On Complex Networks in Atmospheric Dynamics

The atmosphere is a complex system in which large-scale interactions between different flow elements give rise to collective behaviours. For instance, phenomena at widely separated locations (e.g. ENSO and the Indian Monsoon) may evolve coherently, a distribution of vortices may substantially alter the dynamics at a specific location, or similar flow patterns may arise in disconnected regions.

Extracting such features from atmospheric data is crucial for our understanding of climatological phenomena and their global repercussions. Nonetheless, this task remains a significant challenge due to the methodological constraints imposed by high dimensionality, multi-scale dynamics, and non-linearity.

Complex networks have risen as a promising tool to reveal these relationships by simplifying continuous flow data into more tractable discrete graphs. Here, nodes represent flow structures (e.g. fixed points in the Earth's surface or Lagrangian particles) and edges represent their associations (e.g. statistical or material connections). These graphs are a simplified representation of the system but, if expressive enough, can be useful to decompose the underlying interaction structures in a much-simplified way.

Graph theory allows us to reveal the topology of the connectivity patterns, quantify the influence of individual flow elements on the overall dynamics, cluster the flow into groups with similar characteristics, etc. Naturally, depending on how the network is built, different interaction structures with different interpretations can be revealed.

The first objective of this thesis is to bring together graph theory, nonlinear dynamics, and atmospheric physics to develop a simple, versatile, efficient, and consistent toolkit that atmospheric scientists can use to reveal the dynamical structure of atmospheric data. The use of networks in atmospheric sciences dates back only a few decades so there is room for improvement in the efficiency and consistency of the current methodologies.

Moreover, although networks are extremely versatile, atmospheric scientists have focused on three constructions: Eulerian correlation-based networks, Lagrangian transport-based networks, and time-series analysis. This thesis aims to explore these and other alternative relationships like vortical interactions and dynamical similarity, which have been perhaps more actively explored in fluid dynamics.

The second objective of this thesis is to employ this toolkit in a couple of case studies where networks have not been used before to demonstrate their potential in the atmospheric sciences. Networks offer a wide range of applications, with the most immediate ones being the characterisation of the system's dynamics and the benchmarking of models. However, their utility does not stop with analysis, they can also be useful in modelling.

For example, they can be used to build low-order models of atmospheric phenomena, and their ability to capture the system's global interaction structure makes them interesting forms of data to consider when parametrising weather and climate models. Ideally, these case studies will encompass both analysis and modelling uses of networks.

This project aligns the most with the EPSRC Fluid Dynamics and Aerodynamics, and Non-linear Systems Research areas. There are no companies or collaborators involved yet. However, it would be of interest to seek cooperations as with European meteorological centres like the Met Office or the European Centre for Medium-Range Weather Forecasts (ECMWF) to ensure this thesis is both relevant and impactful in the field.