Identification of non-Gaussian parameters in heterogeneous aquifers by a modified probability conditioning method throug
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PAPER
Identification of non-Gaussian parameters in heterogeneous aquifers by a modified probability conditioning method through hydraulic-head assimilation Tian Lan 1 & Xiaoqing Shi 1
&
Yan Chen 2 & Liangping Li 3 & Jichun Wu 1 & Limin Duan 4 & Tingxi Liu 4
Received: 17 February 2020 / Accepted: 13 September 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Parameter estimation with uncertainty quantification is essential in groundwater modeling to ensure model quality; however, parameter estimation, especially for non-Gaussian distributed parameters in highly heterogeneous aquifers, is still a great challenge. The ensemble smoother with multiple data assimilation (ES-MDA) is one of the most popular and effective ensemble-based data assimilation algorithms. However, it only works for multi-Gaussian fields, since two-point statistics are used to estimate the co-relation between parameters and state variables. The probability conditioning method (PCM) has the capability to integrate nonlinear flow data into facies simulation, but it has an assumption of homogeneity within each facies. Full characterization of facies and estimates of hydraulic conductivity within each facies are equally important. This work firstly modifies the original PCM, introducing a new probability assignment method, to consider within-facies heterogeneities, and then it is further combined with the ES-MDA to estimate non-Gaussian distributed hydraulic parameters in a groundwater model. The proposed method is evaluated using a two-facies case and a three-facies case in groundwater modeling. Both cases demonstrate that the modified PCM is effective for facies delineation, especially to identify high heterogeneities in each facies, as well as nonGaussian characteristics with good connectivity within certain facies. The results also show that the performances of data reproduction and model prediction are of high accuracy and low uncertainty, which is attributed to the accurate characterization of the non-Gaussian parameters in the heterogeneous aquifers used. Keywords Non-Gaussian . Heterogeneity . Inverse modeling
Introduction Inverse problems are very important in groundwater modeling since the quality of the groundwater model largely depends on the quality of the model parameters (Gómez-Hernández et al. 2003; Karahan and Ayvaz 2008; Franssen et al. 2009; Zhou
* Xiaoqing Shi [email protected] 1
Key Laboratory of Surficial Geochemistry, Ministry of Education and School of Earth Sciences and Engineering, Nanjing University, Nanjing 210023, China
2
Geoscience Research Centre, Total E&P UK, Westhill, UK
3
Department of Geology and Geological Engineering, South Dakota School of Mines and Technology, Rapid City 57701, USA
4
Water Conservancy and Civil Engineering College, Inner Mongolia Agricultural University, Hohhot 010018, Inner Mongolia, China
et al. 2014). Many studies have focused on parameter estimation in the last few decades (e.g. Carrera et al. 2005; Dagan 1985; Doherty 2004; Gómez-Hernández et al. 2003;
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