The dynamical balance of leading singular vectors in a primitive‐equation model

The dynamical balance of singular vectors (SVs) determined with respect to an energy norm for a primitive-equation atmospheric model is investigated. Partitioning between balanced and unbalanced components is primarily performed in terms of geostrophic and ageostrophic normal modes. Results indicate that if linearized effects of moist convection are not considered, the initial structure of the leading (most rapidly growing) SV is primarily geostrophic, although the ageostrophic part is significant. At the concluding time, however, the structure is almost totally geostrophic. The initially uncorrelated geostrophic and ageostrophic portions of the SV separately evolve into highly correlated structures. These two separately evolved portions therefore reinforce each other, so that the sum of the concluding total perturbation energies of the two portions is less than the corresponding energy of the non-partitioned SV. The high correlations also suggest that the inverse of the tangent linear model would be ill-suited for estimating an initial perturbation given an imperfectly known final one. There is no hint of significant high-frequency inertial gravity-wave activity.