Flood Frequency Analysis and Uncertainty Assessment Based on Bayesian MCMC Method
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摘要: 洪水设计值的计算和不确定性评估是水利工程规划和水资源管理的一个重要课题。以广义极值分布（GEV）作为洪水频率分布线型，通过基于Metropolis-Hastings抽样的贝叶斯马尔科夫链蒙特卡洛（MCMC）方法估计GEV分布参数和洪水设计值的后验概率分布，据此推求不同重现期条件下洪水设计值的点估计和区间估计。结果表明：贝叶斯MCMC方法的参数拟合效果与极大似然估计法相当，但由于其后验概率分布包含参数估计引起的不确定性，在洪水设计值不确定性评估上更有优势；贝叶斯MCMC方法得到的置信区间上限与估计值的距离大于下限与估计值的距离，这种不对称性相比于传统方法所得结果更贴近于实际，使得洪水频率分析结果的可靠性进一步提高。Abstract: The calculation of design flood value and uncertainty assessment is an important subject of hydraulic engineering planning and water resources management. Taking thegGeneralized extreme value (GEV) distribution as the flood frequency distribution line type, the Bayesian Markov chain Monte Carlo (MCMC) method based on Metropolis-Hastings algorithm was employed to evaluate the GEV distribution parameters and posterior probability distributions of the design flood values, and the point estimations and interval estimations of flood design values under different return periods were deduced. The results show that the effect of parameter fitting with Bayesian MCMC method is similar to that from the maximum likelihood estimation (MLE). However, because the posterior probability distribution contains the uncertainty caused by parameter estimation, Bayesian MCMC methods has more advantages in evaluation of the uncertainty of flood design value. The length between upper confidence limits and estimated values are greater than that of the lower confidence limits and estimated values, this asymmetry is more realistic than that from the traditional method, which further improves the reliability of the flood frequency analysis results.
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Keywords:
- flood frequency analysis /
- GEV distribution /
- MCMC /
- Bayesian theory
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百度学术
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