A complex network theory approach to oceanic and atmospheric transport phenomena

Abstract

[EN] The last two decades have seen important advances in the Lagrangian description of transport and mixing in fluid flows driven by concepts from dynamical systems theory, and nowadays several approaches have been developed. Some of such techniques focus on geometric objects - lines, surfaces - separating fluid regions with different properties while others have focussed on computing stretching-like fields in the fluid domain, such as different types of Lyapunov exponents or other Lagrangian descriptors. Finally, there is a line of research focussing on the moving fluid regions themselves, the so-called set-oriented methods. On the other hand many real-world systems can be studied by using the Network paradigm and in the last years Network Theory approaches have been successfully used for geophysical systems in the context of climate networks in which the connections among the different locations represent statistical relationships between climatic time series from these locations, inferred from correlations and other statistical methods. In this thesis we propose a new paradigm linking the network formalism with transport and mixing phenomena in geophysical flows. We analyze directly the network describing the material fluid flow among different locations, which we call flow network. Among other characteristics this network is directed, weighted, spatially embedded and time-dependent. We illustrate the general ideas with an exemplary network derived from a realistic simulation of the surface flow in the Mediterranean sea. We use network-theory tools to analyze them and gain insights into transport processes from a general point of view. We quantitatively relate dispersion and mixing characteristics, classically quantified by Lyapunov exponents, to the degree of the network nodes. A family of network entropies is defined from the network adjacency matrix, and related to the statistics of stretching in the fluid, in particular to the Lyapunov exponent field. We use a network community detection algorithm, Infomap, to partition the network into coherent regions, i.e. areas internally well mixed, but with little fluid interchange between them. We find interesting applications of this approach to marine biology of the Mediterranean Sea. Oceanic dispersal and connectivity have been identified indeed as crucial factors for structuring marine populations and designing Marine Protected Areas (MPAs). Larvae of different pelagic durations and seasons could be modeled as passive tracers advected in a simulated oceanic surface flow from which a flow network is constructed. By ap- plying the Infomap algorithm we extract hydrodynamical provinces from the network that result to be delimited by frontiers which match multi-scale oceanographic features. By examining the repeated occurrence of such boundaries, we identify the spatial scales and geographic structures that would control larval dispersal across the entire seascape. Based on these hydrodynamical units, we study novel connectivity metrics for existing MPAs.

We also define node-by-node proxies measuring local larval retention and exchange. From the analysis of such measures we confirm that retention processes are favored along the coastlines while they are weak in the open ocean due to specific oceanographic conditions. Although these proxies were often studied separately in the literature, we demonstrated that they are inter-related under certain conditions and that their integrated analysis leads to a better understanding of metapopulation dynamics, informing both genetic and demographic connectivities. We also consider paths in weighted and directed temporal networks, introducing tools to compute sets of paths of high probability. We quantify the relative importance of the most probable path between two nodes with respect to the whole set of paths, and to a subset of highly probable paths which incorporate most of the connection probability. These concepts are used to provide alternative definitions of betweenness centrality. We apply these tools to the temporal flow network describing surface currents in the Mediterranean sea. Despite the full transport dynamics is described by a very large number of paths we find that, for realistic time scales, only a very small subset of high probability paths (or even a single most probable one) is enough to characterize global connectivity properties of the network. Finally we apply the same analysis to the atmospheric blocking of eastern Europe and western Russia in summer 2010. We compute the most probable paths followed by fluid particles which reveal the Omega-block skeleton of the event. A hierarchy of sets of highly probable paths is introduced to describe transport pathways when the most probable path alone is not representative enough. These sets of paths have the shape of narrow coherent tubes flowing close to the most probable one. Thus, as for the case of Mediterranean Sea, even when the most probable path is not very significant in terms of its probability, it still identifies the geometry of the transport pathways