Investigating the dynamics of Rossby wave packets using Local Finite Amplitude Wave Activity

Abstract

Upper tropospheric Rossby wave packets (RWPs) are important dynami- cal features, because they may act as precursors to high impact weather and have implications for predictability. In the literature, several meth- ods have been proposed to identify RWPs and describe their dynamics. However, most of these methods are based on linear theory and therefore valid only for small amplitude waves, or theoretically and computationally rather complex when valid for finite amplitude waves. The present work introduces a novel diagnostic to quantify the amplitude of RWPs which holds at finite amplitudes and is particularly amenable to compute from atmospheric data. It is based on the local finite amplitude wave activity (LWA) of N. Nakamura and collaborators, which is extended to the prim- itive equations in isentropic coordinates. LWA is then combined with a zonal filter to remove its intrinsic phase dependence and identify the entire wave packet. The utility of the proposed diagnostics in identifying RWPs is applied first to idealised simulations and then to a specific episode contain- ing large amplitude RWPs. A climatology of Rossby wave activity based on filtered LWA computed from reanalysis data is also presented. Further- more, the LWA diagnostic is used as a metric to quantify the Rossby wave amplitude error up to the planetary scale in an upscale error growth ex- periment. The LWA diagnostic identifies a fourth stage of upscale error growth, which could not been revealed using simply potential vorticity or other phase dependent metrics, since they reach saturation at the synop- tic scale. The LWA diagnostic is then used to analyse the dynamics of Rossby wave packets, with the goal of distinguishing between conservative propagation against the impact of non-conservative processes. Previous re- search focused on the dynamics of the single phases of RWPs or describedthe dynamics of Rossby waves in the zonal average. Our LWA diagnostic achieves both, providing a quantitative framework for the evolution of the RWPs amplitude rather than its individual phases, but at the same time being local in longitude. In this context a budget equation for filtered LWA is derived and its utility is tested in a hierarchy of models and forecast data. The results confirm the ability of the LWA diagnostic to capture the key features of the RWPs dynamics and identifying non-conservative local sources or sinks of wave activity. In agreement with previous studies, diabatic processes are found responsible to considerably affect the RWP evolution, therefore an improvement of the representation of such physical processes operational models may help to reduce the forecast error.