Budget Closures in Data Assimilation: Physical Consistency and Model Error Source Modeling

Data assimilation is a procedure that combines observations with models to improve de-scriptions of the modeled systems, such as the atmosphere and the ocean. Observations correct errors in models on the one hand, and models extrapolate data information in space and time on the other. Data assimilation is widely utilized in atmospheric sci-ences as well as in other disciplines of Earth Science, to help understand the workings of the respective systems. However, because of the data corrections, the temporal evo-lution described by these results are often physically inconsistent. For instance, heat and mass budgets cannot be closed, limiting the utility of the analyses. This article elucidates the nature of these inconsistencies and describes a solution to correct these problems. In particular, so-called smoothing algorithms can x the deciencies ren-dering model solutions physically consistent. Smoothing is half the data assimilation problem often ignored or forgotten in many applications. Smoothing is an inversion of the model that allows explicit estimation of model error sources. In comparison, sequential methods employed in most assimilation systems today are stationary inver