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The ensemble random forest filter (ERFF) is presented as an alternative tothe ensemble Kalman filter (EnKF) for the purpose of inverse modeling. The EnKFis a data assimilation approach that forecasts and updates parameter estimatessequentially in time as observations are being collected. The updating step isbased on the experimental covariances computed from an ensemble of realizationsand the updates are given as linear combinations of the differences betweenobservations and forecasted system state values. The ERFF replaces the linearcombination in the update step with a non-linear function represented by arandom forest. In this way, the non-linear relationships between the parametersto be updated and the observations can be captured and a better updateproduced. The ERFF is demonstrated for the purpose of log-conductivityidentification from piezometric head observations in a number of scenarios withvarying degrees of heterogeneity (log-conductivity variances going from 1 up to6.25 (ln m/d)2), number of realizations in the ensemble (50 or 100), and numberof piezometric head observations (18 or 36). In all scenarios, the ERFF workswell, being able to reconstruct the log-conductivity spatial heterogeneitywhile matching the observed piezometric heads at selected control points. Forbenchmarking purposes the ERFF is compared to the restart EnKF to find that theERFF is superior to the EnKF for the number of ensemble realizations used(small in typical EnKF applications). Only when the number of realizationsgrows to 500, the restart EnKF is able to match the performance of the ERFF,albeit at triple the computational cost.

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