On ellipticity of balance equations for atmospheric dynamics

Abstract

Initial data for atmospheric multi-scale models need to be adjusted in order to ensure small amplitudes of high-frequency oscillations. Different adjustment methods lead to balance conditions in the form of time-independent partial differential systems with appropriate boundary conditions. One of the issues of such systems is a violation of the ellipticity conditions in a part of the problem domain. In this study we present the ellipticity conditions for balance equations based on diagnostic divergence relation with different levels of complexity and explore the existence of non-elliptic regions in the gridded fields of the atmospheric analysis data. It is shown that more physically justifiable balance equations are associated with much sparser and less intensive non-elliptic regions. The obtained results confirm Kasahara’s assumption that ellipticity conditions are violated in the actual atmospheric fields essentially due to approximations made under deriving balance equations.