| Summary: | Climate variability has considerable impact on our society throughout recorded history. If we would like to make informed decisions about our own future, it is essential that we could identify, quantify, understand such climate variability, and then eventually predict it so as to minimize its negative consequences and maximize its positive ones. Complex network theory has been successfully applied to many complex systems. The idea of complex network also has been recently extended to climate studies which is referred to as Climate Network (CN). The novelty of complex network theory is that it maps out the topological features that are related to the physics of the dynamical systems. Therefore, CN is an innovative and powerful tool to investigate the patterns and the dynamics of climate variability. In this thesis, several specific phenomena of climate variability are studied by using the techniques from complex network theory. The first one is the reduction of the Atlantic Meridional Overturning Circulation (MOC). We develop an early warning indicator for a future collapse of the Atlantic MOC. We explore the performance of this indicator using data both from an idealized ocean model and a general circulation model that show such a collapse. We also determine optimal observation locations through quality measures of the indicator, and show that one needs multiple sections in the Atlantic to have a high quality indicator of the MOC collapse. The second phenomenon is the multidecadal variability associated with the Atlantic Multidecadal Oscillation (AMO). We investigate the existence of the westward propagation in the North Atlantic sea surface temperature (SST) observations. We reconstruct CNs by using a linear Pearson correlation measure and a nonlinear mutual information measure of spatial correlations between SST variations. Analysis of the topological properties of CNs shows that the nonlinear measure is better in capturing the main features of propagating patterns from the noisy SST signals than the linear ...
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