Quantifying Monte Carlo Uncertainty in the Ensemble Kalman Filter

We have suggested running multiple EnKF runs with a smaller ensemble size, and have presented a methodology for determining the optimal ensemble batch size for a synthetic 2D model. The optimal combination of ensemble size and number of EnKF runs is clearly case dependent. However, our results suggest that for a given number of forward model runs (n*m), it will be better to perform several EnKF runs with a smaller ensemble size, than one run with a larger number of ensemble members. Technical contributions: 1) Improvement of the EnKF methodology for characterization of posterior pdf by performing multiple runs with smaller ensemble sizes instead of one large run 2) A methodology for optimal choice of ensemble batch size (n) and number of EnKF runs (m) for a fixed total number of ensemble members (m*n). 3) Developed a methodology for uncertainty estimation of the posterior CDF using EnKF.