Analysis of climate dynamics as a complex system: new insights from the development of advanced methodologies in information theory and complex networks.

Growing interest in climate prediction highlights the importance of achieving a better understanding of the underlying mechanisms behind climate variability. One of the dominant modes of interannual climate variability with worldwide weather and socioeconomic impacts is the El Niño Southern Oscillation (ENSO). Different methodologies have been used to improve the understanding of the ENSO dynamics, however research is still needed. During the last two decades the development and use of complex networks theory has led to important advances in the analysis of climate dynamics. Specifically, the analysis of climate networks, that is networks constructed using climate data, has provided valuable insights into different aspects of the climate dynamics that could not be captured using the classic methods frequently used in climatology. The goal of this thesis is to implement and develop new methodologies based on Information Theory quantifiers and Complex Networks for the analysis of climate variability at a variety of temporal scales. Initial work focussed on the use of well-known Information Theory quantifiers to study several dynamical systems including the logistic map and stochastic noises with different degrees of correlation. The Bandt & Pompe methodology, a symbolisation technique for time series analysis is used for the estimation of the probability distribution functions and missing ordinal patterns. Temporal changes in the dynamics of the Holocene ENSO proxy record of the Laguna Pallcacocha sedimentary data were also studied using entropy quantifiers, missing ordinal patterns, the Fisher Information measure, and the Shannon-Jensen Statistical Complexity. The analysis using these Information Theory Quantifiers