地下水流数值模拟概念模型的不确定性分析

Conceptual model is the main uncertainty source of groundwater numerical simulation. Recently, Bayesian Model Averaging (BMA) is widely used in uncertainty analysis of groundwater conceptual model. However, BMA method is hindered in practice application by several problems that include 1) how to construct complete plausible conceptual model set; 2) how to determine conceptual model's prior probability; 3) and the approximation of model's integrated likelihood measure. Therefore, this research is designed for these problems. Firstly, according to the analysis of field hydrogeological condition, the conceptual model set is established by permutation and combination method. Secondly, an improved classification tree method is developed to classify conceptual models, the prior probability is diluted within each model subset, and the optimum prior probability combination is identified by cross validation. Lastly, based on an advanced sampling algorithm, the conceptual model's integrated likelihood measure is estimated by MCMC (Markov Chain Monte Carlo) method. Therefore, the conceptual model uncertainty of groundwater numerical simulation can be effectively treated and assessed, and the efficiency and reliability of BMA predictive distribution is improved based on this project study. In addition, this research is able to provide theory support for groundwater conceptual model uncertainty analysis.

概念模型是地下水数值模拟不确定性的重要来源。贝叶斯模型平均(Bayesian Model Averaging, BMA)是当前处理概念模型不确定性的主要方法。然而，BMA方法在实际应用过程中存在以下几方面的问题：1) 如何建立完备的备择概念模型组；2) 如何确定概念模型的先验概率；3) 概念模型综合似然值的计算。针对这些问题，首先，本项目拟从场地水文地质信息的解析入手，采用排列组合的方式构建备择概念模型组。其次，利用改进的分类树分析方法对备择概念模型进行分组归类，进行先验概率的组内稀释，采用交叉验证的方法识别最优的先验概率组合。最后，利用MCMC(Markov Chain Monte Carlo)方法估计概念模型的综合似然值。因此，本研究拟通过改进及完善BMA方法的理论框架，提升BMA综合预测的效率与可靠性，从而为地下水数值模拟概念模型的不确定性分析提供理论支撑。

地下水数值模拟不确定性主要来自于模型参数、模型结构及观测数据，其中概念模型（模型结构）的不确定性已经受到水文地质工作者的重视。贝叶斯模型平均（Bayesian model averaging）是当前处理概念模型不确定性的主要方法。本项目针对BMA实际应用过程中面对的困难，分别在以下几个方面开展了工作，并取得了相关研究成果。（1）结合研究区的先验信息，通过不确定性条件的排列组合，基于复杂度控制理论，建立一组能够代表研究区水文地质基本特征的概念模型集合；（2）提出了一种基于Adaptive Metropolis的嵌套抽样算法（Nested sampling algorithm），能够对模型边缘似然值进行准确、高效的估计；（3）提出了一种基于自适应稀疏网格-随机配点法（Adaptive sparse grid-stochastic collocation）的替代模型技术，克服了地下水数值模拟概念模型不确定性分析中的计算耗时问题。总之，较好的按照执行计划完成了本项目，很好的完成了项目预期目标。