A Multi-model Data Assimilation Framework Via Ensemble Kalman Filter

The ensemble Kalman filter (EnKF) is a widely-used data assimilation method that has the capacity to sequentially update system parameters and states as new observations become available. One noticeable feature of EnKF is that it not only can provide optimal updates of model parameters and state variables, but also can give the uncertainty associated with them in each assimilation step. The natural system is open and complex, rendering it prone to multiple interpretations and mathematical descriptions. Bayesian model averaging (BMA) is an effective method to account for the uncertainty stemming from the model itself. In this paper, EnKF is embedded into the BMA framework, where individual posterior probability distributions of state vectors after each assimilation step are linearly integrated together through posterior model weights. A two-dimensional illustrative example is employed to demonstrate the proposed multi-model data assimilation approach via EnKF. Results show that statistical bias and uncertainty underestimation can occur when the data assimilation process relies on a single postulated model. The posterior model weight can adjust itself dynamically in time according to its consistency with observations. The performances of log conductivity estimation and head prediction are compared to the standard EnKF method based on the postulated single model and the proposed multi-model EnKF method. Comparisons show that multi-model EnKF performs better in terms of log score and coverage when sufficient observations have been assimilated.