| Citation: |
XIA Chuan’an, WANG Hao, JIAN Wenbin. Estimation of conductivity fields by using a correlation-based localization scheme of iterative ensemble smoother[J]. Hydrogeology & Engineering Geology, 2024, 51(1): 12-21. doi: 10.16030/j.cnki.issn.1000-3665.202303033
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Estimation of conductivity fields by using a correlation-based localization scheme of iterative ensemble smoother
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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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References
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XIA Chuan’an, WANG Hao, JIAN Wenbin. Estimation of conductivity fields by using a correlation-based localization scheme of iterative ensemble smoother[J]. Hydrogeology & Engineering Geology, 2024, 51(1): 12-21. doi: 10.16030/j.cnki.issn.1000-3665.202303033
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Figure 1.
Y reference field and spatial distribution of 16, 48 and 168 monitoring wells
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Figure 2.
Changes of RMSE, SY and Eh obtained through DL_iES and CL_iES with iteration timeswhen N = 50, 100, 500
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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, 500 -
Figure 4.
Maps of Y fields and Y variance
$(\sigma _{\text{Y}}^2)$ estimated through DL_iES and CL_iES at the 20th iteration when Nmon = 16, 48, 168 -
Figure 5.
$\left| {{\rho _{k1}}} \right|$ and${r_{k1}}\left| {{\rho _{k1}}} \right|$ maps considering N = 50, 100, 500, 100000