Abstract
The fact that rainfall data are usually more abundant and more readily regionalized than streamflow data has motivated hydrologists to conceive methods that incorporate the hydrometeorologial information into flood frequency analyses. Some of them, particularly those derived from the French GRADEX method, involve assumptions concerning the relationship between extreme rainfall and flood volumes, under some distributional restrictions. In particular, for rainfall probability distributions exhibiting exponential-like upper tails, it is possible to derive the shape and scale of the probability distribution of flood volumes by hypothesizing the basic properties of such a relationship, under rare and/or extreme conditions. This paper focuses on a parametric mathematical model for the relationship between rare and extreme rainfall and flood volumes under exponentially-tailed distributions. The model is analyzed and fitted to rare and extreme events derived from hydrological simulation of long stochastically-generated synthetic series of rainfall and evaporation for the Indaiá River basin, located in south-central Brazil. The paper also provides a sensitivity analysis of the model parameters in order to better understand flood events under rare and extreme conditions. By working with hydrologically plausible hypothetical events, the modeling approach proved to be a useful way to explore extraordinary rainfall and flood events. The results from this exploratory analysis provide grounds to derive some conclusions regarding the relative positions of the upper tails of the probability distributions of rainfall and flood volumes.
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Acknowledgments
The authors wish to acknowledge the financial support to this research from the Brazilian National Council of Scientific and Technological Development (CNPq), through grant numbered 201526/2010-7 (PDE). The authors wish also to thank both anonymous reviewers for their valuable comments and suggestions.
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Naghettini, M., Gontijo, N.T. & Portela, M.M. Investigation on the properties of the relationship between rare and extreme rainfall and flood volumes, under some distributional restrictions. Stoch Environ Res Risk Assess 26, 859–872 (2012). https://doi.org/10.1007/s00477-011-0530-4
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DOI: https://doi.org/10.1007/s00477-011-0530-4