On the Empirical Orthogonal Functions representation of the ocean circulation

Abstract

Modelling the ocean dynamics is an important part in Earth system models. The understanding of the interplays between ocean and atmosphere is performed through numerical models of important variables, as it is the wind. The wind-driven mid-latitude ocean circulation, for example, includes the subtropical gyres which transport warm water poleward from equatorial regions, and the subpolar gyres that carry cold polar water towards the equator. To the point that Europe, for instance, is warmed by the extension of the Gulf Stream.

A way to reduce a model complexity could be achieved by using the Empirical Orthogonal Functions (EOF) reduction method. The EOF reduction method has been used in the atmosphere before with successful results (Achatz,1997), which opens the possibility of using the method for ocean models, something that has been rarely done. This premise is tested by using a prototype wind-driven barotropic ocean model and applying an additional external forcing to simulate a more realistic setup.

The results of the reconstruction from the EOF reduction method are evaluated by using the optimal assignment and Wasserstein distances among others. Concepts that are mostly used in economy and that offer a new alternative as a method to compare attractors.

The intermediate complexity model tested (Böning,1986), produces attractors that have a phase difference to the reference that are not easy to compare with traditional error calculations methods. Already a small number of EOFs (3-7) suffice to reproduce the essential phase space dynamics and streamfunction. For the principal components, the differences with the reference model decrease when the number of EOFs increases.

This thesis shows that the method of EOF reduction and reconstruction is promising, satisfactory reproductions of the kinetic energy, the streamfunction and the phase space dynamics are also obtained for a modified version of the Böning (1986) model. This is done by including an additional external forcing with coherent spatial structure and stochastic time dependent amplitude. The new force breaks the symmetric structure produced in the unmodified model. This represents a challenge to reproduce with the reconstructed model but for small variations, a satisfactory reproduction is achieved.

Finally, there are many potential improvements and empirical corrections that could be implemented to make the method more efficient. Also, there are more potential prototype ocean models that could represent an advantage for future works.