基于MCMC和ES-MDA方法的地下水数值模型非均质参数场及开采量的反演研究  

Inversion of heterogeneous parameter field and extraction amount of groundwater numerical model based on MCMC and ES-MDA methods

作　　者：刘墉达 陈喜 高满 孟详博 刘维翰 黄日超 LIU Yongda;CHEN Xi;GAO Man;MENG Xiangbo;LIU Weihan;HUANG Richao(Institute of Surface-Earth System Science,School of Earth System Science,Tianjin University,Tianjin 300072,China)

机构地区：[1]天津大学地球系统科学学院表层地球系统科学研究院,天津300072

出　　处：《水利学报》2023年第10期1236-1247,共12页Journal of Hydraulic Engineering

基　　金：国家自然科学基金重点项目(U21A2004)。

摘　　要：马尔科夫链蒙特卡罗方法(MCMC)和多重数据同化集合平滑器方法(ES-MDA)近年来在地下水参数反演得到广泛应用,但对三维多层非均质含水层参数反演精度和计算效率还缺乏对比分析。本文构建了含有基于Karhunen-Loève展开的非均质参数场的潜水和多层承压水含水层案例,并建立了地下水数值模型和基于Kriging方法的替代模型,模拟含水层分层水头变化,探讨了基于替代模型的MCMC、替代模型和数值模型相结合的两阶段MCMC以及ES-MDA方法反演的含水层渗透系数以及开采量。结果表明,针对本文算例,在非均质参数和开采量的反演中,相比而言,两阶段MCMC反演参数精度更高,ES-MDA方法计算效率更高。本研究为地下水数值模型参数反演方法选择提供参考依据。Markov chain Monte Carlo(MCMC)method and Ensemble Smoother Multiple Data Assimilation(ES-MDA)methods have been widely used in groundwater parameter inversion in recent years,but the accuracy and computational efficiency of three-dimensional multi-layer heterogeneous aquifer parameter inversion are still lacking comparative analysis.To this end,we construct a case study of underwater and multilayer confined water aquifers with heterogeneous parameter fields based on Karhunen-Loeve expansion,and establish a numerical groundwater model and an alternative model based on Kriging method to simulate the variation of water head in layers of aquifers.The permeability coefficient and recovery of aquifer obtained from the MCMC based on the alternative model,the two-stage MCMC based on the combination of the alternative model and the numerical model,and the ES-MDA method are discussed.The results show that the two-stage MCMC inversion parameter has the highest accuracy and the ES-MDA method has the highest computational efficiency in the inversion of heterogeneous parameters and mining quantity.This study provides reference for the selection of parameter inversion method of groundwater numerical model.

关 键 词：MCMC算法 ES-MDA算法 替代模型 地下水参数 地下水数值模拟 

分 类 号：TV123[水利工程—水文学及水资源]