A Multi-scale valid time shifting approach in an RRFS-like ensemble based data assimilation system

Valid time shifting (VTS) is a versatile, cost-effective method to increase the background ensemble size for ensemble-based data assimilation (DA) systems. This is accomplished by including ensemble member forecast output at multiple times surrounding the central analysis time within the background ensemble covariances for DA. Despite the demonstrated success of the approach, all early studies adopt a fixed shifting interval, neglecting that phase error can be highly scale dependent. In this study, a new approach to account for scale-dependent phase uncertainty in the time-shifted ensembles is proposed and tested in the RRFS like system. In this approach, smaller scales from short-term time shifting (30-min) are blended together with larger scales taken from a longer time-shifting (2-h). This study adopts a case study setting for better understanding of where and how the multiscale VTS impacts the analysis and forecasts. Results show benefits to the new approach in terms of mesoscale first guesses, and deterministic free forecast benefits when proper parameters are selected. Furthermore, the use of an external ensemble is tested to capture the large-scale shiftings to further limit added computational costs and potentially improve the practicality of VTS for RRFS.