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: Bivariate distributions have been recently employed in hydrologic frequency analysis to analyze the joint probabilistic characteristics of multivariate storm events. This study aims to derive practical solutions of application for the bivariate distribution to estimate design rainfalls corresponding to the desired return periods. Using the Gumbel mixed model, this study constructed rainfall–frequency curves at sample stations in Korea which provide joint relationships between amount, duration, and frequency of storm events. Based on comparisons and analyses of the rainfall–frequency curves derived from univariate and bivariate storm frequency analyses, this study found that conditional frequency analysis provides more appropriate estimates of design rainfalls as it more accurately represents the natural relationship between storm properties than the conventional univariate storm frequency analysis.Stochastic Environmental Research and Risk Assessment 01/2010; 24(3):389-397. · 1.96 Impact Factor
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ABSTRACT: Extreme weather and climatic events can have detrimental effects on society. The coincidence of several factors, themselves not necessarily extreme, can have similar adverse implications, such as a combination of high spring-time temperatures and heavy rainfall. A combination of high temperature and heavy precipitation during spring can produce flooding when run-off due to snow-melt adds to river discharge from the rainfall. Such combined events are often referred to as ‘complex extremes’ (IPCC, Climate change 2001: impact, adaptation andvulnerability. Summary for policymakers. WMO, Geneva, Switzerland, p. 7, 2001) . A likely effect of a climate change is a shift in the frequency of both extremes in traditional sense as well as in complex extreme events. Results from a global climate model were downscaled through a higher-resolution nested regional climate model in order to obtain more realistic descriptions of regional climatic features in Norway. Empirically-based joint frequency distributions (two dimensional histograms) were used to study shifts in the frequency of complex extremes. A slight shift in the joint frequency distributions for spring-time temperature-and-rainfall was detected in downscaled results with HIRHAM from a transient integration with the ECHAM4/OPYC3 climate model following the IS92a emission scenario. The analysis involved values that spanned between ordinary and extreme values of the bivariate distributions complicating the estimation of a representative confidence interval as the data fall in the zone between different types of behaviour. The results from HIRHAM were spatially interpolated and compared with station observations, and substantial biases were revealed, however, the apparent model discrepancy is largely due to great small-scale variability due to a complex physiography. The general temporal trends predicted by the model are nevertheless realistic.Climatic Change 11/2007; 85(3):381-406. · 3.63 Impact Factor