The Gumbel mixed model for flood frequency analysis
ABSTRACT Many hydrological engineering planning, design, and management problems require a detailed knowledge of flood event characteristics, such as flood peak, volume and duration. Flood frequency analysis often focuses on flood peak values, and hence, provides a limited assessment of flood events. This paper proposes the use of the Gumbel mixed model, the bivariate extreme value distribution model with Gumbel marginals, to analyze the joint probability distribution of correlated flood peaks and volumes, and the joint probability distribution of correlated flood volumes and durations. Based on the marginal distributions of these random variables, the joint distributions, the conditional probability functions, and the associated return periods are derived. The model is tested and validated using observed flood data from the Ashuapmushuan river basin in the province of Quebec, Canada. Results indicate that the model is suitable for representing the joint distributions of flood peaks and volumes, as well as flood volumes and durations.
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ABSTRACT: The North Coastal Region of the State of São Paulo, which comprises the Municipalities of Caraguatatuba, São Sebastião, Ilhabela and Ubatuba, is one of the most prone to flooding Brazilian areas, owing to hydrological extreme rainfall events usually coupled with extreme tidal levels. This risk is also high due to human lives and material assets, with increasing population rates and the settling of large Companies such as the Oil industry, with reduced defense measures and works. The catastrophic scenario of the city of Caraguatatuba, in March of 1967, resulted from one of the most serious natural disasters in Brazil, fosters discussions about probabilities of rainfall events and rise in the sea level in coastal areas. Hence, this research is a consequence of this reality. The research presented is founded on an innovative methodology based on the analysis of past data of rainfall stations and tidal stations in the region of the North coastal zone of the State of São Paulo (Brazil). The analysis developed approached the meteorological, hydraulic and statistical knowledge areas. Practical results were used for designing macro-drainage, fluvial and maritime projects, that associate the probability of occurrence of certain types of rainfall coupled with their corresponding increase in tidal levels.Journal of Climatology and Weather Forecasting. 08/2013; 1(1):5.
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ABSTRACT:  The information contained in hyetographs and hydrographs is often synthesized by using key properties such as the peak or maximum value Xp, volume V, duration D, and average intensity I. These variables play a fundamental role in hydrologic engineering as they are used, for instance, to define design hyetographs and hydrographs as well as to model and simulate the rainfall and streamflow processes. Given their inherent variability and the empirical evidence of the presence of a significant degree of association, such quantities have been studied as correlated random variables suitable to be modeled by multivariate joint distribution functions. The advent of copulas in geosciences simplified the inference procedures allowing for splitting the analysis of the marginal distributions and the study of the so-called dependence structure or copula. However, the attention paid to the modeling task has overlooked a more thorough study of the true nature and origin of the relationships that link , and I. In this study, we apply a set of ad hoc bootstrap algorithms to investigate these aspects by analyzing the hyetographs and hydrographs extracted from 282 daily rainfall series from central eastern Europe, three 5 min rainfall series from central Italy, 80 daily streamflow series from the continental United States, and two sets of 200 simulated universal multifractal time series. Our results show that all the pairwise dependence structures between , and I exhibit some key properties that can be reproduced by simple bootstrap algorithms that rely on a standard univariate resampling without resort to multivariate techniques. Therefore, the strong similarities between the observed dependence structures and the agreement between the observed and bootstrap samples suggest the existence of a numerical generating mechanism based on the superposition of the effects of sampling data at finite time steps and the process of summing realizations of independent random variables over random durations. We also show that the pairwise dependence structures are weakly dependent on the internal patterns of the hyetographs and hydrographs, meaning that the temporal evolution of the rainfall and runoff events marginally influences the mutual relationships of , and I. Finally, our findings point out that subtle and often overlooked deterministic relationships between the properties of the event hyetographs and hydrographs exist. Confusing these relationships with genuine stochastic relationships can lead to an incorrect application of multivariate distributions and copulas and to misleading results.Water Resources Research. 06/2013; 49(6).
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ABSTRACT: The North Coastal Region of the State of São Paulo, which comprises the Municipalities of Caraguatatuba, São Sebas-tião, Ilhabela and Ubatuba, is one of the most prone to flooding and debris flow deposition Brazilian areas, owing to hydrological extreme rainfall events usually coupled with extreme tidal levels. This risk is also high due to human lives and material assets, with increasing population rates and the establishment of large Companies such as the Oil industry, with reduced defense/prevention measures and works. The catastrophic scenario of the city of Caraguatatuba, in March 1967, resulting from one of the most serious natural disasters in Brazil, fosters discussions about probabilities of heavy rainfall-caused events and rise in the sea level in coastal areas. Hence, this research is a consequence of this reality. The research is founded on an innovative methodology based on the analysis of past data of rainfall and tidal stations, complemented with debris flow registers in the region of the North coastal zone of the State of São Paulo (Brazil). The analysis developed involved the meteorological, hydraulic, geotechnical and statistical knowledge areas. Practical results are intended to be used for urban planning, designs of macro-drainage, fluvial, maritime projects and debris flow retention structures. These practical applications will then associate the probability of occurrence of certain types of heavy rainfall-caused events such as flooding or debris flow coupled with a corresponding increase in tidal levels.International Journal of Geosciences 09/2013; 4(5B). · 0.26 Impact Factor