A fast, single-iteration ensemble Kalman smoother for sequential data assimilation

Abstract. Ensemble variational methods form the basis of state art for nonlinear, scalable data assimilation, yet current designs may not be cost-effective real-time, short-range forecast systems. We propose a novel estimator in this formalism that is designed applications which error dynamics weakly such as synoptic-scale meteorology. Our method combines 3D sequential filter analysis and retrospective reanalysis classic ensemble Kalman smoother with an iterative simulation 4D smoothers. To rigorously derive contextualize our method, we review related smoothers Bayesian maximum posteriori narrative. then develop intercompare these schemes open-source Julia package DataAssimilationBenchmarks.jl, pseudo-code provided their implementations. This numerical framework, supporting mathematical results, produces extensive benchmarks demonstrating significant performance advantages proposed technique. Particularly, single-iteration (SIEnKS) shown to improve prediction/analysis accuracy simultaneously reduce leading-order computational cost smoothing variety test cases relevant forecasting. long work presents SIEnKS provides theoretical framework further development filters