Wave Activity for Large-Amplitude Disturbances Described by the Primitive Equations on the Sphere

Abstract

Abstract Pseudomomentum and pseudoenergy are both measures of wave activity for disturbances in a fluid, relative to a notional background state. Together they give information on the propagation, growth, and decay of disturbances. Wave activity conservation laws are most readily derived for the primitive equations on the sphere by using isentropic coordinates. However, the intersection of isentropic surfaces with the ground (and associated potential temperature anomalies) is a crucial aspect of baroclinic wave evolution. A new expression is derived for pseudoenergy that is valid for large-amplitude disturbances spanning isentropic layers that may intersect the ground. The pseudoenergy of small-amplitude disturbances is also obtained by linearizing about a zonally symmetric background state. The new expression generalizes previous pseudoenergy results for quasigeostrophic disturbances on the β plane and complements existing large-amplitude results for pseudomomentum. The pseudomomentum and pseudoenergy diagnostics are applied to an extended winter from the European Centre for Medium-Range Weather Forecasts Interim Re-Analysis data. The time series identify distinct phenomena such as a baroclinic wave life cycle where the wave activity in boundary potential temperature saturates nonlinearly almost two days before the peak in wave activity near the tropopause. The coherent zonal propagation speed of disturbances at tropopause level, including distinct eastward, westward, and stationary phases, is shown to be dictated by the ratio of total hemispheric pseudoenergy to pseudomomentum. Variations in the lower-boundary contribution to pseudoenergy dominate changes in propagation speed; phases of westward progression are associated with stronger boundary potential temperature perturbations.