An assessment of global forecast errors due to the spherical geopotential approximation in the shallow-water case

The spherical geopotential approximation (SGA) used in most meteorological global models assumes a spherical shape for the Earth and its geopotential field, together with a horizontally uniform gravity field (for physical consistency). This approximation has largely been used from the outset and is still used in operational meteorological forecast systems. However, the magnitude of the errors linked to this approximation is debated, especially for long integrations. Consistent mathematical models of the atmosphere in the ellipsoidal geopotential approximation (EGA) have recently been developed, thus allowing a clean assessment of the errors linked to using the SGA. Two types of error may be anticipated: those arising due to geometrical distortions and those arising due to the spatial differences in the magnitude of the gravity field. The shallow-water system, which is the minimal framework in which both types of errors are likely to manifest themselves, is used in this study. The link between the pure forecast errors' examined here and the numerical weather prediction (NWP) errors' that would arise in a concrete NWP application (with a data assimilation system) is discussed, in relation to the experimental protocol chosen here. Medium-range forecast errors for idealized fully deterministic flows are first considered in a phenomenological way (phase errors, distortions, etc.) and then some widely documented real cases are examined.