Empirical orthogonal functions (EOF) reduction of ocean circulation models

The ocean circulation is a complex phenomenon since it involves many spatial and temporal scales. Therefore, its simulation requires the application of sophisticated and costly numerical ocean circulation models. A way to reduce the model complexity could be achieved by the so-called EOF reduction method (e. g. Selten 1995, Achatz and Schmitz 1997, Achatz and Branstator 1999). EOFs (empirical orthogonal functions) are eigenvectors of the covariance matrix and they describe typical variability patterns like propagating waves. Since the EOFs form a complete orthogonal basis one can expand any field in terms of such EOFs. The expansion coefficients are called principal components and their time evolution describes the complete system. The dynamical system of the EOF model can be gained by projection of the original tendency equations on the EOF.

This project forms the topic for the PhD of Jairo Segura. He started his study with a wind-driven barotropic model for a rectangular ocean basin. This model is based on Fourier functions and can be formulated as a dynamical system including quadratic nonlinearities. Therefore, it was straightforward to project the dynamics onto new base functions known as EOFs. However, the EOF reduced model reveal a growth of the EOF pattern amplitude (see Figure 1a). The growth appears due to the insufficient representation of the interaction with smaller scales. Professor Dr. Ulrich Achatz (University Frankfurt. a.M.) provided us with an objective empirical correction that yields a much better representation (see Figure 1b). The results were presented at the CliSAP workshop Fundamentals of climate, atmosphere and ocean dynamics (12th - 14th May 2014).

Participating researchers: Jairo Segura and Thomas Frisius

 

 

Figure 1: a) Time evolution of Principal components for the first and second EOFs of the wind driven ocean model (red and green, respectively) and the EOF-reduced model (blue and magenta, respectively), b) as a) but an empirical correction has been includ