eng Understanding and predicting extreme weather events is essential for effective hazard prevention and risk management. However, achieving these objectives is challenging, as such events are often driven by nonlinear and/or multiscale processes, and involve multiple interactions within the climate system. In this thesis we employ complex network-based techniques and stochastic modeling to examine three large-scale weather and climate phenomena recognized for their association with extreme weather conditions: atmospheric blocking events, the El Niño-Southern Oscillation (ENSO), and the Madden-Julian Oscillation (MJO). The first part of the thesis makes use of so-called Lagrangian flow networks to explore the dynamical properties of persistent atmospheric blocking situations, i.e. nearly stationary spatial patterns of air pressure. The networks are constructed by associating nodes to regions of the atmosphere and establishing links based on the material (air) flux between them, resulting in a network representation of the atmospheric circulation. We study the spatial patterns of selected node properties prior to, during and after various Northern Hemisphere summer blocking events. Our results demonstrate the ability of the node degree, entropy and harmonic closeness centrality to trace important spatio-temporal characteristics of these events. In particular, all three measures capture the effective separation of the stationary blocking high from the normal westerly flow and the deviation of the main atmospheric currents around it. While Lagrangian flow networks connect fluid regions based on material transport between them, another approach consists of building the network’s links based on the statistical interdependency between variable time series at different locations. The second study in this thesis explores the application of such functional networks and their percolation properties. We investigate the potential of percolation measures from correlation-based networks for the anticipation of different types of sudden shifts in the state of coupled irregularly oscillating systems. As a paradigmatic model system, with a dynamical behavior which is also present in climatic systems, we choose a ring of diffusively coupled noisy FitzHugh--Nagumo oscillators. We show that percolation measures provide early warnings of the rapid switches between the two states of the system. We clarify the mechanisms behind the percolation transitions in this system. This leads to a better understanding of the factors that make percolation precursors effective as early warning indicators of real-world oscillations and especially of El Niño and La Niña events. Finally, the third study centers on the numerical modeling and theoretical understanding of the Madden--Julian Oscillation. Specifically, we implement and analyze solutions to the stochastic skeleton model, a minimal nonlinear oscillator model for the MJO. This model has been recognized for its ability to reproduce several large-scale features of the MJO. In previous studies, the model's forcing functions were predominantly chosen to be mathematically simple and time-independent. Here, we present solutions to the model with observation-based, time-dependent forcing functions. Our results show that the model, with these more realistic forcing functions, successfully replicates key characteristics of MJO events, such as their lifetime, extent, and amplitude, whose statistics agree well with observations. However, we find that the seasonality of MJO events and the spatial variations in the MJO properties are not well reproduced. Additionally, we study the model's capacity to reflect changes in MJO characteristics under the different phases of ENSO. We find that the model does not capture differences in studied characteristics of MJO events in response to changes in conditions during El Niño, La Niña, and Neutral ENSO.
Noémie Ehstand (Wed,) studied this question.