Reduced-Rank Array Modes of the California Current Observing System

Abstract

The information content of the ocean observing array spanning the U.S. west coast is explored using the reduced-rank array modes (RAMs) derived from a four-dimensional variational (4D-Var) data assimilation system covering a period of three decades. RAMs are an extension of the original formulation of array modes introduced by Bennett (1985) but in the reduced model state-space explored by the 4D-Var system, and reveal the extent to which this space is activated by the observations. The projection of the RAMs onto the empirical orthogonal functions (EOFs) of the 4D-Var background error correlation matrix provides a quantitative measure of the effectiveness of the measurements in observing the circulation. It is found that much of the space spanned by the background error covariance is unconstrained by the present ocean observing system. The RAM spectrum is also used to introduce a new criterion to prevent 4D-Var from overfitting the model to the observations.