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Bibliographic Details
Main Author:	Evensen, Geir (Author)
Format:	Book
Language:	English
Published:	Berlin ; Heidelberg Springer 2009
Edition:	2. ed.
Subjects:	Datenassimilation
Links:	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
Item Description:	Literaturverz. S. 293 - 304
Physical Description:	XXIII, 307 S. graph. Darst. 24 cm
ISBN:	9783642037108

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MARC


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Record in the Search Index

DE-BY-TUM_call_number	0102 MAT 620f 2012 A 4263(2)
DE-BY-TUM_katkey	1855810
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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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edition	2. ed.
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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

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Call Number:	0102 MAT 620f 2012 A 4263(2)
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