title: Networks from flows--from dynamics to topology.
abstract: Complex network approaches have recently been applied to continuous spatial dynamical systems, like climate, successfully uncovering the system's interaction structure. However the relationship between the underlying atmospheric or oceanic flow's dynamics and the estimated network measures have remained largely unclear. We bridge this crucial gap in a bottom-up approach and define a continuous analytical analogue of Pearson correlation networks for advection-diffusion dynamics on a background flow. Analysing complex networks of prototypical flows and from time series data of the equatorial Pacific, we find that our analytical model reproduces the most salient features of these networks and thus provides a general foundation of climate networks. The relationships we obtain between velocity field and network measures show that line-like structures of high betweenness mark transition zones in the flow rather than, as previously thought, the propagation of dynamical information.
authors.affiliation: 1] Potsdam Institute for Climate Impact Research, P.O.Box 601203, 14412 Potsdam, Germany [2] Department of Physics, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany.
authors.forename: Nora
authors.initials: N
authors.lastname: Molkenthin
authors.affiliation: 1] Potsdam Institute for Climate Impact Research, P.O.Box 601203, 14412 Potsdam, Germany [2] Department of Physics, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany [3] Alfred-Wegener-Institute for Polar and Marine Research, Telegrafenberg A43, 14473 Potsdam, Germany.
authors.forename: Kira
authors.initials: K
authors.lastname: Rehfeld
authors.affiliation: Potsdam Institute for Climate Impact Research, P.O.Box 601203, 14412 Potsdam, Germany.
authors.forename: Norbert
authors.initials: N
authors.lastname: Marwan
authors.affiliation: 1] Potsdam Institute for Climate Impact Research, P.O.Box 601203, 14412 Potsdam, Germany [2] Department of Physics, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany [3] Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB243UE, UK.
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths