Extreme value statistics in Raman fiber lasers

We present the numerical study of the statistical properties of the partially coherent quasi-CW high-Q cavity Raman fiber laser. The statistical properties are different for the radiation generated at one or many cavity passes. It is found that rare extreme events are generated at the far spectral wings of the spectrum. The mechanism of the extreme events generation is a turbulent-like four-wave mixing of numerous longitudinal generation modes. © 2011 Optical Society of America.

Modelagem estatística e atribuições dos eventos de precipitação extrema na Amazônia brasileira

Intense precipitation events (IPE) have been causing great social and economic losses in the affected regions. In the Amazon, these events can have serious impacts, primarily for populations living on the margins of its countless rivers, because when water levels are elevated, floods and/or inundations are generally observed. Thus, the main objective of this research is to study IPE, through Extreme Value Theory (EVT), to estimate return periods of these events and identify regions of the Brazilian Amazon where IPE have the largest values. The study was performed using daily rainfall data of the hydrometeorological network managed by the National Water Agency (Agência Nacional de Água) and the Meteorological Data Bank for Education and Research (Banco de Dados Meteorológicos para Ensino e Pesquisa) of the National Institute of Meteorology (Instituto Nacional de Meteorologia), covering the period 1983-2012. First, homogeneous rainfall regions were determined through cluster analysis, using the hierarchical agglomerative Ward method. Then synthetic series to represent the homogeneous regions were created. Next EVT, was applied in these series, through Generalized Extreme Value (GEV) and the Generalized Pareto Distribution (GPD). The goodness of fit of these distributions were evaluated by the application of the Kolmogorov-Smirnov test, which compares the cumulated empirical distributions with the theoretical ones. Finally, the composition technique was used to characterize the prevailing atmospheric patterns for the occurrence of IPE. The results suggest that the Brazilian Amazon has six pluvial homogeneous regions. It is expected more severe IPE to occur in the south and in the Amazon coast. More intense rainfall events are expected during the rainy or transitions seasons of each sub-region, with total daily precipitation of 146.1, 143.1 and 109.4 mm (GEV) and 201.6, 209.5 and 152.4 mm (GPD), at least once year, in the south, in the coast and in the northwest of the Brazilian Amazon, respectively. For the south Amazonia, the composition analysis revealed that IPE are associated with the configuration and formation of the South Atlantic Convergence Zone. Along the coast, intense precipitation events are associated with mesoscale systems, such Squall Lines. In Northwest Amazonia IPE are apparently associated with the Intertropical Convergence Zone and/or local convection.

Regional flood frequency analysis for Newfoundland and Labrador using the L-Moments index-flood method

The L-moments based index-flood procedure had been successfully applied for Regional Flood Frequency Analysis (RFFA) for the Island of Newfoundland in 2002 using data up to 1998. This thesis, however, considered both Labrador and the Island of Newfoundland using the L-Moments index-flood method with flood data up to 2013. For Labrador, the homogeneity test showed that Labrador can be treated as a single homogeneous region and the generalized extreme value (GEV) was found to be more robust than any other frequency distributions. The drainage area (DA) is the only significant variable for estimating the index-flood at ungauged sites in Labrador. In previous studies, the Island of Newfoundland has been considered as four homogeneous regions (A,B,C and D) as well as two Water Survey of Canada's Y and Z sub-regions. Homogeneous regions based on Y and Z was found to provide more accurate quantile estimates than those based on four homogeneous regions. Goodness-of-fit test results showed that the generalized extreme value (GEV) distribution is most suitable for the sub-regions; however, the three-parameter lognormal (LN3) gave a better performance in terms of robustness. The best fitting regional frequency distribution from 2002 has now been updated with the latest flood data, but quantile estimates with the new data were not very different from the previous study. Overall, in terms of quantile estimation, in both Labrador and the Island of Newfoundland, the index-flood procedure based on L-moments is highly recommended as it provided consistent and more accurate result than other techniques such as the regression on quantile technique that is currently used by the government.

On the statistics of transverse permeability of randomly distributed fibers

An RVE–based stochastic numerical model is used to calculate the permeability of randomly generated porous media at different values of the fiber volume fraction for the case of transverse flow in a unidirectional ply. Analysis of the numerical results shows that the permeability is not normally distributed. With the aim of proposing a new understanding on this particular topic, permeability data are fitted using both a mixture model and a unimodal distribution. Our findings suggest that permeability can be fitted well using a mixture model based on the lognormal and power law distributions. In case of a unimodal distribution, it is found, using the maximum-likelihood estimation method (MLE), that the generalized extreme value (GEV) distribution represents the best fit. Finally, an expression of the permeability as a function of the fiber volume fraction based on the GEV distribution is discussed in light of the previous results.

Inundações urbanas: desafios ao ordenamento do território. O caso da Cidade da Praia (Cabo Verde)

Pela sua posição geográfica e particulares condições climáticas, devidas à sua inserção na faixa saheliana com caraterísticas de marcada aridez, Cabo Verde é um arquipélago com condições naturais adversas, pautado principalmente pela seca prolongada. Muitas vezes esta conjuntura é interpolada por curtos períodos de fortes chuvadas que podem originar cheias e inundações nos principais centros urbanos. Os eventos ocorridos revelam consequências graves, desde prejuízos na agricultura, perda de animais, destruição de infra-estruturas, perda de bens materiais e, mesmo, vítimas humanas mortais. Este estudo tem como objetivos principais: (i) perceber os problemas e desafios que se colocam à cidade da Praia (maior centro urbano do país, com forte crescimento e expansão urbana) perante situações de inundação; (ii) contribuir para o maior conhecimento das causas e consequências dessas inundações; (iii) definir quais as áreas de maior suscetibilidade às cheias e quais as que possuem um maior risco potencial. Optou-se por uma metodologia integrada, através do levantamento bibliográfico, cartográfico, numérico e percetivo (com base em entrevistas e inquéritos). Para o estudo das bacias hidrográficas foram calculados índices morfométricos, definidas classes de permeabilidade do substrato geológico e aplicado o método multicritério de Reis (2011) para a definição das áreas suscetíveis às cheias. Analisaram-se as precipitações máximas diárias anuais e respetivos períodos de retorno, com a aplicação do método de Gumbel. A análise de notícias de jornais, referentes ao período compreendido entre 1980 e 2011, foi fundamental para o conhecimento da distribuição espácio-temporal dos eventos perigosos de inundação em Cabo Verde e na cidade da Praia. Os resultados obtidos revelam um significativo grau de suscetibilidade às cheias na cidade da Praia. As áreas de maior risco potencial às inundações encontram-se no setor central da cidade, resultante da conjugação da convergência do escoamento das três ribeiras principais, da elevada densidade populacional e de construção desordenada nos leitos de cheia e nas áreas deprimidas, onde se acumulam as águas.

Inundações Urbanas - Desafios ao Ordenamento do Território - O

Pela sua posição geográfica e particulares condições climáticas, devidas à sua inserção na faixa saheliana com caraterísticas de marcada aridez, Cabo Verde é um arquipélago com condições naturais adversas, pautado principalmente pela seca prolongada. Muitas vezes esta conjuntura é interpolada por curtos períodos de fortes chuvadas que podem originar cheias e inundações nos principais centros urbanos. Os eventos ocorridos revelam consequências graves, desde prejuízos na agricultura, perda de animais, destruição de infra-estruturas, perda de bens materiais e, mesmo, vítimas humanas mortais. Este estudo tem como objetivos principais: (i) perceber os problemas e desafios que se colocam à cidade da Praia (maior centro urbano do país, com forte crescimento e expansão urbana) perante situações de inundação; (ii) contribuir para o maior conhecimento das causas e consequências dessas inundações; (iii) definir quais as áreas de maior suscetibilidade às cheias e quais as que possuem um maior risco potencial. Optou-se por uma metodologia integrada, através do levantamento bibliográfico, cartográfico, numérico e percetivo (com base em entrevistas e inquéritos). Para o estudo das bacias hidrográficas foram calculados índices morfométricos, definidas classes de permeabilidade do substrato geológico e aplicado o método multicritério de Reis (2011) para a definição das áreas suscetíveis às cheias. Analisaram-se as precipitações máximas diárias anuais e respetivos períodos de retorno, com a aplicação do método de Gumbel. A análise de notícias de jornais, referentes ao período compreendido entre 1980 e 2011, foi fundamental para o conhecimento da distribuição espácio-temporal dos eventos perigosos de inundação em Cabo Verde e na cidade da Praia. Os resultados obtidos revelam um significativo grau de suscetibilidade às cheias na cidade da Praia. As áreas de maior risco potencial às inundações encontram-se no setor central da cidade, resultante da conjugação da convergência do escoamento das três ribeiras principais, da elevada densidade populacional e de construção desordenada nos leitos de cheia e nas áreas deprimidas, onde se acumulam as águas.

Climate trends in the municipality of Pelotas, state of Rio Grande do Sul, Brazil

ABSTRACTChanges in the frequency of occurrence of extreme weather events have been pointed out as a likely impact of global warming. In this context, this study aimed to detect climate change in series of extreme minimum and maximum air temperature of Pelotas, State of Rio Grande do Sul, (1896 - 2011) and its influence on the probability of occurrence of these variables. We used the general extreme value distribution (GEV) in its stationary and non-stationary forms. In the latter case, GEV parameters are variable over time. On the basis of goodness-of-fit tests and of the maximum likelihood method, the GEV model in which the location parameter increases over time presents the best fit of the daily minimum air temperature series. Such result describes a significant increase in the mean values of this variable, which indicates a potential reduction in the frequency of frosts. The daily maximum air temperature series is also described by a non-stationary model, whose location parameter decreases over time, and the scale parameter related to sample variance rises between the beginning and end of the series. This result indicates a drop in the mean of daily maximum air temperature values and increased dispersion of the sample data.

Identification and ranking of extraordinary rainfall events over northwest Italy: the role of Atlantic moisture

An objective identification and ranking of extraordinary rainfall events for Northwest Italy is established using time series of annual precipitation maxima for 1938–2002 at over 200 stations. Rainfall annual maxima are considered for five reference durations (1, 3, 6, 12, and 24 h). In a first step, a day is classified as an extraordinary rainfall day when a regional threshold calculated on the basis of a two-components extreme value distribution is exceeded for at least one of the stations. Second, a clustering procedure taking into account the different rainfall durations is applied to the identified 163 events. Third, a division into six clusters is chosen using Ward's distance criteria. It is found that two of these clusters include the seven strongest events as quantified from a newly developed measure of intensity which combines rainfall intensities and spatial extension. Two other clusters include the weakest 72% historical events. The obtained clusters are analyzed in terms of typical synoptic characteristics. The two top clusters are characterized by strong and persistent upper air troughs inducing not only moisture advection from the North Atlantic into the Western Mediterranean but also strong northward flow towards the southern Alpine ranges. Humidity transports from the North Atlantic are less important for the weaker clusters. We conclude that moisture advection from the North Atlantic plays a relevant role in the magnitude of the extraordinary events over Northwest Italy.

Loss potentials associated with European windstorms under future climate conditions

Possible changes in the frequency and intensity of windstorms under future climate conditions during the 21st century are investigated based on an ECHAM5 GCM multi-scenario ensemble. The intensity of a storm is quantified by the associated estimated loss derived with using an empirical model. The geographical focus is ‘Core Europe’, which comprises countries of Western Europe. Possible changes of losses are analysed by comparing ECHAM5 GCM data for recent (20C, 1960 to 2000) and future climate conditions (B1, A1B, A2; 2060 to 2100), each with 3 ensemble members. Changes are quantified using both rank statistics and return periods (RP) estimated by fitting an extreme value distribution using the peak over threshold method to potential storm losses. The estimated losses for ECHAM5 20C and reanalysis events show similar statistical features in terms of return periods. Under future climate conditions, all climate scenarios show an increase in both frequency and magnitude of potential losses caused by windstorms for Core Europe. Future losses that are double the highest ECHAM5 20C loss are identified for some countries. While positive changes of ranking are significant for many countries and multiple scenarios, significantly shorter RPs are mostly found under the A2 scenario for return levels correspondent to 20 yr losses or less. The emergence time of the statistically significant changes in loss varies from 2027 to 2100. These results imply an increased risk of occurrence of windstorm-associated losses, which can be largely attributed to changes in the meteorological severity of the events. Additionally, factors such as changes in the cyclone paths and in the location of the wind signatures relative to highly populated areas are also important to explain the changes in estimated losses.

Dowscaling estocástico para extremos climáticos via interpolação espacial

Present day weather forecast models usually cannot provide realistic descriptions of local and particulary extreme weather conditions. However, for lead times of about a small number of days, they provide reliable forecast of the atmospheric circulation that encompasses the subscale processes leading to extremes. Hence, forecasts of extreme events can only be achieved through a combination of dynamical and statistical analysis methods, where a stable and significant statistical model based on prior physical reasoning establishes posterior statistical-dynamical model between the local extremes and the large scale circulation. Here we present the development and application of such a statistical model calibration on the besis of extreme value theory, in order to derive probabilistic forecast for extreme local temperature. The dowscaling applies to NCEP/NCAR re-analysis, in order to derive estimates of daily temperature at Brazilian northeastern region weather stations

The estimation of statistical parameters for local alignment score distributions

The distribution of optimal local alignment scores of random sequences plays a vital role in evaluating the statistical significance of sequence alignments. These scores can be well described by an extreme-value distribution. The distribution’s parameters depend upon the scoring system employed and the random letter frequencies; in general they cannot be derived analytically, but must be estimated by curve fitting. For obtaining accurate parameter estimates, a form of the recently described ‘island’ method has several advantages. We describe this method in detail, and use it to investigate the functional dependence of these parameters on finite-length edge effects.

A unified statistical framework for sequence comparison and structure comparison

We present an approach for assessing the significance of sequence and structure comparisons by using nearly identical statistical formalisms for both sequence and structure. Doing so involves an all-vs.-all comparison of protein domains [taken here from the Structural Classification of Proteins (scop) database] and then fitting a simple distribution function to the observed scores. By using this distribution, we can attach a statistical significance to each comparison score in the form of a P value, the probability that a better score would occur by chance. As expected, we find that the scores for sequence matching follow an extreme-value distribution. The agreement, moreover, between the P values that we derive from this distribution and those reported by standard programs (e.g., blast and fasta validates our approach. Structure comparison scores also follow an extreme-value distribution when the statistics are expressed in terms of a structural alignment score (essentially the sum of reciprocated distances between aligned atoms minus gap penalties). We find that the traditional metric of structural similarity, the rms deviation in atom positions after fitting aligned atoms, follows a different distribution of scores and does not perform as well as the structural alignment score. Comparison of the sequence and structure statistics for pairs of proteins known to be related distantly shows that structural comparison is able to detect approximately twice as many distant relationships as sequence comparison at the same error rate. The comparison also indicates that there are very few pairs with significant similarity in terms of sequence but not structure whereas many pairs have significant similarity in terms of structure but not sequence.

Out-of-equilibrium dynamical fluctuations in glassy systems

"In this paper we extend the earlier treatment of out-of-equilibrium mesoscopic fluctuations in glassy systems in several significant ways. First, via extensive simulations, we demonstrate that models of glassy behavior without quenched disorder display scalings of the probability of local two-time correlators that are qualitatively similar to that of models with short-ranged quenched interactions. The key ingredient for such scaling properties is shown to be the development of a criticallike dynamical correlation length, and not other microscopic details. This robust data collapse may be described in terms of a time-evolving "extreme value" distribution. We develop a theory to describe both the form and evolution of these distributions based on a effective sigma model approach."

Bayesian analysis of extreme events with threshold estimation

The aim of this paper is to analyze extremal events using Generalized Pareto Distributions (GPD), considering explicitly the uncertainty about the threshold. Current practice empirically determines this quantity and proceeds by estimating the GPD parameters based on data beyond it, discarding all the information available be10w the threshold. We introduce a mixture model that combines a parametric form for the center and a GPD for the tail of the distributions and uses all observations for inference about the unknown parameters from both distributions, the threshold inc1uded. Prior distribution for the parameters are indirectly obtained through experts quantiles elicitation. Posterior inference is available through Markov Chain Monte Carlo (MCMC) methods. Simulations are carried out in order to analyze the performance of our proposed mode1 under a wide range of scenarios. Those scenarios approximate realistic situations found in the literature. We also apply the proposed model to a real dataset, Nasdaq 100, an index of the financiai market that presents many extreme events. Important issues such as predictive analysis and model selection are considered along with possible modeling extensions.

A subsampling approach to estimating the distribution of diversing statistics with application to assessing financial market risks

In this paper we propose a subsampling estimator for the distribution ofstatistics diverging at either known rates when the underlying timeseries in strictly stationary abd strong mixing. Based on our results weprovide a detailed discussion how to estimate extreme order statisticswith dependent data and present two applications to assessing financialmarket risk. Our method performs well in estimating Value at Risk andprovides a superior alternative to Hill's estimator in operationalizingSafety First portofolio selection.