地面沉降模型的参数全局敏感性
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摘要
为了提高地面沉降模型(COMPAC模型)参数自动校正(或反演)的效率,降低不确定性,使用Sobol'全局敏感性分析方法,以静态和动态的方式分别计算上海市地面沉降模型中5个参数(弱透水层渗透系数、塑性贮水率、弹性贮水率、前期最低水位和含水层贮水率)的一阶、交互和总敏感度,讨论不同变形阶段和参数区间对敏感度计算结果的影响,得出以下结论. 1)含水层贮水率的敏感度较小,说明该参数对模拟结果的影响有限,该模型不能准确地反演该参数. 2)各参数敏感度在不同变形阶段存在明显的差异,在弹性变形阶段,土层变形量主要受弱透水层弹性贮水率的影响;塑性变形阶段变形量主要受弱透水层塑性贮水率、渗透系数和前期最低水位的影响,说明模型可在弹性变形和塑性变形2个阶段分别校正参数. 3)模型参数的交互敏感度较大,但通过分析观测数据,确定参数的合理区间,可以减小交互敏感度,即减小了"异参同效"性,降低了参数校正或反演的不确定性.
Sobol' method was used to conduct a global sensitivity analysis of five parameters in the land subsidence model of Shanghai city in order to reduce the model uncertainty and enhance efficiency of the calibration(or inversion) on land subsidence model. The parameters were as follows: Kv(vertical hydraulic conductivity of the aquitards), Sskv(aquitard nonrecoverable skeletal specific storage), Sske(aquitard recoverable skeletal specific storage), PPmax(initial preconsolidation stress within the aquitards) and Ssk(skeletal specific of the aquifer). Total sensitivity, the first-order sensitivity and interaction sensitivity indexes were calculated on the response variable of mean square error(MSE). Then the impact of the parameter range and time series result simulated by land subsidence model on sensitivity analysis was discussed. 1) Ssk shows low sensitivity, which implies its less influence on simulated deformation. Ssk can be fixed at a given value when the model is calibrated or inversed. 2) Parameters sensitivity in different deformation phases shows different characteristics: Sske shows the most influence on deformation during elastic deformation phase; Kv, PPmax and Sskv show the most influence on deformation during plastic deformation phase. This implies the parameters in land subsidence model can be calibrated by each of two deformation phases. 3) The interaction sensitivity of parameters shows high value. This implies that the model may encounter equifinality when it is calibrated. The possibility of equifinality can be decreased when the range of PPmax is reduced for sensitivity analysis by analyzing the curve of groundwater level and deformation.
Sobol' method was used to conduct a global sensitivity analysis of five parameters in the land subsidence model of Shanghai city in order to reduce the model uncertainty and enhance efficiency of the calibration(or inversion) on land subsidence model. The parameters were as follows: Kv(vertical hydraulic conductivity of the aquitards), Sskv(aquitard nonrecoverable skeletal specific storage), Sske(aquitard recoverable skeletal specific storage), PPmax(initial preconsolidation stress within the aquitards) and Ssk(skeletal specific of the aquifer). Total sensitivity, the first-order sensitivity and interaction sensitivity indexes were calculated on the response variable of mean square error(MSE). Then the impact of the parameter range and time series result simulated by land subsidence model on sensitivity analysis was discussed. 1) Ssk shows low sensitivity, which implies its less influence on simulated deformation. Ssk can be fixed at a given value when the model is calibrated or inversed. 2) Parameters sensitivity in different deformation phases shows different characteristics: Sske shows the most influence on deformation during elastic deformation phase; Kv, PPmax and Sskv show the most influence on deformation during plastic deformation phase. This implies the parameters in land subsidence model can be calibrated by each of two deformation phases. 3) The interaction sensitivity of parameters shows high value. This implies that the model may encounter equifinality when it is calibrated. The possibility of equifinality can be decreased when the range of PPmax is reduced for sensitivity analysis by analyzing the curve of groundwater level and deformation.
引文
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[23]WAGENER T,MCINTYRE N,LEES M J,et al.Towards reduced uncertainty in conceptual rainfallrunoff modelling:dynamic identifiability analysis[J].Hydrological Processes,2003,17(2):455-476.
[24]SHEN S,MA L,XU Y,et al.Interpretation of increased deformation rate in aquifer IV due to groundwater pumping in Shanghai[J].Canadian Geotechnical Journal,2013,50(11):1129-1142.
[25]罗跃,叶淑君,吴吉春,等.上海市地下水位大幅抬升条件下土层变形特征分析[J].高校地质学报,2015,21(2):243-254.LUO Yue,YE Shu-jun,WU Ji-chun,et al.Characterization of land subsidence during recovery of groundwater levels in Shanghai[J].Geological Journal of China Universities,2015,21(2):243-254.
[26]PIANOSI F,SARRAZIN F,WAGENER T.A Matlab toolbox for global sensitivity analysis[J].Environmental Modelling and Software,2015,70(C):80-85.
[2]MIURA N,HAYASHI S,MADHAV M R,et al.Problems of subsidence and their mitigation in Saga Plain,Japan[C]//Proceedings of the 5th International Symposium on Land Subsidence.Netherlands:IAHS-AISH,1995:463-470.
[3]PHIEN W N,GIAO P H,NUTALAYA P.Land subsidence in Bangkok,Thailand[J].Engineering Geology,2006,82(4):187-201.
[4]CHEN C,HU J,LU C,et al.Thirty-year land elevation change from subsidence to uplift following the termination of groundwater pumping and its geological implications in the Metropolitan Taipei Basin,Northern Taiwan[J].Engineering Geology,2007,95(1):30-47.
[5]CALDERHEAD A I,MARTEL A,ALASSET P,et al.Land subsidence induced by groundwater pumping,monitored by D-InSAR and field data in the Toluca Valley,Mexico[J].Canadian Journal of Remote Sensing,2010,36(1):9-23.
[6]SNEED M.Measurement of land subsidence using interferometry,Coachella Valley,California[C]//Proceedings of the 8th International Symposium on Land Subsidence.Mexico:IAHS-AISH,2010:260-263.
[7]GAMBOLATI G,PUTTI M.A comparison of lanczos and optimization methods in the partial solution of sparse symmetrical eigenproblems[J].International Journal for Numerical Methods in Engineering,1994,37(4):605-621.
[8]GALLOWAY D L,BURBEY T J.Review:regional land subsidence accompanying groundwater extraction[J].Hydrogeology Journal,2011,19(8):1459-1486.
[9]HELM D C.One-dimensional simulation of aquifer system compaction near pixley,california.1.constant parameters[J].Water Resources Research,1975,11(3):465-478.
[10]薛禹群,张云,叶淑君,等.我国地面沉降若干问题研究[J].高校地质学报,2006,12(2):153-160.XUE Yu-qun,ZHANG yun,YE Shu-jun,et al.Research on the problems of land subsidence in China[J].Geological Journal of China Universities,2006,12(2):153-160.
[11]WU J,SHI X,YE S,et al.Numerical simulation of viscoelastoplastic land subsidence due to groundwater Overdrafting in Shanghai,China[J].Journal of Hydrologic Engineering,2010,15(3):223-236.
[12]YE S,LUO Y,WU J,et al.Three-dimensional numerical modeling of land subsidence in Shanghai,China[J].Hydrogeology Journal,2016,24(3):695-709.
[13]YE S,XUE Y,WU J,et al.Modeling visco-elastic-plastic deformation of soil with modified Merchant model[J].Environmental Earth Sciences,2012,66(5):1497-1504.
[14]LUO Y,YE S,WU J,et al.A modified inverse procedure for calibrating parameters in a land subsidence model and its field application in Shanghai,China[J].Hydrogeology Journal,2016,24(3):711-725.
[15]BEVEN K,FREER J.Equifinality,data assimilation,and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUEmethodology[J].Journal of Hydrology,2001,249(1-4):11-29.
[16]YAN T,BURBEY T J.The value of subsidence data in ground water model calibration[J].Ground Water,2008,46(4):538-550.
[17]HOFFMANN J,ZEBKER H A,GALLOWAY D L,et al.Seasonal subsidence and rebound in Las Vegas Valley,Nevada,observed by synthetic aperture radar interferometry[J].Water Resources Research,2001,37(6):1551-1566.
[18]SALTELLI A.Global sensitivity analysis:the primer[M].England:Wiley,2008:11.
[19]郑菲,施小清,吴吉春,等.深部咸水层CO2地质封存数值模拟参数的全局敏感性分析:以苏北盆地盐城组为例[J].吉林大学学报:地球科学版,2014,44(01):310-318.ZHENG Fei,SHI Xiao-qing,WU Ji-chun,et al.Global parametric sensitivity analysis numerical simulation for CO2 geological sequestration in saline aquifers:a case study of Yancheng formation in Subei basin[J].Journal of Jilin University:Earth Science Edition,2014,44(01):310-318.
[20]宋晓猛,孔凡哲,占车生,等.基于统计理论方法的水文模型参数敏感性分析[J].水科学进展,2012,23(05):642-649.SONG Xiao-meng,KONG Fan-zhe,ZHAN Chesheng,et al.Sensitivity analysis of hydrological model parameters using a statistical theoryapproach[J].Advances in Water Science,2012,23(05):642-649.
[21]张质明.基于不确定性分析的WASP水质模型研究[D].北京:首都师范大学,2013.ZHANG Zhi-ming.Study of WASP model based on uncertainty analysis[D].Beijing:Capital Normal University,2013.
[22]REUSSER D E,BUYTAERT W,ZEHE E.Temporal dynamics of model parameter sensitivity for computationally expensive models with the Fourier amplitude sensitivity test[J].Water Resources Research,2011,47(7):197-203.
[23]WAGENER T,MCINTYRE N,LEES M J,et al.Towards reduced uncertainty in conceptual rainfallrunoff modelling:dynamic identifiability analysis[J].Hydrological Processes,2003,17(2):455-476.
[24]SHEN S,MA L,XU Y,et al.Interpretation of increased deformation rate in aquifer IV due to groundwater pumping in Shanghai[J].Canadian Geotechnical Journal,2013,50(11):1129-1142.
[25]罗跃,叶淑君,吴吉春,等.上海市地下水位大幅抬升条件下土层变形特征分析[J].高校地质学报,2015,21(2):243-254.LUO Yue,YE Shu-jun,WU Ji-chun,et al.Characterization of land subsidence during recovery of groundwater levels in Shanghai[J].Geological Journal of China Universities,2015,21(2):243-254.
[26]PIANOSI F,SARRAZIN F,WAGENER T.A Matlab toolbox for global sensitivity analysis[J].Environmental Modelling and Software,2015,70(C):80-85.