Abstract

The rapid increase of computing power is making global non-hydrostatic simulations affordable. A natural approach is to extend the formulation to include the non-hydrostatic effect. The advantage of this approach is that the existing data assimilation and tools require minimal changes. ECMWF and JMA seem to pursue this approach. ECMWF has achieved TL7999 (corresponding to approximately 2.5 km) with a fast Lendre transform using the butterfly algorithm (Nils Wedi, pers. comm.). Hiromasa Yoshimura (MRI/JMA) has built a non-hydrostatic version of JMA GSM using double Fourier series. Their formulations are based on Laprise (1992) that proposes the vertical co-ordinates based on hydrostatic pressure. Juang (1992, 2000) also adopts hydrostatic sigmaco-ordinates in the vertical but there are subtle differences. The latter introduces the hydrostatic temperature. In a limited-area model, such as MSM , the hydrostatic temperature may be given externally. In a GCM , however, the hyd rostatic temperature must be determined internally if is not time-independent. We investigated the two formations and found the assumption of the hydrostatic state of Laprise (1992) may be used to diagnose the hydrostatic temperature within MSM . Similarly the hydrostatic assumption of Arakawa and Konor (2009) can be used. MSM is found to run stably with any of these diagnosed hydrostatic states. The diagnosed hydrostatic temperature would enable the application of the formulation of MSM to the global domain.