.. [Asch16] Asch M., Bocquet M., Nodet M., *Data Assimilation - Methods, Algorithms and Applications*, SIAM, 2016
-.. [GilBellosta15] Gil Bellosta C. J., *rPython: Package Allowing R to Call Python*, CRAN, 2015, https://cran.r-project.org/web/packages/rPython/ and http://rpython.r-forge.r-project.org/
-
-.. [Bouttier99] Bouttier B., Courtier P., *Data assimilation concepts and methods*, Meteorological Training Course Lecture Series, ECMWF, 1999
+.. [Bishop01] Bishop C. H., Etherton B. J., Majumdar S. J., *Adaptive sampling with the ensemble transform Kalman filter. Part I: theoretical aspects*, Monthly Weather Review, 129, pp.420–436, 2001
.. [Bocquet04] Bocquet M., *Introduction aux principes et méthodes de l'assimilation de données en géophysique*, Lecture Notes, 2014
+.. [Bouttier99] Bouttier B., Courtier P., *Data assimilation concepts and methods*, Meteorological Training Course Lecture Series, ECMWF, 1999
+
.. [Buchinsky98] Buchinsky M., *Recent Advances in Quantile Regression Models: A Practical Guidline for Empirical Research*, Journal of Human Resources, 33(1), pp.88-126, 1998
.. [Burgers98] Burgers G., Van Leuween P. J., Evensen G., *Analysis scheme in the Ensemble Kalman Filter*, Monthly Weather Review, 126, 1719–1724, 1998
.. [Courtier94] Courtier P., Thépaut J.-N., Hollingsworth A., *A strategy for operational implementation of 4D-Var, using an incremental approach*, Quarterly Journal of the Royal Meteorological Society, 120, pp.1367–1387, 1994
+.. [Courtier97] Courtier P., *Dual formulation of four-dimensional variational assimilation*, Quarterly Journal of the Royal Meteorological Society, 123, pp.2449-2461, 1997
+
.. [Das11] Das S., Suganthan P. N., *Differential Evolution: A Survey of the State-of-the-art*, IEEE Transactions on Evolutionary Computation, 15(1), pp.4-31, 2011
.. [Das16] Das S., Mullick S. S., Suganthan P. N., *Recent Advances in Differential Evolution - An Updated Survey*, Swarm and Evolutionary Computation, 27, pp.1-30, 2016
.. [Evensen03] Evensen G., *The Ensemble Kalman Filter: theoretical formulation and practical implementation*, Seminar on Recent developments in data assimilation for atmosphere and ocean, ECMWF, 8 to 12 September 2003
+.. [GilBellosta15] Gil Bellosta C. J., *rPython: Package Allowing R to Call Python*, CRAN, 2015, https://cran.r-project.org/web/packages/rPython/ and http://rpython.r-forge.r-project.org/
+
.. [Glover89] Glover F., *Tabu Search-Part I*, ORSA Journal on Computing, 1(2), pp.190-206, 1989
.. [Glover90] Glover F., *Tabu Search-Part II*, ORSA Journal on Computing, 2(1), pp.4-32, 1990
.. [WikipediaUKF] Wikipedia, *Unscented Kalman Filter*, https://en.wikipedia.org/wiki/Unscented_Kalman_filter
.. [Zhu97] Zhu C., Byrd R. H., Nocedal J., *L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization*, ACM Transactions on Mathematical Software, 23(4), pp.550-560, 1997
+
+.. [Zupanski05] Zupanski M., *Maximum likelihood ensemble filter: Theoretical aspects*, Monthly Weather Review, 133, pp.1710–1726, 2005
+
tui
reference
license
+ bibliography
+ notations
glossary
genindex
- notations
- bibliography
* :ref:`search`
which is usually designed as the "*3D-Var*" function (see for example
[Talagrand97]_). The terms "*3D-Var*", "*3D-VAR*" and "*3DVAR*" are equivalent.
+There exists various variants of this algorithm. The following stable and robust formulations are proposed here:
+
+.. index::
+ pair: Variant ; 3DVAR
+ pair: Variant ; 3DVAR-VAN
+ pair: Variant ; 3DVAR-Incr
+ pair: Variant ; 3DVAR-PSAS
+
+- "3DVAR" (3D Variational analysis, see [Lorenc86]_, [LeDimet86]_, [Talagrand97]_), original and very robust algorithm,
+- "3DVAR-VAN" (3D Variational Analysis with No inversion of B, see [Lorenc88]_), similar algorithm but avoiding inversion of the covariance matrix B,
+- "3DVAR-Incr" (Incremental 3DVAR, see [Courtier94]_), cheaper algorithm but involving an approximation of non-linear operators,
+- "3DVAR-PSAS" (Physical-space Statistical Analysis Scheme for 3DVAR, see [Courtier97]_, [Cohn98]_), algorithm sometimes more cheap because it operates in another space, but involving an approximation of non-linear operators.
+
+It is recommended to use the original 3DVAR.
+
.. ------------------------------------ ..
.. include:: snippets/Header2Algo02.rst
to evaluate on small systems. One can verify the linearity of the operators
with the help of the :ref:`section_ref_algorithm_LinearityTest`.
-There exists a lot of variants of this algorithm. Stable and robust ones are proposed here:
+There exists a lot of variants of this algorithm. The following stable and robust formulations are proposed here:
-- "EnKF" (Ensemble Kalman Filter), original stochastic algorithm, allowing consistent treatment of non-linear evolution operator,
+.. index::
+ pair: Variant ; EnKF
+ pair: Variant ; ETKF
+ pair: Variant ; ETKF-N
+ pair: Variant ; MLEF
+ pair: Variant ; IEnKF
+
+- "EnKF" (Ensemble Kalman Filter, see [Evensen94]_), original stochastic algorithm, allowing consistent treatment of non-linear evolution operator,
- "ETKF" (Ensemble-Transform Kalman Filter), deterministic EnKF algorithm, allowing treatment of non-linear evolution operator with a lot less members (one recommends to use a number of members on the order of 10 or even sometimes less),
- "ETKF-N" (Ensemble-Transform Kalman Filter of finite size N), ETKF algorithm of "finite size N", yhat doesn't need inflation that is often required with the other algorithms,
-- "MLEF" (Maximum Likelihood Kalman Filter), deterministic EnKF scheme, allowing in addition the consistent treament of non-linear observation operator,
+- "MLEF" (Maximum Likelihood Kalman Filter, see [Zupanski05]_), deterministic EnKF scheme, allowing in addition the consistent treament of non-linear observation operator,
- "IEnKF" (Iterative_EnKF), deterministic EnKF scheme, improving treament of operators non-linearities.
Without being a universal recommandation, one recommend to use EnKF as a reference algorithm, and the other algorithms (in this order) as means to obtain less costly data assimilation with hopefully the same quality.
- [Evensen94]_
- [Burgers98]_
- [Evensen03]_
+- [Zupanski05]_
- [WikipediaEnKF]_
*Predifined name*. This key allows to choose one of the possible variants
for the main algorithm. The default variant is the original "3DVAR", and the
possible ones are
- "3DVAR" (3D Variational analysis, see [Lorenc86]_, [LeDimet86]_, [Talagrand97]_),
- "3DVAR-VAN" (3D Variational Analysis with No inversion of B, see [Lorenc88]_),
- "3DVAR-Incr" (Incremental 3DVAR, see [Courtier94]_),
- "3DVAR-PSAS" (Physical-space Statistical Analysis Scheme for 3DVAR, see [Cohn98]_),
+ "3DVAR" (3D Variational analysis),
+ "3DVAR-VAN" (3D Variational Analysis with No inversion of B),
+ "3DVAR-Incr" (Incremental 3DVAR),
+ "3DVAR-PSAS" (Physical-space Statistical Analysis Scheme for 3DVAR),
It is highly recommended to keep the default value.
Exemple :
.. [Asch16] Asch M., Bocquet M., Nodet M., *Data Assimilation - Methods, Algorithms and Applications*, SIAM, 2016
-.. [GilBellosta15] Gil Bellosta C. J., *rPython: Package Allowing R to Call Python*, CRAN, 2015, https://cran.r-project.org/web/packages/rPython/ and http://rpython.r-forge.r-project.org/
-
-.. [Bouttier99] Bouttier B., Courtier P., *Data assimilation concepts and methods*, Meteorological Training Course Lecture Series, ECMWF, 1999
+.. [Bishop01] Bishop C. H., Etherton B. J., Majumdar S. J., *Adaptive sampling with the ensemble transform Kalman filter. Part I: theoretical aspects*, Monthly Weather Review, 129, pp.420–436, 2001
.. [Bocquet04] Bocquet M., *Introduction aux principes et méthodes de l'assimilation de données en géophysique*, Lecture Notes, 2014
+.. [Bouttier99] Bouttier B., Courtier P., *Data assimilation concepts and methods*, Meteorological Training Course Lecture Series, ECMWF, 1999
+
.. [Buchinsky98] Buchinsky M., *Recent Advances in Quantile Regression Models: A Practical Guidline for Empirical Research*, Journal of Human Resources, 33(1), pp.88-126, 1998
.. [Burgers98] Burgers G., Van Leuween P. J., Evensen G., *Analysis scheme in the Ensemble Kalman Filter*, Monthly Weather Review, 126, 1719–1724, 1998
.. [Courtier94] Courtier P., Thépaut J.-N., Hollingsworth A., *A strategy for operational implementation of 4D-Var, using an incremental approach*, Quarterly Journal of the Royal Meteorological Society, 120, pp.1367–1387, 1994
+.. [Courtier97] Courtier P., *Dual formulation of four-dimensional variational assimilation*, Quarterly Journal of the Royal Meteorological Society, 123, pp.2449-2461, 1997
+
.. [Das11] Das S., Suganthan P. N., *Differential Evolution: A Survey of the State-of-the-art*, IEEE Transactions on Evolutionary Computation, 15(1), pp.4-31, 2011
.. [Das16] Das S., Mullick S. S., Suganthan P. N., *Recent Advances in Differential Evolution - An Updated Survey*, Swarm and Evolutionary Computation, 27, pp.1-30, 2016
.. [Evensen03] Evensen G., *The Ensemble Kalman Filter: theoretical formulation and practical implementation*, Seminar on Recent developments in data assimilation for atmosphere and ocean, ECMWF, 8 to 12 September 2003
+.. [GilBellosta15] Gil Bellosta C. J., *rPython: Package Allowing R to Call Python*, CRAN, 2015, https://cran.r-project.org/web/packages/rPython/ and http://rpython.r-forge.r-project.org/
+
.. [Glover89] Glover F., *Tabu Search-Part I*, ORSA Journal on Computing, 1(2), pp.190-206, 1989
.. [Glover90] Glover F., *Tabu Search-Part II*, ORSA Journal on Computing, 2(1), pp.4-32, 1990
.. [Zhu97] Zhu C., Byrd R. H., Nocedal J., *L-BFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization*, ACM Transactions on Mathematical Software, 23(4), pp.550-560, 1997
+.. [Zupanski05] Zupanski M., *Maximum likelihood ensemble filter: Theoretical aspects*, Monthly Weather Review, 133, pp.1710–1726, 2005
+
*Nota Bene* : un lien vers la version française de chaque page Wikipédia se
trouve dans le sous-menu "*Languages*". Les deux versions sont complémentaires
car, même si souvent le contenu en anglais est plus fourni, les informations
tui
reference
license
+ bibliography
+ notations
glossary
genindex
- notations
- bibliography
* :ref:`search`
exemple [Talagrand97]_). Les dénominations "*3D-Var*", "*3D-VAR*" et "*3DVAR*"
sont équivalentes.
+Il existe diverses variantes de cet algorithme. On propose ici des formulations stables et robustes suivantes :
+
+.. index::
+ pair: Variant ; 3DVAR
+ pair: Variant ; 3DVAR-VAN
+ pair: Variant ; 3DVAR-Incr
+ pair: Variant ; 3DVAR-PSAS
+
+- "3DVAR" (3D Variational analysis, voir [Lorenc86]_, [LeDimet86]_, [Talagrand97]_), algorithme d'origine et très robuste,
+- "3DVAR-VAN" (3D Variational Analysis with No inversion of B, voir [Lorenc88]_), algorithme similaire mais permettant d'éviter l'inversion de la matrice de covariance B,
+- "3DVAR-Incr" (Incremental 3DVAR, voir [Courtier94]_), algorithme plus économique mais impliquant une approximation des opérateurs non-linéaires,
+- "3DVAR-PSAS" (Physical-space Statistical Analysis Scheme for 3DVAR, voir [Courtier97]_, [Cohn98]_), algorithme parfois plus économique car opérant dans un autre espace, mais impliquant une approximation des opérateurs non-linéaires.
+
+On recommande d'utiliser le 3DVAR d'origine.
+
.. ------------------------------------ ..
.. include:: snippets/Header2Algo02.rst
coûteux en évaluations sur de petits systèmes. On peut vérifier la linéarité
des opérateurs à l'aide de l':ref:`section_ref_algorithm_LinearityTest`.
-Il existe de nombreuses variantes de cet algorithme. On propose ici des formes stables et robustes suivantes :
+Il existe de nombreuses variantes de cet algorithme. On propose ici des formulations stables et robustes suivantes :
-- "EnKF" (Ensemble Kalman Filter), algorithme stochastique original, permettant de traiter de manière consistante un opérateur d'évolution non-linéaire,
+.. index::
+ pair: Variant ; EnKF
+ pair: Variant ; ETKF
+ pair: Variant ; ETKF-N
+ pair: Variant ; MLEF
+ pair: Variant ; IEnKF
+
+- "EnKF" (Ensemble Kalman Filter, voir [Evensen94]_), algorithme stochastique original, permettant de traiter de manière consistante un opérateur d'évolution non-linéaire,
- "ETKF" (Ensemble-Transform Kalman Filter), algorithme déterministe d'EnKF, permettant de traiter un opérateur d'évolution non-linéaire avec beaucoup moins de membres (on recommande d'utiliser un nombre de membres de l'ordre de 10 ou même parfois moins),
- "ETKF-N" (Ensemble-Transform Kalman Filter of finite size N), algorithme d'ETKF dit de "taille finie N", évitant de recourir à une inflation souvent nécessaire avec les autres algorithms
-- "MLEF" (Maximum Likelihood Kalman Filter), schéma déterministe d'EnKF, permettant en plus de traiter de manière consistante un opérateur d'observation non-linéaire),
+- "MLEF" (Maximum Likelihood Kalman Filter, voir [Zupanski05]_), schéma déterministe d'EnKF, permettant en plus de traiter de manière consistante un opérateur d'observation non-linéaire),
- "IEnKF" (Iterative_EnKF), schéma déterministe d'EnKF, améliorant le traitement des non-linéarités des opérateurs.
Sans pouvoir prétendre à l'universalité, on recommande d'utiliser l'EnKF comme référence, et les autres algorithmes (dans l'ordre) comme des moyens pour obtenir une assimilation de données plus économique et de qualité éventuellement similaire.
- [Evensen94]_
- [Burgers98]_
- [Evensen03]_
+- [Zupanski05]_
- [WikipediaEnKF]_
*Nom prédéfini*. Cette clé permet de choisir l'une des variantes possibles
pour l'algorithme principal. La variante par défaut est le "3DVAR" d'origine,
et les choix possibles sont
- "3DVAR" (3D Variational analysis, voir [Lorenc86]_, [LeDimet86]_, [Talagrand97]_),
- "3DVAR-VAN" (3D Variational Analysis with No inversion of B, voir [Lorenc88]_),
- "3DVAR-Incr" (Incremental 3DVAR, voir [Courtier94]_),
- "3DVAR-PSAS" (Physical-space Statistical Analysis Scheme for 3DVAR, voir [Cohn98]_),
+ "3DVAR" (3D Variational analysis),
+ "3DVAR-VAN" (3D Variational Analysis with No inversion of B),
+ "3DVAR-Incr" (Incremental 3DVAR),
+ "3DVAR-PSAS" (Physical-space Statistical Analysis Scheme for 3DVAR),
Il est fortement conseillé de conserver la valeur par défaut.
Exemple :
