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一种改进的地下水模型结构不确定性分析方法

孙晓卓 曾献奎 吴吉春 孙媛媛

孙晓卓, 曾献奎, 吴吉春, 孙媛媛. 一种改进的地下水模型结构不确定性分析方法[J]. 水文地质工程地质. doi: 10.16030/j.cnki.issn.1000-3665.202012061
引用本文: 孙晓卓, 曾献奎, 吴吉春, 孙媛媛. 一种改进的地下水模型结构不确定性分析方法[J]. 水文地质工程地质. doi: 10.16030/j.cnki.issn.1000-3665.202012061
SUN Xiaozhuo, ZENG Xiankui, WU Jichun, SUN Yuanyuan. An improved method of groundwater model structural uncertainty analysis[J]. Hydrogeology & Engineering Geology. doi: 10.16030/j.cnki.issn.1000-3665.202012061
Citation: SUN Xiaozhuo, ZENG Xiankui, WU Jichun, SUN Yuanyuan. An improved method of groundwater model structural uncertainty analysis[J]. Hydrogeology & Engineering Geology. doi: 10.16030/j.cnki.issn.1000-3665.202012061

一种改进的地下水模型结构不确定性分析方法

doi: 10.16030/j.cnki.issn.1000-3665.202012061
基金项目: 国家重点研发计划“场地土壤污染成因与治理技术”重点专项(2018YFC1800604);国家自然科学基金项目(42072272)
详细信息
    作者简介:

    孙晓卓(1998-),女,硕士研究生,主要从事地下水数值模拟研究。E-mail:1249879295@qq.com

    通讯作者:

    曾献奎(1985-),男,副教授,主要从事地下水数值模拟研究。E-mail:zengxiankui@yeah.net

  • 中图分类号: P641.2

An improved method of groundwater model structural uncertainty analysis

  • 摘要: 高斯过程回归(GPR)是一种基于贝叶斯理论的监督学习算法,在基于数据驱动(DDM)的模型结构不确定性分析中具有广泛应用。目前研究中通常假设物理参数和超参独立并进行联立识别,这会导致参数补偿。文章提出两步识别DDM量化模型结构误差,并通过2个地下水模型案例,分别在不考虑模型结构误差、考虑模型结构误差(联立识别DDM、两步识别DDM)的情况下,对比分析了参数识别和模型预测结果。结果表明,不考虑模型结构误差直接进行参数识别时,为补偿结构误差,物理参数会过度拟合,从而影响模型预测效果。基于DDM刻画模型结构偏差时,物理参数和超参的独立性假设会影响参数识别结果。提出的两步识别DDM法没有假设物理参数和超参独立,能够减少参数过度拟合效应,从而更准确刻画结构误差,有效提高了模型的预测性能。
  • 图  1  两步识别DDM法计算步骤图

    Figure  1.  Flow chart of the two-stage based DDM method

    图  2  模型识别和验证数据点的位置

    Figure  2.  Location of model observation wells during calibration and validation periods

    图  3  识别得到的模型参数和超参边缘后验分布

    Figure  3.  Identified marginal posterior distributions of model parameters and hyperparameters

    图  4  定流量非完整井流模型示意图

    Figure  4.  Diagrammatic representation of partially penetrating well pumping at a constant rate

    图  5  模型识别和验证数据点的位置

    Figure  5.  Location of model observation wells during calibration and validation periods

    图  6  识别得到的模型参数和超参边缘后验分布

    Figure  6.  Identified marginal posterior distributions of model parameters and hyperparameters

    表  1  模型参数的先验分布

    Table  1.   Prior distributions of model parameters

    参数先验分布
    Co/(mol·L−1Uniform on [45.0,52.0]
    V/(cm·d−1Uniform on [45.0,52.0]
    λGamma, k=5, θ=0. 2, on [0.1,0.8]
    σExponential, μ=0. 25, on [3.0,10.0]
    σδUniform on [0.1,0.5]
    下载: 导出CSV

    表  2  模型预测性能指标统计结果

    Table  2.   Statistics of model prediction performance

    识别期验证期
    RMSEMAEMRE RMSEMAEMRE
    不考虑结构误差4.60564.10560.19748.95836.76990.2279
    联立识别DDM5.31654.95210.22258.23566.38890.2240
    两步识别DDM4.65004.29160.20947.77705.62550.2068
    下载: 导出CSV

    表  3  模型参数的先验分布

    Table  3.   Prior distributions of model parameters

    参数先验分布
    Krr/(m·d−1Uniform on [8.0,14.0]
    M/dUniform on [75.0,90.0]
    λGamma, k=5, θ=0. 2, on [0.2,0.6]
    σExponential, μ=0. 25, on [5.0,10.0]
    σδUniform on [0.05,0.5]
    下载: 导出CSV

    表  4  模型预测性能指标统计结果

    Table  4.   Statistics of model prediction performance

    识别期验证期
    RMSEMAEMRE RMSEMAEMRE
    不考虑结构误差5.20843.55910.22263.57643.17280.4488
    联立识别DDM8.13807.98430.65761.89121.52490.2253
    两步识别DDM8.03907.78210.63151.71841.35890.1954
    下载: 导出CSV
  • [1] 薛禹群. 中国地下水数值模拟的现状与展望[J]. 高校地质学报,2010,16(1):1 − 6. [XUE Yuqun. Present situation and prospect of groundwater numerical simulation in China[J]. Geological Journal of China Universities,2010,16(1):1 − 6. (in Chinese with English abstract) doi:  10.3969/j.issn.1006-7493.2010.01.001
    [2] DUMEDAH G, WALKER J P. Assessment of model behavior and acceptable forcing data uncertainty in the context of land surface soil moisture estimation[J]. Advances in Water Resources,2017,101:23 − 36. doi:  10.1016/j.advwatres.2017.01.001
    [3] 高烨, 梁收运, 王申宁, 等. 地下水数值模拟不确定性分析研究进展[J]. 地下水,2020,42(1):28 − 31. [GAO Ye, LIANG Shouyun, WANG Shenning, et al. Research progress on uncertainty analysis of groundwater numerical simulation[J]. Ground Water,2020,42(1):28 − 31. (in Chinese with English abstract)
    [4] REFSGAARD J C, VAN DER SLUIJS J P, BROWN J, et al. A framework for dealing with uncertainty due to model structure error[J]. Advances in Water Resources,2006,29(11):1586 − 1597. doi:  10.1016/j.advwatres.2005.11.013
    [5] WATSON T A, DOHERTY J E, CHRISTENSEN S. Parameter and predictive outcomes of model simplification[J]. Water Resources Research,2013,49(7):3952 − 3977. doi:  10.1002/wrcr.20145
    [6] WU J C, ZENG X K. Review of the uncertainty analysis of groundwater numerical simulation[J]. Chinese Science Bulletin,2013,58(25):3044 − 3052. doi:  10.1007/s11434-013-5950-8
    [7] DOHERTY J, WELTER D. A short exploration of structural noise[J]. Water Resources Research,2010,46(5):W05525.
    [8] DOHERTY J, CHRISTENSEN S. Use of paired simple and complex models to reduce predictive bias and quantify uncertainty[J]. Water Resources Research,2011,47(12):W12534.
    [9] ERDAL D, NEUWEILER I, HUISMAN J A. Estimating effective model parameters for heterogeneous unsaturated flow using error models for bias correction[J]. Water Resources Research,2012,48(6):W06530.
    [10] WHITE J T, DOHERTY J E, HUGHES J D. Quantifying the predictive consequences of model error with linear subspace analysis[J]. Water Resources Research,2014,50(2):1152 − 1173. doi:  10.1002/2013WR014767
    [11] DRAPER D. Assessment and propagation of model uncertainty[J]. Journal of the Royal Statistical Society:Series B (Methodological),1995,57(1):45 − 70. doi:  10.1111/j.2517-6161.1995.tb02015.x
    [12] HOETING J A, MADIGAN D, VOLINSKY R C T. Bayesian model averaging: a tutorial[J]. Statistical Science,1999,14(4):382 − 401.
    [13] 杜新忠, 李叙勇, 王慧亮, 等. 基于贝叶斯模型平均的径流模拟及不确定性分析[J]. 水文,2014,34(3):6 − 10. [DU Xinzhong, LI Xuyong, WANG Huiliang, et al. Multi-model ensemble runoff simulation based on Bayesian model averaging method and model structure uncertainty analysis[J]. Journal of China Hydrology,2014,34(3):6 − 10. (in Chinese with English abstract) doi:  10.3969/j.issn.1000-0852.2014.03.002
    [14] 王亮. 贝叶斯模型平均方法研究综述与展望[J]. 技术经济与管理研究,2016(3):19 − 23. [WANG Liang. Overview and prospect of Bayesian model averaging[J]. Technoeconomics & Management Research,2016(3):19 − 23. (in Chinese with English abstract) doi:  10.3969/j.issn.1004-292X.2016.03.004
    [15] 王倩, 师鹏飞, 宋培兵, 等. 基于贝叶斯模型平均法的洪水集合概率预报[J]. 水电能源科学,2016,34(6):64 − 66. [WANG Qian, SHI Pengfei, SONG Peibing, et al. Multi-model ensemble flood probability forecasting based on BMA[J]. Water Resources and Power,2016,34(6):64 − 66. (in Chinese with English abstract)
    [16] 江善虎, 任立良, 刘淑雅, 等. 基于贝叶斯模型平均的水文模型不确定性及集合模拟[J]. 中国农村水利水电,2017(1):107 − 112. [JIANG Shanhu, REN Liliang, LIU Shuya, et al. An analysis of hydrological modeling and ensemble simulation uncertainty using the Bayesian model averaging[J]. China Rural Water and Hydropower,2017(1):107 − 112. (in Chinese with English abstract) doi:  10.3969/j.issn.1007-2284.2017.01.025
    [17] ROJAS R, FEYEN L, DASSARGUES A. Conceptual model uncertainty in groundwater modeling: Combining generalized likelihood uncertainty estimation and Bayesian model averaging[J]. Water Resources Research,2008,44(12):W12418.
    [18] LIU Z, MERWADE V. Separation and prioritization of uncertainty sources in a raster based flood inundation model using hierarchical Bayesian model averaging[J]. Journal of Hydrology,2019,578:124100. doi:  10.1016/j.jhydrol.2019.124100
    [19] LU D, YE M, CURTIS G P. Maximum likelihood Bayesian model averaging and its predictive analysis for groundwater reactive transport models[J]. Journal of Hydrology,2015,529(3):1859 − 1873.
    [20] CAO T T, ZENG X K, WU J C, et al. Integrating MT-DREAMzs and nested sampling algorithms to estimate marginal likelihood and comparison with several other methods[J]. Journal of Hydrology,2018,563:750 − 765. doi:  10.1016/j.jhydrol.2018.06.055
    [21] DEMISSIE Y K, VALOCCHI A J, MINSKER B S, et al. Integrating a calibrated groundwater flow model with error-correcting data-driven models to improve predictions[J]. Journal of Hydrology,2009,364(3/4):257 − 271.
    [22] KHALIL A, ALMASRI M N, MCKEE M, et al. Applicability of statistical learning algorithms in groundwater quality modeling[J]. Water Resources Research,2005,41(5):W05010.
    [23] TESORIERO A J, GRONBERG J A, JUCKEM P F, et al. Predicting redox-sensitive contaminant concentrations in groundwater using random forest classification[J]. Water Resources Research,2017,53(8):7316 − 7331. doi:  10.1002/2016WR020197
    [24] XU T F, VALOCCHI A J. A Bayesian approach to improved calibration and prediction of groundwater models with structural error[J]. Water Resources Research,2015,51(11):9290 − 9311. doi:  10.1002/2015WR017912
    [25] XU T F, VALOCCHI A J, YE M, et al. Quantifying model structural error: Efficient Bayesian calibration of a regional groundwater flow model using surrogates and a data-driven error model[J]. Water Resources Research,2017,53(5):4084 − 4105. doi:  10.1002/2016WR019831
    [26] PAN Y, ZENG X K, XU H X, et al. Assessing human health risk of groundwater DNAPL contamination by quantifying the model structure uncertainty[J]. Journal of Hydrology,2020,584:124690. doi:  10.1016/j.jhydrol.2020.124690
    [27] REICHERT P, SCHUWIRTH N. Linking statistical bias description to multiobjective model calibration[J]. Water Resources Research,2012,48(9):W09543.
    [28] BRYNJARSDÓTTIR J, OʼHAGAN A. Learning about physical parameters: the importance of model discrepancy[J]. Inverse Problems,2014,30(11):114007. doi:  10.1088/0266-5611/30/11/114007
    [29] KENNEDY M C, O'HAGAN A. Bayesian calibration of computer models[J]. Journal of the Royal Statistical Society:Series B Statistical Methodology,2001,63(3):425 − 464. doi:  10.1111/1467-9868.00294
    [30] RASMUSSEN C E, WILLIAMS C K I. Gaussian processes for machine learning[M]. Cambridge: MIT Press, 2006: 69-106.
    [31] VRUGT J A, BRAAK C J F T, DIKS C G H, et al. Accelerating Markov Chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling[J]. International Journal of Nonlinear Sciences & Numerical Simulation,2009,10(3):273 − 290.
    [32] LALOY E, VRUGT J A. High-dimensional posterior exploration of hydrologic models using multiple-try DREAM(ZS) and high-performance computing[J]. Water Resources Research,2012,50(3):182 − 205.
    [33] KASS R E, RAFTERY A E. Bayesian factors[J]. Journal of the American statistical association,1995,90(430):773 − 795. doi:  10.1080/01621459.1995.10476572
    [34] LIU P G, ELSHALL A S, YE M, et al. Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods[J]. Water Resources Research,2016,52(2):734 − 758. doi:  10.1002/2014WR016718
    [35] SMOLYAK S A. Quadrature and interpolation formulas for tensor products of certain classes of functions[J]. Soviet Math Dokl,1963(4):240 − 243.
    [36] MA X, ZABARAS N. An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations[J]. Journal of Computational Physics,2009,228(8):3084 − 3113. doi:  10.1016/j.jcp.2009.01.006
    [37] ZENG X K, YE M, BURKARDT J, et al. Evaluating two sparse grid surrogates and two adaptation criteria for groundwater Bayesian uncertainty quantification[J]. Journal of Hydrology,2016,535:120 − 134. doi:  10.1016/j.jhydrol.2016.01.058
    [38] 侯泽宇, 卢文喜, 王宇. 基于替代模型的地下水DNAPLs污染源反演识别[J]. 中国环境科学,2019,39(1):188 − 195. [HOU Zeyu, LU Wenxi, WANG Yu. Surrogate-based source identification of DNAPLs-contaminated groundwater[J]. China Environmental Science,2019,39(1):188 − 195. (in Chinese with English abstract) doi:  10.3969/j.issn.1000-6923.2019.01.021
    [39] 高鑫宇, 曾献奎, 吴吉春. 基于改进稀疏网格替代模拟的地下水DNAPLs运移不确定性分析[J]. 水文地质工程地质,2020,47(1):1 − 10. [GAO Xinyu, ZENG Xiankui, WU Jichun. Uncertainty analysis of groundwater DNAPLs migration based on improved sparse grids surrogate model[J]. Hydrogeology & Engineering Geology,2020,47(1):1 − 10. (in Chinese with English abstract)
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  • 收稿日期:  2020-12-15
  • 修回日期:  2021-02-18

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