On-line and off-line data assimilation in palaeoclimatology: a case study

Different ensemble-based data assimilation (DA) approaches for palaeoclimate reconstructions have been recently undertaken, but no systematic comparison among them has been attempted. We compare an off-line and an on-line ensemble-based method, with the testing period being the 17th century, which led into the Maunder Minimum. We use a low-resolution version of Max Planck Institute for Meteorology Earth System Model (MPI-ESM) to assimilate the Past Global Changes (PAGES) 2k continental temperature reconstructions. In the off-line approach, the ensemble for the entire simulation period is generated first and then the ensemble is used in combination with the empirical information to produce the analysis. In contrast, in the on-line approach, the ensembles are generated sequentially for sub-periods based on the analysis of previous sub-periods. Both schemes perform better than the simulations without DA. The on-line method would be expected to perform better if the assimilation led to states of the slow components of the climate system that are close to reality and the system had sufficient memory to propagate this information forward in time. In our comparison, which is based on analysing correlations and differences between the analysis and the proxy-based reconstructions, we find similar skill for both methods on the continental and hemispheric scales. This indicates either a lack of control of the slow components in our setup or a lack of skill in the information propagation on decadal timescales. Additional experiments are however needed to check whether the conclusions reached in this particular setup are valid in other cases. Although the performance of the two schemes is similar and the on-line method is more difficult to implement, the temporal consistency of the analysis in the on-line method makes it in general preferable