A New Inverse Modeling Approach for Hydraulic Conductivity Estimation Based on Gaussian Mixtures

This study proposes a new inverse algorithm to estimate the hydraulic conductivity (K) distribution based on a Gaussian Mixture Model that significantly reduces the number of parameters to be estimated during the inversion process. Moreover, a new objective function that increases the sensitivity of...

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Bibliographic Details
Published in:Water resources research 2020-09, Vol.56 (9), p.n/a
Main Authors: Minutti, Carlos, Illman, Walter A., Gomez, Susana
Format: Article
Language:English
Subjects:
Algorithms
aquifer heterogeneity
Bayesian analysis
Computational efficiency
Computer applications
Computing time
Geostatistics
groundwater modeling
Heterogeneity
Hydraulic conductivity
hydraulic tomography
Hydraulics
inverse modeling
model comparison
Objective function
Parameter estimation
Parameter sensitivity
Parameters
Probabilistic models
Pumping
Pumping tests
Tests
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Summary:This study proposes a new inverse algorithm to estimate the hydraulic conductivity (K) distribution based on a Gaussian Mixture Model that significantly reduces the number of parameters to be estimated during the inversion process. Moreover, a new objective function that increases the sensitivity of parameters using the spatial derivatives of hydraulic heads is introduced, and the algorithm is further improved by including a Bayes estimator that takes advantage of different possible solutions. The developed approach is tested through multiple synthetic experiments consisting of 250 randomly generated K fields resulting in different levels of heterogeneity and the use of different number of pumping tests, with a total of 1,000 cases of two‐dimensional configuration. A large number of cases are considered to ensure that our findings and conclusions are not based on a single realization. Results revealed significant improvements to K estimates, computational time, and predictions of independently conducted tests not used in the calibration effort when compared to a geostatistical inverse approach. Overall, our results reveal that the Gaussian Mixture inversion approach is able to achieve similar or higher levels of accuracy using half of the pumping tests and 20% of the computational time compared to a geostatistical inversion approach. Key Points New algorithm based on Gaussian mixtures is developed for hydraulic conductivity estimation It is faster and more accurate than geostatistical inversion, based on tests with multiple synthetic experiments Use of spatial derivatives in the objective function improves estimates
ISSN:0043-1397
1944-7973
DOI:10.1029/2019WR026531