Data assimilation for re-analyses: potential gains from full use of post-analysis-time observations

In recent years a number of operational meteorological centres have completed multidecadal reanalyses of their observation records using a version of their operational analysis systems. These operational systems aim to approximate the best possible analysis of the atmospheric state at a given time using all observations made prior to that time, and require major resources to produce. Re-analyses are made with the same real-time systems because they can be done as marginal activities on the back of operational efforts. In this paper, we examine some of the salient differences between the use of optimal real-time analyses and optimal retrospective analyses in the context of a simple linear system. In this case, the optimal real-time analysis could be obtained by the Kalman filter. When observations are available both before and after the analysis time the additional information can, in principle, be exploited to improve on the Kalman filter analysis. For linear systems the optimal retrospective analysis is given by the Kalman smoother, which combines a forward and backward Kalman filter. Results comparing these methods are presented which demonstrate the importance of using all the available data for a retrospective analysis. While using all future data is not yet tractable for retrospective meteorological analyses, such techniques are of use for more limited re-analysis.