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

The ensemble random forest filter (ERFF) is presented as an alternative to the ensemble Kalman filter (EnKF) for the purpose of inverse modeling. The EnKF is a data assimilation approach that forecasts and updates parameter estimates sequentially in time as observations are being 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. In 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 the purpose of log-conductivity identification from piezometric head observations in a number of 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, being able to reconstruct 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 is able to match the performance of the ERFF, albeit at triple the computational cost.