Spatio-temporal Extreme Events Research Articles

Extreme events in a broad-area semiconductor laser with coherent injection

Spatiotemporal extreme events are interesting phenomena, both from a fundamental point of view, as manifestations of complexity in dynamical systems, and for their possible applications in different research fields. Here, we present some recent results for extreme events in spatially extended semiconductor laser systems (broad-area vertical cavity surface-emitting lasers) with coherent injection. We study the statistics of spatiotemporal intensity peaks occurring in the transverse $(x,y)$ section of the field perpendicular to the light propagation direction and identify regions in the parameter space where extreme events are more likely to occur. Searching for precursors of these phenomena, we concentrate, on the one hand, on the spatiotemporal dynamics of the field phase and, in particular, on the presence of optical vortices in the vicinity of an extreme event. On the other hand, we focus on the laser gain dynamics and the phase-space trajectories of the system close to the occurrence of an extreme event. Both these complementary approaches are successful and allow us to shed some light on potential prediction strategies.

A Comparative Tour through the Simulation Algorithms for Max-Stable Processes

Being the max-analogue of α-stable stochastic processes, max-stable processes form one of the fundamental classes of stochastic processes. With the arrival of sufficient computational capabilities, they have become a benchmark in the analysis of spatiotemporal extreme events. Simulation is often a necessary part of inference of certain characteristics, in particular for future spatial risk assessment. In this article, we give an overview over existing procedures for this task, put them into perspective of one another and use some new theoretical results to make comparisons with respect to their properties.

Generation of spatio-temporal extreme events in noise-like pulses NPE mode-locked fibre laser.

We experimentally study spatio-temporal generation of extreme events in the radiation of NPE mode-locked fibre laser generating noise-like pulses. We show that new pulses starts from high-intensity spatio-temporal structure which consist of mainly 3 subsequent pulses which are both separated over fast and slow evolution time. Statistical analysis of the noise-like pulse evolution over round-trips shows that the pulse width and intensity varies with a period of around 85 round-trips which does not change from pulse to pulse. The intensity probability density function has a heavy tail originated only from events of pulse formation.

Spatiotemporal extreme events in a laser with a saturable absorber

We study extreme events occurring in the transverse $(x,y)$ section of the field emitted by a broad-area semiconductor laser with a saturable absorber. The spatio-temporal events on which we perform the statistical analysis are identified as maxima of the field intensity in the 3D space $(x,y,t)$. We identify regions in the parameter space where extreme events are more likely to occur and we study the connection of those extreme events with the cavity solitons that are known to exist in the same system, both stationary and self-pulsing.

Chaos and extreme events in an azimuthally polarized Nd:GdVO4 laser with pump modulation.

Nonlinear dynamics and extreme events were explored in a spatially distributed polarization laser based on an azimuthally polarized Nd:GdVO4 laser with pump modulation. When the modulation frequency approached the relaxation oscillation frequency, a period-doubling route to chaos was observed with an increasing modulation depth, and spatiotemporal extreme events occurred with the generation of the chaos. An efficient azimuthal polarization was kept, even though the intensity fluctuated in the chaotic region.

Modeling Spatio-Temporal Extreme Events Using Graphical Models

We propose a novel statistical model to describe spatio-temporal extreme events. The model can be used, for instance, to estimate extreme-value temporal pattern such as seasonality and trend, and further to predict the distribution of extreme events in the future. Such model usually involves thousands or even millions of variables in the spatio-temporal domain, whereas only one single observation is available for each location and time point. To address this challenge, previous works usually employ learning and inference methods that are computationally burdensome, and therefore are prohibitive for large-scale data. Moreover, they assume that the shape and scale parameters of the extreme-value distributions are constant across the spatio-temporal domain, which is often too restrictive in practice. In this paper, we break through these limitations by exploring graphical models to capture the highly structured dependencies among the parameters of extreme-value distributions. Furthermore, we develop an efficient stochastic variational inference (SVI) algorithm to learn the parameters of the resulting non-Gaussian graphical model. The computational complexity of the SVI algorithm is sublinear in the number of variables, thus enabling the proposed model to tackle large-scale spatio-temporal data in real-life applications. Results of both synthetic and real data demonstrate the effectiveness of the proposed approach.

Statistics of Extremes

Statistics of extremes concerns inference for rare events. Often the events have never yet been observed, and their probabilities must therefore be estimated by extrapolation of tail models fitted to available data. Because data concerning the event of interest may be very limited, efficient methods of inference play an important role. This article reviews this domain, emphasizing current research topics. We first sketch the classical theory of extremes for maxima and threshold exceedances of stationary series. We then review multivariate theory, distinguishing asymptotic independence and dependence models, followed by a description of models for spatial and spatiotemporal extreme events. Finally, we discuss inference and describe two applications. Animations illustrate some of the main ideas.

Extreme events in gross primary production: a characterization across continents

Abstract. Climate extremes can affect the functioning of terrestrial ecosystems, for instance via a reduction of the photosynthetic capacity or alterations of respiratory processes. Yet the dominant regional and seasonal effects of hydrometeorological extremes are still not well documented and in the focus of this paper. Specifically, we quantify and characterize the role of large spatiotemporal extreme events in gross primary production (GPP) as triggers of continental anomalies. We also investigate seasonal dynamics of extreme impacts on continental GPP anomalies. We find that the 50 largest positive extremes (i.e., statistically unusual increases in carbon uptake rates) and negative extremes (i.e., statistically unusual decreases in carbon uptake rates) on each continent can explain most of the continental variation in GPP, which is in line with previous results obtained at the global scale. We show that negative extremes are larger than positive ones and demonstrate that this asymmetry is particularly strong in South America and Europe. Our analysis indicates that the overall impacts and the spatial extents of GPP extremes are power-law distributed with exponents that vary little across continents. Moreover, we show that on all continents and for all data sets the spatial extents play a more important role for the overall impact of GPP extremes compared to the durations or maximal GPP. An analysis of possible causes across continents indicates that most negative extremes in GPP can be attributed clearly to water scarcity, whereas extreme temperatures play a secondary role. However, for Europe, South America and Oceania we also identify fire as an important driver. Our findings are consistent with remote sensing products. An independent validation against a literature survey on specific extreme events supports our results to a large extent.

Detection and attribution of large spatiotemporal extreme events in Earth observation data

Latest climate projections suggest that both frequency and intensity of climate extremes will be substantially modified over the course of the coming decades. As a consequence, we need to understand to what extent and via which pathways climate extremes affect the state and functionality of terrestrial ecosystems and the associated biogeochemical cycles on a global scale. So far the impacts of climate extremes on the terrestrial biosphere were mainly investigated on the basis of case studies, while global assessments are widely lacking. In order to facilitate global analysis of this kind, we present a methodological framework that firstly detects spatiotemporally contiguous extremes in Earth observations, and secondly infers the likely pathway of the preceding climate anomaly. The approach does not require long time series, is computationally fast, and easily applicable to a variety of data sets with different spatial and temporal resolutions. The key element of our analysis strategy is to directly search in the relevant observations for spatiotemporally connected components exceeding a certain percentile threshold. We also put an emphasis on characterization of extreme event distribution, and scrutinize the attribution issue. We exemplify the analysis strategy by exploring the fraction of absorbed photosynthetically active radiation (fAPAR) from 1982 to 2011. Our results suggest that the hot spots of extremes in fAPAR lie in Northeastern Brazil, Southeastern Australia, Kenya and Tanzania. Moreover, we demonstrate that the size distribution of extremes follow a distinct power law. The attribution framework reveals that extremes in fAPAR are primarily driven by phases of water scarcity.

Controlling spatio-temporal extreme events by decreasing the localized energy

The problem of controlling extreme events in spatially extended dynamical systems is investigated in this Letter. Based on observations of the system state, the control technique we proposed locally decreases the spatial energy of the amplitude in the vicinity of the highest burst, without needs of any knowledge or prediction of the system model. Considering the specific Complex Ginzburg–Landau equation, we provide theoretical analysis for designing the localized state feedback controller. More exactly, a simple control law by varying a damping parameter at control region is chose to achieve the control. Numerical simulations and statistic analysis demonstrate that extreme events can be efficiently suppressed by our strategy. In particular, the cost of the control and the tolerant time delay in applying the control is considered in detail.