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- ItemSimilarity estimators for irregular and age-uncertain time series(München : European Geopyhsical Union, 2014) Rehfeld, K.; Kurths, J.Paleoclimate time series are often irregularly sampled and age uncertain, which is an important technical challenge to overcome for successful reconstruction of past climate variability and dynamics. Visual comparison and interpolation-based linear correlation approaches have been used to infer dependencies from such proxy time series. While the first is subjective, not measurable and not suitable for the comparison of many data sets at a time, the latter introduces interpolation bias, and both face difficulties if the underlying dependencies are nonlinear. In this paper we investigate similarity estimators that could be suitable for the quantitative investigation of dependencies in irregular and age-uncertain time series. We compare the Gaussian-kernel-based cross-correlation (gXCF, Rehfeld et al., 2011) and mutual information (gMI, Rehfeld et al., 2013) against their interpolation-based counterparts and the new event synchronization function (ESF). We test the efficiency of the methods in estimating coupling strength and coupling lag numerically, using ensembles of synthetic stalagmites with short, autocorrelated, linear and nonlinearly coupled proxy time series, and in the application to real stalagmite time series. In the linear test case, coupling strength increases are identified consistently for all estimators, while in the nonlinear test case the correlation-based approaches fail. The lag at which the time series are coupled is identified correctly as the maximum of the similarity functions in around 60–55% (in the linear case) to 53–42% (for the nonlinear processes) of the cases when the dating of the synthetic stalagmite is perfectly precise. If the age uncertainty increases beyond 5% of the time series length, however, the true coupling lag is not identified more often than the others for which the similarity function was estimated. Age uncertainty contributes up to half of the uncertainty in the similarity estimation process. Time series irregularity contributes less, particularly for the adapted Gaussian-kernel-based estimators and the event synchronization function. The introduced link strength concept summarizes the hypothesis test results and balances the individual strengths of the estimators: while gXCF is particularly suitable for short and irregular time series, gMI and the ESF can identify nonlinear dependencies. ESF could, in particular, be suitable to study extreme event dynamics in paleoclimate records. Programs to analyze paleoclimatic time series for significant dependencies are included in a freely available software toolbox.
- ItemTopological data analysis of contagion maps for examining spreading processes on networks([London] : Nature Publishing Group UK, 2015) Taylor, Dane; Klimm, Florian; Harrington, Heather A.; Kramár, Miroslav; Mischaikow, Konstantin; Porter, Mason A.; Mucha, Peter J.Social and biological contagions are influenced by the spatial embeddedness of networks. Historically, many epidemics spread as a wave across part of the Earth’s surface; however, in modern contagions long-range edges—for example, due to airline transportation or communication media—allow clusters of a contagion to appear in distant locations. Here we study the spread of contagions on networks through a methodology grounded in topological data analysis and nonlinear dimension reduction. We construct ‘contagion maps’ that use multiple contagions on a network to map the nodes as a point cloud. By analysing the topology, geometry and dimensionality of manifold structure in such point clouds, we reveal insights to aid in the modelling, forecast and control of spreading processes. Our approach highlights contagion maps also as a viable tool for inferring low-dimensional structure in networks.
- ItemA new climate dataset for systematic assessments of climate change impacts as a function of global warming(München : European Geopyhsical Union, 2012) Heinke, J.; Ostberg, S.; Schaphoff, S.; Frieler, K.; Müller, C.; Gerten, D.; Meinshausen, M.; Lucht, W.Interactions between food demand, biomass energy and forest preservation are driving both food prices and land-use changes, regionally and globally. This study presents a new model called Nexus Land-Use version 1.0 which describes these interactions through a generic representation of agricultural intensification mechanisms within agricultural lands. The Nexus Land-Use model equations combine biophysics and economics into a single coherent framework to calculate crop yields, food prices, and resulting pasture and cropland areas within 12 regions inter-connected with each other by international trade. The representation of cropland and livestock production systems in each region relies on three components: (i) a biomass production function derived from the crop yield response function to inputs such as industrial fertilisers; (ii) a detailed representation of the livestock production system subdivided into an intensive and an extensive component, and (iii) a spatially explicit distribution of potential (maximal) crop yields prescribed from the Lund-Postdam-Jena global vegetation model for managed Land (LPJmL). The economic principles governing decisions about land-use and intensification are adapted from the Ricardian rent theory, assuming cost minimisation for farmers. In contrast to the other land-use models linking economy and biophysics, crops are aggregated as a representative product in calories and intensification for the representative crop is a non-linear function of chemical inputs. The model equations and parameter values are first described in details. Then, idealised scenarios exploring the impact of forest preservation policies or rising energy price on agricultural intensification are described, and their impacts on pasture and cropland areas are investigated.
- ItemUnderstanding flood regime changes in Europe: A state-of-the-art assessment(Göttingen : Copernicus GmbH, 2014) Hall, J.; Arheimer, B.; Borga, M.; Brázdil, R.; Claps, P.; Kiss, A.; Kjeldsen, T.R.; Kriauĉuniene, J.; Kundzewicz, Z.W.; Lang, M.; Llasat, M.C.; Macdonald, N.; McIntyre, N.; Mediero, L.; Merz, B.; Merz, R.; Molnar, P.; Montanari, A.; Neuhold, C.; Parajka, J.; Perdigão, R.A.P.; Plavcová, L.; Rogger, M.; Salinas, J.L.; Sauquet, E.; Schär, C.; Szolgay, J.; Viglione, A.; Blöschl, G.There is growing concern that flooding is becoming more frequent and severe in Europe. A better understanding of flood regime changes and their drivers is therefore needed. The paper reviews the current knowledge on flood regime changes in European rivers that has traditionally been obtained through two alternative research approaches. The first approach is the data-based detection of changes in observed flood events. Current methods are reviewed together with their challenges and opportunities. For example, observation biases, the merging of different data sources and accounting for nonlinear drivers and responses. The second approach consists of modelled scenarios of future floods. Challenges and opportunities associated with flood change scenarios are discussed such as fully accounting for uncertainties in the modelling cascade and feedbacks. To make progress in flood change research, we suggest that a synthesis of these two approaches is needed. This can be achieved by focusing on long duration records and flood-rich and flood-poor periods rather than on short duration flood trends only, by formally attributing causes of observed flood changes, by validating scenarios against observed flood regime dynamics, and by developing low-dimensional models of flood changes and feedbacks. The paper finishes with a call for a joint European flood change research network.
- ItemThe role of orbital forcing, carbon dioxide and regolith in 100 kyr glacial cycles(München : European Geopyhsical Union, 2011) Ganopolski, A.; Calov, R.The origin of the 100 kyr cyclicity, which dominates ice volume variations and other climate records over the past million years, remains debatable. Here, using a comprehensive Earth system model of intermediate complexity, we demonstrate that both strong 100 kyr periodicity in the ice volume variations and the timing of glacial terminations during past 800 kyr can be successfully simulated as direct, strongly nonlinear responses of the climate-cryosphere system to orbital forcing alone, if the atmospheric CO2 concentration stays below its typical interglacial value. The existence of long glacial cycles is primarily attributed to the North American ice sheet and requires the presence of a large continental area with exposed rocks. We show that the sharp, 100 kyr peak in the power spectrum of ice volume results from the long glacial cycles being synchronized with the Earth's orbital eccentricity. Although 100 kyr cyclicity can be simulated with a constant CO2 concentration, temporal variability in the CO2 concentration plays an important role in the amplification of the 100 kyr cycles.
- ItemThe Nexus Land-Use model version 1.0, an approach articulating biophysical potentials and economic dynamics to model competition for land-use(München : European Geopyhsical Union, 2012) Souty, F.; Brunelle, T.; Dumas, P.; Dorin, B.; Ciais, P.; Crassous, R.; Müller, C.; Bondeau, A.Interactions between food demand, biomass energy and forest preservation are driving both food prices and land-use changes, regionally and globally. This study presents a new model called Nexus Land-Use version 1.0 which describes these interactions through a generic representation of agricultural intensification mechanisms within agricultural lands. The Nexus Land-Use model equations combine biophysics and economics into a single coherent framework to calculate crop yields, food prices, and resulting pasture and cropland areas within 12 regions inter-connected with each other by international trade. The representation of cropland and livestock production systems in each region relies on three components: (i) a biomass production function derived from the crop yield response function to inputs such as industrial fertilisers; (ii) a detailed representation of the livestock production system subdivided into an intensive and an extensive component, and (iii) a spatially explicit distribution of potential (maximal) crop yields prescribed from the Lund-Postdam-Jena global vegetation model for managed Land (LPJmL). The economic principles governing decisions about land-use and intensification are adapted from the Ricardian rent theory, assuming cost minimisation for farmers. In contrast to the other land-use models linking economy and biophysics, crops are aggregated as a representative product in calories and intensification for the representative crop is a non-linear function of chemical inputs. The model equations and parameter values are first described in details. Then, idealised scenarios exploring the impact of forest preservation policies or rising energy price on agricultural intensification are described, and their impacts on pasture and cropland areas are investigated.
- ItemReliability of inference of directed climate networks using conditional mutual information(Basel : MDPI, 2013) Hlinka, Jaroslav; Hartman, David; Vejmelka, Martin; Runge, Jakob; Marwan, Norbert; Kurths, Jürgen; Paluš, MilanAcross geosciences, many investigated phenomena relate to specific complex systems consisting of intricately intertwined interacting subsystems. Such dynamical complex systems can be represented by a directed graph, where each link denotes an existence of a causal relation, or information exchange between the nodes. For geophysical systems such as global climate, these relations are commonly not theoretically known but estimated from recorded data using causality analysis methods. These include bivariate nonlinear methods based on information theory and their linear counterpart. The trade-off between the valuable sensitivity of nonlinear methods to more general interactions and the potentially higher numerical reliability of linear methods may affect inference regarding structure and variability of climate networks. We investigate the reliability of directed climate networks detected by selected methods and parameter settings, using a stationarized model of dimensionality-reduced surface air temperature data from reanalysis of 60-year global climate records. Overall, all studied bivariate causality methods provided reproducible estimates of climate causality networks, with the linear approximation showing higher reliability than the investigated nonlinear methods. On the example dataset, optimizing the investigated nonlinear methods with respect to reliability increased the similarity of the detected networks to their linear counterparts, supporting the particular hypothesis of the near-linearity of the surface air temperature reanalysis data.
- ItemA simple conceptual model of abrupt glacial climate events(Göttingen : Copernicus GmbH, 2007) Braun, H.; Ganopolski, A.; Christl, M.; Chialvo, D.R.Here we use a very simple conceptual model in an attempt to reduce essential parts of the complex nonlinearity of abrupt glacial climate changes (the so-called Dansgaard-Oeschger events) to a few simple principles, namely (i) the existence of two different climate states, (ii) a threshold process and (iii) an overshooting in the stability of the system at the start and the end of the events, which is followed by a millennial-scale relaxation. By comparison with a so-called Earth system model of intermediate complexity (CLIMBER-2), in which the events represent oscillations between two climate states corresponding to two fundamentally different modes of deep-water formation in the North Atlantic, we demonstrate that the conceptual model captures fundamental aspects of the nonlinearity of the events in that model. We use the conceptual model in order to reproduce and reanalyse nonlinear resonance mechanisms that were already suggested in order to explain the characteristic time scale of Dansgaard-Oeschger events. In doing so we identify a new form of stochastic resonance (i.e. an overshooting stochastic resonance) and provide the first explicitly reported manifestation of ghost resonance in a geosystem, i.e. of a mechanism which could be relevant for other systems with thresholds and with multiple states of operation. Our work enables us to explicitly simulate realistic probability measures of Dansgaard-Oeschger events (e.g. waiting time distributions, which are a prerequisite for statistical analyses on the regularity of the events by means of Monte-Carlo simulations). We thus think that our study is an important advance in order to develop more adequate methods to test the statistical significance and the origin of the proposed glacial 1470-year climate cycle.
- ItemOcean rogue waves and their phase space dynamics in the limit of a linear interference model([London] : Macmillan Publishers Limited, part of Springer Nature, 2016) Birkholz, Simon; Brée, Carsten; Veselić, Ivan; Demircan, Ayhan; Steinmeyer, GünterWe reanalyse the probability for formation of extreme waves using the simple model of linear interference of a finite number of elementary waves with fixed amplitude and random phase fluctuations. Under these model assumptions no rogue waves appear when less than 10 elementary waves interfere with each other. Above this threshold rogue wave formation becomes increasingly likely, with appearance frequencies that may even exceed long-term observations by an order of magnitude. For estimation of the effective number of interfering waves, we suggest the Grassberger-Procaccia dimensional analysis of individual time series. For the ocean system, it is further shown that the resulting phase space dimension may vary, such that the threshold for rogue wave formation is not always reached. Time series analysis as well as the appearance of particular focusing wind conditions may enable an effective forecast of such rogue-wave prone situations. In particular, extracting the dimension from ocean time series allows much more specific estimation of the rogue wave probability.