Análise de frequência de vazões mínimas

Orientador : Profa. Dra. Miriam Rita Moro MineDissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Engenharia de Recursos Hídricos e Ambiental. Defesa: Curitiba, 01/12/2014Inclui referências : f.79-83Área de concentração:Recursos HídricosResumo: Na teoria de valores extremos, a análise de máximos sempre atrai mais atenção do que a de mínimos. Ainda há muitos detalhes a serem descobertos e esclarecidos para mínimos em relação às propriedades das funções de distribuições de probabilidade. O reconhecimento crescente da importância das vazões mínimas para a viabilidade de ecossistemas, para a sustentabilidade da economia e como sentinela das mudanças climáticas, faz com que o estudo de extremos mínimos torne-se cada vez mais importante. O objetivo desta dissertação é compensar em parte a falta de tratamento teórico sobre extremos mínimos e, especificamente, vazões mínimas. O método está dividido em duas abordagens: a análise convencional e a análise assintótica. Na análise convencional foram ajustadas as distribuições de Weibull e Lognormal de dois parâmetros às séries de vazões mínimas anuais e mínimas médias móveis de 7 dias de duração. Em seguida, foram aplicados os testes de aderência Qui-Quadrado e Kolmogorov-Smirnov. O estudo da abordagem da análise assintótica foi baseado no artigo de Gottschalk et al., 2013, e nesta pesquisa é dada ênfase ao Método do Bloco (BM). Duas distribuições "mãe", aqui entendidas como as distribuições de todas as vazões médias diárias, com comportamento de potência para vazões mínimas, são investigadas: i) Distribuição Gama; ii) Distribuição Lognormal de dois parâmetros. Busca-se demonstrar que essas distribuições pertencem ao domínio mínimo de atração da distribuição de Weibull, isto é, amostras de mínimos dessas duas distribuições, assintoticamente tenderão à distribuição de Weibull. A teoria estudada nesta dissertação é aplicada a 11 estações fluviométricas da bacia hidrográfica do rio Iguaçu com séries de dados de 48 anos. A partir da análise convencional, conclui-se que a distribuição Lognormal foi a que apresentou melhor ajuste segundo o teste ??2, na quase totalidade das estações. Porém, para a maioria das estações, a distribuição de Weibull também obteve um bom ajuste com o mesmo teste de aderência. Verificouse que a distribuição Gama, com relação aos mínimos, tende a uma função de potência em consequência da distribuição de Weibull, e a Lognormal não apresenta bom ajuste para 3 das estações da bacia do rio Iguaçu. Isto não foi suficiente para rejeitar a distribuição Lognormal como uma boa candidata para modelar vazões mínimas, devido à análise dos parâmetros. Observou-se que a assimetria das séries de vazões médias diárias das estações da bacia do rio Iguaçu é maior do que a assimetria da distribuição de Weibull, e tem bom ajuste à distribuição Lognormal. Os parâmetros ??, ?? e ????, das séries de vazões mínimas anuais moduladas, se ajustaram bem à distribuição Lognormal. Em conformidade com os estudos da análise convencional prefere-se indicar a LN2 do que a W2 para estudos de vazões mínimas na bacia hidrográfica do rio Iguaçu.Abstract: In extreme value theory analysis maximums, always attracts more attention than the minimums. There are still many details to be discovered and clarified to minimums in relation to the properties of distribution functions. The growing recognition of the importance of minimum flows for the viability of ecosystems, sustainability of the economy and as a sentinel of climate change, makes the minimum extremes study become increasingly important. The aim of this work is to offset in part the lack of theoretical treatment of extreme minimum and specifically minimum flows. The method has two approaches, the conventional analysis and the asymptotic analysis. In conventional analysis were adjusted the Weibull and Lognormal 2 parameters distributions to the series of annual minimum flows and minimum averages of 7 days. Then were applied the tests Qui-Square and Kolmogorov-Smirnov. The study of the asymptotic analysis was based on the paper of Gottschalk et al., 2013 and this research emphasis is given to the block method (BM). Two parent distributions here understood as the distributions of all average daily flow rates with power behavior for low flows are investigated: i) Gamma distribution; ii) Lognormal distribution. The aim is to demonstrate that these distributions belong to a minimum domain of attraction of the Weibull distribution, that is, minimal samples of these two distributions asymptotically tend to Weibull distribution. The theory studied in this thesis is applied to 11 gauged stations of the Iguaçu river basin with 48-year data series. From the conventional analysis it is concluded that the Lognormal distribution presents the best fit according to the ??2 test. However, for most stations Weibull distribution has also achieved a good fit with the same test. It was found that the Gamma distribution with respect to the minimum tends to a power function as a result of the Weibull distribution and the Lognormal presents no good fit for three stations of the Iguaçu River basin. This was not enough to reject the Lognormal distribution as a good candidate to model minimum flows, because of the parameters analysis. It was observed that the asymmetry of the average daily flow of the Iguaçu River basin gauged stations series is higher than the asymmetry of the Weibull distribution, and has good fit to Lognormal distribution. The parameters ??, ?? and ????, of the annual minimum flows modulated series, had goof fit to the Lognormal distribution. In accordance with the studies of conventional analysis is preferred to indicate the LN2 than W2 for studies of minimum flows in the catchment area of the Iguaçu River.Abstract: In extreme value theory analysis maximums, always attracts more attention than the minimums. There are still many details to be discovered and clarified to minimums in relation to the properties of distribution functions. The growing recognition of the importance of minimum flows for the viability of ecosystems, sustainability of the economy and as a sentinel of climate change, makes the minimum extremes study become increasingly important. The aim of this work is to offset in part the lack of theoretical treatment of extreme minimum and specifically minimum flows. The method has two approaches, the conventional analysis and the asymptotic analysis. In conventional analysis were adjusted the Weibull and Lognormal 2 parameters distributions to the series of annual minimum flows and minimum averages of 7 days. Then were applied the tests Qui-Square and Kolmogorov-Smirnov. The study of the asymptotic analysis was based on the paper of Gottschalk et al., 2013 and this research emphasis is given to the block method (BM). Two parent distributions here understood as the distributions of all average daily flow rates with power behavior for low flows are investigated: i) Gamma distribution; ii) Lognormal distribution. The aim is to demonstrate that these distributions belong to a minimum domain of attraction of the Weibull distribution, that is, minimal samples of these two distributions asymptotically tend to Weibull distribution. The theory studied in this thesis is applied to 11 gauged stations of the Iguaçu river basin with 48-year data series. From the conventional analysis it is concluded that the Lognormal distribution presents the best fit according to the ??2 test. However, for most stations Weibull distribution has also achieved a good fit with the same test. It was found that the Gamma distribution with respect to the minimum tends to a power function as a result of the Weibull distribution and the Lognormal presents no good fit for three stations of the Iguaçu River basin. This was not enough to reject the Lognormal distribution as a good candidate to model minimum flows, because of the parameters analysis. It was observed that the asymmetry of the average daily flow of the Iguaçu River basin gauged stations series is higher than the asymmetry of the Weibull distribution, and has good fit to Lognormal distribution. The parameters ??, ?? and ????, of the annual minimum flows modulated series, had goof fit to the Lognormal distribution. In accordance with the studies of conventional analysis is preferred to indicate the LN2 than W2 for studies of minimum flows in the catchment area of the Iguaçu River