scholarly journals Extreme events: dynamics, statistics and prediction

2011 ◽  
Vol 18 (3) ◽  
pp. 295-350 ◽  
Author(s):  
M. Ghil ◽  
P. Yiou ◽  
S. Hallegatte ◽  
B. D. Malamud ◽  
P. Naveau ◽  
...  

Abstract. We review work on extreme events, their causes and consequences, by a group of European and American researchers involved in a three-year project on these topics. The review covers theoretical aspects of time series analysis and of extreme value theory, as well as of the deterministic modeling of extreme events, via continuous and discrete dynamic models. The applications include climatic, seismic and socio-economic events, along with their prediction. Two important results refer to (i) the complementarity of spectral analysis of a time series in terms of the continuous and the discrete part of its power spectrum; and (ii) the need for coupled modeling of natural and socio-economic systems. Both these results have implications for the study and prediction of natural hazards and their human impacts.

2010 ◽  
Vol 10 (20) ◽  
pp. 10021-10031 ◽  
Author(s):  
H. E. Rieder ◽  
J. Staehelin ◽  
J. A. Maeder ◽  
T. Peter ◽  
M. Ribatet ◽  
...  

Abstract. In this study ideas from extreme value theory are for the first time applied in the field of stratospheric ozone research, because statistical analysis showed that previously used concepts assuming a Gaussian distribution (e.g. fixed deviations from mean values) of total ozone data do not adequately address the structure of the extremes. We show that statistical extreme value methods are appropriate to identify ozone extremes and to describe the tails of the Arosa (Switzerland) total ozone time series. In order to accommodate the seasonal cycle in total ozone, a daily moving threshold was determined and used, with tools from extreme value theory, to analyse the frequency of days with extreme low (termed ELOs) and high (termed EHOs) total ozone at Arosa. The analysis shows that the Generalized Pareto Distribution (GPD) provides an appropriate model for the frequency distribution of total ozone above or below a mathematically well-defined threshold, thus providing a statistical description of ELOs and EHOs. The results show an increase in ELOs and a decrease in EHOs during the last decades. The fitted model represents the tails of the total ozone data set with high accuracy over the entire range (including absolute monthly minima and maxima), and enables a precise computation of the frequency distribution of ozone mini-holes (using constant thresholds). Analyzing the tails instead of a small fraction of days below constant thresholds provides deeper insight into the time series properties. Fingerprints of dynamical (e.g. ENSO, NAO) and chemical features (e.g. strong polar vortex ozone loss), and major volcanic eruptions, can be identified in the observed frequency of extreme events throughout the time series. Overall the new approach to analysis of extremes provides more information on time series properties and variability than previous approaches that use only monthly averages and/or mini-holes and mini-highs.


2010 ◽  
Vol 10 (5) ◽  
pp. 12765-12794 ◽  
Author(s):  
H. E. Rieder ◽  
J. Staehelin ◽  
J. A. Maeder ◽  
T. Peter ◽  
M. Ribatet ◽  
...  

Abstract. In this study ideas from extreme value theory are for the first time applied in the field of stratospheric ozone research, because statistical analysis showed that previously used concepts assuming a Gaussian distribution (e.g. fixed deviations from mean values) of total ozone data do not adequately address the structure of the extremes. We show that statistical extreme value methods are appropriate to identify ozone extremes and to describe the tails of the Arosa (Switzerland) total ozone time series. In order to accommodate the seasonal cycle in total ozone, a daily moving threshold was determined and used, with tools from extreme value theory, to analyse the frequency of days with extreme low (termed ELOs) and high (termed EHOs) total ozone at Arosa. The analysis shows that the Generalized Pareto Distribution (GPD) provides an appropriate model for the frequency distribution of total ozone above or below a mathematically well-defined threshold, thus providing a statistical description of ELOs and EHOs. The results show an increase in ELOs and a decrease in EHOs during the last decades. The fitted model represents the tails of the total ozone data set with high accuracy over the entire range (including absolute monthly minima and maxima), and enables a precise computation of the frequency distribution of ozone mini-holes (using constant thresholds). Analyzing the tails instead of a small fraction of days below constant thresholds provides deeper insight into the time series properties. Fingerprints of dynamical (e.g. ENSO, NAO) and chemical features (e.g. strong polar vortex ozone loss), and major volcanic eruptions, can be identified in the observed frequency of extreme events throughout the time series. Overall the new approach to analysis of extremes provides more information on time series properties and variability than previous approaches that use only monthly averages and/or mini-holes and mini-highs.


Risks ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 51
Author(s):  
Anthony Medford

Best practice life expectancy has recently been modeled using extreme value theory. In this paper we present the Gumbel autoregressive model of order one—Gumbel AR(1)—as an option for modeling best practice life expectancy. This class of model represents a neat and coherent framework for modeling time series extremes. The Gumbel distribution accounts for the extreme nature of best practice life expectancy, while the AR structure accounts for the temporal dependence in the time series. Model diagnostics and simulation results indicate that these models present a viable alternative to Gaussian AR(1) models when dealing with time series of extremes and merit further exploration.


2017 ◽  
Vol 21 (5) ◽  
pp. 2421-2448 ◽  
Author(s):  
Johannes Christoph Haas ◽  
Steffen Birk

Abstract. To improve the understanding of how aquifers in different alluvial settings respond to extreme events in a changing environment, we analyze standardized time series of groundwater levels (Standardized Groundwater level Index – SGI), precipitation (Standardized Precipitation Index – SPI), and river stages of three subregions within the catchment of the river Mur (Austria). Using correlation matrices, differences and similarities between the subregions, ranging from the Alpine upstream part of the catchment to its shallow foreland basin, are identified and visualized. Generally, river stages exhibit the highest correlations with groundwater levels, frequently affecting not only the wells closest to the river, but also more distant parts of the alluvial aquifer. As a result, human impacts on the river are transferred to the aquifer, thus affecting the behavior of groundwater levels. Hence, to avoid misinterpretation of groundwater levels in this type of setting, it is important to account for the river and human impacts on it. While the river is a controlling factor in all of the subregions, an influence of precipitation is evident too. Except for deep wells found in an upstream Alpine basin, groundwater levels show the highest correlation with a precipitation accumulation period of 6 months (SPI6). The correlation in the foreland is generally higher than that in the Alpine subregions, thus corresponding to a trend from deeper wells in the Alpine parts of the catchment towards more shallow wells in the foreland. Extreme events are found to affect the aquifer in different ways. As shown with the well-known European 2003 drought and the local 2009 floods, correlations are reduced under flood conditions, but increased under drought. Thus, precipitation, groundwater levels and river stages tend to exhibit uniform behavior under drought conditions, whereas they may show irregular behavior during floods. Similarly, correlations are found to be weaker in years with little snow as compared with those with much snow. This is in agreement with typical aquifer response times over 1 month, suggesting that short events such as floods will not affect much of the aquifer, whereas a long-term event such as a drought or snow-rich winter will. Splitting the time series into periods of 12 years reveals a tendency towards higher correlations in the most recent time period from 1999 to 2010. This time period also shows the highest number of events with SPI values below −2. The SGI values behave in a similar way only in the foreland aquifer, whereas the investigated Alpine aquifers exhibit a contrasting behavior with the highest number of low SGI events in the time before 1986. This is a result of overlying trends and suggests that the groundwater levels within these subregions are more strongly influenced by direct human impacts, e.g., on the river, than by changes in precipitation. Thus, direct human impacts must not be ignored when assessing climate change impacts on alluvial aquifers situated in populated valleys.


Author(s):  
Zhigang Wei ◽  
Pingsha Dong ◽  
Litang Gao ◽  
Robert Kurth

Risk based treatment of degradation and failure in engineering components is an important topic in recent years with an emphasis on obtaining more detailed information for extreme events. Fatigue damage and life degradation caused by variable amplitude cyclic loading is dominated by such extreme events, and can be properly treated with the extreme value theory, which could help understand the damage nature of the fatigue damage process as well as to provide more efficient and robust approaches for engineering applications. In this paper, advanced extreme value theory is reviewed first. Methods such as peak counting, block maxima, and peaks over thresholds are investigated and compared in this paper with an emphasis on the relationship between the extreme value theory and the existing methods for fatigue life assessment. A few simple examples of uniaxial and multi-axial fatigue life assessment process are provided and the results are discussed. It is found that, if properly used, the extreme value theories can improve the efficiency of fatigue life assessment. Finally, a hybrid time- and frequency-based multi-axial fatigue life assessment procedure is proposed for wide band loadings.


2011 ◽  
Vol 11 (10) ◽  
pp. 2741-2753 ◽  
Author(s):  
R. Sobradelo ◽  
J. Martí ◽  
A. T. Mendoza-Rosas ◽  
G. Gómez

Abstract. The Canary Islands are an active volcanic region densely populated and visited by several millions of tourists every year. Nearly twenty eruptions have been reported through written chronicles in the last 600 yr, suggesting that the probability of a new eruption in the near future is far from zero. This shows the importance of assessing and monitoring the volcanic hazard of the region in order to reduce and manage its potential volcanic risk, and ultimately contribute to the design of appropriate preparedness plans. Hence, the probabilistic analysis of the volcanic eruption time series for the Canary Islands is an essential step for the assessment of volcanic hazard and risk in the area. Such a series describes complex processes involving different types of eruptions over different time scales. Here we propose a statistical method for calculating the probabilities of future eruptions which is most appropriate given the nature of the documented historical eruptive data. We first characterize the eruptions by their magnitudes, and then carry out a preliminary analysis of the data to establish the requirements for the statistical method. Past studies in eruptive time series used conventional statistics and treated the series as an homogeneous process. In this paper, we will use a method that accounts for the time-dependence of the series and includes rare or extreme events, in the form of few data of large eruptions, since these data require special methods of analysis. Hence, we will use a statistical method from extreme value theory. In particular, we will apply a non-homogeneous Poisson process to the historical eruptive data of the Canary Islands to estimate the probability of having at least one volcanic event of a magnitude greater than one in the upcoming years. This is done in three steps: First, we analyze the historical eruptive series to assess independence and homogeneity of the process. Second, we perform a Weibull analysis of the distribution of repose time between successive eruptions. Third, we analyze the non-homogeneous Poisson process with a generalized Pareto distribution as the intensity function.


Economical ◽  
2020 ◽  
Vol 1 (1(22)) ◽  
pp. 115-131
Author(s):  
Ірина Кладченко ◽  

Improving of the methodological tools for the national economies behavior’s forecasting in the context of increasing the validity and analytical characteristics of state economic strategies in conditions of high volatility, lack of trend stability and non-stationary dynamics of external and internal socio-economic processes by implementing interdisciplinary methods of Fourier analysis and their adaptation to the specifics of the socio-economic systems’ functioning and development. Methodology. The forecasting’s targeting as an important independent stage in the process of analytical assessment of the balance of development is performed on the basis of structuring, division into stages, systematization, and grouping. Justification of the interdisciplinary approach for forecasting of national economic system’s development is carried out by methods of analysis and synthesis, comparison and practical testing. Establishment of the economic dynamics’ structural regularities and forecasting of a trajectory of national economy development are executed by harmonic and spectral analysis of the dynamic systems’ fluctuating processes. The results. The paper’s attention is focused on the specific features of macroeconomic dynamics’ time series as a basis for the forecasting of national economies development, namely their short duration, non-stationary, aperiodic, polyharmonic and their impact on the formation of adequate methodological support for forecasting. The possibility and efficiency of spectral and harmonic methods using for analysis oscillating processes of national economic system’s development are substantiated. A harmonic model of Ukraine's economic development’s trajectory during 1991-2020 is formed, which allowed to analyze the fluctuating component of the macroeconomic indicators’ dynamics on the basis of actual data that included all the initial information contained in the time series. By distinguishing economic cycles, their amplitude-frequency characteristics, the current phase of Ukrainian economy’s development is characterized. On the basis of the economic dynamics’ model, being used the indicator of annual GDP growth, forecasting is executed and short-term, average-term and long-term tendencies Ukraine’s economy’s development are established. Scientific novelty. The extending of theoretical and methodological tools for forecasting of main trends in national economies, based on harmonic and spectral analysis, is allowed to form a structural approach to the analysis of economic dynamics in the context of selection of its decisive harmonics and basing on their characteristics to make conclusions about the current level and projected national economic systems’ development. Practical significance. The adapted and regulated procedure of harmonic and spectral analysis of socio-economic systems’ oscillating processes became the basis for forecasting the level, rates and proportions of national economic systems development.


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