scholarly journals Fitting a Generalised Extreme Value Distribution to Four Candidate Annual Maximum Flood Heights Time Series Models in the Lower Limpopo River Basin of Mozambique

2019 ◽  
Author(s):  
Daniel Maposa
Keyword(s):  
Time Series ◽  
River Basin ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Time Series Models ◽  
Annual Maximum ◽  
Generalised Extreme Value Distribution

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.

Prediction of Airgap Statistics for Fixed Offshore Platforms

2011 ◽  
Author(s):  
A. Naess ◽  
O. Gaidai
Keyword(s):  
Time Series ◽  
Random Field ◽  
Wave Field ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Air Gap ◽  
Value Distribution ◽  
Extreme Value Statistics ◽  
Offshore Platforms ◽  
Spatial Extremes

Air gap statistics for offshore platforms is directly related to the extreme value statistics of the random ocean wave field. The present paper describes a new method for predicting the extreme values of a random wave field in both space and time. The method relies on the use of data provided by measurements or Monte Carlo simulation combined with a technique for estimating the extreme value distribution of a recorded time series. The time series in question represents the spatial extremes of the random field at each point in time. The time series is constructed by sampling the available realization of the random field over a suitable grid defining the domain in question and extracting the extreme value. This is done for each time point of a suitable time grid. Thus, a time series of spatial extremes is produced. This time series provides the basis for estimating the extreme value distribution using recently developed techniques for time series, which results in an accurate practical procedure for solving a very difficult problem. This procedure is applied to the prediction of air gap statistics for a jacket structure.

scholarly journals CALCULATION OF CLIMATE LOADS DESIGN VALUES ACCORDING TO THE PROBABILITY MODEL OF ANNUAL MAXIMUM SERIES

2021 ◽  
Vol 12 (23) ◽  
pp. 61-71
Author(s):  
Mykola Pashynskyi ◽  
◽  
Victor Pashynskyi ◽  
Evgeniy Klymenko ◽  
◽  
...  
Keyword(s):  
Probabilistic Model ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Generalized Extreme Value Distribution ◽  
Type I ◽  
Annual Maximum ◽  
Generalized Extreme Value ◽  
Characteristic Values ◽  
Distribution Type

The aim of this work is to improve a method for determining the characteristic values of climatic loads according to a probabilistic model of the annual maxima sequence, by choosing a rational type of generalized extreme value distribution law. An analysis is provided regarding the suitability of using four types of distributions for describing a data collection of maximum values of climatic loads. Using example data from the meteorological stations of Ukraine, it is found that for coefficients of variation smaller than 0.85–1.0, it is advisable to use the double exponential Gumbel distribution (generalized extreme value distribution type-I), and at higher values of the coefficient of variation, it is advisable to use the Weibull distribution (generalized extreme value distribution type-III). Recommendations are provided for considering the accuracy in the estimations of the characteristic values of loads according to the probabilistic model for the annual maximum value series.

scholarly journals Extreme Storm Surge estimation and projection through the Metastatistical Extreme Value Distribution

2021 ◽  
Author(s):  
Maria Francesca Caruso ◽  
Marco Marani
Keyword(s):  
Time Series ◽  
Sea Level ◽  
Return Period ◽  
Extreme Value Distribution ◽  
Storm Surges ◽  
Extreme Value ◽  
Value Distribution ◽  
Sample Sizes ◽  
Sea Levels ◽  
Calibration Sample

Abstract. Accurate estimates of the probability of extreme sea levels are pivotal for assessing risk and the design of coastal defense structures. This probability is typically estimated by modelling observed sea-level records using one of a few statistical approaches. In this study we comparatively apply the Generalized Extreme Value (GEV) distribution, based on Block Maxima (BM) and Peak-Over-Threshold (POT) formulations, and the recently Metastatistical Extreme Value Distribution (MEVD) to four long time series of sea-level observations distributed along European coastlines. A cross-validation approach, dividing available data in separate calibration and test sub-samples, is used to compare their performances in high-quantile estimation. To address the limitations posed by the length of the observational time series, we quantify the estimation uncertainty associated with different calibration sample sizes, from 5 to 30 years. Focusing on events with a high return period, we find that the GEV-based approaches and MEVD perform similarly when considering short samples (5 years), while the MEVD estimates outperform the traditional methods when longer calibration sample sizes (10-30 years) are considered. We then investigate the influence of sea-level rise through 2100 on storm surges frequencies. The projections indicate an increase in the height of storm surges for a fixed return period that are spatially heterogeneous across the coastal locations explored.

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