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Academic Commons Search Resultsen-usAdvanced spectral methods for climatic time series
http://academiccommons.columbia.edu/catalog/ac:151633
Ghil, Michael; Allen, M. R.; Dettinger, M. D.; Ide, K.; Kondrashov, D.; Mann, M. E.; Robertson, Andrew W.; Saunders, A.; Tian, Y.; Varadi, F.; Yiou, P.http://hdl.handle.net/10022/AC:P:14382Tue, 14 Aug 2012 00:00:00 +0000The analysis of univariate or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical field of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory. In this review we describe the connections between time series analysis and nonlinear dynamics, discuss signal-to-noise enhancement, and present some of the novel methods for spectral analysis. The various steps, as well as the advantages and disadvantages of these methods, are illustrated by their application to an important climatic time series, the Southern Oscillation Index. This index captures major features of interannual climate variability and is used extensively in its prediction. Regional and global sea surface temperature data sets are used to illustrate multivariate spectral methods. Open questions and further prospects conclude the review.Atmospheric sciences, Physical oceanographyawr2001International Research Institute for Climate and SocietyArticlesA Hierarchy of Data-Based ENSO Models
http://academiccommons.columbia.edu/catalog/ac:151563
Kondrashov, D.; Kravtsov, S.; Robertson, Andrew W.; Ghil, Michaelhttp://hdl.handle.net/10022/AC:P:14360Tue, 14 Aug 2012 00:00:00 +0000Global sea surface temperature (SST) evolution is analyzed by constructing predictive models that best describe the dataset's statistics. These inverse models assume that the system's variability is driven by spatially coherent, additive noise that is white in time and are constructed in the phase space of the dataset's leading empirical orthogonal functions. Multiple linear regression has been widely used to obtain inverse stochastic models; it is generalized here in two ways. First, the dynamics is allowed to be nonlinear by using polynomial regression. Second, a multilevel extension of classic regression allows the additive noise to be correlated in time; to do so, the residual stochastic forcing at a given level is modeled as a function of variables at this level and the preceding ones. The number of variables, as well as the order of nonlinearity, is determined by optimizing model performance. The two-level linear and quadratic models have a better El Niño–Southern Oscillation (ENSO) hindcast skill than their one-level counterparts. Estimates of skewness and kurtosis of the models' simulated Niño-3 index reveal that the quadratic model reproduces better the observed asymmetry between the positive El Niño and negative La Niña events. The benefits of the quadratic model are less clear in terms of its overall, cross-validated hindcast skill; this model outperforms, however, the linear one in predicting the magnitude of extreme SST anomalies. Seasonal ENSO dependence is captured by incorporating additive, as well as multiplicative forcing with a 12-month period into the first level of each model. The quasi-quadrennial ENSO oscillatory mode is robustly simulated by all models. The "spring barrier" of ENSO forecast skill is explained by Floquet and singular vector analysis, which show that the leading ENSO mode becomes strongly damped in summer, while nonnormal optimum growth has a strong peak in December.Atmospheric sciences, Climate changeawr2001International Research Institute for Climate and SocietyArticles