A comparison between a Monte Carlo implementation of retrospective optimal interpolation and an ensemble Kalman filter in nonlinear dynamics

Abstract

To more correctly estimate the error covariance of an evolved state of a nonlinear dynamical System, the second and higher-order moments of the prior error need to be known. Analogous to the extension of a Kalman filter into an EnKF, an ensemble retrospective optimalinterpolation (EnROI) technique was derived using the Monte Carlo method from ROI. In contrast to the deterministic version of ROI, the background error covariance is represented by a background ensemble in EnROI. By sequentially applying EnROI to a moving limited analysis window and exploiting the forecast from the average of the background ensemble of En-ROI as a guess field, the computation costs for EnROI can be reduced.nKF, an ensemble retrospective optimalinterpolation (EnROI) technique was derived using the Monte Carlo method from ROI. In contrast to the deterministic version of ROI, the background error covariance is represented by a background ensemble in EnROI. By sequentially applying EnROI to a moving limited analysis window and exploiting the forecast from the average of the background ensemble of En-ROI as a guess field, the computation costs for EnROI can be reduced.