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Flood frequency analysis employing Bayesian regional regression and imperfect historical information.

机译：利用贝叶斯区域回归和不完善的历史信息进行洪水频率分析。

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This thesis focuses on development of a Bayesian methodology for analysis of regional Generalized Least Squares (GLS) regression models, and the use of regional regression models and imperfect historical and palaeoflood information to reduce the uncertainty in flood quantile estimators.; The first part of this thesis develops a Bayesian approach to flood frequency analysis with imperfect historical information. A Markov Chain Monte Carlo algorithm provides the posterior distributions of the parameters of lognormal and log Pearson Type 3 distributions, flood quantiles, and flood damage estimators. An example shows that the Bayesian approach provides a better description of the actual uncertainty in some flood quantiles and other functions of the parameters than asymptotic approximations that use the Fisher Information matrix. In addition, the Bayesian MCMC algorithm avoids the numerical problems the Maximum Likelihood procedure faces when fitting the LP3 distribution. The proposed MCMC algorithm provides a computationally and conceptually simple way of appropriately incorporating into flood frequency analysis the joint distribution of possible errors in rating curves and individual observations, which is clearly important when dealing with historical and paleoflood information.; The second part of the thesis, develops an operational Bayesian methodology for the Generalized Least Squares (GLS) model for regionalization of hydrologic data. The new approach allows computation of the posterior distributions of the parameters and the model-error variance using a convenient quasi-analytic approach. It provides both a measure of the precision of the model error variance that the traditional GLS lacks, and a more reasonable description of the possible values of the model error variance in cases where the model error variance is small compared to the sampling errors, which is often the case for regionalization of shape parameters. Examples illustrate the differences among Ordinary, Weighted, and GLS models, and the method-of-moments, maximum likelihood, and Bayesian estimators of the model error variance. A flood frequency analysis for three sites in the Illinois River basin illustrates the ability of regional information on the shape parameter to increase the precision of flood quantile estimators.
机译：本文的重点是开发一种用于分析区域广义最小二乘（GLS）回归模型的贝叶斯方法，以及使用区域回归模型和不完善的历史和古洪水信息来减少洪水分位数估计量的不确定性。本文的第一部分提出了一种具有不完善历史信息的贝叶斯洪水频率分析方法。马尔可夫链蒙特卡罗算法提供了对数正态和对数Pearson Type 3分布，洪水分位数和洪水破坏估计量的参数的后验分布。一个示例表明，与使用Fisher信息矩阵的渐近逼近相比，贝叶斯方法可以更好地描述某些洪水分位数和参数的其他函数中的实际不确定性。此外，贝叶斯MCMC算法避免了在拟合LP3分布时最大似然法面临的数值问题。提出的MCMC算法提供了一种在计算上和概念上简单的方法，可以将洪水等级分析中可能误差的联合分布适当地纳入洪水频率分析中，这在处理历史和古洪水信息时显然很重要。论文的第二部分为水文数据的区域化开发了广义最小二乘（GLS）模型的可操作贝叶斯方法。新方法允许使用方便的准分析方法计算参数的后验分布和模型误差方差。它既提供了传统GLS缺乏的模型误差方差的精度的度量，又提供了在模型误差方差与采样误差相比较小的情况下模型误差方差的可能值的更合理描述。形状参数区域化通常是这种情况。示例说明了普通模型，加权模型和GLS模型之间的差异，以及模型误差方差的矩量法，最大似然法和贝叶斯估计量。对伊利诺伊河流域三个地点的洪水频率分析表明，形状参数上的区域信息能够提高洪水分位数估计量的精度。

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