Bayesian Analysis for Uncertainty and Risk in a Groundwater Numerical Model's Predictions
Bayesian Analysis for Uncertainty and Risk in a Groundwater Numerical Model's Predictions
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DOI：
10.1080/10807039.2011.618419
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发表时间：
2011-11
期刊：
影响因子：
--
通讯作者：
Jichun Wu;Le Lu;Tian Tang
中科院分区：
文献类型：
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作者：
Jichun Wu;Le Lu;Tian Tang
地下水模拟通常依赖于一些假设和近似的现实，因为真实的水文系统远比我们可以用数学描述的复杂。在对实际问题进行模型预测的不确定性分析时，这类模型的误差是不可忽略的。随着规模和复杂性的增加，相关的不确定性急剧增加。在这项研究中，贝叶斯不确定性分析方法的确定性模型的预测。从场地特征中获得的水文地质参数的地质统计学被视为贝叶斯定理中的先验参数分布。然后，马尔可夫链蒙特卡罗方法被用来产生后验统计分布的模型的预测，观测到的水文系统的行为的条件。最后，通过将该方法应用于MODFLOW抽水试验模型，给出了一系列合成实例，以测试其能力和效率，以评估模型预测不确定性的各种来源。模型的参数敏感性，简化和观测误差的影响，预测不确定性进行评估。对结果进行统计分析，以提供具有相关预测误差的确定性预测。根据贝叶斯结果进行风险分析，绘制权衡曲线，为地下水资源开采决策提供参考。
ABSTRACT Groundwater modeling typically relies on some hypothesis and approximations of reality, as the real hydrologic systems are far more complex than we can mathematically characterize. This kind of a model's errors cannot be neglected in the uncertainty analysis for a model's predictions in practical issues. As the scale and complexity increase, the associated uncertainties boost dramatically. In this study, a Bayesian uncertainty analysis method for a deterministic model's predictions is presented. The geostatistics of hydrogeologic parameters obtained from site characterization are treated as the prior parameter distribution in the Bayes’ theorem. Then the Markov-Chain Monte Carlo method is used to generate the posterior statistical distribution of the model's predictions, conditional to the observed hydrologic system behaviors. Finally, a series of synthetic examples are given by applying this method to a MODFLOW pumping test model, to test its capability and efficiency in order to assess various sources of the model's prediction uncertainty. The impacts of the model's parameter sensitivity, simplification, and observation errors to predict uncertainty are evaluated, respectively. The results are analyzed statistically to provide deterministic predictions with associated prediction errors. Risk analysis is also derived from the Bayesian results to draw tradeoff curves for decision-making about exploitation of groundwater resources.