Assessing the influence of observations on the analysis in ensemble-based data assimilation systems

Convection-permitting numerical weather prediction (NWP) is crucial for forecasting high-impact weather events such as heavy precipitation, storms, floods, wind gusts and fog. The assimilation of observations plays a significant role in improving the forecasting skill of these weather events. To make better use of existing observations and guide the design of future observation networks, accurately assessing the influence of assimilated observations is essential. The degrees of freedom for signal (DFS) has long been used to assess the influence of observations on the analysis. While various methods exist for calculating the DFS in variational data assimilation (DA) systems, calculating the DFS in ensemble-based DA systems (e.g., the ensemble transform Kalman filter) is a largely unexplored area. Since ensemble-based DA systems are becoming increasingly dominant for convection-permitting NWP, practical implementation of the DFS in such DA systems is needed. Unlike in variational DA systems, the background error covariance matrix is not static in ensemble-based DA methods. Consequently, the DFS calculated at each assimilation step measures the observation influence for a certain background error covariance matrix. This means that the DFS estimates are flow dependent. In addition, domain localisation of observations is often used in ensemble-based DA systems (e.g., local ensemble transform Kalman filter). This implies that the DFS should be calculated locally. In this work, we propose novel approaches for calculating the DFS in ensemble-based DA systems and investigate existing approaches applicable to such systems. We establish their consistency under idealised conditions and discuss their differences in practical applications. To validate our theoretical findings, we conduct simple numerical experiments using JEDI (Joint Effort for Data assimilation Integration) developed by JCSDA (Joint Center for Satellite Data Assimilation).  Our results provide useful information for assessing the influence of observations in ensemble-based DA systems. This work is financially supported by the Met Office and is fully in line with the Met Office’s strategy and its ongoing development of the next generation data assimilation and observation processing system.