[{"key":"dc.contributor.author","value":"Monahan, Adam Hugh","language":null},{"key":"dc.date.accessioned","value":"2009-07-15T17:12:18Z","language":null},{"key":"dc.date.available","value":"2009-07-15T17:12:18Z","language":null},{"key":"dc.date.issued","value":"2000","language":null},{"key":"dc.identifier.uri","value":"http:\/\/hdl.handle.net\/2429\/10829","language":null},{"key":"dc.description.abstract","value":"A nonlinear generalisation of Principal Component Analysis (PCA), denoted Nonlinear\r\nPrincipal Component Analysis (NLPCA), is introduced and applied to the analysis of\r\nclimate data. This method is implemented using a 5-layer feed-forward neural network\r\nintroduced originally in the chemical engineering literature. The method is described\r\nand details of its implementation are addressed. It is found empirically that NLPCA\r\npartitions variance in the same fashion as does PCA, that is, that the sum of the total\r\nvariance of the NLPCA approximation with the total variance of the residual from the\r\noriginal data is equal to the total variance of the original data. An important distinction\r\nis drawn between a modal P-dimensional NLPCA analysis, in which P successive 1D\r\napproximations are determined iteratively so that the approximation is the sum of P\r\nnonlinear functions of one variable, and a nonmodal analysis, in which the P-dimensional\r\nNLPCA approximation is determined as a nonlinear non-additive function of P variables.\r\nNonlinear Principal Component Analysis is first applied to a data set sampled from\r\nthe Lorenz attractor. It is found that the NLPCA approximations are much more representative\r\nof the data than are the corresponding PCA approximations. In particular, the\r\n1D and 2D NLPCA approximations explain 76% and 99.5% of the total variance, respectively,\r\nin contrast to 60% and 95% explained by the 1D and 2D PCA approximations.\r\nWhen applied to a data set consisting of monthly-averaged tropical Pacific Ocean sea\r\nsurface temperatures (SST), the modal 1D NLPCA approximation describes average variability\r\nassociated with the El Nino\/Southern Oscillation (ENSO) phenomenon, as does\r\nthe 1D PCA approximation. The NLPCA approximation, however, characterises the\r\nasymmetry in spatial pattern of SST anomalies between average warm and cold events\r\n(manifested in the skewness of the distribution) in a manner that the PCA approximation\r\ncannot. The second NLPCA mode of SST is found to characterise differences\r\nin ENSO variability between individual events, and in particular is consistent with the\r\ncelebrated 1977 \"regime shift\". A 2D nonmodal NLPCA approximation is determined,\r\nthe interpretation of which is complicated by the fact that a secondary feature extraction\r\nproblem has to be carried out to interpret the results. It is found that this approximation\r\ncontains much the same information as that provided by the modal analysis. A modal\r\nNLPC analysis of tropical Indo-Pacific sea level pressure (SLP) finds that the first mode\r\ndescribes average ENSO variability in this field, and also characterises an asymmetry in\r\nSLP fields between average warm and cold events. No robust nonlinear mode beyond the\r\nfirst could be found.\r\nNonlinear Principal Component Analysis is used to find the optimal nonlinear approximation to SLP data produced by a 1001 year integration of the Canadian Centre for\r\nClimate Modelling and Analysis (CCCma) coupled general circulation model (CGCM1).\r\nThis approximation's associated time series is strongly bimodal and partitions the data\r\ninto two distinct regimes. The first and more persistent regime describes a standing oscillation whose signature in the mid-troposphere is alternating amplification and attenuation\r\nof the climatological ridge over Northern Europe. The second and more episodic\r\nregime describes mid-tropospheric split-flow south of Greenland. Essentially the same\r\nstructure is found in the 1D NLPCA approximation of the 500mb height field itself. In\r\na 500 year integration with atmospheric CO2 at four times pre-industrial concentrations,\r\nthe occupation statistics of these preferred modes of variability change, such that the\r\nepisodic split-flow regime occurs less frequently while the standing oscillation regime\r\noccurs more frequently.\r\nFinally, a generalisation of Kramer\u2019s NLPCA using a 7-layer autoassociative neural\r\nnetwork is introduced to address the inability of Kramer\u2019s original network to find P-dimensional\r\nstructure topologically different from the unit cube in RP. The example of\r\nan ellipse is considered, and it is shown that the approximation produced by the 7-layer\r\nnetwork is a substantial improvement over that produced by the 5-layer network. [Scientific formulae used in this abstract could not be reproduced.]","language":"en"},{"key":"dc.format.extent","value":"8824754 bytes","language":null},{"key":"dc.format.mimetype","value":"application\/pdf","language":null},{"key":"dc.language.iso","value":"eng","language":"en"},{"key":"dc.publisher","value":"University of British Columbia","language":null},{"key":"dc.rights","value":"For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https:\/\/open.library.ubc.ca\/terms_of_use.","language":null},{"key":"dc.title","value":"Nonlinea principal component analysis of climate data","language":"en"},{"key":"dc.type","value":"Text","language":null},{"key":"dc.degree.name","value":"Doctor of Philosophy - PhD","language":"en"},{"key":"dc.degree.discipline","value":"Oceanography","language":null},{"key":"dc.degree.grantor","value":"University of British Columbia","language":null},{"key":"dc.date.graduation","value":"2000-05","language":"en"},{"key":"dc.type.text","value":"Thesis\/Dissertation","language":"en"},{"key":"dc.description.affiliation","value":"Science, Faculty of","language":"en"},{"key":"dc.description.affiliation","value":"Earth, Ocean and Atmospheric Sciences, Department of","language":null},{"key":"dc.degree.campus","value":"UBCV","language":"en"},{"key":"dc.description.scholarlevel","value":"Graduate","language":"en"}]