An Analog Offline EnKF for Paleoclimate Data Assimilation

An analog offline ensemble Kalman filter (AOEnKF) is proposed, which constructs ensemble priors from a control climate simulation for each assimilation time based on an analog criterion using proxy observations. Even though AOEnKF is an offline scheme and is therefore computationally economical, it has the ability to capture "flow-dependent" background error covariances that help spread observation information through climate fields. Extensive tests in the Lorenz05 model demonstrate that, compared to the online cycling EnKF (CEnKF), AOEnKF generates smaller posterior errors and requires much less computational cost. Compared to the commonly applied offline EnKF (OEnKF), AOEnKF has the advantages of having a more accurate prior ensemble mean and "flow-dependent" background error covariances, even though the assimilation time scale is beyond significant forecast skill of the climate model. With varying ensemble sizes, sample sizes, observation error covariances and observing networks, AOEnKFs generally produce statistically significant error reduction relative to OEnKF, especially for larger sample sizes, increased observation uncertainties and sparser observing networks. The AOEnKF can be applied based on either the error of state variables from observations (AOEnKF_E) or the spatial correlation of state variables with observations (AOEnKF_C), with generally comparable results.