Article

# Application of Bayesian approach to hydrological frequency analysis

Department of Geosciences, University of Nevada, Las Vegas, NV 89154, USA

Science China Technological Sciences (Impact Factor: 1.11). 05/2011; 54(5):1183-1192. DOI: 10.1007/s11431-010-4229-4 - [Show abstract] [Hide abstract]

**ABSTRACT:**To develop national economy and use the water resources and hydropower resources sufficiently, a lot of high arch dams, with the height of more than 200 m, have been and will be built in China. Although arch dams have good mechanical behavior, there is still failure possibility due to the huge water pressure and high stress level in dam, complex topographic and geologic conditions, formidable environment and high intensity earthquake. As one of the three main aspects concerning the safety of high arch dam, the study on global destruction, has been elaborated in the literatures, and research advance in the other two aspects, namely the failure risk and local damage of high arch dams, will be reviewed in this paper. In recent years, the failure risk of high arch dams has been investigated, and the model for identifying dam failure risk factors has been established. It is shown that the foundation deterioration and strong earthquake are the major risk sources for high dam failure. With the fault tree method, the failure mode and failure probability of high arch dams are studied, and the principle for determining failure mode and the method of calculating failure probability are proposed. Meanwhile, the determination principle of acceptable risk standard for high arch dam was proposed, and the acceptable risk rate and the acceptable standard value of various risk losses were given. For the local damage of arch dam, it is pointed out that the local damage belongs to the strength failure at material level. The study on local failure mechanism of arch dam is reviewed, based on the theories that from traditional strength theory to damage mechanics and meso-mechanics theory. Aiming at the cracking, the main pattern of local failure of high concrete dam, the research advances in the analysis methods and cracking criteria for smeared crack model and discrete crack model are summarized, and the research findings of preventive measures for local failure are shown.Chinese Science Bulletin 12/2012; 57(36). · 1.37 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**As an important tool for the description and analysis of hydrological processes, the watershed hydrological model has been increasingly applied to watershed hydrological simulations and water resource management. However, in most cases, model parameters are only determined in a calibration scheme which fits the modeled data to observations, thus significant uncertainties exist in the model parameters. How to quantitatively evaluate the uncertainties in model parameters and the resulting uncertainty impacts on model simulations has always been a question which has attracted much attention. In this study, two methods based on the bootstrap method (specifically, the model-based bootstrap and block bootstrap) are used to analyze the parameter uncertainties in the case of the SWAT (Soil and Water Assessment Tool) model applied to a hydrological simulation of the Dongliao River Watershed. Then, the uncertainty ranges of five sensitivity parameters are obtained. The calculated variation coefficients and the variable parameter contributions show that, among the five parameters, ESCO and CN2 have relatively high uncertainties: the variation coefficients and contribution rates are 23.98 and 70%, 14.43 and 18%, respectively. The three remaining parameters have relatively low uncertainties. We compare the two uncertainty ranges of parameters acquired by the two bootstrap methods, and find that the uncertainty ranges of parameters acquired by the block bootstrap are narrower than those acquired by the model-based bootstrap. Further analysis of the effects of parameter uncertainties on the model simulation reveals that the parameter uncertainties have great impacts on results of the model simulation, and in the model calibration stage 60%–70% of runoff observations were within the corresponding 95% confidence interval. The uncertainty in the model simulation during the flood season (i.e. the wet period) is relatively higher than that during the dry season.Science China Technological Sciences 01/2013; 57(1). · 1.11 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The hydrological frequency analysis (HFA) is the foundation for the hydraulic engineering design and water resources management. Hydrological extreme observations or samples are the basis for HFA; the representativeness of a sample series to the population distribution is extremely important for the estimation reliability of the hydrological design value or quantile. However, for most of hydrological extreme data obtained in practical application, the size of the samples is usually small, for example, in China about 40 ∼ 50 years. Generally, samples with small size cannot completely display the statistical properties of the population distribution, thus leading to uncertainties in the estimation of hydrological design values. In this paper, a new method based on bootstrap is put forward to analyze the impact of sampling uncertainty on the design value. By bootstrap resampling technique, a large number of bootstrap samples are constructed from the original flood extreme observations; the corresponding design value or quantile is estimated for each bootstrap sample, so that the sampling distribution of design value is constructed; based on the sampling distribution, the uncertainty of quantile estimation can be quantified. Compared with the conventional approach, this method provides not only the point estimation of a design value but also quantitative evaluation on uncertainties of the estimation.Mathematical Problems in Engineering 06/2013; 2013. · 1.08 Impact Factor

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