answer in real time with a window of approximately one hour to run a medium-range global forecast such that it can be delivered in time to its customers worldwide. While computational efficiency remains one of the most pressing needs of NWP, it is an open question how to most efficiently use the computer power available over the next twenty years, while seeking the most accurate and cost-effective solution. At the same time, there are significant scientific challenges to increase resolution further, changes to the governing equations, and how sub-gridscale (SGS) processes are represented. ECMWF plans to implement a global horizontal resolution of approximately 10km by 2015 for its assimilation and deterministic forecast system, and approximately 20km for the ensemble prediction system (EPS). The scales resolved at these resolutions are still hydrostatic and the efficiency of the contemporary hydrostatic, semi-Lagrangian, semi-imp licit solution procedure using the spectral transform method is likely to remain a relevant benchmark. However, due to the relative cost increase of the Legendre transforms compared to the gridpoint computations, very high resolution spectral models may become prohibitively expensive. Moreover, spectral-to-gridpoint transformations require data-rich global communications at every timestep that may become too expensive on massively parallel computers. Recent progress in the development of fast spherical harmonics transforms (Tygert, 2008,2010) based on the butterfly scheme (OíNeil et al, 2010) mitigate the computational expense of the spectral transforms. Results are presented that demonstrate the cost-effectiveness of the fast Legendre transforms (FLT) on the ibm_power7 architecture. The FLTs save both memory and computing time enabling the "world's first" successful T7999 (or equivalently ~2.5km horizontal resolution) global weather forecast with a spectral transform model.
Tygert, M., Fast algorithms for spherical harmonic expansions, II, J. of Comput. Physics, Vol. 227 (8), 2008, 4260-4279.
Tygert, M., Fast algorithms for spherical harmonic expansions, III, J. of Comput. Physics, Vol. 229 (18), 2010, 6181-6192.
OíNeil, M., F. Woolfe, V. Rohklin, An algorithm for the rapid evaluation of special function transforms, Appl. Comput. Harmon. Anal., Vol. 28(2), 2010, 203-226.