A random interacting network model for complex networks

This paper was developed within the scope of the DAAD-DST PPP-Indien project 55516784 (INT/FRG/DAAD/P-215) which funded exchange visits between the two participating institutes. B.G. was supported by the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP. J.K. acknowledges financial support from the Government of the Russian Federation (Agreement No. 14.Z50.31.0033). S.M.S. would like to thank University Grants Comission, New Delhi for the financial assistance as an SRF. B.G. and A.R. thank Niklas Boers for stimulating discussions and comments.Peer reviewedPublisher PD

Spatial analyses of precipitation climatology using Climate Networks

Im folgenden wird ein Verfahren dargestellt welches die Möglichkeit bietet komplexe räumliche Zusammenhänge zwischen Niederschlagsereignissen quantitativ in Klimanetzwerke zu fassen und diese auf vielfältige Arten und Weisen zu analysieren. In dem Maße wie synchronisiert Niederschlagsereignisse zwischen Raumpunkten auftreten, in dem Maße sind diese Raumpunkte in Event Synchronization Klimanetzwerken verbunden. Zum einen wird das bestehende Ähnlichkeitsmaß der Ereignissynchronisation verbessert und erweitert, und zum anderen werden verschiedene, zum Teil neue, statistische Methoden zur Netzwerkanalyse vorgestellt und erläutert. Klimanetzwerke sind räumlich eingebettete Netzwerke und die statistisch zu zeigende Abhängigkeit der Ähnlichkeit vom räumlichen Abstand führt zu einer vom Raum nicht unabängigen Netzwerkstruktur. Dies ist in einer Vielzahl von Fällen ein ungewünschter Effekt und es wird eine Methodik entwickelt wie dieser statistisch quantifiziert werden kann. Des weiteren werden zwei weitere neue Netzwerkstatistiken vorgestellt. Einerseits das neue Netzwerkmaß Directionality und andererseits eine Netzwerkreduktion welche Klimanetzwerke auf Klimanetzwerke mit weitreichenden Verbindungen reduziert. Dieser neue Ansatz steht gewissermaßen im Gegensatz zur klassischen Klimanetzwerkkonstruktion die vor allem zu kurzreichweitigen Verbindungen führt. Das neue Netzwerkmaß Directionality gibt für jeden Raumpunkt des Netzwerks eine dominante Raumrichtung der Netzwerkverbindungen an und kann dadurch z.B. für bestimmte Event Synchronization Klimanetzwerke Isochronen abbilden.In the following an approach to the analysis of spatial structures of precipitation event synchronizations is presented. By estimating the synchronicity of precipitation events between points in space, a spatial similarity network is constructed. These Climate Networks can be analyzed statistically in various ways. However, the similarity measure Event Synchronization that will be presented, as well as the concept of Climate Networks, is more general. Climate Network precipitation analyses are done in the applications part in order to present improvements to existing methodologies, as well as novel ones. On one hand, the existing similarity measure Event Synchronization will be refined and extended to a weighted and continuous version, and on the other hand, new methods for statistical analyses of Climate Networks will be presented. Climate Networks are spatially embedded networks and the probability of a link between two nodes decreases with the distance between these nodes. In other words, Climate Network topologies depend on the spatial embedding. Often this effect is distracting and should be considered as a bias in Climate Network statistics. This thesis provides a methodology to estimate this bias and to correct network measures for it. Furthermore, two novel graph statistics are introduced. First, the novel network measure Directionality, and second, a network coarse-graining approach that reduces Climate Networks to Climate Networks of teleconnections, i.e., long-ranged interrelations. This new approach is in contrast to existing Climate Network construction schemes, since commonly most links are short. The novel network measure Directionality provides a dominant direction of links in the embedding space. For undirected Event Synchronization networks this measure is applied for the estimation of Isochrones, i.e., lines of synchronous event occurrences

Clustering River Profiles to Classify Geomorphic Domains

The structure and organization of river networks has been used for decades to investigate the influence of climate and tectonics on landscapes. The majority of these studies either analyze rivers in profile view by extracting channel steepness or calculate planform metrics such as drainage density. However, these techniques rely on the assumption of homogeneity: that intrinsic and external factors are spatially or temporally invariant over the measured profile. This assumption is violated for the majority of Earth's landscapes, where variations in uplift rate, rock strength, climate, and geomorphic process are almost ubiquitous. We propose a method for classifying river profiles to identify landscape regions with similar characteristics by adapting hierarchical clustering algorithms developed for time series data. We first test our clustering on two landscape evolution scenarios and find that we can successfully cluster regions with different erodibility and detect the transient response to sudden base level fall. We then test our method in two real landscapes: first in Bitterroot National Forest, Idaho, where we demonstrate that our method can detect transient incision waves and the topographic signature of fluvial and debris flow process regimes; and second, on Santa Cruz Island, California, where our technique identifies spatial patterns in lithology not detectable through normalized channel steepness analysis. By calculating channel steepness separately for each cluster, our method allows the extraction of more reliable steepness metrics than if calculated for the landscape as a whole. These examples demonstrate the method's ability to disentangle fluvial morphology in complex lithological and tectonic settings

Boundary effects in network measures of spatially embedded networks

In studies of spatially confined networks, network measures can lead to false conclusions since most measures are boundary affected. This is especially the case if boundaries are artificial and not inherent in the underlying system of interest (e.g., borders of countries). An analytical estimation of boundary effects is not trivial due to the complexity of measures. The straightforward approach we propose here is to use surrogate networks that provide estimates of boundary effects in graph statistics. This is achieved by using spatially embedded random networks as surrogates that have approximately the same link probability as a function of spatial link lengths. The potential of our approach is demonstrated for an analysis of spatial patterns in characteristics of regional climate networks. As an example networks derived from daily rainfall data and restricted to the region of Germany are considered

Abrupt transitions in time series with uncertainties

Most time series techniques tend to ignore data uncertainties, which results in inaccurate conclusions. Here, Goswami et al. represent time series as a sequence of probability density functions, and reliably detect abrupt transitions by identifying communities in probabilistic recurrence networks