scholarly journals Extreme Value Statistics of the Total Energy in an Intermediate-Complexity Model of the Midlatitude Atmospheric Jet. Part I: Stationary Case

2007 ◽  
Vol 64 (7) ◽  
pp. 2137-2158 ◽  
Author(s):  
Mara Felici ◽  
Valerio Lucarini ◽  
Antonio Speranza ◽  
Renato Vitolo
Keyword(s):  
Time Series ◽  
Total Energy ◽  
Goodness Of Fit ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Stationary Time Series ◽  
Return Level ◽  
Extreme Value Statistics ◽  
Intermediate Complexity

Abstract A baroclinic model of intermediate complexity for the atmospheric jet at middle latitudes is used as a stochastic generator of atmosphere-like time series. In this case, time series of the total energy of the system are considered. Statistical inference of extreme values is applied to sequences of yearly maxima extracted from the time series in the rigorous setting provided by extreme value theory. The generalized extreme value (GEV) family of distributions is used here as a basic model, both for its qualities of simplicity and its generality. Several physically plausible values of the parameter TE, which represents the forced equator-to-pole temperature gradient and is responsible for setting the average baroclinicity in the atmospheric model, are used to generate stationary time series of the total energy. Estimates of the three GEV parameters—location, scale, and shape—are inferred by maximum likelihood methods. Standard statistical diagnostics, such as return level and quantile–quantile plots, are systematically applied to assess goodness-of-fit. The GEV parameters of location and scale are found to have a piecewise smooth, monotonically increasing dependence on TE. The shape parameter also increases with TE but is always negative, as is required a priori by the boundedness of the total energy. The sensitivity of the statistical inferences is studied with respect to the selection procedure of the maxima: the roles occupied by the length of the sequences of maxima and by the length of data blocks over which the maxima are computed are critically analyzed. Issues related to model sensitivity are also explored by varying the resolution of the system. The method used in this paper is put forward as a rigorous framework for the statistical analysis of extremes of observed data, to study the past and present climate and to characterize its variations.

scholarly journals Extreme Value Statistics of the Total Energy in an Intermediate-Complexity Model of the Midlatitude Atmospheric Jet. Part II: Trend Detection and Assessment

2007 ◽  
Vol 64 (7) ◽  
pp. 2159-2175 ◽  
Author(s):  
Mara Felici ◽  
Valerio Lucarini ◽  
Antonio Speranza ◽  
Renato Vitolo
Keyword(s):  
Time Series ◽  
Total Energy ◽  
Extreme Values ◽  
Linear Time ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Trend Detection ◽  
Ratio Test ◽  
Scale Parameters ◽  
Baroclinic Model

Abstract A baroclinic model for the atmospheric jet at middle latitudes is used as a stochastic generator of nonstationary time series of the total energy of the system. A linear time trend is imposed on the parameter TE, descriptive of the forced equator-to-pole temperature gradient and responsible for setting the average baroclinicity in the model. The focus lies on establishing a theoretically sound framework for the detection and assessment of trend at extreme values of the generated time series. This problem is dealt with by fitting time-dependent generalized extreme value (GEV) models to sequences of yearly maxima of the total energy. A family of GEV models is used in which the location μ and scale parameters σ depend quadratically and linearly on time, respectively, while the shape parameter ξ is kept constant. From this family, a GEV model is selected with Akaike’s information criterion, complemented by the likelihood ratio test and by assessment through standard graphical diagnostics. The inferred location and scale parameters are found to depend in a rather smooth way on time and, therefore, on TE. In particular, power-law dependences of μ and σ on TE are obtained, in analogy with the results of a previous work where the same baroclinic model was run with fixed values of TE spanning the same range as in this case. It is emphasized under which conditions the adopted approach is valid.

scholarly journals Characteristics of Extreme Value Statistics of Annual Maximum Monthly Precipitation in East Asia Calculated Using an Earth System Model of Intermediate Complexity

Atmosphere ◽  
2020 ◽  
Vol 11 (12) ◽  
pp. 1273
Author(s):  
Tosiyuki Nakaegawa ◽  
Takuro Kobashi ◽  
Hirotaka Kamahori
Keyword(s):  
Time Series ◽  
Extreme Precipitation ◽  
Extreme Value ◽  
Nonstationary Time Series ◽  
Return Level ◽  
Extreme Value Statistics ◽  
Extreme Value Analysis ◽  
Monthly Precipitation ◽  
Annual Maximum ◽  
Value Analysis

Extreme precipitation is no longer stationary under a changing climate due to the increase in greenhouse gas emissions. Nonstationarity must be considered when realistically estimating the amount of extreme precipitation for future prevention and mitigation. Extreme precipitation with a certain return level is usually estimated using extreme value analysis under a stationary climate assumption without evidence. In this study, the characteristics of extreme value statistics of annual maximum monthly precipitation in East Asia were evaluated using a nonstationary historical climate simulation with an Earth system model of intermediate complexity, capable of long-term integration over 12,000 years (i.e., the Holocene). The climatological means of the annual maximum monthly precipitation for each 100-year interval had nonstationary time series, and the ratios of the largest annual maximum monthly precipitation to the climatological mean had nonstationary time series with large spike variations. The extreme value analysis revealed that the annual maximum monthly precipitation with a return level of 100 years estimated for each 100-year interval also presented a nonstationary time series which was normally distributed and not autocorrelated, even with the preceding and following 100-year interval (lag 1). Wavelet analysis of this time series showed that significant periodicity was only detected in confined areas of the time–frequency space.

Statistics of Extreme Wind Speeds and Wave Heights by the Bivariate ACER Method

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Arvid Naess ◽  
Oleh Karpa
Keyword(s):  
Time Series ◽  
Extreme Value Distribution ◽  
Offshore Structures ◽  
Accurate Estimate ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Extreme Value Statistics ◽  
Wind Speeds ◽  
Wave Heights

In the reliability engineering and design of offshore structures, probabilistic approaches are frequently adopted. They require the estimation of extreme quantiles of oceanographic data based on the statistical information. Due to strong correlation between such random variables as, e.g., wave heights and wind speeds (WS), application of the multivariate, or bivariate in the simplest case, extreme value theory is sometimes necessary. The paper focuses on the extension of the average conditional exceedance rate (ACER) method for prediction of extreme value statistics to the case of bivariate time series. Using the ACER method, it is possible to provide an accurate estimate of the extreme value distribution of a univariate time series. This is obtained by introducing a cascade of conditioning approximations to the true extreme value distribution. When it has been ascertained that this cascade has converged, an estimate of the extreme value distribution has been obtained. In this paper, it will be shown how the univariate ACER method can be extended in a natural way to also cover the case of bivariate data. Application of the bivariate ACER method will be demonstrated for measured coupled WS and wave height data.

scholarly journals Extreme value theory and return time statistics for dispersing billiard maps and flows, Lozi maps and Lorenz-like maps

2011 ◽  
Vol 31 (5) ◽  
pp. 1363-1390 ◽  
Author(s):  
CHINMAYA GUPTA ◽  
MARK HOLLAND ◽  
MATTHEW NICOL
Keyword(s):  
Time Series ◽  
Hyperbolic Systems ◽  
Return Time ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Distributed Processes ◽  
Return Time Statistics ◽  
Generic Points ◽  
Lozi Maps

AbstractIn this paper we establish extreme value statistics for observations on a class of hyperbolic systems: planar dispersing billiard maps and flows, Lozi maps and Lorenz-like maps. In particular, we show that for time series arising from Hölder observations on these systems which are maximized at generic points the successive maxima of the time series are distributed according to the corresponding extreme value distributions for independent identically distributed processes. These results imply an exponential law for the hitting and return time statistics of these dynamical systems.

scholarly journals Automatic threshold and run parameter selection: a climatology for extreme hourly precipitation in Switzerland

2014 ◽  
Vol 120 (3-4) ◽  
pp. 403-416 ◽  
Author(s):  
S. Fukutome ◽  
M. A. Liniger ◽  
M. Süveges
Keyword(s):  
Time Series ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Return Level ◽  
High Threshold ◽  
Hourly Precipitation ◽  
Four Seasons ◽  
Increasing Demand ◽  
Short Time

Abstract Extreme value analyses of a large number of relatively short time series are in increasing demand in environmental sciences and design. Here, we present an automated procedure for the peaks-over-threshold (POT) approach to extreme value theory and use it to provide a climatology of extreme hourly precipitation in Switzerland. The POT approach fits the generalized Pareto distribution (GPD) to independent exceedances above some high threshold. To guarantee independence, the time series is pruned: exceedances separated by less than a fixed interval called the run parameter are considered a cluster, and all but the cluster maxima are discarded. We propose the automation of an existing graphical method for joint selection of threshold and run parameter. Hourly precipitation is analyzed at 59 stations of the MeteoSwiss observational network over the period 1981–2010. The four seasons are considered separately. When necessary, a simple detrending is applied. Results suggest that unnecessarily large run parameters have adverse effects on the estimation of the GPD parameters. The proposed method yields mean cluster sizes that reflect the seasonal and geographical variation of lag dependence of hourly precipitation. The climatology, as represented by the return level maps and Alpine cross-section, mirror known aspects of the Swiss climate. Unlike for daily precipitation, summer thunderstorm tracks are visible in the seasonal frequency of events, rather than in the amplitude of rare events.

scholarly journals Topics in data analysis using R in extreme value theory

2013 ◽  
Vol 10 (1) ◽  
Author(s):  
Helena Penalva ◽  
Manuela Neves
Keyword(s):  
Applied Sciences ◽  
Data Analysis ◽  
Open Source Software ◽  
Extreme Value Theory ◽  
Extreme Values ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Statistics ◽  
Data Sets ◽  
Statistics Of Extremes

The statistical Extreme Value Theory has grown gradually from the beginning of the 20th century. Its unquestionable importance in applications was definitely recognized after Gumbel's book in 1958, Statistics of Extremes. Nowadays there is a wide number of applied sciences where extreme value statistics are largely used. So, accurately modeling extreme events has become more and more important and the analysis requires tools that must be simple to use but also should consider complex statistical models in order to produce valid inferences. To deal with accurate, friendly, free and open-source software is of great value for practitioners and researchers. This paper presents a review of the main steps for initializing a data analysis of extreme values in R environment. Some well documented packages are briefly described and two data sets will be considered for illustrating the use of some functions.

scholarly journals Non-stationary Extreme Value Analysis: a simplified approach for Earth science applications

2016 ◽  
Author(s):  
Lorenzo Mentaschi ◽  
Michalis Vousdoukas ◽  
Evangelos Voukouvalas ◽  
Ludovica Sartini ◽  
Luc Feyen ◽  
...  
Keyword(s):  
Time Series ◽  
Extreme Values ◽  
Extreme Value ◽  
Stationary Time Series ◽  
Alternative Methods ◽  
Extreme Value Analysis ◽  
Accurate Estimation ◽  
Residual Water ◽  
Value Analysis ◽  
Simplified Approach

Abstract. Statistical approaches to study extreme events require by definition long time series of data. The climate is subject to natural and anthropogenic variations at different temporal scales, leaving their footprint on the frequency and intensity of climatic and hydrological extremes, therefore assumption of stationarity is violated and alternative methods to conventional stationary Extreme Value Analysis (EVA) need to be adopted. In this study we introduce the Transformed-Stationary (TS) methodology for non-stationary EVA. This approach consists in (i) transforming a non-stationary time series into a stationary one to which the stationary EVA theory can be applied; and (ii) reverse-transforming the result into a non-stationary extreme value distribution. As a transformation we propose and discuss a simple time-varying normalization of the signal and show that it allows a comprehensive formulation of non stationary GEV/GPD models with constant shape parameter. A validation of the methodology is carried out on time series of significant wave height, residual water level, and river discharge, which show varying degrees of long-term and seasonal variability. The results from the proposed approach are comparable with the ones from (a) a stationary EVA on quasi-stationary slices of non stationary series and (b) the previously applied non stationary EVA approach. However, the proposed technique comes with advantages in both cases, as in contrast to (a) it uses the whole time horizon of the series for the estimation of the extremes, allowing for a more accurate estimation of large return levels; and with respect to (b) it decouples the detection of non-stationary patterns from the fitting of the extreme values distribution. As a result the steps of the analysis are simplified and intermediate diagnostics are possible. In particular the transformation can be carried out by means of simple statistical techniques such as low-pass filters based on running mean and standard deviation, and the fitting procedure is a stationary one with a few degrees of freedom and easy to implement and control. An open-source MATLAB toolbox has been developed to cover this methodology, available at https://bitbucket.org/menta78/tseva.

Statistics of Extreme Wind Speeds and Wave Heights by the Bivariate ACER Method

2013 ◽  
Author(s):  
Arvid Naess ◽  
Oleh Karpa
Keyword(s):  
Time Series ◽  
Extreme Value Distribution ◽  
Offshore Structures ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Extreme Value Statistics ◽  
Wind Speeds ◽  
Wave Heights ◽  
Extreme Wind Speeds

In the reliability engineering and design of offshore structures probabilistic approaches are frequently adopted. They require the estimation of extreme quantiles of oceanographic data based on the statistical information. Due to strong correlation between such random variables as e.g. wave heights and wind speeds, application of the multivariate, or bivariate in the simplest case, extreme value theory is sometimes necessary. The paper focuses on the extension of the ACER method for prediction of extreme value statistics to the case of bivariate time series. Using the ACER method it is possible to provide an estimate of the exact extreme value distribution of a univariate time series. This is obtained by introducing a cascade of conditioning approximations to the exact extreme value distribution. When this cascade has converged, an estimate of the exact distribution has been obtained. In this paper it will be shown how the univariate ACER method can be extended in a natural way to also cover the case of bivariate data. Application of the bivariate ACER method will also be demonstrated at the measured coupled wind speed and wave height data.

scholarly journals Chinese Sunspot Drawings and Their Digitizations-(VI) Extreme Value Theory Applied to the Sunspot Number Series from the Purple Mountain Observatory

Atmosphere ◽  
2021 ◽  
Vol 12 (9) ◽  
pp. 1176
Author(s):  
Yan-Qing Chen ◽  
Sheng Zheng ◽  
Yan-Shan Xiao ◽  
Shu-Guang Zeng ◽  
Tuan-Hui Zhou ◽  
...  
Keyword(s):  
Sunspot Number ◽  
Extreme Value Theory ◽  
Extreme Values ◽  
Threshold Value ◽  
Value Theory ◽  
Extreme Value ◽  
Return Level ◽  
Block Maxima ◽  
First Time

Based on the daily sunspot number (SN) data (1954–2011) from the Purple Mountain Observatory, the extreme value theory (EVT) is employed for the research of the long-term solar activity. It is the first time that the EVT is applied on the Chinese SN. Two methods are used for the research of the extreme events with EVT. One method is the block maxima (BM) approach, which picks the maximum SN value of each block. Another one is the peaks-over-threshold (POT) approach. After a declustering process, a threshold value (here it is 300) is set to pick the extreme values. The negative shape parameters are obtained by the two methods, respectively, indicating that there is an upper bound for the extreme SN value. Only one value of the N-year return level (RL) is estimated: N = 19 years. For N = 19 years, the RL values of SN obtained by two methods are similar with each other. The RL values are found to be 420 for the POT method and the BM method. Here, the trend of 25th solar cycle is predicted to be stronger, indicating that the length of meridional forms of atmospheric circulation will be increased.

scholarly journals Dry months in the agricultural region of Ribeirão Preto, state of São Paulo-Brazil: an study based on the extreme value theory

2014 ◽  
Vol 34 (5) ◽  
pp. 992-1000 ◽  
Author(s):  
Gabriel C. Blain
Keyword(s):  
Extreme Value Theory ◽  
Goodness Of Fit ◽  
Standardized Precipitation Index ◽  
Generalized Pareto Distribution ◽  
Extreme Value Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Return Level ◽  
Probability Of Occurrence ◽  
Goodness Of Fit Tests

The application of the Extreme Value Theory (EVT) to model the probability of occurrence of extreme low Standardized Precipitation Index (SPI) values leads to an increase of the knowledge related to the occurrence of extreme dry months. This sort of analysis can be carried out by means of two approaches: the block maxima (BM; associated with the General Extreme Value distribution) and the peaks-over-threshold (POT; associated with the Generalized Pareto distribution). Each of these procedures has its own advantages and drawbacks. Thus, the main goal of this study is to compare the performance of BM and POT in characterizing the probability of occurrence of extreme dry SPI values obtained from the weather station of Ribeirão Preto-SP (1937-2012). According to the goodness-of-fit tests, both BM and POT can be used to assess the probability of occurrence of the aforementioned extreme dry SPI monthly values. However, the scalar measures of accuracy and the return level plots indicate that POT provides the best fit distribution. The study also indicated that the uncertainties in the parameters estimates of a probabilistic model should be taken into account when the probability associated with a severe/extreme dry event is under analysis.

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