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Earth’s climate is a complex dynamical system. Its underlying components interact with eachother in linear or nonlinear ways on multiple several spatial and time scales creating possiblepositive and negative feedback loops. Understanding and studying such a system is a difficultchallenge with crucial implications on our society but requires data mining through anextremely large and complex amount of data. In particular, the investigation ofchanges in dynamical and statistical properties in the climate of the past represents aninvaluable opportunity to understand interactions between external forcing (e.g., orbitalparameters) and the internal variability of the climate system. Given a simulatedclimate field embedded on a two dimensional grid, we propose a new methodology to(i) quantify nonlinear changes in variability in simulated climate fields by meansof an information entropy quantifier, (ii) identify regions that undergo changes inentropy in a homogeneous way and (iii) investigate the time dependency of theconnectivity patterns between these regions. To address these points, we analyze twoglobal transient simulations ran with the IPSL Earth system model from mid- to lateHolocene (6000 years BP to 1950). These simulations differ according to theirhorizontal resolution (3.75ox 1.89ovs. 2.5ox 1.27o), their hydrological component(2 vs. 11 layers) and the way vegetation interacts with climate (prescribed versusdynamic). Specifically, we focus on the variability and connectivity of two fields: seasurface temperature (SST) and precipitation. Time resolution is monthly. For agiven field, the input of the algorithm is a two dimensional grid with detrendedanomalies embedded in it. We consider time windows of 100 years of data every20 years and for each time window we compute the entropy of every time seriesembedded in the grid. The entropy serves as a measure of complexity of time series andits computation depends on recurrence plots, an advanced nonlinear data analysistechnique. The product of this first step is then a spatio-temporal entropy field.We then use δ-MAPS, a dimensionality reduction methodology recently proposedby the authors, to reduce the dimensionality of the entropy field by identifyingsemi-autonomous components, referred to as "domains". Domains are defined as spatiallycontiguous, possibly overlapping, structures that undergo changes in entropy in ahomogeneous way. This allows to study both past climate regime shifts and their spatialheterogeneity. Finally, given two sets of domains (in the SST and precipitation fields),for each time window, we compute their signals and infer a functional network ofnetworks (NoN) between them. The NoN is a weighted and potentially directed graphwhich, in a single framework, quantify the interactions between domains in the samefield and the dependency among domains of different fields. A first analysis of thetime dependency of domains’ complexity and of their NoN topology is presented. [ABSTRACT FROM AUTHOR]