Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 11 3 2004 10.5194/npg-11-393-2004 http://www.nonlin-processes-geophys.net/11/393/2004/ http://www.nonlin-processes-geophys.net/11/393/2004/npg-11-393-2004.html http://www.nonlin-processes-geophys.net/11/393/2004/npg-11-393-2004.pdf 393 398 2004-09-13 Nonlinear dimensionality reduction in climate data A. J. Gámez C. S. Zhou A. Timmermann J. Kurths Institut für Physik, Universität Potsdam, Postfach 601553, D-14415 Potsdam, Germany Leibniz Institut für Meereswissenschaften, IfM-GEOMAR, Düsternbrooker Weg 20, D-24105 Kiel, Germany Linear methods of dimensionality reduction are useful tools for handling and interpreting high dimensional data. However, the cumulative variance explained by each of the subspaces in which the data space is decomposed may show a slow convergence that makes the selection of a proper minimum number of subspaces for successfully representing the variability of the process ambiguous. The use of nonlinear methods can improve the embedding of multivariate data into lower dimensional manifolds. In this article, a nonlinear method for dimensionality reduction, Isomap, is applied to the sea surface temperature and thermocline data in the tropical Pacific Ocean, where the El Niño-Southern Oscillation (ENSO) phenomenon and the annual cycle phenomena interact. Isomap gives a more accurate description of the manifold dimensionality of the physical system. The knowledge of the minimum number of dimensions is expected to improve the development of low dimensional models for understanding and predicting ENSO.