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We present here two promising techniques for the application of the complexnetwork approach to continuous spatio-temporal systems that have been developedin the last decade and show large potential for future application anddevelopment of complex systems analysis. First, we discuss the transforming ofa time series from such systems to a complex network. The natural approach isto calculate the recurrence matrix and interpret such as the adjacency matrixof an associated complex network, called recurrence network. Using complexnetwork measures, such as transitivity coefficient, we demonstrate that thisapproach is very efficient for identifying qualitative transitions inobservational data, e.g., when analyzing paleoclimate regime transitions.Second, we demonstrate the use of directed spatial networks constructed fromspatio-temporal measurements of such systems that can be derived from thesynchronized-in-time occurrence of extreme events in different spatial regions.Although there are many possibilities to investigate such spatial networks, wepresent here the new measure of network divergence and how it can be used todevelop a prediction scheme of extreme rainfall events.

Complex network based techniques to identify extreme events and (sudden) transitions in spatio-temporal systems