Dynamical Decomposition of Low-Frequency Tendencies

Abstract

A nearly complete vorticity equation is used to diagnose the tendency components of the low-frequency variations of the 500-mb streamfunction induced by various internal linear-nonlinear interaction processes. With the aid of a special composite technique (?phase-shifting? method) that effectively records the observations in a coordinate system moving with an identifiable low-frequency pattern, the authors are able to separate the internal interactions that primarily act to make low-frequency waves propagate from those that are mostly responsible for development/maintenance/decay (?maintenance? for brevity) of low-frequency transients. It is found that the low-frequency transients are maintained primarily by two nonlinear interaction processes: one is the vorticity flux of high-frequency eddies and the other is the interaction of low-frequency transients and stationary waves. It is also found that an individual propagation tendency component may be much larger than a maintenance tendency component. In particular, the beta effect and the advection of the low-frequency vorticity by the zonally averaged climatological wind are the dominant terms among the propagation tendency components. But there is a great deal of cancellation among the propagation tendency components. As a result, the net magnitude of the tendency components describing propagation is only slightly larger than those relating to maintenance of low-frequency waves. From a forecast point of view, both propagation and forcing terms are equally important if an accurate forecast beyond a few days is required.