My colleague Anthony Fillion has investigated quasi-static strategies in the context of ensemble variational data assimilation. Quasi-static variational data assimilation had been developed by Pires, Talagrand and Vautard (1996) for 4D-Var in a significant nonlinear context where the background cost function may have multiple local minima which could easily cripple the analysis. His study generalizes this idea to 4D EnVar techniques, where the transfer of statistics from one cycle to the next plays a significant role. It is illustrated with the Iterative Ensemble Kalman Smoother, an exemplar of nonlinear 4D EnVar algorithms. Analytical results are obtained in simple linear cases. The quasi-static algorithms that we developed are then applied successfully to Lorenz low-order models and allow, in the absence of model error, extra long data assimilation window with a proper cycling. A heuristic argument helps estimate the optimal legnth of the window.
This study has been published in the Nonlinear Processes in Geophysics special edition dedicated to the legacy of Anna Trevisan. It is entitled Quasi static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother .