基于高斯过程回归的地下水模型结构不确定性分析与控制
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摘要
目前针对模型结构不确定性的研究方法主要为贝叶斯模型平均方法,而该方法受到模型权重计算困难等影响,应用受限。基于数据驱动的模型结构误差统计学习方法最近得到关注。研究采用高斯过程回归方法对地下水模型结构误差进行统计模拟,并将DREAMzs算法与高斯过程回归相结合,对地下水模型和统计模型的参数同时进行识别。基于此方法,分别以理想岩溶裂隙海水入侵过程和溶质运移柱体实验为例,进行地下水数值模拟及预测结果的不确定性分析。相对于不考虑模型结构误差条件的不确定性分析,结果表明,考虑结构误差之后,能够明显减少参数识别过程中的参数补偿影响,且能显著提高模型的预测性能。因此,基于高斯过程回归的模型结构不确定性分析可以一定程度控制地下水数值模拟的不确定性,提高模型预测可靠性。
Nowadays,the main analysis method for groundwater model structural uncertainty is the Bayesian model averaging(BMA) method.But BMA suffers from the difficulty of model weight estimation,which makes its application infeasible.More attention is recently paid to the data-driven based model structural error analysis method.In this paper,the groundwater model structural error is statistically learnt based on Gaussian process regression,and then the parameters of the groundwater model and statistical model are identified simultaneously by combining the DREAMzs and Gaussian process regression algorithms.With this method,the uncertainty of groundwater model parameters and prediction results are analyzed.In addition,a synthetic numerical simulation of seawater intrusion in a karst fissure area and a solute transport column experiment are taken as case studies.In contrast with the uncertainty analysis without considering the model structural error,the impact of parameter compensation is significantly reduced by considering the model structural error.Moreover,the model prediction performance is also improved.Therefore,based on the model structural uncertainty analysis method proposed in this paper,the uncertainty of groundwater modeling can be reduced tosome extent,as well the reliability of groundwater model prediction can be improved.
Nowadays,the main analysis method for groundwater model structural uncertainty is the Bayesian model averaging(BMA) method.But BMA suffers from the difficulty of model weight estimation,which makes its application infeasible.More attention is recently paid to the data-driven based model structural error analysis method.In this paper,the groundwater model structural error is statistically learnt based on Gaussian process regression,and then the parameters of the groundwater model and statistical model are identified simultaneously by combining the DREAMzs and Gaussian process regression algorithms.With this method,the uncertainty of groundwater model parameters and prediction results are analyzed.In addition,a synthetic numerical simulation of seawater intrusion in a karst fissure area and a solute transport column experiment are taken as case studies.In contrast with the uncertainty analysis without considering the model structural error,the impact of parameter compensation is significantly reduced by considering the model structural error.Moreover,the model prediction performance is also improved.Therefore,based on the model structural uncertainty analysis method proposed in this paper,the uncertainty of groundwater modeling can be reduced tosome extent,as well the reliability of groundwater model prediction can be improved.
引文
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[22]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):257-271.
[23]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.
[24]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.
[25]CARRERA J,NEUMAN S P.Estimation of aquifer parameters under transient and steady state conditions:1.maximum likelihood method incorporating prior information[J].Water Resources Research,1986,22(2):199-210.
[26]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.
[27]RASMUSSEN C,WILLIAMS C.Gaussian processes for machine learning[M].Cambridge:MIT Press,2006:69-106.
[28]LANGEVIN C D,THORNE J R D T,DAUSMAN AM,et al.SEAWAT version 4:A computer program for simulation of multi-species solute and heat transport[R].Reston,Virginia:US Geological Survey,2008.
[29]BRYNJARSDTTIR J,O'HAGAN A.Learning about physical parameters:the importance of model discrepancy[J].Inverse Problems,2014,30(11):.
[30]LV X,GAO B,SUN Y,et al.Effects of grain size and structural heterogeneity on the transport and retention of nano-TiO2in saturated porous media[J].Science of The Total Environment,2016,563/564:987-995.
[31]HARBAUGH A W.MODFLOW-2005,the USGeological Survey modular groundwater model-the groundwater flow process[R].Reston:US Geological Survey,2005.
[32]ZHENG C,WANG P P.MT3DMS:A modular ThreeDimensional multispecies transport model for simulation of advection,dispersion and chemical reactions of contaminants in groundwater systems[R].Vicksburg,Mississippi:US Army Engineer Research and Development Center,1999.
[33]BENSON D A,SCHUMER R,MEERSCHAERT MM,et al.Fractional dispersion,Lévy Motion,and the MADE tracer tests[J].Transport in Porous Media,2001,42(1/2):211-240.
[2]吴吉春,陆乐.地下水模拟不确定性分析[J].南京大学学报(自然科学版),2011,47(3):227-234.[WU J C,LU L.Uncertainty analysis for groundwater modeling[J].Journal of Nanjing University(Natural Sciences),2011,47(3):227-234.(in Chinese)]
[3]WATSON T A,DOHERTY J E,CHRISTENSEN S.Parameter and predictive outcomes of model simplification[J].Water Resources Research,2013,49(7):3952-3977.
[4]WU J C,ZENG X K.Review of the uncertainty analysis of groundwater numerical simulation[J].Chinese Science Bulletin,2013,58(25):3044-3052.
[5]束龙仓,朱元生.地下水资源评价中的不确定性因素分析[J].水文地质工程地质,2000,27(6):6-8.[SHU L C,ZHU Y S.Analysis of uncertainties in groundwater resource evaluation[J].Hydrogeology&Engineering Geology,2000,27(6):6-8.(in Chinese)]
[6]束龙仓,陶玉飞,刘佩贵.考虑水文地质参数不确定性的地下水补给量可靠度计算[J].水利学报,2008,39(3):346-350.[SHU L C,TAO Y F,LIUP G.Reliability calculation method for groundwater recharge in consideration of uncertainty of hydrogeological parameters[J].Journal of Hydraulic Engineering,2008,39(3):346-350.(in Chinese)]
[7]KUNSTMANN H,KINZELBACH W,SIEGFRIED T.Conditional first-order second-moment method and its application to the quantification of uncertainty in groundwater modeling[J].Water Resources Research,2002,38(4):1-6.
[8]DETTINGER M D,WILSON J L.First order analysis of uncertainty in numerical models of groundwater flow part:1.Mathematical development[J].Water Resources Research,1981,17(1):149-161.
[9]于勇,翟远征,郭永丽,等.基于不确定性的地下水污染风险评价研究进展[J].水文地质工程地质,2013,40(1):115-123.[YU Y,ZHAI Y Z,GUO Y L,et al.Risk assessment of groundwater pollution based on uncertainty[J].Hydrogeology&Engineering Geology,2013,40(1):115-123.(in Chinese)]
[10]BEVEN K,BINLEY A.The future of distributed models-model calibration and uncertainty prediction[J].Hydrological Processes,1992,6(3):279-298.
[11]HASSAN A E,BEKHIT H M,CHAPMAN J B.Using Markov Chain Monte Carlo to quantify parameter uncertainty and its effect on predictions of a groundwater flow model[J].Environmental Modelling&Software,2009,24(6):749-763.
[12]HASSAN A E,BEKHIT H M,CHAPMAN J B.Uncertainty assessment of a stochastic groundwater flow model using GLUE analysis[J].Journal of Hydrology,2008,362(1):89-109.
[13]陆乐,吴吉春,陈景雅.基于贝叶斯方法的水文地质参数识别[J].水文地质工程地质,2008,35(5):58-63.[LU L,WU J C,CHEN J Y.Identification of hydrogeological parameters based on the Bayesian method[J].Hydrogeology&Engineering Geology,2008,35(5):58-63.(in Chinese)]
[14]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,2011,10(3):273-290.
[15]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.
[16]SADEGH M,VRUGT J A.Approximate Bayesian Computation using Markov Chain Monte Carlo simulation:DREAM(ABC)[J].Water Resources Research,2015,50(8):6767-6787.
[17]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(48):2061-2066.
[18]DOHERTY J,WELTER D.A short exploration of structural noise.[J].Water Resources Research,2010,46(5):W5525.
[19]NEUMAN S P.Maximum likelihood Bayesian averaging of uncertain model predictions[J].Stochastic Environmental Research&Risk Assessment,2003,17(5):291-305.
[20]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.
[21]PARRISH M A,MORADKHANI H,DECHANT CM.Toward reduction of model uncertainty:Integration of Bayesian model averaging and data assimilation[J].Water Resources Research,2012,48(3):3519.
[22]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):257-271.
[23]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.
[24]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.
[25]CARRERA J,NEUMAN S P.Estimation of aquifer parameters under transient and steady state conditions:1.maximum likelihood method incorporating prior information[J].Water Resources Research,1986,22(2):199-210.
[26]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.
[27]RASMUSSEN C,WILLIAMS C.Gaussian processes for machine learning[M].Cambridge:MIT Press,2006:69-106.
[28]LANGEVIN C D,THORNE J R D T,DAUSMAN AM,et al.SEAWAT version 4:A computer program for simulation of multi-species solute and heat transport[R].Reston,Virginia:US Geological Survey,2008.
[29]BRYNJARSDTTIR J,O'HAGAN A.Learning about physical parameters:the importance of model discrepancy[J].Inverse Problems,2014,30(11):.
[30]LV X,GAO B,SUN Y,et al.Effects of grain size and structural heterogeneity on the transport and retention of nano-TiO2in saturated porous media[J].Science of The Total Environment,2016,563/564:987-995.
[31]HARBAUGH A W.MODFLOW-2005,the USGeological Survey modular groundwater model-the groundwater flow process[R].Reston:US Geological Survey,2005.
[32]ZHENG C,WANG P P.MT3DMS:A modular ThreeDimensional multispecies transport model for simulation of advection,dispersion and chemical reactions of contaminants in groundwater systems[R].Vicksburg,Mississippi:US Army Engineer Research and Development Center,1999.
[33]BENSON D A,SCHUMER R,MEERSCHAERT MM,et al.Fractional dispersion,Lévy Motion,and the MADE tracer tests[J].Transport in Porous Media,2001,42(1/2):211-240.