An online data assimilation method to assimilate time-averaged observations

Knowledge of past climate conditions is invaluable to understand the climate system. Recently, data assimilation (DA) has been applied to reconstruct paleoclimate, using proxy data such as tree-ring width and isotopic composition in ice sheets. 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. Especially, the temporal resolution of proxy data is significantly lower (seasonal at best) 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. Up until now, several DA methods have been proposed for paleoclimate, and successfully reconstructed the paleoclimate. However, 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 developed a new online data assimilation method to treat temporally-averaged observations like proxy data, building upon the previous studies exploring online DA. We performed idealized OSSE experiments using an intermediate AGCM known as the SPEEDY model. We will show comparison results with offline DA and other online DA methods and their response to the temporal resolution of the observations.