Revisiting Online and Offline Data Assimilation Comparison for Paleoclimate Reconstruction: An Idealized OSSE Study

Data assimilation (DA) has been applied to estimate the time-mean state, such as annual mean surface temperature for paleoclimate reconstruction. There are two types of DA for this purpose: online-DA and offline-DA. The online-DA estimates both time-mean states (analyses) and initial conditions for subsequent DA cycles, while the offline-DA only estimates the time-mean analyses. If there is sufficiently long predictability in the system of interest compared to the temporal resolution of the observations, online-DA is expected to outperform offline-DA by utilizing information in the initial conditions. However, previous studies failed to show the superiority of online-DA when time-averaged observations are assimilated, and the reason has not been investigated thoroughly. This study compares online-DA and offline-DA and investigates the relation to the predictability using an intermediate complexity general circulation model with perfect-model observing system simulation experiments. The result shows that the online-DA outperforms offline-DA when the length of predictability is longer than the averaging time of the observations. We also found that the longer the predictability, the more skillful the online-DA. Here, the ocean plays a crucial role in extending predictability, which helps online-DA to outperform offline-DA. Interestingly, the observations of near-surface air temperature over land are highly valuable to update the ocean variables in the analysis steps, suggesting the importance of using cross-domain covariance information between the atmosphere and the ocean when online-DA is applied to reconstruct paleoclimate.