Extreme rainfall from Tropical Cyclones described through the Metastatistical Extreme Value Distribution

2020 ◽  
Author(s):  
Arianna Miniussi ◽  
Marco Marani ◽  
Gabriele Villarini
Keyword(s):  
Tropical Cyclones ◽  
Heavy Rainfall ◽  
Daily Rainfall ◽  
Extreme Value Distribution ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Single Component ◽  
Accurate Estimation ◽  
Rainfall Events

<p>Tropical Cyclones (TCs) represent a threat in several areas of the world, among which the Eastern/South-Eastern United States are one of the highly impacted regions. In addition to the frequently analyzed hazards related to the strong winds and storm surges associated with TCs, they are also responsible for heavy rainfall, which can affect areas located very far from the storm center. The accurate estimation of rainfall extremes is crucial in several TC-related impacts, such as engineering design of buildings and prevention/protection measures, flood mapping, risk estimation and mitigation, insurance and re-insurance purposes, policy-making support. Statistical approaches considering the physical drivers of hydrological phenomena, besides their conceptual relevance, can help reducing the estimation uncertainty of extremes. Under these premises, here we use the Metastatistical Extreme Value Distribution (MEVD), a recent approach that improves the estimation of high-return period values over the traditional Extreme Value Theory. We leverage the property of the MEVD to explicitly include in the statistical formulation different rainfall-generating phenomena and we examine the potential advantage of distinguishing TC-induced and non-TC rainfall events in the estimation of extremes. Hence, we apply the MEVD both in a single-component formulation (i.e., assuming that all rainfall events are generated by one single mechanism, so that they can be described by the same probability distribution) and a mixed-population formulation (i.e., separating non-TC and TC-induced rainfall events) to long time series of daily precipitation in six American metropolitan areas, historically known for being impacted by TCs. Moreover, due to the characteristic time scale of these mechanisms, which can significantly influence precipitation for several days, we focus also on aggregated values of rainfall on consecutive days. We find that the mixed approach is advantageous in some cases when looking at daily rainfall, especially when there is a rather uniform frequency of TC events over years. When considering cumulative rainfall on time windows of three days, we show that the reduction of the estimation error by the mixed MEVD is generally higher than in the case of daily rainfall and it is consistent for all the cases studied, except for Houston. A possible reason for the mixed MEVD not to outperform the single-component MEVD in this area is the presence of tornadic supercell convective mechanisms, which also generate heavy rainfall though concentrated in short time intervals.</p>

Convergence rates for the ultimate and pentultimate approximations in extreme-value theory

1982 ◽  
Vol 14 (04) ◽  
pp. 833-854 ◽  
Author(s):  
Jonathan P. Cohen
Keyword(s):  
Extreme Value Theory ◽  
Convergence Rates ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Rates Of Convergence ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Type I ◽  
Type Ii

Let F be a distribution in the domain of attraction of the type I extreme-value distribution Λ(x). In this paper we derive uniform rates of convergence of Fn to Λfor a large class of distributions F. We also generalise the penultimate approximation of Fisher and Tippett (1928) and show that for many F a type II or type III extreme-value distribution gives a better approximation than the limiting type I distribution.

Convergence rates for the ultimate and pentultimate approximations in extreme-value theory

1982 ◽  
Vol 14 (4) ◽  
pp. 833-854 ◽  
Author(s):  
Jonathan P. Cohen
Keyword(s):  
Extreme Value Theory ◽  
Convergence Rates ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Rates Of Convergence ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Type I ◽  
Type Ii

Let F be a distribution in the domain of attraction of the type I extreme-value distribution Λ(x). In this paper we derive uniform rates of convergence of Fn to Λfor a large class of distributions F. We also generalise the penultimate approximation of Fisher and Tippett (1928) and show that for many F a type II or type III extreme-value distribution gives a better approximation than the limiting type I 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.

scholarly journals The transformed-stationary approach: a generic and simplified methodology for non-stationary extreme value analysis

2016 ◽  
Vol 20 (9) ◽  
pp. 3527-3547 ◽  
Author(s):  
Lorenzo Mentaschi ◽  
Michalis Vousdoukas ◽  
Evangelos Voukouvalas ◽  
Ludovica Sartini ◽  
Luc Feyen ◽  
...  
Keyword(s):  
Time Series ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Value Distribution ◽  
Stationary Time Series ◽  
Alternative Methods ◽  
Extreme Value Analysis ◽  
Accurate Estimation ◽  
Residual Water ◽  
Value Analysis

Abstract. Statistical approaches to study extreme events require, by definition, long time series of data. In many scientific disciplines, these series are often subject to variations at different temporal scales that affect the frequency and intensity of their extremes. Therefore, the assumption of stationarity is violated and alternative methods to conventional stationary extreme value analysis (EVA) must be adopted. Using the example of environmental variables subject to climate change, in this study we introduce the transformed-stationary (TS) methodology for non-stationary EVA. This approach consists of (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 enables a comprehensive formulation of non-stationary generalized extreme value (GEV) and generalized Pareto distribution (GPD) models with a 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 results from (a) a stationary EVA on quasi-stationary slices of non-stationary series and (b) the established method for non-stationary EVA. However, the proposed technique comes with advantages in both cases. For example, in contrast to (a), the proposed technique uses the whole time horizon of the series for the estimation of the extremes, allowing for a more accurate estimation of large return levels. Furthermore, with respect to (b), it decouples the detection of non-stationary patterns from the fitting of the extreme value 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 the running mean and the standard deviation, and the fitting procedure is a stationary one with a few degrees of freedom and is easy to implement and control. An open-source MATLAB toolbox has been developed to cover this methodology, which is available at https://github.com/menta78/tsEva/ (Mentaschi et al., 2016).

Uniform rates of convergence in extreme-value theory

1982 ◽  
Vol 14 (03) ◽  
pp. 600-622 ◽  
Author(s):  
Richard L. Smith
Keyword(s):  
Extreme Value Theory ◽  
Error Term ◽  
Extreme Value Distribution ◽  
Rates Of Convergence ◽  
Value Theory ◽  
Extreme Value ◽  
Value Distribution ◽  
Convergence In Distribution ◽  
Principal Error ◽  
Close Parallel

Rates of convergence are derived for the convergence in distribution of renormalised sample maxima to the appropriate extreme-value distribution. Related questions which are discussed include the estimation of the principal error term and the optimality of the renormalising constants. Throughout the paper a close parallel is drawn with the theory of slow variation with remainder. This theory is used in proving most of the results. Some applications are discussed, including some models of importance in reliability.

scholarly journals The exact extreme value distribution – applied study

2017 ◽  
Vol 5 (2) ◽  
pp. 87
Author(s):  
Aisha Fayomi ◽  
Neamat Qutb ◽  
Ohoud Al-Beladi
Keyword(s):  
Estimation Method ◽  
Simulated Data ◽  
Daily Rainfall ◽  
Extreme Value Distribution ◽  
Real Data ◽  
Value Theory ◽  
Extreme Value ◽  
Data Set ◽  
Applied Study ◽  
Extreme Value Model

Extreme value theory is used to develop models for describing the distribution of extreme events. Exact extreme value or compound distri-bution which is based on the theory of the maximum of random variables of random numbers is one of the most important models that are applicable in various situations, for instance of interest, it uses partial duration series (PDF) data to analyze extreme hydrological. As part of our earlier study, the parameters of this model were estimated by two methods, maximum likelihood (ML) and Bayesian- based on non-informative and informative priors. Moreover, a comparative study using simulated data showed that the Bayesian based on informative prior is the best estimation method. In this paper, a real data set taken from records of the largest daily rainfall data of Jeddah city in Saudi Arabia is used to fit the model when the parameters are estimated by Bayesian method. A comparative applied study indicates that the exact extreme value model under Bayesian estimates (BE) of its parameters provides appropriate fit for this data set and it is more applicable than the same model when the parameters are estimated by ML method and other three classical extreme value models.

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