Exploring Online Data Assimilation for Paleoclimate Reconstruction Using an Idealized OSSE Framework

Knowledge of past climate conditions is crucial to understand the climate system. Recently, data assimilation (DA) has been applied to reconstruct paleoclimate, in which proxy data such as tree-ring width and isotopic composition in ice sheets are used. DA has long been used for forecasting the weather and is a well-established method. However, the DA algorithms used for weather forecasts cannot be directly applied to paleoclimate due to the different temporal resolution, spatial extent, and type of information contained within the observation data. The temporal resolution and spatial distribution of proxy data are significantly lower (seasonal at best) and sparser than the present-day observations used for weather forecasts. Therefore, DA applied to paleoclimate is only loosely linked to the methods used in the more mature field of weather forecasting. Several DA methods have been proposed for paleoclimate reconstruction, and paleoclimate studies using DA have successfully determined the mechanisms behind the past climate changes. Most of the previous studies have not used the analysis to provide a first guess for the next cycle, the method known as offline DA, assuming that the observations are temporally too coarse to constrain the model simulation. However, an advantage of DA is to accumulate the observed information into the model state in both space and time in a physically consistent way by cycling the analysis to the simulation, the method known as online DA. In this study, we first investigate correlations between the time-averaged observation and the short-time-scale model state using an intermediate AGCM known as the SPEEDY model. Based on the results, we perform idealized, perfect-model OSSE experiments to evaluate several online DA techniques assimilating time-averaged observation data.