Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother
The analysis in nonlinear variational data assimilation is the solution of a non-quadratic minimization. Thus, the analysis efficiency relies on its ability to locate a global minimum of the cost function. If this minimization uses a Gauss–Newton (GN) method, it is critical for the starting point...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2018-04-01
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| Series: | Nonlinear Processes in Geophysics |
| Online Access: | https://www.nonlin-processes-geophys.net/25/315/2018/npg-25-315-2018.pdf |
| Summary: | The analysis in nonlinear variational data assimilation is the solution of a
non-quadratic minimization. Thus, the analysis efficiency relies on its
ability to locate a global minimum of the cost function. If this minimization
uses a Gauss–Newton (GN) method, it is critical for the starting point to be
in the attraction basin of a global minimum. Otherwise the method may
converge to a <i>local</i> extremum, which degrades the analysis. With
chaotic models, the number of local extrema often increases with the temporal
extent of the data assimilation window, making the former condition harder to
satisfy. This is unfortunate because the assimilation performance also
increases with this temporal extent. However, a quasi-static (QS)
minimization may overcome these local extrema. It accomplishes this by
gradually injecting the observations in the cost function. This method was
introduced by Pires et al. (1996) in a 4D-Var context.
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We generalize this approach to four-dimensional strong-constraint nonlinear
ensemble variational (EnVar) methods, which are based on both a nonlinear
variational analysis and the propagation of dynamical error statistics via an
ensemble. This forces one to consider the cost function minimizations in the
broader context of cycled data assimilation algorithms. We adapt this QS
approach to the iterative ensemble Kalman smoother (IEnKS), an exemplar of
nonlinear deterministic four-dimensional EnVar methods. Using low-order
models, we quantify the positive impact of the QS approach on the IEnKS,
especially for long data assimilation windows. We also examine the
computational cost of QS implementations and suggest cheaper algorithms. |
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| ISSN: | 1023-5809 1607-7946 |