Significance of Non-Elliptic Regions in Balanced Flows of the Tropical Atmosphere

Abstract

Recently, questions were raised concerning the ellipticity condition of the traditional balance equation, related to the application of nonlinear normal mode initialization for primitive equation prediction models. We investigate, in this paper, the occurrence of non-elliptic regions, using the FWE level IIIb analyses of the European Centre for Medium Range Weather Forecasts. We found that non-elliptic regions are ubiquitous in the tropics. For the traditional balance equation, non-elliptic regions are not realizable in the sense that balanced flows are not physically possible. To reconcile this dilemma, we postulate that the traditional balance equation lacks an additional term due, for example, to the effects of subgrid-scale motions. We evaluated this additional term as the residual by computing each term in the balance equation. This additional term modifies the ellipticity criterion of the balance equation. We call the modified ellipticity condition the realizability condition. This study concludes that the non-elliptic regions found in the tropics satisfy the realizability condition when this additional term in the balance equation is considered. This suggests that the apparent dilemma may be resolved by taking into account presently lacking physical processes in achieving the dynamical balance between the mass and wind fields, if the FGGE level IIIb analyses are supposed to be correct.