2 Copyright (C) 2008-2021 EDF R&D
4 This file is part of SALOME ADAO module.
6 This library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
11 This library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
16 You should have received a copy of the GNU Lesser General Public
17 License along with this library; if not, write to the Free Software
18 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
20 See http://www.salome-platform.org/ or email : webmaster.salome@opencascade.com
22 Author: Jean-Philippe Argaud, jean-philippe.argaud@edf.fr, EDF R&D
24 .. index:: single: 3DVAR
25 .. index:: single: 3D-Var
26 .. _section_ref_algorithm_3DVAR:
28 Algorithme de calcul "*3DVAR*"
29 ------------------------------
31 .. ------------------------------------ ..
32 .. include:: snippets/Header2Algo01.rst
34 Cet algorithme réalise une estimation d'état par minimisation variationnelle de
35 la fonctionnelle :math:`J` d'écart classique en assimilation de données
38 .. math:: J(\mathbf{x})=(\mathbf{x}-\mathbf{x}^b)^T.\mathbf{B}^{-1}.(\mathbf{x}-\mathbf{x}^b)+(\mathbf{y}^o-H(\mathbf{x}))^T.\mathbf{R}^{-1}.(\mathbf{y}^o-H(\mathbf{x}))
40 qui est usuellement désignée comme la fonctionnelle "*3D-Var*" (voir par
41 exemple [Talagrand97]_). Les dénominations "*3D-Var*", "*3D-VAR*" et "*3DVAR*"
44 Il existe diverses variantes de cet algorithme. On propose ici les formulations
45 stables et robustes suivantes :
49 pair: Variant ; 3DVAR-VAN
50 pair: Variant ; 3DVAR-Incr
51 pair: Variant ; 3DVAR-PSAS
53 - "3DVAR" (3D Variational analysis, voir [Lorenc86]_, [LeDimet86]_, [Talagrand97]_), algorithme classique d'origine, très robuste, opérant dans l'espace du modèle,
54 - "3DVAR-VAN" (3D Variational Analysis with No inversion of B, voir [Lorenc88]_), algorithme similaire, opérant dans l'espace du modèle, mais permettant d'éviter l'inversion de la matrice de covariance B,
55 - "3DVAR-Incr" (Incremental 3DVAR, voir [Courtier94]_), algorithme plus économique que les précédents, mais impliquant une approximation des opérateurs non-linéaires,
56 - "3DVAR-PSAS" (Physical-space Statistical Analysis Scheme for 3DVAR, voir [Courtier97]_, [Cohn98]_), algorithme parfois plus économique car opérant dans l'espace des observations, mais impliquant une approximation des opérateurs non-linéaires.
58 On recommande fortement d'utiliser le "3DVAR" d'origine. Les algorithmes
59 "3DVAR" et "3DVAR-Incr" (et pas les autres) permettent la modification du point
60 initial de leur minimisation, mais ce n'est pas recommandé.
62 .. ------------------------------------ ..
63 .. include:: snippets/Header2Algo02.rst
65 .. include:: snippets/Background.rst
67 .. include:: snippets/BackgroundError.rst
69 .. include:: snippets/Observation.rst
71 .. include:: snippets/ObservationError.rst
73 .. include:: snippets/ObservationOperator.rst
75 .. ------------------------------------ ..
76 .. include:: snippets/Header2Algo03AdOp.rst
78 .. include:: snippets/BoundsWithNone.rst
80 .. include:: snippets/CostDecrementTolerance.rst
82 .. include:: snippets/GradientNormTolerance.rst
84 .. include:: snippets/InitializationPoint.rst
86 .. include:: snippets/MaximumNumberOfSteps.rst
88 .. include:: snippets/Minimizer_xDVAR.rst
90 .. include:: snippets/NumberOfSamplesForQuantiles.rst
92 .. include:: snippets/ProjectedGradientTolerance.rst
94 .. include:: snippets/Quantiles.rst
96 .. include:: snippets/SetSeed.rst
98 .. include:: snippets/SimulationForQuantiles.rst
100 StoreSupplementaryCalculations
101 .. index:: single: StoreSupplementaryCalculations
103 *Liste de noms*. Cette liste indique les noms des variables supplémentaires
104 qui peuvent être disponibles au cours du déroulement ou à la fin de
105 l'algorithme, si elles sont initialement demandées par l'utilisateur. Cela
106 implique potentiellement des calculs ou du stockage coûteux. La valeur par
107 défaut est une liste vide, aucune de ces variables n'étant calculée et
108 stockée par défaut sauf les variables inconditionnelles. Les noms possibles
109 sont dans la liste suivante : [
111 "APosterioriCorrelations",
112 "APosterioriCovariance",
113 "APosterioriStandardDeviations",
114 "APosterioriVariances",
117 "CostFunctionJAtCurrentOptimum",
119 "CostFunctionJbAtCurrentOptimum",
121 "CostFunctionJoAtCurrentOptimum",
122 "CurrentIterationNumber",
128 "InnovationAtCurrentState",
129 "JacobianMatrixAtBackground",
130 "JacobianMatrixAtOptimum",
131 "KalmanGainAtOptimum",
132 "MahalanobisConsistency",
135 "SampledStateForQuantiles",
137 "SimulatedObservationAtBackground",
138 "SimulatedObservationAtCurrentOptimum",
139 "SimulatedObservationAtCurrentState",
140 "SimulatedObservationAtOptimum",
141 "SimulationQuantiles",
145 ``{"StoreSupplementaryCalculations":["BMA", "CurrentState"]}``
147 .. include:: snippets/Variant_3DVAR.rst
149 .. ------------------------------------ ..
150 .. include:: snippets/Header2Algo04.rst
152 .. include:: snippets/Analysis.rst
154 .. include:: snippets/CostFunctionJ.rst
156 .. include:: snippets/CostFunctionJb.rst
158 .. include:: snippets/CostFunctionJo.rst
160 .. ------------------------------------ ..
161 .. include:: snippets/Header2Algo05.rst
163 .. include:: snippets/Analysis.rst
165 .. include:: snippets/APosterioriCorrelations.rst
167 .. include:: snippets/APosterioriCovariance.rst
169 .. include:: snippets/APosterioriStandardDeviations.rst
171 .. include:: snippets/APosterioriVariances.rst
173 .. include:: snippets/BMA.rst
175 .. include:: snippets/CostFunctionJ.rst
177 .. include:: snippets/CostFunctionJAtCurrentOptimum.rst
179 .. include:: snippets/CostFunctionJb.rst
181 .. include:: snippets/CostFunctionJbAtCurrentOptimum.rst
183 .. include:: snippets/CostFunctionJo.rst
185 .. include:: snippets/CostFunctionJoAtCurrentOptimum.rst
187 .. include:: snippets/CurrentIterationNumber.rst
189 .. include:: snippets/CurrentOptimum.rst
191 .. include:: snippets/CurrentState.rst
193 .. include:: snippets/ForecastState.rst
195 .. include:: snippets/IndexOfOptimum.rst
197 .. include:: snippets/Innovation.rst
199 .. include:: snippets/InnovationAtCurrentState.rst
201 .. include:: snippets/JacobianMatrixAtBackground.rst
203 .. include:: snippets/JacobianMatrixAtOptimum.rst
205 .. include:: snippets/KalmanGainAtOptimum.rst
207 .. include:: snippets/MahalanobisConsistency.rst
209 .. include:: snippets/OMA.rst
211 .. include:: snippets/OMB.rst
213 .. include:: snippets/SampledStateForQuantiles.rst
215 .. include:: snippets/SigmaObs2.rst
217 .. include:: snippets/SimulatedObservationAtBackground.rst
219 .. include:: snippets/SimulatedObservationAtCurrentOptimum.rst
221 .. include:: snippets/SimulatedObservationAtCurrentState.rst
223 .. include:: snippets/SimulatedObservationAtOptimum.rst
225 .. include:: snippets/SimulationQuantiles.rst
227 .. ------------------------------------ ..
228 .. include:: snippets/Header2Algo09.rst
230 .. include:: scripts/simple_3DVAR.rst
232 .. literalinclude:: scripts/simple_3DVAR.py
234 .. include:: snippets/Header2Algo10.rst
236 .. literalinclude:: scripts/simple_3DVAR.res
238 .. ------------------------------------ ..
239 .. include:: snippets/Header2Algo06.rst
241 - :ref:`section_ref_algorithm_Blue`
242 - :ref:`section_ref_algorithm_ExtendedBlue`
243 - :ref:`section_ref_algorithm_LinearityTest`
245 .. ------------------------------------ ..
246 .. include:: snippets/Header2Algo07.rst