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Ongoing climate change is known to cause an increase in the frequency and amplitude of local temperature and precipitation extremes in many regions of the Earth. While gradual changes in the climatological conditions have already been shown to strongly influence plant flowering dates, the question arises if and how extremes specifically impact the timing of this important phenological phase. Studying this question calls for the application of statistical methods that are tailored to the specific properties of event time series. Here, we employ event coincidence analysis, a novel statistical tool that allows assessing whether or not two types of events exhibit similar sequences of occurrences in order to systematically quantify simultaneities between meteorological extremes and the timing of the flowering of four shrub species across Germany. Our study confirms previous findings of experimental studies by highlighting the impact of early spring temperatures on the flowering of the investigated plants. However, previous studies solely based on correlation analysis do not allow deriving explicit estimates of the strength of such interdependencies without further assumptions, a gap that is closed by our analysis. In addition to direct impacts of extremely warm and cold spring temperatures, our analysis reveals statistically significant indications of an influence of temperature extremes in the autumn preceding the flowering.
Observed recent and expected future increases in frequency and intensity of climatic extremes in central Europe may pose critical challenges for domestic tree species. Continuous dendrometer recordings provide a valuable source of information on tree stem radius variations, offering the possibility to study a tree's response to environmental influences at a high temporal resolution. In this study, we analyze stem radius variations (SRV) of three domestic tree species (beech, oak, and pine) from 2012 to 2014. We use the novel statistical approach of event coincidence analysis (ECA) to investigate the simultaneous occurrence of extreme daily weather conditions and extreme SRVs, where extremes are defined with respect to the common values at a given phase of the annual growth period. Besides defining extreme events based on individual meteorological variables, we additionally introduce conditional and joint ECA as new multivariate extensions of the original methodology and apply them for testing 105 different combinations of variables regarding their impact on SRV extremes. Our results reveal a strong susceptibility of all three species to the extremes of several meteorological variables. Yet, the inter-species differences regarding their response to the meteorological extremes are comparatively low. The obtained results provide a thorough extension of previous correlation-based studies by emphasizing on the timings of climatic extremes only. We suggest that the employed methodological approach should be further promoted in forest research regarding the investigation of tree responses to changing environmental conditions.
Ongoing climate change is known to cause an increase in the frequency and amplitude of local temperature and precipitation extremes in many regions of the Earth. While gradual changes in the climatological conditions have already been shown to strongly influence plant flowering dates, the question arises if and how extremes specifically impact the timing of this important phenological phase. Studying this question calls for the application of statistical methods that are tailored to the specific properties of event time series. Here, we employ event coincidence analysis, a novel statistical tool that allows assessing whether or not two types of events exhibit similar sequences of occurrences in order to systematically quantify simultaneities between meteorological extremes and the timing of the flowering of four shrub species across Germany. Our study confirms previous findings of experimental studies by highlighting the impact of early spring temperatures on the flowering of the investigated plants. However, previous studies solely based on correlation analysis do not allow deriving explicit estimates of the strength of such interdependencies without further assumptions, a gap that is closed by our analysis. In addition to direct impacts of extremely warm and cold spring temperatures, our analysis reveals statistically significant indications of an influence of temperature extremes in the autumn preceding the flowering.
Observed recent and expected future increases in frequency and intensity of climatic extremes in central Europe may pose critical challenges for domestic tree species. Continuous dendrometer recordings provide a valuable source of information on tree stem radius variations, offering the possibility to study a tree's response to environmental influences at a high temporal resolution. In this study, we analyze stem radius variations (SRV) of three domestic tree species (beech, oak, and pine) from 2012 to 2014. We use the novel statistical approach of event coincidence analysis (ECA) to investigate the simultaneous occurrence of extreme daily weather conditions and extreme SRVs, where extremes are defined with respect to the common values at a given phase of the annual growth period. Besides defining extreme events based on individual meteorological variables, we additionally introduce conditional and joint ECA as new multivariate extensions of the original methodology and apply them for testing 105 different combinations of variables regarding their impact on SRV extremes. Our results reveal a strong susceptibility of all three species to the extremes of several meteorological variables. Yet, the inter-species differences regarding their response to the meteorological extremes are comparatively low. The obtained results provide a thorough extension of previous correlation-based studies by emphasizing on the timings of climatic extremes only. We suggest that the employed methodological approach should be further promoted in forest research regarding the investigation of tree responses to changing environmental conditions.
The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state vectors in the studied system’s state space reconstructed by means of time-delay embedding as the key characteristic that should guide the corresponding choice for obtaining an adequate resolution of a recurrence plot. Specifically, we present an empirical description of the distance distribution, focusing on characteristic changes of its shape with increasing embedding dimension. Our results suggest that selecting the recurrence threshold according to a fixed percentile of this distribution reduces the dependence of recurrence characteristics on the embedding dimension in comparison with other commonly used threshold selection methods. Numerical investigations on some paradigmatic model systems with time-dependent parameters support these empirical findings.
Recurrence plots (RPs) provide an intuitive tool for visualizing the (potentially multi-dimensional) trajectory of a dynamical system in state space. In case only univariate observations of the system’s overall state are available, time-delay embedding has become a standard procedure for qualitatively reconstructing the dynamics in state space. The selection of a threshold distance 𝜀
, which distinguishes close from distant pairs of (reconstructed) state vectors, is known to have a substantial impact on the recurrence plot and its quantitative characteristics, but its corresponding interplay with the embedding dimension has not yet been explicitly addressed. Here, we point out that the results of recurrence quantification analysis (RQA) and related methods are qualitatively robust under changes of the (sufficiently high) embedding dimension only if the full distribution of pairwise distances between state vectors is considered for selecting 𝜀, which is achieved by consideration of a fixed recurrence rate.
The oceans and atmosphere interact via a multiplicity of feedback mechanisms, shaping to a large extent the global climate and its variability. To deepen our knowledge of the global climate system, characterizing and investigating this interdependence is an important task of contemporary research. However, our present understanding of the underlying large-scale processes is greatly limited due to the manifold interactions between essential climatic variables at different temporal scales. To address this problem, we here propose to extend the application of complex network techniques to capture the interdependence between global fields of sea-surface temperature (SST) and precipitation (P) at multiple temporal scales. For this purpose, we combine time-scale decomposition by means of a discrete wavelet transform with the concept of coupled climate network analysis. Our results demonstrate the potential of the proposed approach to unravel the scale-specific interdependences between atmosphere and ocean and, thus, shed light on the emerging multiscale processes inherent to the climate system, which traditionally remain undiscovered when investigating the system only at the native resolution of existing climate data sets. Moreover, we show how the relevant spatial interdependence structures between SST and P evolve across time-scales. Most notably, the strongest mutual correlations between SST and P at annual scale (8-16 months) concentrate mainly over the Pacific Ocean, while the corresponding spatial patterns progressively disappear when moving toward longer time-scales. Published under license by AIP Publishing.
Motivated by the successful Karlsruhe dynamo experiment, a relatively low-dimensional dynamo model is proposed. It is based on a strong truncation of the magnetohydrodynamic (MHD) equations with an external forcing of the Roberts type and the requirement that the model system satisfies the symmetries of the full MHD system, so that the first symmetry-breaking bifurcations can be captured. The backbone of the Roberts dynamo is formed by the Roberts flow, a helical mean magnetic field and another part of the magnetic field coupled to these two by triadic mode interactions. A minimum truncation model (MTM) containing only these energetically dominating primary mode triads is fully equivalent to the widely used first-order smoothing approximation. However, it is shown that this approach works only in the limit of small wave numbers of the excited magnetic field or small magnetic Reynolds numbers ($Rm ll 1$). To obtain dynamo action under more general conditions, secondary mode
We investigate the dynamo effect in a flow configuration introduced by G. O. Roberts in 1972. Based on a clear energetic hierarchy of Fourier components on the steady-state dynamo branch, an approximate model of interacting modes is constructed covering all essential features of the complete system but allowing simulations with a minimum amount of computation time. We use this model to study the excitation mechanism of the dynamo, the transition from stationary to time-dependent dynamo solutions and the characteristic properties of the latter ones.
As a non-contact process laser beam melt ablation offers several advantages compared to conventional processing mechanisms. During ablation the surface of the workpiece is molten by the energy of a CO2-laser beam, this melt is then driven out by the impulse of an additional process gas. Although the idea behind laser beam melt ablation is rather simple, the process itself has a major limitation in practical applications: with increasing ablation rate surface quality of the workpiece processed declines rapidly. With different ablation rates different surface structures can be distinguished, which can be characterised by suitable surface parameters. The corresponding regimes of pattern formation are found in linear and non-linear statistical properties of the recorded process emissions as well. While the ablation rate can be represented in terms of the line-energy, this parameter does not provide sufficient information about the full behaviour of the system. The dynamics of the system is dominated by oscillations due to the laser cycle but includes some periodically driven non-linear processes as well. Upon the basis of the measured time series, a corresponding model is developed. The deeper understanding of the process can be used to develop strategies for a process control.
As a non-contact process laser beam melt ablation offers several advantages compared to conventional processing mechanisms. During ablation the surface of the workpiece is molten by the energy of a CO2-laser beam, this melt is then driven out by the impulse of an additional process gas. Although the idea behind laser beam melt ablation is rather simple, the process itself has a major limitation in practical applications: with increasing ablation rate surface quality of the workpiece processed declines rapidly. With different ablation rates different surface structures can be distinguished, which can be characterised by suitable surface parameters. The corresponding regimes of pattern formation are found in linear and non-linear statistical properties of the recorded process emissions as well. While the ablation rate can be represented in terms of the line-energy, this parameter does not provide sufficient information about the full behaviour of the system. The dynamics of the system is dominated by oscillations due to the laser cycle but includes some periodically driven non-linear processes as well. Upon the basis of the measured time series, a corresponding model is developed. The deeper understanding of the process can be used to develop strategies for a process control.