Aljoscha Rheinwalt

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.

The South American rainfall dipole: A complex network analysis of extreme events

Intraseasonal rainfall variability of the South American monsoon system is characterized by a pronounced dipole between southeastern South America and southeastern Brazil. Here we analyze the dynamical properties of extreme rainfall events associated with this dipole by combining a nonlinear synchronization measure with complex networks. We make the following main observations: (i) Our approach reveals the dominant synchronization pathways of extreme events for the two dipole phases, (ii) while extreme rainfall synchronization in the tropics is directly driven by the trade winds and their deflection by the Andes mountains, extreme rainfall propagation in the subtropics is mainly dictated by frontal systems, and (iii) the well-known rainfall dipole is, in fact, only the most prominent mode of an oscillatory pattern that extends over the entir ec ontinent. This provides further evidence that the influence of Rossby waves, which cause frontal systems over South America and impact large-scale circulation patterns, extends beyond the equator.

Non-linear time series analysis of precipitation events using regional climate networks for Germany

AbstractSynchronous occurrences of heavy rainfall events and the study of their relation in time and space are of large socio-economical relevance, for instance for the agricultural and insurance sectors, but also for the general well-being of the population. In this study, the spatial synchronization structure is analyzed as a regional climate network constructed from precipitation event series. The similarity between event series is determined by the number of synchronous occurrences. We propose a novel standardization of this number that results in synchronization scores which are not biased by the number of events in the respective time series. Additionally, we introduce a new version of the network measure directionality that measures the spatial directionality of weighted links by also taking account of the effects of the spatial embedding of the network. This measure provides an estimate of heavy precipitation isochrones by pointing out directions along which rainfall events synchronize. We propose a climatological interpretation of this measure in terms of propagating fronts or event traces and confirm it for Germany by comparing our results to known atmospheric circulation patterns.

The size distribution of spatiotemporal extreme rainfall clusters around the globe

The scaling behavior of rainfall has been extensively studied both in terms of event magnitudes and in terms of spatial extents of the events. Different heavy-tailed distributions have been proposed as candidates for both instances, but statistically rigorous treatments are rare. Here we combine the domains of event magnitudes and event area sizes by a spatiotemporal integration of 3-hourly rain rates corresponding to extreme events derived from the quasi-global high-resolution rainfall product Tropical Rainfall Measuring Mission 3B42. A maximum likelihood evaluation reveals that the distribution of spatiotemporally integrated extreme rainfall cluster sizes over the oceans is best described by a truncated power law, calling into question previous statements about scale-free distributions. The observed subpower law behavior of the distributions tail is evaluated with a simple generative model, which indicates that the exponential truncation of an otherwise scale-free spatiotemporal cluster size distribution over the oceans could be explained by the existence of land masses on the globe.

Abrupt transitions in time series with uncertainties

Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Niño-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an ‘uncertainty-aware’ framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon.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.

Teleconnections in Climate Networks: A Network-of-Networks Approach to Investigate the Influence of Sea Surface Temperature Variability on Monsoon Systems

We analyze large-scale interdependencies between sea surface temperature (SST) and rainfall variability. We propose a novel climate network construction scheme which we call teleconnection climate networks (TCN). On account of this analysis, gridded SST and rainfall data sets are coarse grained by merging grid points that are dynamically similar to each other. The resulting clusters of time series are taken as the nodes of the TCN. The SST and rainfall systems are investigated as two separate climate networks, and teleconnections within the individual climate networks are studied with special focus on dipolar patterns. Our analysis reveals a pronounced rainfall dipole between Southeast Asia and the Afghanistan-Pakistan region, and we discuss the influences of Pacific SST anomalies on this dipole.

A Complex Network Approach to Investigate the Spatiotemporal Co-variability of Extreme Rainfall

The analysis of spatial patterns of co-variability of extreme rainfall is challenging because traditional techniques based on principal component analysis of the covariance matrix only capture the first two statistical moments of the data distribution and are thus not suitable to analyze the behavior in the tails of the respective distributions. Here, we describe an alternative to these techniques which is based on the combination of a nonlinear synchronization measure and complex network theory. This approach allows to derive spatial patterns encoding the co-variability of extreme rainfall at different locations. By introducing suitable network measures, the methodology can be used to perform climatological analysis but also for statistical prediction of extreme rainfall events. We introduce the methodological framework and present applications to high-spatiotemporal resolution rainfall data (TRMM 3B42) over South America.

Network-based flow accumulation for point clouds: Facet-Flow Networks (FFN)

Point clouds provide high-resolution topographic data which is often classified into bare-earth, vegetation, and building points and then filtered and aggregated to gridded Digital Elevation Models (DEMs) or Digital Terrain Models (DTMs). Based on these equally-spaced grids flow-accumulation algorithms are applied to describe the hydrologic and geomorphologic mass transport on the surface. In this contribution, we propose a stochastic point-cloud filtering that, together with a spatial bootstrap sampling, allows for a flow accumulation directly on point clouds using Facet-Flow Networks (FFN). Additionally, this provides a framework for the quantification of uncertainties in point-cloud derived metrics such as Specific Catchment Area (SCA) even though the flow accumulation itself is deterministic.

A random interacting network model for complex networks

We propose a RAndom Interacting Network (RAIN) model to study the interactions between a pair of complex networks. The model involves two major steps: (i) the selection of a pair of nodes, one from each network, based on intra-network node-based characteristics, and (ii) the placement of a link between selected nodes based on the similarity of their relative importance in their respective networks. Node selection is based on a selection fitness function and node linkage is based on a linkage probability defined on the linkage scores of nodes. The model allows us to relate within-network characteristics to between-network structure. We apply the model to the interaction between the USA and Schengen airline transportation networks (ATNs). Our results indicate that two mechanisms: degree-based preferential node selection and degree-assortative link placement are necessary to replicate the observed inter-network degree distributions as well as the observed inter-network assortativity. The RAIN model offers the possibility to test multiple hypotheses regarding the mechanisms underlying network interactions. It can also incorporate complex interaction topologies. Furthermore, the framework of the RAIN model is general and can be potentially adapted to various real-world complex systems.

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. Results for the region of Germany are compared to results from subregions of that region.