Estimation of conductivity fields by using a correlation-based localization scheme of iterative ensemble smoother
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摘要: 在地下水流和溶质运移问题中，有较多研究基于物理距离局域化集合同化方法反演水文地质参数。当反演参数与观测信息之间不存在物理距离时，这种方法不适用。为了克服这个局限，通过渗透系数与水头信息之间的相关性计算局域化方法的阻滞因子，构建基于相关性的局域化迭代集合平滑方法。为了方便比较，将该方法和一种基于物理距离的局域化迭代集合平滑一同用于同化水头信息反演二维孔隙承压含水层的渗透系数场。算例中考虑了不同集合大小、观测误差及观测数量等因子的组合，便于分析它们对渗透系数反演精度的影响。研究结果显示：（1）在所有算例中新方法得到的渗透系数均方根误差RMSE范围为[0.8307, 0.9590]，都小于基于物理距离方法的均方根误差，范围为[0.8394, 1.0000]；（2）基于物理距离的方法得到渗透系数场空间上存在不连续性，而新方法的结果不存在此现象。文章提出了一种新的基于相关性局域化迭代平滑方法，该方法不需要依赖参数与观测信息之间的物理距离且参数反演精度高于基于物理距离的方法，可作为参数反演的科学工具。Abstract: In the studies of groundwater flow and solute transport, many efforts have been made to estimate hydrogeological parameters through physical-distance based localization schemes of ensemble assimilation approaches. However, these methods are unavailable when there are no physical distances between parameters and observations. To avoid this limitation, we calculate the tapering factors in terms of the correlation coefficients between parameters and observations and develop a novel correlation-based localization scheme of iterative ensemble smoother. For the purpose of comparison, a physical distance-based scheme of iterative ensemble smoother together with the new approach are used to assimilate hydraulic head information and estimate the hydraulic conductivity field of a 2D confined aquifer. Among the test cases, we consider different configurations of ensemble size, observation error and number of observations, and their impacts on the accuracy of conductivity estimation can be well explored. The results show that (1) the root mean square error of hydraulic conductivity, RMSE, obtained through the new approach for each test case of interest, is lower than its counterpart through the physical distance-based approach, with the RMSE ranges of [0.8307, 0.9590] and [0.8394, 1.0000] for all test cases through the two approaches, respectively. (2) The estimated conductivity field has discontinuities when using the physical distance-based approach, but this does not happen when using the new approach. In this study, we develop a novel correlation-based localization scheme of iterative ensemble smoother, which is free of the definitions of physical distances between parameters and observations, yields higher accuracy of parameter estimation in comparison with the physical distance-based approach, and can be a useful tool for estimating hydrogeological parameters.
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图 1 Y参考场和16，48，168口监测井空间分布图
Figure 1. Y reference field (a); spatial distribution of (b) 16, (c) 48 and (d) 168 monitoring wells
图 2 由DL_iES和CL_iES在N = 50，100和500时得到的RMSE，SY和Eh随迭代次数变化的曲线
Figure 2. Changes of (a) RMSE, (b) SY, and (c) Eh obtained through DL_iES and CL_iES with iteration times when N = 50, 100 or 500
图 3 当N = 50，100或500时，通过DL_iES和CL_iES在第20次迭代后获得的Y估计场和Y方差($\sigma _{\text{Y}}^2$)估计场
Figure 3. Maps of Y fields and Y variance $(\sigma _{\text{Y}}^2)$ estimated through DL_iES and CL_iES at the 20th iteration when N = 50, 100 or 500
图 4 在Nmon = 16，48或168时，通过DL_iES和CL_iES在第20次迭代后获得的Y估计场和Y方差($\sigma _{\text{Y}}^2$)估计场
Figure 4. Maps of Y fields Y variance, $(\sigma _{\text{Y}}^2)$ estimated through DL_iES and CL_iES at the 20th iteration when Nmon = 16, 48, or 168
图 5 当N = 50，100，500或100000的$\left| {{\rho _{k1}}} \right|$及${r_{k1}}\left| {{\rho _{k1}}} \right|$分布图
注：图中红色圆圈代表最靠近点（0，0）的监测井位置为观测水头的固定点。
Figure 5. $\left| {{\rho _{k1}}} \right|$ and ${r_{k1}}\left| {{\rho _{k1}}} \right|$ maps considering N = 50 (first column), 100 (second), 500 (third) or 100,000 (fourth)
表 1 第1组第20次迭代后DL_iES和CL_iES得到的RMSE、SY和Eh值
Table 1. Final values of RMSE, SY and Eh through DL_iES and CL_iES for Group 1 at the 20th iteration
参数 模型 集合大小 50 100 500 RMSE DL_iES 1.0000 0.9779 0.8394 CL_iES 0.9590 0.9151 0.8307 SY DL_iES 0.9901 0.9689 0.7887 CL_iES 0.9359 0.9016 0.8424 Eh DL_iES 0.1132 0.1115 0.0829 CL_iES 0.1059 0.0978 0.0858 
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表 2 第2组第20次迭代后DL_iES和CL_iES得到的RMSE、SY和Eh值
Table 2. Final values of RMSE, SY and Eh through DL_iES and CL_iES for Group 2 at the 20th iteration
参数 模型 观测误差 0.1 0.01 0.001 RMSE DL_iES 0.9744 0.9779 0.9801 CL_iES 0.91868 0.9151 0.9162 SY DL_iES 0.9691 0.9689 0.9690 CL_iES 0.90294 0.9016 0.9015 Eh DL_iES 0.2728 0.1115 0.0789 CL_iES 0.26774 0.0978 0.0571
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表 3 第3组第20次迭代后DL_iES和CL_iES得到的RMSE、SY和Eh值
Table 3. Final values of RMSE, SY and Eh through DL_iES and CL_iES for Group 3 at the 20th iteration
参数 模型 观测数量 16 48 168 RMSE DL_iES 0.9999 0.9779 0.9575 CL_iES 0.9537 0.9151 0.8974 SY DL_iES 0.9862 0.9689 0.9543 CL_iES 0.9281 0.9016 0.8850 Eh DL_iES 0.1023 0.1115 0.1090 CL_iES 0.0948 0.0978 0.0932
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表 4 第4组第20次迭代后CL_iES得到的RMSE、SY和Eh值
Table 4. Final values of RMSE, SY and Eh through CL_iES for Group 4 at the 20th iteration
参数 相关系数高斯白噪音标准差的倍数 1.0 1.5 2.0 2.5 3.0 RMSE 0.8782 0.8920 0.9151 0.9443 0.9706 SY 0.8367 0.8715 0.9016 0.9273 0.9500 Eh 0.0901 0.0936 0.0978 0.1027 0.1071
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[1] 杨运,吴吉春,骆乾坤,等. 考虑预报偏差的迭代式集合卡尔曼滤波在地下水水流数据同化中的应用[J]. 水文地质工程地质,2022,49(6):13 − 23. [YANG Yun,WU Jichun,LUO Qiankun,et al. Application of the bias aware Ensemble Kalman Filter with Confirming Option (Bias-CEnKF) in groundwater flow data assimilation[J]. Hydrogeology & Engineering Geology,2022,49(6):13 − 23. (in Chinese with English abstract) YANG Yun, WU Jichun, LUO Qiankun, et al . Application of the bias aware Ensemble Kalman Filter with Confirming Option （Bias-CEnKF） in groundwater flow data assimilation[J]. Hydrogeology & Engineering Geology,2022 ,49 （6 ）:13 −23 . （in Chinese with English abstract）[2] 宗成元,康学远,施小清,等. 基于多点地质统计与集合平滑数据同化方法识别非高斯渗透系数场[J]. 水文地质工程地质,2020,47(2):1 − 8. [ZONG Chengyuan,KANG Xueyuan,SHI Xiaoqing,et al. Characterization of non-Gaussian hydraulic conductivity fields using multiple-point geostatistics and ensemble smoother with multiple data assimilation method[J]. Hydrogeology & Engineering Geology,2020,47(2):1 − 8. (in Chinese with English abstract) ZONG Chengyuan, KANG Xueyuan, SHI Xiaoqing, et al . Characterization of non-Gaussian hydraulic conductivity fields using multiple-point geostatistics and ensemble smoother with multiple data assimilation method[J]. Hydrogeology & Engineering Geology,2020 ,47 （2 ）:1 −8 . （in Chinese with English abstract）[3] MO Shaoxing,ZABARAS N,SHI Xiaoqing,et al. Deep autoregressive neural networks for high-dimensional inverse problems in groundwater contaminant source identification[J]. Water Resources Research,2019,55(5):3856 − 3881. doi: 10.1029/2018WR024638 [4] XIA Chuanan,HU B X,TONG Juxiu,et al. Data assimilation in density-dependent subsurface flows via localized iterative ensemble Kalman filter[J]. Water Resources Research,2018,54(9):6259 − 6281. doi: 10.1029/2017WR022369 [5] ZHANG Jiangjiang,LIN Guang,LI Weixuan,et al. An iterative local updating ensemble smoother for estimation and uncertainty assessment of hydrologic model parameters with multimodal distributions[J]. Water Resources Research,2018,54(3):1716 − 1733. doi: 10.1002/2017WR020906 [6] CHEN Zi,GÓMEZ-HERNÁNDEZ J J,XU Teng,et al. Joint identification of contaminant source and aquifer geometry in a sandbox experiment with the restart ensemble Kalman filter[J]. Journal of Hydrology,2018,564:1074 − 1084. doi: 10.1016/j.jhydrol.2018.07.073 [7] 李丽敏,温宗周,董勋凯,等. 基于矩阵奇异值分解约束型无迹粒子滤波的滑坡位移预测模型研究[J]. 水土保持通报,2019,39(1):132 − 136. [LI Limin,WEN Zongzhou,DONG Xunkai,et al. Landslide displacement prediction model based on singular value decomposition constrained unscented particle filter[J]. Bulletin of Soil and Water Conservation,2019,39(1):132 − 136. (in Chinese with English abstract) LI Limin, WEN Zongzhou, DONG Xunkai, et al . Landslide displacement prediction model based on singular value decomposition constrained unscented particle filter[J]. Bulletin of Soil and Water Conservation,2019 ,39 （1 ）:132 −136 . （in Chinese with English abstract）[8] 薛长虎. 基于改进粒子滤波的大型滑坡数据同化方法研究[D]. 武汉:武汉大学,2019 [XUE Changhu. Research on data assimilation method of large landslide based on improved particle filter[D]. Wuhan:Wuhan University,2019. (in Chinese with English abstract) XUE Changhu. Research on data assimilation method of large landslide based on improved particle filter[D]. Wuhan: Wuhan University, 2019. （in Chinese with English abstract） [9] ZHANG Hongqin,TIAN Xiangjun. A multigrid nonlinear least squares four-dimensional variational data assimilation scheme with the advanced research weather research and forecasting model[J]. Journal of Geophysical Research:Atmospheres,2018,123(10):5116 − 5129. [10] LUO Xiaodong,BHAKTA T. Automatic and adaptive localization for ensemble-based history matching[J]. Journal of Petroleum Science and Engineering,2020,184:106559. doi: 10.1016/j.petrol.2019.106559 [11] LUO Xiaodong,LORENTZEN R,VALESTRAND R,et al. Correlation-based adaptive localization for ensemble-based history matching:applied to the norne field case study[Z]. Spe Norway One Day Seminar. Norway. 2018:SPE-191305-MS. 10.2118/191305-MS. [12] BISHOP C H,HODYSS D. Adaptive ensemble covariance localization in ensemble 4D-VAR state estimation[J]. Monthly Weather Review,2011,139(4):1241 − 1255. doi: 10.1175/2010MWR3403.1 [13] CHEN Yan,ZHANG Dongxiao. Data assimilation for transient flow in geologic formations via ensemble Kalman filter[J]. Advances in Water Resources,2006,29(8):1107 − 1122. doi: 10.1016/j.advwatres.2005.09.007 [14] TONG Juxiu,HU B X,YANG Jinzhong. Assimilating transient groundwater flow data via a localized ensemble Kalman filter to calibrate a heterogeneous conductivity field[J]. Stochastic Environmental Research and Risk Assessment,2012,26(3):467 − 478. doi: 10.1007/s00477-011-0534-0 [15] NAN Tongchao,WU Jichun. Groundwater parameter estimation using the ensemble Kalman filter with localization[J]. Hydrogeology Journal,2011,19(3):547 − 561. doi: 10.1007/s10040-010-0679-9 [16] 南统超,吴吉春. 集合卡尔曼滤波估计水文地质参数的局域化修正[J]. 水科学进展,2010,21(5):613 − 621. [NAN Tongchao,WU Jichun. Localization corrections for the estimation of hydrogeological parameters using ensemble Kalman filter[J]. Advances in Water Science,2010,21(5):613 − 621. (in Chinese with English abstract) NAN Tongchao, WU Jichun . Localization corrections for the estimation of hydrogeological parameters using ensemble Kalman filter[J]. Advances in Water Science,2010 ,21 （5 ）:613 −621 . （in Chinese with English abstract）[17] SOARES R V,MASCHIO C,SCHIOZER D J. A novel localization scheme for scalar uncertainties in ensemble-based data assimilation methods[J]. Journal of Petroleum Exploration and Production Technology,2019,9(4):2497 − 2510. doi: 10.1007/s13202-019-0727-5 [18] FURRER R,BENGTSSON T. Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants[J]. Journal of Multivariate Analysis,2007,98(2):227 − 255. doi: 10.1016/j.jmva.2006.08.003 [19] MIYOSHI T. An adaptive covariance localization method with the LETKF[C]//14th Symposium on Integrated Observing and Assimilation Systems for the Atmosphere,Oceans,and Land Surface (IOAS-AOLS). Atlanta:Americian Meterological Society,2010. [20] XIA Chuanan,LUO Xiaodong,HU B X,et al. Data assimilation with multiple types of observation boreholes via the ensemble Kalman filter embedded within stochastic moment equations[J]. Hydrology and Earth System Sciences,2021,25(4):1689 − 1709. doi: 10.5194/hess-25-1689-2021 [21] SONG Xuehang,SHI Liangsheng,YE Ming,et al. Numerical comparison of iterative ensemble Kalman filters for unsaturated flow inverse modeling[J]. Vadose Zone Journal,2014,13(2):1 − 12. [22] 周研来,郭生练,郭家力,等. VIC模型参数的地区分布规律及在无资料流域的移用[J]. 水资源研究,2012,1(3):56 − 63. [ZHOU Yanlai,GUO Shenglian,GUO Jiali,et al. Regional Distribution of the VIC Model Parameters and Application in Ungauged Basins [J]. Journal of Water Resources Research,2012,1(3):56 − 63 (in Chinese with English Abstrct) ZHOU Yanlai, GUO Shenglian, GUO Jiali, et al . Regional Distribution of the VIC Model Parameters and Application in Ungauged Basins [J]. Journal of Water Resources Research,2012 ,1 （3 ）:56 −63 （in Chinese with English Abstrct）[23] 石鸿蕾,郝奇琛,邵景力,等. 基于多源数据的弱透水层水文地质参数反演研究——以呼和浩特盆地某淤泥层为例[J]. 水文地质工程地质,2021,48(2):1 − 7. [SHI Honglei,HAO Qichen,SHAO Jingli,et al. Research on hydrogeological parameter inversion of an aquitard based on multi-source data:A case study of a silt layer in the Hohhot Basin[J]. Hydrogeology & Engineering Geology,2021,48(2):1 − 7. (in Chinese with English abstract) SHI Honglei, HAO Qichen, SHAO Jingli, et al . Research on hydrogeological parameter inversion of an aquitard based on multi-source data: A case study of a silt layer in the Hohhot Basin[J]. Hydrogeology & Engineering Geology,2021 ,48 （2 ）:1 −7 . （in Chinese with English abstract）[24] BEAR J. Hydraulics of groundwater[M]. New York:McGraw-Hill Book Co,1979. [25] LUO Xiaodong,STORDAL A S,LORENTZEN R J,et al. Iterative ensemble smoother as an approximate solution to a regularized minimum-average-cost problem:theory and applications[J]. SPE Journal,2015,20(5):962 − 982. doi: 10.2118/176023-PA [26] ZHANG Hongqin,TIAN Xiangjun. An efficient local correlation matrix decomposition approach for the localization implementation of ensemble-based assimilation methods[J]. Journal of Geophysical Research:Atmospheres,2018,123(7):3556 − 3573. [27] ANDERSON T W. An introduction to multivariate statistical analysis[M]. 3rd ed. Hoboken,NJ:Wiley-Interscience,2003. -
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