Ensemble random forest filter: An alternative to the ensemble Kalman filter for inverse modeling

[EN] The ensemble random forest filter (ERFF) is presented as an alternative to the ensemble Kalman filter (EnKF) for inverse modeling. The EnKF is a data assimilation approach that forecasts and updates parameter estimates sequentially in time as observations are collected. The updating step is based on the experimental covariances computed from an ensemble of realizations, and the updates are given as linear combinations of the differences between observations and forecasted system state values. The ERFF replaces the linear combination in the update step with a non-linear function represented by a random forest. This way, the non-linear relationships between the parameters to be updated and the observations can be captured, and a better update produced. The ERFF is demonstrated for log-conductivity identification from piezometric head observations in several scenarios with varying degrees of heterogeneity (log-conductivity variances going from 1 up to 6.25 (ln m/d)2), number of realizations in the ensemble (50 or 100), and number of piezometric head observations (18 or 36). In all scenarios, the ERFF works well, reconstructing the log-conductivity spatial heterogeneity while matching the observed piezometric heads at selected control points. For benchmarking purposes, the ERFF is compared to the restart EnKF to find that the ERFF is superior to the EnKF for the number of ensemble realizations used (small in typical EnKF applications). Only when the number of realizations grows to 500 the restart EnKF can match the performance of the ERFF, albeit at more than double the computational cost.The authors acknowledge grant PID2019-109131RB-I00 funded by MCIN/AEI/10.13039/501100011033 and project InTheMED, which is part of the PRIMA Programme supported by the European Union's Horizon 2020 Research and Innovation Programme under Grant Agreement No 1923.A. Godoy, V.; Napa-García, GF.; Gómez-Hernández, JJ. (2022). Ensemble random forest filter: An alternative to the ensemble Kalman filter for inverse modeling. Journal of Hydrology. 615:1-13. https://doi.org/10.1016/j.jhydrol.2022.12864211361

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

[EN] The ensemble smoother with multiple data assimilation (ES-MDA) coupled to a normal-score transformation is used to fit a Langmuir isotherm curve to estimate its parameters (Sm and b) and their uncertainty. The highlights of this work are threefold: (1) the ES-MDA can be used as a curve fitting procedure, (2) the ES-MDA provides also a full uncertainty quantification about the fitted parameters, and (3) for the specific case of the Langmuir isotherm, parameter Sm is well identified with little uncertainty, while parameter b is well identified with a larger uncertainty, indicating that solute concentrations are more sensitive to Sm than to b. As a by-product, the number of samples required to characterize the joint uncertainty of Langmuir isotherm parameters is also investigated; it can be concluded that the minimum number of samples to use is six, with best results obtained with eight samples, a value larger than the number recommended in the literature.This research has been supported by the Spanish Ministry of Science and Innovation through project number PID2019-109131RB-I00 and by the Schlumberger Foundation by means of the program Faculty for the Future.Godoy, VA.; Napa-García, GF.; Gómez-Hernández, JJ. (2022). Ensemble Smoother with Multiple Data Assimilation as a Tool for Curve Fitting and Parameter Uncertainty Characterization: Example Applications to Fit Nonlinear Sorption Isotherms. Mathematical Geosciences. 54(4):807-825. https://doi.org/10.1007/s11004-021-09981-780782554

Deep Learning-based inverse modeling of a tank model of a channelized aquifer

Inverse modeling plays a fundamental role in the subsurface characterization of aquifers, given the scarcity of available data. Several techniques have been proposed in the literature and tested using synthetic examples. However, one of the big criticisms of these techniques is the lack of demonstra- tions in real cases. In this context, this study presents the application of two of the most advanced inverse modeling techniques: the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) and Deep Learning-based inverse modeling (DL), for the characterization of the non-Gaussian hy- draulic conductivity field of a 2D tank model of an aquifer. The experiment consisted of the release of a fluorescent solution from a point source on a horizontal flow field (constant head imposed to the left and right boundaries of the model). The physical model was built with glass beads of two sizes, forming a homogeneous low hydraulic conductivity matrix with sub-horizontal high conductivity channels embedded. The inverse problem pursued the identification of the hydraulic conductivity from measurements of the solute concentration at given locations and times. Prior field realizations were generated using multiple-point geostatistics to resemble the channel patterns observed on the physical model. The efficiency and accuracy of both techniques in terms of computational time and error/dispersion in hydraulic conductivity and solute concentration are evaluated