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.

Extreme Value Analysis of Tropical Cyclone Trapped-Fetch Waves

2007 ◽  
Vol 46 (10) ◽  
pp. 1501-1522 ◽  
Author(s):  
Allan W. MacAfee ◽  
Samuel W. K. Wong
Keyword(s):  
Gulf Of Mexico ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Return Level ◽  
Direct Result ◽  
Extreme Value Analysis ◽  
Wind Fields ◽  
Value Analysis ◽  
Output Information

Abstract Many of the extreme ocean wave events generated by tropical cyclones (TCs) can be explained by examining one component of the spectral wave field, the trapped-fetch wave (TFW). Using a Lagrangian TFW model, a parametric model representation of the local TC wind fields, and the National Hurricane Center’s hurricane database archive, a dataset of TFWs was created from all TCs in the Atlantic Ocean, Gulf of Mexico, and Caribbean Sea from 1851 to 2005. The wave height at each hourly position along a TFW trajectory was sorted into 2° × 2° latitude–longitude grid squares. Five grid squares (north of Hispaniola, Gulf of Mexico, Carolina coast, south of Nova Scotia, and south of Newfoundland) were used to determine if extreme value theory could be applied to the extremes in the TFW dataset. The statistical results justify accepting that a generalized Pareto distribution (GPD) model with a threshold of 6 m could be fitted to the data: the datasets were mostly modeled adequately, and much of the output information was useful. Additional tests were performed by sorting the TFW data into the marine areas in Atlantic Canada, which are of particular interest to the Meteorological Service of Canada because of the high ocean traffic, offshore drilling activities, and commercial fishery. GPD models were fitted, and return periods and the 95% confidence intervals (CIs) for 10-, 15-, and 20-m return levels were computed. The results further justified the use of the GPD model; hence, extension to the remaining grid squares was warranted. Of the 607 grid squares successfully modeled, the percentage of grid squares with finite lower (upper) values for the 10-, 15-, and 20-m return level CIs were 100 (80), 94 (53), and 90 (16), respectively. The lower success rate of 20-m TFW CIs was expected, given the rarity of 20-m TFWs: of the 5 713 625 hourly TFW points, only 13 958, or 0.24%, were 20 m or higher. Overall, the distribution of the successfully modeled grid squares in the data domain agreed with TFW theory and TC climatology. As a direct result of this study, the summary datasets and return level plots were integrated into application software for use by risk managers. A description of the applications illustrates their use in addressing various questions on extreme TFWs.

scholarly journals Vertical structure of extreme currents in the Faroe-Bank Channel

2005 ◽  
Vol 23 (6) ◽  
pp. 1977-1986 ◽  
Author(s):  
C. Carollo ◽  
I. Astin ◽  
J. Graff
Keyword(s):  
Extreme Value Theory ◽  
General Circulation ◽  
Regional Scale ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Horizontal Resolution ◽  
Return Level ◽  
Near Surface ◽  
Deep Waters

Abstract. Extreme currents are studied with the aim of understanding their vertical and spatial structures in the Faroe-Bank Channel. Acoustic Doppler Current Profiler time series recorded in 3 deployments in this channel were investigated. To understand the main features of extreme events, the measurements were separated into their components through filtering and tidal analysis before applying the extreme value theory to the surge component. The Generalized Extreme Value (GEV) distribution and the Generalized Pareto Distribution (GPD) were used to study the variation of surge extremes from near-surface to deep waters. It was found that this component alone is not able to explain the extremes measured in total currents, particularly below 500 m. Here the mean residual flow enhanced by tidal rectification was found to be the component feature dominating extremes. Therefore, it must be taken into consideration when applying the extreme value theory, not to underestimate the return level for total currents. Return value speeds up to 250 cm s–1 for 50/250 years return period were found for deep waters, where the flow is constrained by the topography at bearings near 300/330° It is also found that the UK Meteorological Office FOAM model is unable to reproduce either the magnitude or the form for the extremes, perhaps due to its coarse vertical and horizontal resolution, and is thus not suitable to model extremes on a regional scale. Keywords. Oceanography: Physical (Currents; General circulation; General or miscellaneous)

scholarly journals EXTREME VALUE ANALYSIS FOR MODELING HIGH PM10 LEVEL IN JOHOR BAHRU

2015 ◽  
Vol 76 (1) ◽  
Author(s):  
Nor Azrita Mohd Amin ◽  
Mohd Bakri Adam ◽  
Ahmad Zaharin Aris
Keyword(s):  
Generalized Pareto Distribution ◽  
Pollution Index ◽  
Extreme Value Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Generalized Extreme Value Distribution ◽  
Return Level ◽  
Extreme Value Analysis ◽  
Value Analysis ◽  
Pm10 Level

Extreme value theory is a very well-known statistical analysis for modeling extreme data in environmental management. The main focus is to compare the generalized extreme value distribution (GEV) and the generalized Pareto distribution (GPD) for modeling extreme data in terms of estimated parameters and return levels. The maximum daily PM10 data for Johor Bahru monitoring station based on a 14 years database (1997-2010) were analyzed. It is found that the parameters estimated are more comparable if the extracted numbers of extreme series for both models are much more similar. The 10-years return value for GEV is  while for GPD is . Based on the threshold choice plot, threshold  is chosen and the corresponding 10-years return level is . According to the air pollution index in Malaysia, this value is categorized as hazardous.

How to a priori select ordinary distributions in flood frequency analysis when applying the Metastatistical Extreme Value approach

2021 ◽  
Author(s):  
Sumra Mushtaq ◽  
Arianna Miniussi ◽  
Ralf Merz ◽  
Stefano Basso
Keyword(s):  
Time Series ◽  
A Priori ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
High Threshold ◽  
Log Normal ◽  
Effective Use ◽  
Short Time

<p>Standard flood frequency analyses hinge on unrealistic asymptotic assumptions, use a small portion of the data available (annual maxima or a few values above a high threshold only), and are ill-suited for short time series. Lately, the Metastatistical Extreme Value Distribution (MEVD) has gained momentum in the study of extremes, as it relaxes the assumptions on which traditional methods are based and makes a more effective use of the information at hand. Moreover, it is more flexible in the choice of the distribution of the ordinary events (i.e., events belonging to the bulk of the distribution, in contrast to annual maxima), hence giving room for selecting the statistical method that better describes the data.</p><p>In this work, we leverage the flexibility of the MEVD and develop an approach to a priori select the distribution of ordinary peaks according to the ratio between their empirical 99th and 90th percentiles, and apply it to daily mean streamflow time series from 183 gauges in Germany. Based on the value of this ratio, we choose either the Generalized Gamma or the Log-Normal distributions to describe ordinary peaks that show lighter or heavier tails respectively. This distinction allows us to improve the estimation of the magnitude of floods with high return periods in 117 basins of a 64 % on average and to reduce under-/over-estimation issues, when compared to a MEVD application in which the ordinary distribution is chosen regardless the tail features of the underlying data.</p>

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.

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 events in total ozone over Arosa – Part 1: Application of extreme value theory

2010 ◽  
Vol 10 (20) ◽  
pp. 10021-10031 ◽  
Author(s):  
H. E. Rieder ◽  
J. Staehelin ◽  
J. A. Maeder ◽  
T. Peter ◽  
M. Ribatet ◽  
...  
Keyword(s):  
Time Series ◽  
Frequency Distribution ◽  
Extreme Events ◽  
Extreme Value Theory ◽  
Total Ozone ◽  
Volcanic Eruptions ◽  
Value Theory ◽  
Extreme Value ◽  
Data Set ◽  
Ozone Data

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.

scholarly journals Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory

1997 ◽  
Vol 27 (1) ◽  
pp. 117-137 ◽  
Author(s):  
Alexander J. McNeil
Keyword(s):  
Extreme Value Theory ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Parametric Curve ◽  
Excess Loss ◽  
Generalized Pareto ◽  
Fire Insurance ◽  
Loss Severity ◽  
Parametric Curve Fitting

AbstractGood estimates for the tails of loss severity distributions are essential for pricing or positioning high-excess loss layers in reinsurance. We describe parametric curve-fitting methods for modelling extreme historical losses. These methods revolve around the generalized Pareto distribution and are supported by extreme value theory. We summarize relevant theoretical results and provide an extensive example of their application to Danish data on large fire insurance losses.

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