Impact of Distribution Type in Bayes Probability Flood Forecasting

Li, Wei; Zhou, Jianzhong; Sun, Huaiwei; Feng, Kuaile; Zhang, Hairong; Tayyab, Muhammad

doi:10.1007/s11269-016-1557-6

Cited by 16 publications

(6 citation statements)

References 50 publications

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“…The cumulative distribution expressions are shown in Table 1, let u, v be random variables; Φ is known as a generator function of the copula and Φ −1 is the inverse of Φ; θ is the copula parameter. More details on the theoretical properties of various copulas can also be found in [55].…”

Section: Copula Functionmentioning

confidence: 99%

Using the Apriori Algorithm and Copula Function for the Bivariate Analysis of Flash Flood Risk

Zhong

Wang

Jiang

et al. 2020

Water

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Flash flooding is a phenomenon characterized by multiple variables. Few studies have focused on the extracted variables involved in flash flood risk and the joint probability distribution of the extracted variables. In this paper, a novel methodology that integrates the Apriori algorithm and copula function is presented and used for a flood risk analysis of Arizona in the United States. Due to the various rainfall indices affecting the flash flood risk, when performing the Apriori algorithm, the accumulated 3-h rainfall and accumulated 6-h rainfall were extracted as the most fitting rainfall indices. After comparing the performance of copulas, the Frank copula was found to exhibit the best fit for the flash flood hazard; thus, it was used for a bivariate joint probability analysis. The bivariate joint distribution functions of P–Q, PA–Q, PB–Q, and D–Q were established, and the results showed an increasing trend of flash flood risk with increases in the rainfall indices and peak flow; however, the risk displayed the least significant relation with the duration of the flash flood. These results are expected to be useful for risk analysis and decision making regarding flash floods.

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Section: Copula Functionmentioning

confidence: 99%

Using the Apriori Algorithm and Copula Function for the Bivariate Analysis of Flash Flood Risk

Zhong

Wang

Jiang

et al. 2020

Water

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“…The Bayesian forecasting system (BFS) provides an ideal theoretical framework that could be developed for different purposes using the probabilistic forecasting of inputs via any deterministic hydrologic model (Krzysztofowicz 1999;Biondi and De Luca, 2013a, b;Han et al 2014). The hydrologic uncertainty processor (HUP), a key part of Bayesian probability prediction, was created under the assumption that rainfall was certain, which could simultaneously quantify the uncertainty of the hydrologic model and parameters (Krzysztofowicz and Maranzano 2004;Maranzano and Krzysztofowicz 2004;Li et al 2017;Feng et al 2019).…”

Section: Introductionmentioning

confidence: 99%

A Hydrologic Uncertainty Processor Using Linear Derivation in the Normal Quantile Transform Space

Zhou

Feng

Liu

et al. 2020

Water Resour Manage

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Hydrological forecasting plays an important role in basin flood control systems, and the uncertainty of hydrological forecasting is helpful to reveal basin hydrological characteristics and provide support to decision makers in formulating water resources management schemes. The hydrologic uncertainty processor (HUP) has been widely employed in hydrological uncertainty prediction. However, in the HUP normal quantile transform (NQT) space, the posteriori distribution is derived from the Bayesian theory. This increases the difficulty of the theory and calculations. In this paper, a new method is proposed to deduce the posterior residual equation, and the HUP-Gaussian mixture model (HUP-GMM) is adopted to simplify the calculations. By maintaining the original hypothesis, since the posterior residual is known to follow a normal distribution, the posterior linear correlation equation can be directly assumed without prior and likelihood inferences. In particular, the complex Bayesian inference is replaced with simple linear equations. By converting the linear equation into the original space, we obtain a new method consisting of the HUP linear GMM (HUP-LG). In the study area, the parameters of the HUP-LG and HUP-GMM in the NQT space are calculated, and corresponding expressions of the probability density in the original space are obtained. The results reveal that the HUP-LG simplifies the calculation process in the NQT space, and attains the same performance as that of the HUP-GMM.

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“…The Bayesian forecasting system (BFS) provides an ideal theoretical framework that could be developed for different purposes using probabilistic forecasting of inputs via any deterministic hydrological model (Krzysztofowicz 1999). The hydrological uncertainty processor (HUP), a key part of Bayesian probability prediction, was created under the assumption that rainfall was certain, which could simultaneously quantify the uncertainty of the hydrological model and parameters (Li et al 2017).…”

Section: Introductionmentioning

confidence: 99%

Hydrological Uncertainty Processor (HUP) with Estimation of the Marginal Distribution by a Gaussian Mixture Model

Feng

Zhou

Liu

et al. 2019

Water Resour Manage

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Uncertainty assessments of hydrological prediction results can reflect additional hydrological information and reveal important hydrological characteristics of river basins, which is of great significance to disaster prevention and reduction. The hydrological uncertainty processor (HUP), which is a key part of the Bayesian forecasting system (BFS), has derived a variety of methods for hydrological uncertainty forecasting. The HUP allows for any form of marginal distributions of hydrological data and does not require a unified estimation structure for the marginal distribution function. The Gaussian mixture model (GMM) is a probability distribution estimation model that can approximate any probability distribution with arbitrary precision. In this paper, the GMM was used to estimate the marginal distribution of observed and modelled data, and this method is called HUP-GMM. The uncertainty of river discharge at the Yichang hydrological station on the main stem of the Yangtze River in China is predicted by the HUP-GMM. The Weibull and Gamma distributions, which are commonly used hydrological probability distributions, are compared to analyse the performance of the GMM. In June, when the measured flow h 3 is 13,850 m 3 /s and the GMM, Gamma and Weibull distributions are used, the prior probabilities are 1.63E-04, 1.05E-04 and 9.50E-05 and the posterior probabilities are 2.57E-04, 1.61E-04 and 1.38E-04, respectively. In September, when the measured flow h 3 is 35,400 m 3 /s and the GMM, Gamma and Weibull distributions are used, the prior probabilities are 5.98E-05, 2.21E-05 and 2.18E-05 and the posterior probabilities are 1.64E-04, 9.15E-05 and 8.43E-05, respectively. The results show that the performance of the uncertainty estimation of the prior and posterior probability distributions in the HUP-GMM has been improved.

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Impact of Distribution Type in Bayes Probability Flood Forecasting

Cited by 16 publications

References 50 publications

Using the Apriori Algorithm and Copula Function for the Bivariate Analysis of Flash Flood Risk

Using the Apriori Algorithm and Copula Function for the Bivariate Analysis of Flash Flood Risk

A Hydrologic Uncertainty Processor Using Linear Derivation in the Normal Quantile Transform Space

Hydrological Uncertainty Processor (HUP) with Estimation of the Marginal Distribution by a Gaussian Mixture Model

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