Variational Implicit Normal Mode Initialization

It is shown that implicit normal mode initialization can be combined with a variational technique, in order to control the relative magnitudes of the changes to the analyzed mass and wind fields. Since the initialization procedure is expressed entirely in physical space, the use of locally varying weights in the variational integral becomes more straightforward than in previous efforts to combine variational methods with normal mode initialization. We present details of the application to a finite-element model of the shallow water equations on a stereographic projection. It is demonstrated that the use of variational initialization can change the slowly evolving component of the subsequent forecast, as well as eliminate the unrealistic fast component.