genES-MDA: A generic open-source software package to solve inverse problems via the Ensemble Smoother with Multiple Data Assimilation

Todaro, Valeria; D’Oria, Marco; Tanda, Maria Giovanna; Gómez‐Hernández, J. Jaime

doi:10.1016/j.cageo.2022.105210

Cited by 9 publications

(5 citation statements)

References 43 publications

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“…There are many applications of ES-MDA for the estimation of source information or model parameters (Bao et al, 2020;Chen, Xu, et al, 2023;Rafiee & Reynolds, 2017;Todaro et al, 2021Todaro et al, , 2022Xu et al, 2021Xu et al, , 2022. After referring to these studies, the ensemble size and the number of iterations were set to 300 and 5, respectively.…”

Section: Ensemble Smoother With Multiple Data Assimilationmentioning

confidence: 99%

A Comparison of Inversion Methods for Surrogate‐Based Groundwater Contamination Source Identification With Varying Degrees of Model Complexity

Chang,

Guo,

Chen

et al. 2024

Water Resources Research

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Accurate identification of groundwater contamination sources is important for designing efficacious site remediation strategies. Currently, the methods for identifying contamination sources mainly fall into three distinct categories: simulation optimization, Bayesian inference, and data assimilation. Each method has its own advantages and disadvantages under specific site conditions. To evaluate the applicability of these methods, we chose one representative inversion algorithm from each category, namely the Improved Butterfly Optimization Algorithm (IBOA) for simulation optimization, the Ensemble Smoother with Multiple Data Assimilation (ES‐MDA) for data assimilation, and the DiffeRential Evolution Adaptive Metropolis with a Snooker Update and Sampling from a Past Archive (DREAM(ZS)) for Bayesian inference. We conducted a comprehensive evaluation of these methods' performance under different model complexities, employing a surrogate model as a substitute for the complex forward model. By addressing two distinct problems involving conservative pollutant transport and Light Non‐Aqueous Phase Liquid (LNAPL) transport with biodegradation, we employed four criteria (elapsed time, result accuracy, posterior probability distribution, and noise resistance) for evaluation. The findings unequivocally indicate that DREAM(ZS) outperforms others in terms of result accuracy and posterior probability distribution. It also adeptly navigates the interrelations among disparate unknown variables. The strength of ES‐MDA lies in its efficiency. It achieves relatively satisfactory results with a reduced computational burden. In contrast, IBOA underperforms in both test problems. In terms of resistance to noise, both DREAM(ZS) and ES‐MDA perform better than IBOA does.

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Section: Ensemble Smoother With Multiple Data Assimilationmentioning

confidence: 99%

A Comparison of Inversion Methods for Surrogate‐Based Groundwater Contamination Source Identification With Varying Degrees of Model Complexity

Chang,

Guo,

Chen

et al. 2024

Water Resources Research

View full text Add to dashboard Cite

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“…Without going into mathematical derivation details, we briefly overview the workflow of ES-MDA. Detailed information on ES-MDA algorithm can be found in the reference (Emerick & Reynolds, 2013;Evensen, 2018;Le et al, 2016;Ranazzi & Sampaio, 2019;Todaro et al, 2022).…”

Section: Es-mda Inversionmentioning

confidence: 99%

“…To ensure the assimilation performance, the specification of covariances of measurement error is crucial. Here, we define measurement covariances by setting the standard deviation according to the relationship (Todaro et al, 2022): 3𝜎 = 𝑝/100 • 𝑦 𝑜𝑏𝑠 , where p is a user-defined parameter and 𝑦 𝑜𝑏𝑠 is the observation value. We set 𝑝 = 1, 𝑝 = 0.1 for tracer and pressure data, respectively.…”

Section: Onetime Aperture Inversionmentioning

confidence: 99%

A Multi-stage inversion framework for dynamic fracture characterization and long-term thermal performance prediction in an Enhanced Geothermal System

Zhang,

2024

Preprint

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Fractures play important roles in fluid and heat flow during heat extraction from an enhanced geothermal system (EGS). Quantifying the associated uncertainties in fractures is critical for predicting long-term thermal performance of EGSs. Considerable advancements have been made regarding the inversion of fracture characteristics such as aperture distribution. However, most previous studies assumed a constant fracture aperture to simplify the inversion, while both experimental and numerical results indicated significant variations in fracture aperture due to complex thermo-hydro-mechanical (THM) coupled processes during heat extraction. This study introduces a multi-stage inversion framework that integrates the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) with a THM coupled model to capture the dynamic evolution of fracture aperture. The framework executes multiple aperture inversions at different times during EGS operation. In each inversion stage, we use ES-MDA to invert for fracture aperture by assimilating tracer data, and then perform THM modeling to analyze fracture aperture evolution under coupled THM processes and predict thermal performance. We propose a principle to assure a smooth transition between two consecutive inversion stages, that the posterior aperture fields obtained in an inversion stage are used as the prior aperture fields for the following stage, and the temperature field simulated in the previous inversion stage serves as the initial temperature field for the following stage. Application of the framework to a synthetic field-scale EGS model demonstrates its efficacy in capturing the dynamic evolution of fracture aperture, resulting in more accurate thermal predictions compared with previous inversion methods assuming constant fracture aperture.

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“…Furthermore, the general software package genES-MDA, developed by Todaro et al (2022), integrates various variants of ES, providing a convenient solution for solving inverse problems. However, it's crucial to note that the reparameterization and updating process may lead to the loss of certain essential features, and the Gaussian assumption remains inherent in the employed DA methods.…”

Section: Introductionmentioning

confidence: 99%

A Deep Learning-Based Data Assimilation Approach to Characterizing Coastal Aquifers Amid Non-linearity and Non-Gaussianity Challenges

Cao,

Zhang,

Gan

et al. 2024

Preprint

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Seawater intrusion (SI) poses a substantial threat to water security in coastal regions, where numerical models play a pivotal role in supporting groundwater management and protection. However, the inherent heterogeneity of coastal aquifers introduces significant uncertainties into SI predictions, potentially diminishing their effectiveness in management decisions. Data assimilation (DA) offers a solution by integrating various types of observational data with the model to characterize heterogeneous coastal aquifers. Traditional DA techniques, like ensemble smoother using the Kalman formula (ES) and Markov chain Monte Carlo, face challenges when confronted with the non-linearity, non-Gaussianity, and high-dimensionality issues commonly encountered in aquifer characterization. In this study, we introduce a novel DA approach rooted in deep learning (DL), referred to as ES, aimed at effectively characterizing coastal aquifers with varying levels of heterogeneity. We systematically investigate a range of factors that impact the performance of ES, including the number and types of observations, the degree of aquifer heterogeneity, the structure and training options of the DL models. Our findings reveal that ES excels in characterizing heterogeneous aquifers under non-linear and non-Gaussian conditions. Comparison between ES and ES under different experimentation settings underscores the robustness of ES. Conversely, in certain scenarios, ES displays noticeable biases in the characterization results, especially when measurement data from non-linear and discontinuous processes are used. To optimize the efficacy of ES, attention must be given to the design of the DL model and the selection of observational data, which are crucial to ensure the universal applicability of this DA method.

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genES-MDA: A generic open-source software package to solve inverse problems via the Ensemble Smoother with Multiple Data Assimilation

Cited by 9 publications

References 43 publications

A Comparison of Inversion Methods for Surrogate‐Based Groundwater Contamination Source Identification With Varying Degrees of Model Complexity

A Comparison of Inversion Methods for Surrogate‐Based Groundwater Contamination Source Identification With Varying Degrees of Model Complexity

A Multi-stage inversion framework for dynamic fracture characterization and long-term thermal performance prediction in an Enhanced Geothermal System

A Deep Learning-Based Data Assimilation Approach to Characterizing Coastal Aquifers Amid Non-linearity and Non-Gaussianity Challenges

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