Assessing the Influence of Observations in Ensemble‐Based Data Assimilation Systems

Abstract The skill of numerical weather forecasts strongly depends on the quality of the initial conditions (analyses), which are created by assimilating observations into previous short‐range model forecasts. Therefore, it is important to carefully assess the influence of different observations on the analysis. The degrees of freedom for signal (DFS) is a useful metric for quantifying this influence. While DFS has long been used in variational data assimilation (DA) systems, its application in ensemble‐based DA systems remains limited. In this study, we propose two novel approaches for estimating the DFS in ensemble‐based systems. One approach uses the weighting vector calculated in ensemble transform Kalman filters, while the other uses the innovation vector and observation‐space increment vector. We also propose a new strategy for implementing the DFS approaches in the presence of domain localization, which first estimates DFS locally and then aggregates the results to derive a global DFS value for each observation. Our numerical results show that the DFS per observation decreases as the localization radius increases. More generally, the proposed DFS approaches and implementation strategy have the potential to be used in practice to inform the optimization of observation networks and DA systems.