A Budget Equation for the Amplitude of Rossby Wave Packets Based on Finite-Amplitude Local Wave Activity

Abstract

AbstractRecently, the authors proposed a novel diagnostic to quantify the amplitude of Rossby wave packets. This diagnostic extends the local finite-amplitude wave activity (LWA) of N. Nakamura and collaborators to the primitive-equations framework and combines it with a zonal filter to remove the phase dependence. In the present work, this diagnostic is used to investigate the dynamics of upper-tropospheric Rossby wave packets, with a particular focus on distinguishing between conservative dynamics and nonconservative processes. For this purpose, a budget equation for filtered LWA is derived and its utility is tested in a hierarchy of models. Idealized simulations with a barotropic and a dry primitive-equation model confirm the ability of the LWA diagnostic to identify nonconservative local sources or sinks of wave activity. In addition, the LWA budget is applied to forecast data for an episode in which the amplitude of an upper-tropospheric Rossby wave packet was poorly represented. The analysis attributes deficiencies in the Rossby wave packet amplitude to the misrepresentation of diabatic processes and illuminates the importance of the upper-level divergent outflow as a source for the error in the wave packet amplitude.