Ensemble Smoother with Multiple Data Assimilation as a Tool for Curve Fitting and Parameter Uncertainty Characterization: Example Applications to Fit Nonlinear Sorption Isotherms

Godoy, Vanessa A.; Napa-García, Gian Franco; Gómez‐Hernández, J. Jaime

doi:10.1007/s11004-021-09981-7

Cited by 4 publications

(1 citation statement)

References 32 publications

(36 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, there are many cases in practice in which the empirical data do not adequately fit these types of functions but correspond to two different behaviours dependent on the variation of the independent variable. This study presents a new type of single variable function, named the function of double asymptote, which allows the acceptance of new empirical laws, unlike other more complex processes such as the one shown in Godoy et al [1], and those showing a single asymptote are usually studied using the empirical Hurst's law [2]. A function of double asymptote of a single variable is one that presents an infinite approximation to a straight line (horizontal, vertical, or oblique), i.e., an asymptotic behaviour, at two different values, and these functions have been called y 2A (x).…”

Section: Introductionmentioning

confidence: 99%

New Empirical Laws in Geosciences: A Successful Proposal

Díaz-Curiel,

Biosca,

Arévalo-Lomas

et al. 2023

Applied Sciences

View full text Add to dashboard Cite

The importance of empirical versus theoretical laws is a controversial issue in many scientific fields, the latter being generally accepted and the relevance of which is not discussed here. As in other areas, there are well-known theoretical and empirical formulas in geosciences that do not adequately represent the reality of a given phenomenon. Quantitative comparison of geophysical and petrophysical results with data from the other multiple fields that comprise the geosciences compels a high exigency to avoid discontinuities in existing relationships. However, the proposal of new empirical laws that more accurately reflect a given phenomenon is often considered insufficient to contradict existing formulas. The aim of this work is to defend the development of new empirical laws by showing that they constitute a true model of analysed behaviour if certain criteria are followed. This defence is especially needed when non-linearisable functions are required to fit the empirical data. To achieve this aim, this study shows the established algebraic function as a function of a single variable, whose main advantage is its application to phenomena of a geological nature that show two differentiated behaviours as the variable x is increased. A series of five examples of different phenomena related to geosciences is selected to demonstrate the level of accuracy that new empirical laws can reach in contrast to the widely accepted historical relationships.

show abstract

Section: Introductionmentioning

confidence: 99%

New Empirical Laws in Geosciences: A Successful Proposal

Díaz-Curiel,

Biosca,

Arévalo-Lomas

et al. 2023

Applied Sciences

View full text Add to dashboard Cite

show abstract

Coupled hydrogeophysical inversion through ensemble smoother with multiple data assimilation and convolutional neural network for contaminant plume reconstruction

Fagandini,

Todaro,

Escada

et al. 2024

Stoch Environ Res Risk Assess

View full text Add to dashboard Cite

In the field of groundwater, accurate delineation of contaminant plumes is critical for designing effective remediation strategies. Typically, this identification poses a challenge as it involves solving an inverse problem with limited concentration data available. To improve the understanding of contaminant behavior within aquifers, hydrogeophysics emerges as a powerful tool by enabling the combination of non-invasive geophysical techniques (i.e., electrical resistivity tomography—ERT) and hydrological variables. This paper investigates the potential of the Ensemble Smoother with Multiple Data Assimilation method to address the inverse problem at hand by simultaneously assimilating observed ERT data and scattered concentration values from monitoring wells. A novelty aspect is the integration of a Convolutional Neural Network (CNN) to replace and expedite the expensive geophysical forward model. The proposed approach is applied to a synthetic case study, simulating a tracer test in an unconfined aquifer. Five scenarios are compared, allowing to explore the effects of combining multiple data sources and their abundance. The outcomes highlight the efficacy of the proposed approach in estimating the spatial distribution of a concentration plume. Notably, the scenario integrating apparent resistivity with concentration values emerges as the most promising, as long as there are enough concentration data. This underlines the importance of adopting a comprehensive approach to tracer plume mapping by leveraging different types of information. Additionally, a comparison was conducted between the inverse procedure solved using the full geophysical forward model and the CNN model, showcasing comparable performance in terms of results, but with a significant acceleration in computational time.

show abstract

Experimental sandbox tracer tests to characterize a two-facies aquifer via an ensemble smoother

et al. 2023

View full text Add to dashboard Cite

Estimating aquifer properties and their spatial variability is the most challenging part of groundwater flow and transport simulations. In this work, an ensemble Kalman-based method, the ensemble smoother with multiple data assimilation (ES-MDA), is applied to infer the characteristics of a binary field by means of tracer test data collected in an experimental sandbox. Two different approaches are compared: the first one aims at estimating the hydraulic conductivity over the whole field assuming that the rest of the hydraulic and transport parameters are known by applying the standard ES-MDA method; the second one couples the ES-MDA with a truncated Gaussian model to simultaneously estimate the spatial distribution of two geological lithotypes and their main hydraulic and transport properties. Both procedures are tested following a fully parameterized approach and a pilot point approach. A synthetic case that mimics the sandbox experiment was developed to test the capability of the proposed methods and find out their optimal configurations to be used for the real case. The results show that the ES-MDA coupled with a truncated Gaussian model outperforms the standard ES-MDA and it reproduces well the binary field and the aquifer properties also in the presence of large measurement errors. The fully parametrized and pilot point approaches lead to comparable solutions, with less computation time required by the pilot point approach.

show abstract

Ensemble Smoother with Multiple Data Assimilation as a Tool for Curve Fitting and Parameter Uncertainty Characterization: Example Applications to Fit Nonlinear Sorption Isotherms

Cited by 4 publications

References 32 publications

New Empirical Laws in Geosciences: A Successful Proposal

New Empirical Laws in Geosciences: A Successful Proposal

Coupled hydrogeophysical inversion through ensemble smoother with multiple data assimilation and convolutional neural network for contaminant plume reconstruction

Experimental sandbox tracer tests to characterize a two-facies aquifer via an ensemble smoother

Contact Info

Product

Resources

About