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...
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doaj-b0d0ec4fd01c4246bd6388c6fbf605ae2020-11-24T22:44:09ZengCopernicus PublicationsNonlinear Processes in Geophysics1023-58091607-79462018-04-012531533410.5194/npg-25-315-2018Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smootherA. Fillion0A. Fillion1M. Bocquet2S. Gratton3CEREA, Joint Laboratory École des Ponts ParisTech and EDF R&D, Université Paris-Est, Champs-sur-Marne, FranceCERFACS, Toulouse, FranceCEREA, Joint Laboratory École des Ponts ParisTech and EDF R&D, Université Paris-Est, Champs-sur-Marne, FranceINPT-IRIT, Toulouse, FranceThe 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. <br><br> 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.https://www.nonlin-processes-geophys.net/25/315/2018/npg-25-315-2018.pdf |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
A. Fillion A. Fillion M. Bocquet S. Gratton |
spellingShingle |
A. Fillion A. Fillion M. Bocquet S. Gratton Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother Nonlinear Processes in Geophysics |
author_facet |
A. Fillion A. Fillion M. Bocquet S. Gratton |
author_sort |
A. Fillion |
title |
Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother |
title_short |
Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother |
title_full |
Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother |
title_fullStr |
Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother |
title_full_unstemmed |
Quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble Kalman smoother |
title_sort |
quasi-static ensemble variational data assimilation: a theoretical and numerical study with the iterative ensemble kalman smoother |
publisher |
Copernicus Publications |
series |
Nonlinear Processes in Geophysics |
issn |
1023-5809 1607-7946 |
publishDate |
2018-04-01 |
description |
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.
<br><br>
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. |
url |
https://www.nonlin-processes-geophys.net/25/315/2018/npg-25-315-2018.pdf |
work_keys_str_mv |
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