Data assimilation: the ensemble Kalman filter
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
2009
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 293 - 304 |
| Beschreibung: | XXIII, 307 S. graph. Darst. 24 cm |
| ISBN: | 9783642037108 |
Internformat
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| 100 | 1 | |a Evensen, Geir |e Verfasser |0 (DE-588)132448394 |4 aut | |
| 245 | 1 | 0 | |a Data assimilation |b the ensemble Kalman filter |c Geir Evensen |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c 2009 | |
| 300 | |a XXIII, 307 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 500 | |a Literaturverz. S. 293 - 304 | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS LIST OF SYMBOLS XVII 1 INTRODUCTION 1 2 STATISTICAL DEFINITIONS
5 2.1 PROBABILITY DENSITY FUNCTION 5 2.2 STATISTICAL MOMENTS 8 2.2.1
EXPECTED VALUE 8 2.2.2 VARIANCE 8 2.2.3 COVARIANCE 9 2.3 WORKING WITH
SAMPLES FROM A DISTRIBUTION 9 2.3.1 SAMPLE MEAN 9 2.3.2 SAMPLE VARIANCE
10 2.3.3 SAMPLE COVARIANCE 10 2.4 STATISTICS OF RANDOM FIELDS 10 2.4.1
SAMPLE MEAN 10 2.4.2 SAMPLE VARIANCE 10 2.4.3 SAMPLE COVARIANCE 11 2.4.4
CORRELATION 11 2.5 BIAS 11 2.6 CENTRAL LIMIT THEOREM 12 3 ANALYSIS
SCHEME 13 3.1 SCALAR CASE 13 3.1.1 STATE-SPACE FORMULATION 13 3.1.2
BAYESIAN FORMULATION 15 3.2 EXTENSION TO SPATIAL DIMENSIONS 16 3.2.1
BASIC FORMULATION 16 3.2.2 EULER-LAGRANGE EQUATION 17 3.2.3 REPRESENTER
SOLUTION 19 3.2.4 REPRESENTER MATRIX 20 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/995338817 DIGITALISIERT DURCH XII CONTENTS 3.2.5 ERROR
ESTIMATE 20 3.2.6 UNIQUENESS OF THE SOLUTION 21 3.2.7 MINIMIZATION OF
THE PENALTY FUNCTION 23 3.2.8 PRIOR AND POSTERIOR VALUE OF THE PENALTY
FUNCTION 24 3.3 DISCRETE FORM 24 4 SEQUENTIAL DATA ASSIMILATION 27 4.1
LINEAR DYNAMICS 27 4.1.1 KALMAN FILTER FOR A SCALAR CASE 28 4.1.2 KALMAN
FILTER FOR A VECTOR STATE 29 4.1.3 KALMAN FILTER WITH A LINEAR ADVECTION
EQUATION 29 4.2 NONLINEAR DYNAMICS 32 4.2.1 EXTENDED KALMAN FILTER FOR
THE SCALAR CASE 32 4.2.2 EXTENDED KALMAN FILTER IN MATRIX FORM 33 4.2.3
EXAMPLE USING THE EXTENDED KALMAN FILTER 35 4.2.4 EXTENDED KALMAN FILTER
FOR THE MEAN 36 4.2.5 DISCUSSION 37 4.3 ENSEMBLE KALMAN FILTER 38 4.3.1
REPRESENTATION OF ERROR STATISTICS 38 4.3.2 PREDICTION OF ERROR
STATISTICS 39 4.3.3 ANALYSIS SCHEME 41 4.3.4 DISCUSSION 43 4.3.5 EXAMPLE
WITH A QG MODEL 44 5 VARIATIONAL INVERSE PROBLEMS 47 5.1 SIMPLE
ILLUSTRATION 47 5.2 LINEAR INVERSE PROBLEM 50 5.2.1 MODEL AND
OBSERVATIONS 50 5.2.2 MEASUREMENT FUNCTIONAL 51 5.2.3 COMMENT ON THE
MEASUREMENT EQUATION 51 5.2.4 STATISTICAL HYPOTHESIS 52 5.2.5 WEAK
CONSTRAINT VARIATIONAL FORMULATION 52 5.2.6 EXTREMUM OF THE PENALTY
FUNCTION 53 5.2.7 EULER-LAGRANGE EQUATIONS 53 5.2.8 STRONG CONSTRAINT
APPROXIMATION 55 5.2.9 SOLUTION BY REPRESENTER EXPANSIONS 55 5. CONTENTS
XIII 6 NONLINEAR VARIATIONAL INVERSE PROBLEMS 71 6.1 EXTENSION TO
NONLINEAR DYNAMICS 71 6.1.1 GENERALIZED INVERSE FOR THE LORENZ EQUATIONS
72 6.1.2 STRONG CONSTRAINT ASSUMPTION 73 6.1.3 SOLUTION OF THE WEAK
CONSTRAINT PROBLEM 76 6.1.4 MINIMIZATION BY THE GRADIENT DESCENT METHOD
77 6.1.5 MINIMIZATION BY GENETIC ALGORITHMS 78 6.2 EXAMPLE WITH THE
LORENZ EQUATIONS 82 6.2.1 ESTIMATING THE MODEL ERROR COVARIANCE 82 6.2.2
TIME CORRELATION OF THE MODEL ERROR COVARIANCE 83 6.2.3 INVERSION
EXPERIMENTS 84 6.2.4 DISCUSSION 92 7 PROBABILISTIC FORMULATION 95 7.1
JOINT PARAMETER AND STATE ESTIMATION 95 7.2 MODEL EQUATIONS AND
MEASUREMENTS 96 7.3 BAYESIAN FORMULATION 97 7.3.1 DISCRETE FORMULATION
98 7.3.2 SEQUENTIAL PROCESSING OF MEASUREMENTS 99 7.4 SUMMARY 101 8
GENERALIZED INVERSE 103 8.1 GENERALIZED INVERSE FORMULATION 103 8.1.1
PRIOR DENSITY FOR THE POORLY KNOWN PARAMETERS 103 8.1.2 PRIOR DENSITY
FOR THE INITIAL CONDITIONS 104 8.1.3 PRIOR DENSITY FOR THE BOUNDARY
CONDITIONS 104 8.1.4 PRIOR DENSITY FOR THE MEASUREMENTS 105 8.1.5 PRIOR
DENSITY FOR THE MODEL ERRORS 105 8.1.6 CONDITIONAL JOINT DENSITY 107 8.2
SOLUTION METHODS FOR THE GENERALIZED INVERSE PROBLEM 108 8.2.1
GENERALIZED INVERSE FOR A SCALAR MODEL 108 8.2.2 EULER-LAGRANGE
EQUATIONS 109 8.2.3 ITERATION IN A ILL 8.2. XJV CONTENTS 9.7.1 ENKF WITH
LINEAR NOISE FREE MODEL 129 9.7.2 ENKS USING ENKF AS A PRIOR 130 9.8
EXAMPLE WITH THE LORENZ EQUATIONS 131 9.8.1 DESCRIPTION OF EXPERIMENTS
131 9.8.2 ASSIMILATION EXPERIMENT 132 9.9 DISCUSSION 137 10 STATISTICAL
OPTIMIZATION 139 10.1 DEFINITION OF THE MINIMIZATION PROBLEM 139 10.1.1
PARAMETERS 140 10.1.2 MODEL 140 10.1.3 MEASUREMENTS 140 10.1.4 COST
FUNCTION 141 10.2 BAYESIAN FORMALISM 141 10.3 SOLUTION BY ENSEMBLE
METHODS 142 10.3.1 VARIANCE MINIMIZING SOLUTION 144 10.3.2 ENKS SOLUTION
144 10.4 EXAMPLES 145 10.5 DISCUSSION 154 11 SAMPLING STRATEGIES FOR THE
ENKF 157 11.1 INTRODUCTION 157 11.2 SIMULATION OF REALIZATIONS 158
11.2.1 INVERSE FOURIER TRANSFORM 159 11.2.2 DEFINITION OF FOURIER
SPECTRUM 159 11.2.3 SPECIFICATION OF COVARIANCE AND VARIANCE 160 11.3
SIMULATING CORRELATED FIELDS 162 11.4 IMPROVED SAMPLING SCHEME 163
11.4.1 THEORETICAL FOUNDATION 164 11.4.2 IMPROVED SAMPLING ALGORITHM 165
11.4.3 PROPERTIES OF THE IMPROVED SAMPLING 166 11.5 MODEL AND
MEASUREMENT NOISE 168 11.6 GENERATION OF A RANDOM ORTHOGONAL MATRIX 169
11.7 EXPERIMENTS 169 11.7.1 OVERVIEW OF EXPERIMENTS 170 11.7.2 IMPACT
FROM ENSEMBLE SIZE 172 11.7.3 IMPACT OF IMPROVED SAMPLING FOR THE
INITIAL ENSEMBLE .. 173 11.7. CONTENTS XV 12 MODEL ERRORS 177 12.1
SIMULATION OF MODEL ERRORS 177 12.1.1 DETERMINATION OF P 177 12.1.2
PHYSICAL MODEL 178 12.1.3 VARIANCE GROWTH DUE TO THE STOCHASTIC FORCING
178 12.1.4 UPDATING MODEL NOISE USING MEASUREMENTS 182 12.2 SCALAR MODEL
182 12.3 VARIATIONAL INVERSE PROBLEM 183 12.3.1 PRIOR STATISTICS 183
12.3.2 PENALTY FUNCTION 184 12.3.3 EULER-LAGRANGE EQUATIONS 184 12.3.4
ITERATION OF PARAMETER 185 12.3.5 SOLUTION BY REPRESENTER EXPANSIONS 185
12.3.6 VARIANCE GROWTH DUE TO MODEL ERRORS 186 12.4 FORMULATION AS A
STOCHASTIC MODEL 187 12.5 EXAMPLES 187 12.5.1 CASE AO 188 12.5.2 CASE AL
191 12.5.3 CASE B 191 12.5.4 CASE C 194 12.5.5 DISCUSSION 195 13 SQUARE
ROOT ANALYSIS SCHEMES 197 13.1 SQUARE ROOT ALGORITHM FOR THE ENKF
ANALYSIS 197 13.1.1 UPDATING THE ENSEMBLE MEAN 198 13.1.2 UPDATING THE
ENSEMBLE PERTURBATIONS 198 13.1.3 PROPERTIES OF THE SQUARE ROOT SCHEME
200 13.1.4 FINAL UPDATE EQUATION 203 13.1.5 ANALYSIS UPDATE USING A
SINGLE MEASUREMENT 204 13.1.6 ANALYSIS UPDATE USING A DIAGONAL C 205
13.2 EXPERIMENTS 205 13.2.1 OVERVIEW OF EXPERIMENTS 206 13.2.2 IMPACT OF
THE SQUARE ROOT ANALYSIS ALGORITHM 207 14 RANK ISSUES 211 14.1 PSEUDO
INVERSE OF C XVI CONTENTS 14.3.1 DERIVATION OF THE PSEUDO INVERSE 223
14.3.2 ANALYSIS SCHEMES USING A LOW-RANK C ET 224 14.4 IMPLEMENTATION OF
THE ANALYSIS SCHEMES 225 14.5 RANK ISSUES RELATED TO THE USE OF A
LOW-RANK C E* 226 14.6 EXPERIMENTS WITH M » N 228 14.7 VALIDITY OF
ANALYSIS EQUATION 233 14.8 SUMMARY 235 15 SPURIOUS CORRELATIONS,
LOCALIZATION, AND INFLATION 237 15.1 SPURIOUS CORRELATIONS 237 15.2
INFLATION 239 15.3 AN ADAPTIVE COVARIANCE INFLATION METHOD 240 15.4
LOCALIZATION 241 15.5 ADAPTIVE LOCALIZATION METHODS 242 15.6 A
LOCALIZATION AND INFLATION EXAMPLE 243 16 AN OCEAN PREDICTION SYSTEM 255
16.1 INTRODUCTION 255 16.2 SYSTEM CONFIGURATION AND ENKF IMPLEMENTATION
256 16.3 NESTED REGIONAL MODELS 259 16.4 SUMMARY 260 17 ESTIMATION IN AN
OIL RESERVOIR SIMULATOR 263 17.1 INTRODUCTION 263 17.2 EXPERIMENT 265
17.2.1 PARAMETERIZATION 266 17.2.2 STATE VECTOR 267 17.3 RESULTS 269
17.4 SUMMARY 272 A OTHER ENKF ISSUES 273 A.I NONLINEAR MEASUREMENTS IN
THE ENKF 273 A.2 ASSIMILATION OF NON-SYNOPTIC MEASUREMENTS 275 A.3 TIME
DIFFERENCE DATA 276 A.
|
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| author | Evensen, Geir |
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| ctrlnum | (OCoLC)458747607 (DE-599)DNB995338817 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Geologie / Paläontologie Technik Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV040136801 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:17:43Z |
| institution | BVB |
| isbn | 9783642037108 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024993834 |
| oclc_num | 458747607 |
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| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | XXIII, 307 S. graph. Darst. 24 cm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| spelling | Evensen, Geir Verfasser (DE-588)132448394 aut Data assimilation the ensemble Kalman filter Geir Evensen 2. ed. Berlin ; Heidelberg Springer 2009 XXIII, 307 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 293 - 304 Datenassimilation (DE-588)4803260-8 gnd rswk-swf Datenassimilation (DE-588)4803260-8 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-03711-5 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024993834&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Evensen, Geir Data assimilation the ensemble Kalman filter Datenassimilation (DE-588)4803260-8 gnd |
| subject_GND | (DE-588)4803260-8 |
| title | Data assimilation the ensemble Kalman filter |
| title_auth | Data assimilation the ensemble Kalman filter |
| title_exact_search | Data assimilation the ensemble Kalman filter |
| title_full | Data assimilation the ensemble Kalman filter Geir Evensen |
| title_fullStr | Data assimilation the ensemble Kalman filter Geir Evensen |
| title_full_unstemmed | Data assimilation the ensemble Kalman filter Geir Evensen |
| title_short | Data assimilation |
| title_sort | data assimilation the ensemble kalman filter |
| title_sub | the ensemble Kalman filter |
| topic | Datenassimilation (DE-588)4803260-8 gnd |
| topic_facet | Datenassimilation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024993834&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT evensengeir dataassimilationtheensemblekalmanfilter |