On Variational Normal Mode Initialization

Abstract

The variational problem of initial data specification from observations with the strong constraint of the elimination of transient gravity waves through nonlinear normal mode balancing is reconsidered. The exact formulation of this problem is contrasted to the approximate formulation previously given by Daley. Through the judicious use of model normal modes, an alternative algorithm is developed which allows the use of confidence weights which reflect the fidelity of observations in a more realistic manner than previously possible. In particular, longitudinally varying confidence weights can be utilized. Examples of the use of this technique using the Machenhauer and the second-order Baer-Tribbia initialization are given. An attempt to ascertain the validity of Daley's method demonstrates the accuracy of this approximation and justifies its continued use.