Continuous formulations of the ensemble Kalman filter:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2013
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 107 S. Ill., graph. Darst. |
Internformat
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Datensatz im Suchindex
| _version_ | 1804152837578424320 |
|---|---|
| adam_text | CONTENTS
1 INTRODUCTION 1
1.1 DATA ASSIMILATION 1
1.2 FOCUS OF THIS WORK 3
1.3 OUTLINE 4
2 BASICS 7
2.1 THE FILTERING PROBLEM 7
2.2 THE KALMAN FILTER 9
2.3 THE EXTENDED KALMAN FILTER 13
2.4 PARTICLE FILTERS 14
2.4.1 EXAMPLE: DEGENERATION OF PARTICLE WEIGHTS 18
2.5 THE ENSEMBLE KALMAN FILTER 21
2.5.1 EXAMPLE: FORM OF THE PRIOR 24
2.6 THE ENSEMBLE TRANSFORM KALMAN FILTER 25
3 TIME-CONTINUOUS FILTERS 31
3.1 THE KALMAN-BUCY FILTER 31
3.2 THE ENSEMBLE KALMAN-BUCY FILTER 32
3.3 CONNECTION TO INTERMITTENT DATA ASSIMILATION 33
3.4 THE MOLLIFIED ENKF 37
4 DEALING WITH SMALL ENSEMBLE SIZES 41
4.1 MINIMIZING THE EFFECTS OF SMALL ENSEMBLE SIZES 42
4.1.1 COVARIANCE INFLATION 42
4.1.2 CONTINUOUS COVARIANCE INFLATION 43
4.1.3 COVARIANCE LOCALIZATION 44
4.1.4 R-LOCALIZATION 48
4.2 NUMERICAL EXPERIMENTS 49
4.2.1 EXPERIMENTAL SETUP 49
4.2.2 RESULTS 51
IX
HTTP://D-NB.INFO/1064946097
CONTENTS
5 DYNAMICAL BALANCES 57
5.1 THE SLOW-FAST LORENZ96 MODEL 57
5.2 BALANCE IN THE SHALLOW WATER EQUATIONS 60
5.3 NUMERICAL RESULTS 62
5.3.1 INFLUENCE OF THE LOCALIZATION RADIUS 63
5.3.2 INFLUENCE OF THE MOLLIFICATION INTERVAL 70
6 CONCLUSION 73
A DERIVATION OF THE CONTINUOUS INFLATION CENKF 77
B THE ICON SHALLOW WATER MODEL 83
B.L THE MODEL 83
B.2 DISCRETIZATION 83
B.2.1 SPACE DISTRETIZATION 83
B.2.2 TIME DISCRETIZATION 84
B.3 EXPERIMENTAL SETTING 85
B.3.1 INITIAL CONDITIONS 85
B.3.2 PARAMETERS 85
B.3.3 INITIAL ENSEMBLES 86
C RESULTS FOR THE LORENZ96 MODEL 89
C.L IMPACT OF THE TIME-STEPPING ON THE CENKF 89
C.L.L RMS ERRORS FOR THE FORWARD EULER METHOD WITH DIFFERENT TIME
STEP SIZES 89
C.1.2 STABILITY FOR THE FORWARD EULER METHOD WITH DIFFERENT TIME
STEP SIZES 93
C.1.3 RMS ERRORS AND STABILITY FOR THE EULER-HEUN METHOD WITH
ADAPTIVE TIME STEP SIZE 96
C.2 COMPARISON OF DIFFERENT ALGORITHMS 97
C.2.1 RMS ERROR FOR DIFFERENT ALGORITHMS 97
C.2.2 STABILITY FOR DIFFERENT ALGORITHMS 99
C.3 RESULTS FOR THE CONTINUOUS INFLATION CENKF 101
C.3.1 RMS ERRORS FOR DIFFERENT TIME-STEPPING SCHEMES 101
C.3.2 STABILITY FOR DIFFERENT TIME-STEPPING SCHEMES 102
BIBLIOGRAPHY 103
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| any_adam_object | 1 |
| author | Bergemann, Kay |
| author_GND | (DE-588)1067122923 |
| author_facet | Bergemann, Kay |
| author_role | aut |
| author_sort | Bergemann, Kay |
| author_variant | k b kb |
| building | Verbundindex |
| bvnumber | BV042275785 |
| ctrlnum | (OCoLC)900442314 (DE-599)GBV798472731 |
| dewey-full | 518.28 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.28 |
| dewey-search | 518.28 |
| dewey-sort | 3518.28 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Thesis Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV042275785 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:17:04Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027713258 |
| oclc_num | 900442314 |
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| owner_facet | DE-12 DE-188 |
| physical | X, 107 S. Ill., graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| record_format | marc |
| spelling | Bergemann, Kay Verfasser (DE-588)1067122923 aut Continuous formulations of the ensemble Kalman filter von Kay Bergemann 2013 X, 107 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Potsdam, Univ., Diss., 2013 Kalman-Filter (DE-588)4130759-8 gnd rswk-swf Datenassimilation (DE-588)4803260-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kalman-Filter (DE-588)4130759-8 s Datenassimilation (DE-588)4803260-8 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027713258&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bergemann, Kay Continuous formulations of the ensemble Kalman filter Kalman-Filter (DE-588)4130759-8 gnd Datenassimilation (DE-588)4803260-8 gnd |
| subject_GND | (DE-588)4130759-8 (DE-588)4803260-8 (DE-588)4113937-9 |
| title | Continuous formulations of the ensemble Kalman filter |
| title_auth | Continuous formulations of the ensemble Kalman filter |
| title_exact_search | Continuous formulations of the ensemble Kalman filter |
| title_full | Continuous formulations of the ensemble Kalman filter von Kay Bergemann |
| title_fullStr | Continuous formulations of the ensemble Kalman filter von Kay Bergemann |
| title_full_unstemmed | Continuous formulations of the ensemble Kalman filter von Kay Bergemann |
| title_short | Continuous formulations of the ensemble Kalman filter |
| title_sort | continuous formulations of the ensemble kalman filter |
| topic | Kalman-Filter (DE-588)4130759-8 gnd Datenassimilation (DE-588)4803260-8 gnd |
| topic_facet | Kalman-Filter Datenassimilation Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027713258&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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