Conditioning Multi-Gaussian Groundwater Flow Parameters to Transient Hydraulic Head and Flowrate Data With Iterative Ensemble Smoothers: A Synthetic Case Study

Lam, Dan-Thuy; Kerrou, Jaouher; Renard, Philippe; Benabderrahmane, H.; Perrochet, Pierre

doi:10.3389/feart.2020.00202

Cited by 5 publications

(9 citation statements)

References 39 publications

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“…The distribution features of hydraulic conductivity of the test site are controlled by the direction of the fractured and conduit network, prescribing a general trend of NE-SW. Assume that the transfer probability is consistent in the lateral and vertical directions (Langousis et al, 2018). However, the mean length of each hydrofacies in the lateral direction relative to the vertical direction is difficult to determine because of the lack of direct measurement data.…”

Section: Transition Probability Geostatisticsmentioning

confidence: 99%

“…The main advantages of ensemble‐based methods in the context of HT are that uncertainties from different sources can be dealt with directly; the covariance matrix between states can be easily estimated from a finite ensemble of stochastic simulations without sensitivity analysis, which greatly reduces the computational burden (Schoeniger et al, 2012); and the posterior ensemble of parameters conditioned on collected state measurements is a set of possible solutions, reflecting the heterogeneity of aquifers, rather than a single optimal solution (Zovi et al, 2017), and can be further analysed for uncertainty. Many studies have compared the performance of the above methods for parameter inversion (Emerick & Reynolds, 2013a; Evensen, 2018; Lam et al, 2020). In general, ensemble smoother with multiple data assimilation (ES‐MDA) is better in hydrogeological parameter estimation.…”

Section: Introductionmentioning

confidence: 99%

“…An attractive approach to model highly heterogeneous aquifers is transition probability geostatistics (T-PROGS), which is a Markov chain classification indicator method (Carle & Fogg, 1996). As a technique for describing the configuration of hydrostratigraphical units, the T-PROGS takes into account local heterogeneity while honouring measured data (Langousis et al, 2018). The application of this method in fractured or karst aquifers usually involves selecting several realizations from the conditional simulations to construct the initial ensemble separately and comparing the final estimates of the different realizations (Blessent et al, 2011;Park et al, 2004;Wang et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

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Identification of hydraulic conductivity field of a karst aquifer by using transition probability geostatistics and discrete cosine transform with an ensemble method

Duan

Deng

Chu

et al. 2022

Hydrological Processes

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Knowledge of the spatial distribution characteristics of hydraulic parameters is essential for the management and protection of karst groundwater resources. In this study, we propose a workflow integrating the transition probability geostatistics (T‐PROGS) and the discrete cosine transform (DCT) with the ensemble smoother with multiple data assimilation (ES‐MDA) method to map the hydraulic conductivity of karst aquifers that usually follow a multimodal distribution. The priori parameter ensemble is constructed from the T‐PROGS and transformed into an approximately Gaussian distributed coefficient field containing critical spatial structural features about the aquifer using DCT. The ES‐MDA method is employed to update the DCT coefficients by assimilating the measurements. In addition, a postprocessing process based on cumulative distribution function (CDF) mapping is used to address the problem of parameters gradually tending to a Gaussian distribution after updating using the ES‐MDA and the inappropriate selection of initial parameter values. In practice, the limited amount of available data makes it difficult to fully capture the spatial distribution of the parameters in the initial ensemble of a single realization. Therefore, we suggest a new strategy for structuring the initial ensemble by mixing samples from multiple realizations. We then apply the proposed approach to four single realization models and a combined multiple realizations model in a field hydraulic tomography investigation of a real karst aquifer. The computed results show that this method can effectively identify the characteristics of the spatial distribution of hydraulic conductivity in karst aquifers. Compared with an individual realization model, the uncertainty of the hydraulic conductivity estimated by the combined multiple realizations model is significantly reduced. Therefore, including more uncertainty of the aquifer in the initial ensemble is beneficial to improve the accuracy of the parameter estimation.

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Section: Transition Probability Geostatisticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Identification of hydraulic conductivity field of a karst aquifer by using transition probability geostatistics and discrete cosine transform with an ensemble method

Duan

Deng

Chu

et al. 2022

Hydrological Processes

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“…The key aspect of ES-MDA is to perform iterative ES corrections of the parameters by assimilating the data of the previous iteration, when PESTPP-IES optimizes directly an objective function using a modified form of the Levenberg-Marquardt algorithm. Lam et al (2020) showed a comparison of different Iterative Ensemble Smoothers, including PESTPP-IES and ES-MDA. It was shown that PESTPP-IES approach outperforms ES-MDA when the ensemble size is relatively small (200 in the study) but that ES-MDA tends to improve with an increase of the ensemble size, while PESTPP-IES does not.…”

Section: Introductionmentioning

confidence: 99%

“…It was shown that PESTPP-IES approach outperforms ES-MDA when the ensemble size is relatively small (200 in the study) but that ES-MDA tends to improve with an increase of the ensemble size, while PESTPP-IES does not. ES-MDA has been successfully applied in groundwater studies (Kang et al, 2019;Lam et al, 2020;Xu et al, 2022). One important underlying assumption is that the state variables and parameters are normally distributed (and even multi-Gaussian).…”

Section: Introductionmentioning

confidence: 99%

Stochastic multi-fidelity joint hydrogeophysical inversion of consistent geological models

Néven

Schorpp²,

Renard³

2022

Front. Water

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In Quaternary deposits, the characterization of subsurface heterogeneity and its associated uncertainty is critical when dealing with groundwater resource management. The combination of different data types through joint inversion has proven to be an effective way to reduce final model uncertainty. Moreover, it allows the final model to be in agreement with a wider spectrum of data available on site. However, integrating them stochastically through an inversion is very time-consuming and resource expensive, due to the important number of physical simulations needed. The use of multi-fidelity models, by combining low-fidelity inexpensive and less accurate models with high-fidelity expensive and accurate models, allows one to reduce the time needed for inversion to converge. This multiscale logic can be applied for the generation of Quaternary models. Most Quaternary sedimentological models can be considered as geological units (large scale), populated with facies (medium scale), and finally completed by physical parameters (small scale). In this paper, both approaches are combined. A simple and fast time-domain EM 1D geophysical direct problem is used to first constrain a simplified stochastic geologically consistent model, where each stratigraphic unit is considered homogeneous in terms of facies and parameters. The ensemble smoother with multiple data assimilation (ES-MDA) algorithm allows generating an ensemble of plausible subsurface realizations. Fast identification of the large-scale structures is the main point of this step. Once plausible unit models are generated, high-fidelity transient groundwater flow models are incorporated. The low-fidelity models are populated stochastically with heterogeneous facies and their associated parameter distribution. ES-MDA is also used for this task by directly inferring the property values (hydraulic conductivity and resistivity) from the generated model. To preserve consistency, geophysical and hydrogeological data are inverted jointly. This workflow ensures that the models are geologically consistent and are therefore less subject to artifacts due to localized poor-quality data. It is able to robustly estimate the associated uncertainty with the final model. Finally, due to the simplification of both the direct problem and the geology during the low-fidelity part of the inversion, it greatly reduces the time required to converge to an ensemble of complex models while preserving consistency.

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Groundwater contaminated source estimation based on adaptive correction iterative ensemble smoother with an auto lightgbm surrogate

Pan

Bai

2023

Journal of Hydrology

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Conditioning Multi-Gaussian Groundwater Flow Parameters to Transient Hydraulic Head and Flowrate Data With Iterative Ensemble Smoothers: A Synthetic Case Study

Cited by 5 publications

References 39 publications

Identification of hydraulic conductivity field of a karst aquifer by using transition probability geostatistics and discrete cosine transform with an ensemble method

Identification of hydraulic conductivity field of a karst aquifer by using transition probability geostatistics and discrete cosine transform with an ensemble method

Stochastic multi-fidelity joint hydrogeophysical inversion of consistent geological models

Groundwater contaminated source estimation based on adaptive correction iterative ensemble smoother with an auto lightgbm surrogate

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