Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother

摘要

The analysis in nonlinear variational data assimilation is the solution of anon-quadratic minimization. Thus, the analysis efficiency relies on itsability to locate a global minimum of the cost function. If this minimizationuses a Gauss–Newton (GN) method, it is critical for the starting point to bein the attraction basin of a global minimum. Otherwise the method mayconverge to a local extremum, which degrades the analysis. Withchaotic models, the number of local extrema often increases with the temporalextent of the data assimilation window, making the former condition harder tosatisfy. This is unfortunate because the assimilation performance alsoincreases with this temporal extent. However, a quasi-static (QS)minimization may overcome these local extrema. It accomplishes this bygradually injecting the observations in the cost function. This method wasintroduced by Pires et al. (1996) in a 4D-Var context.We generalize this approach to four-dimensional strong-constraint nonlinearensemble variational (EnVar) methods, which are based on both a nonlinearvariational analysis and the propagation of dynamical error statistics via anensemble. This forces one to consider the cost function minimizations in thebroader context of cycled data assimilation algorithms. We adapt this QSapproach to the iterative ensemble Kalman smoother (IEnKS), an exemplar ofnonlinear deterministic four-dimensional EnVar methods. Using low-ordermodels, we quantify the positive impact of the QS approach on the IEnKS,especially for long data assimilation windows. We also examine thecomputational cost of QS implementations and suggest cheaper algorithms.