Unit:
Department of PhysicsLibrary of the School of Science
Dissertation committee:
1. George Kallos: Emeritus Professor, National & Kapodistrian University of Athens School of Physics Division of Environment Physics - Meteorology
2. Takvor H. Soukissian: Research Director, Hellenic Centre for Marine Research - Institute of Oceanography, Anavissos
3. Kostas A. Belibassakis: Professor, School of Naval Architecture & Marine Eng. NTUA
4. George N. Galanis: Professor, Hellenic Naval Academy
5. Helena Flocas: Professor, National & Kapodistrian University of Athens School of Physics Division of Environment Physics - Meteorology
6. Sofianos Sarantis: Associate Professor, National & Kapodistrian University of Athens School of Physics Division of Environment Physics - Meteorology
7. Nikolaos Themelis: Assistant Professor, School of Naval Architecture & Marine Eng. NTUA
Original Title:
Statistical Modeling of Extreme Environmental Values
Translated title:
Statistical Modeling of Extreme Environmental Values
Summary:
The accurate estimation of extreme values for metocean parameters (e.g., wind speed) plays a crucial role in the marine renewable energy industry and in coastal and offshore engineering applications. Typical challenges that arise in these fields of interest among others are the limited source of information in samples, commonly associated by the scarcity of long datasets, and the accurate estimation of the underlying dependence structure of the stochastic models that can be used for inference on applied problems with extremes.
The present analysis, aims to assess the effect of the asymptotic distributional behavior of two types of extreme wind speed sampling data that form the basis of all subsequent predictions in the long term time scale. The first type of sampling data considered will be subsets of observations extracted from blocks of annual length and the second type are subset of observations exceeding a high enough threshold. The challenges closely related to the special attributes that form these types of sampling data motivate the present thesis which focuses on constructing and improving extreme value models to assess the risk associated to extreme wind speed episodes. In particular, in this thesis we focus on
• The identification of the combined effects of the samples of wind speed that influence the stability of the parameter estimates as well as the efficiency of the estimators to the modelling of extremes.
• Providing alternative methods of modelling extremes of wind speed that are less known to the relative fields of interest and infer to demonstrate better in comparison to the standard modelling approach.
• Extending the formulation of the stationary model of extremes to the parameterization of a nonstationary model in order to incorporate subject specific knowledge in the presence of trends under the assumption of climate wind changes.
• Extending the classical methods that identify the dependence structure in sample of observations in order to effectively model the extremes that are irregularly spaced in time. Specifically, the reconstruction of a dependent sample of extremes that are irregularly spaced in time is focused on relatively small samples of wind speed where the scarcity of long and complete time series is a common restriction in climatological studies.
In this setting, the statistical analysis of the most used and less known estimators that model the extremes of wind speed is inferred from a twofold approach. A simulation study is performed first to assess the effect of the sample size to the estimators of the asymptotic distribution that model extremes. The evaluation of the simulation results is based on several statistical measures. Afterwards, the optimum methods from the simulation analysis are applied to wind speed datasets of different sample size and different direction step of sampling. The evaluation is based on datasets originated from databases of relatively moderate horizontan resolution to the regional locations at the North Sea, at the Pacific coast of central America and at the eastern Atlantic Ocean where these locations are exposed to a strong wind climate with evidence of extreme wind speeds. Inference of the sample size effect and the directional step of sampling to the demonstration of the model estimators is made on the obtained 50- and 100-year wind speed design values. From this assessment, the combind method of moments is advised as the suitable method when the sample size is limited.
Other challenges that motivated this study is the modelling of extremes when the extremal characteristics are expected not constant over time. To this effect, seasonality and long-term trends are probably the main reasons that influence the stationary hypothesis of the wind speed processes. In this part of this study, an attempt is made to model the possible trends of extremes in the long-term behavior of the process. Since in practice the trend is unknown, various formulations of the trend as a function of time are assessed to represent the extremes of wind speed when the stationary assumption is not valid in order to alleviate the bias effect from the attempt of de-trending the process before the time series is used. Statistical tests challenged the modeling of the trend of rejection or not in favor of stationarity. For the extremes of non-stationary sequences and the application to wind speed design values, our analysis is based on coarse historical data of long datasets at regional locations at the North Sea where trends are notable to influence the wind speed variability. From this assessment, the simplest form of parameterization in the parameters of the extreme value distribution is advised in modeling extremes when stationarity is violated.
Another common problem of design to assess risk associated to extremes of wind speed in met-ocean fields of interest, is the scarcity of long datasets. To this limitation, many applications utilize as many as possible extremes from the available dataset by re-sampling to a subset of extremes. However, the re-samples are often affected by dependency and the diagnostics related to the independence limitations is usually violated when the observations of these samples are irregularly spaced in time. To alleviate this effect, a resampling strategy is proposed that effectively models extremes irregularly in time when re-sampling of relatively small datasets of wind speed is advised. The proposed DeCA Uncorrelated (DeCAUn) model provides an improvement to the current physical De-Clustering Algorithm (DeCA) modelling the samples of DeCA irregularly in time.
Specifically, the resampling strategy proposed analyzes the correlation effect in samples based on the extention of the standard correlation operator setting weight functions to observations irregularly spaced in time. To infer in terms of precision and variability, design value estimates and confidence bounds of the demonstration of the proposed model are evaluated based on the standard approaches that model extremes. The use of a high resolution database is crucial to derive detailed data to follow-up the requirements of the resampling strategy to short and irregularly samples near the offshore regions of Europe where the demonstration of DeCAUn to wind speed is challenged from the highly dependent regional effects (surface roughness, landmass, etc.). However, to assess the effect of larger sample sizes to the limiting distribution of the excesses that will infer effectively the modelling of DeCAUn, larger samples of wind speed from a fairly coarse resolution database are also required for evaluation. From this assessment, the proposed model demonstrated as an alternative re-sampling strategy for extreme wind speed projections when samples are irregularly spaced in time.
These challenges motivate the present thesis to assess the risk associated to extreme wind speed episodes for direct potential application to the relevant fields of interest. In particular, the most important findings from this assessment in extremes are outlined in the following:
• Based on the evaluation using different sample sizes of wind speed data from both the simulation study and applications, the combind method of moments outperforms, in many respects, compared to the standard likelihood approach. Overall, regarding the design values it is evident that sample sizes greater than 35 years are necessary for a substantial reduction of epistemic uncertainty.
• Under the proviso of nonstationarity at locations where the natural climate variability in extreme wind speeds is challenged, the linear form of parameterization in the parameters of the extreme value distribution will model effectively the trends in extremes.
• For sample periods of wind speed greater than 15 years, the re-samples of DeCAUn demonstrated effective projections in terms of precision and variability.
• The resampling strategy proposed in this setting showed systematically stronger rate of convergence to the asymptotic properties of the extreme value distribution particularly for wind speed datasets of higher spatial resolution and a less stronger rate of convergence for datasets of lower resolution.
Main subject category:
Science
Keywords:
Extreme wind speed, Return period, GEV parameter estimation methods, Block maxima method, DeCA model, GPD distribution, Threshold selection, Irregularly sample time series, Wind speed design values, Extreme Value Analysis, Similarity, De-clustering, POT, modelling irregular samples, slotting autocorrelation, Non-rectangular Kernel, irregular Correlation estimator
Number of references:
430
