Detection and stochastic modeling of nonlinear signatures in the geopotential height field of an atmospheric general circulation model:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Sankt Augustin
Asgard-Verl.
2003
|
| Series: | Bonner meteorologische Abhandlungen
58 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 157 S. Ill., graph. Darst. : 30 cm |
| ISBN: | 3537878583 |
Staff View
MARC
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| 100 | 1 | |a Berner, Judith |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Detection and stochastic modeling of nonlinear signatures in the geopotential height field of an atmospheric general circulation model |c Judith Berner |
| 264 | 1 | |a Sankt Augustin |b Asgard-Verl. |c 2003 | |
| 300 | |a VIII, 157 S. |b Ill., graph. Darst. : 30 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Bonner meteorologische Abhandlungen |v 58 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010416836 | |
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| _version_ | 1807229081190662144 |
|---|---|
| adam_text |
CONTENTS
1
INTRODUCTION
1
1.1
STRUCTURE
OF
THESIS
.
3
2
THE
DATA
SET
6
3
THE
EMPIRICAL
ORTHOGONAL
FUNCTION
BASIS
7
3.1
SPATIAL
PATTERNS
.
7
3.2
DECORRELATION
TIMES
OF
THE
LEADING
PCS
.
11
3.3
DISCUSSION
.
14
4
PDF
AND
PHASE-SPACE
DYNAMICS
OF
Z
5O
OHPA
15
4.1
PROBABILITY
DENSITY
FUNCTION
AND
MUTUAL
DENSITY
INFORMATION
(MID)
.
15
4.2
PHASE-SPACE
VELOCITIES
.
17
4.3
DISCUSSION
.
23
5
DETECTING
NONLINEAR
SIGNATURES
25
5.1
WHAT
IS
A
NONLINEAR
SIGNATURE?
.
25
5.2
A
MEASURE
FOR
NON-NORMALITY:
THE
PEARSON-STATISTIC
.
26
5.3
THE
IMPORTANCE
OF
THE
NONLINEAR
VELOCITIES
.
27
5.4
NONLINEAR
PHASE
SPACES
PLANES
.
27
6
SDES
AND
THE
FOKKER-PLANCK
EQ.
34
6.1
STOCHASTIC
DIFFERENTIAL
EQUATIONS
(SDES)
.
35
6.2
DEFINITION
OF
A
MARKOV
PROCESS
.
35
6.3
SPECIAL
CASE
OF
A
SDE:
THE
GENERAL
LANGEVIN
EQUATION
.
35
6.4
ITO
AND
STRATONOVITCH
SDES
.
36
6.5
THE
KRAMERS-MOYAL
EXPANSION
.
37
6.6
THE
FOKKER-PLANCK
EQUATION
.
38
6.6.1
UNIQUENESS
OF
THE
GENERAL
LANGEVIN
EQ
.
39
7
DECORRELATION
TIMES
40
7.1
DECORRELATION
TIMES
FOR
LINEAR
MARKOV
MODELS
.
41
7.2
DECORRELATION
TIMES
FOR
A
RED-NOISE
MODEL
.
43
7.3
DISCUSSION
AND
VALIDITY
FOR
NONLINEAR
MODELS
.
45
7.4
DECORRELATION
RATES
IN
THE
GCM
.
47
7.5
DISCUSSION
.
48
8
FITTING
THE
FOKKER-PLANCK
EQUATION
51
8.1
DRIFT
AND
DIFFUSION
COEFFICIENTS
OF
THE
GCM
DATA
.
52
8.1.1
DRIFT
VECTORS
.
52
8.1.2
DIFFUSION
MATRIX
.
52
8.1.3
FINITE-DIFFERENCE
ERROR
CORRECTION
.
55
8.1.4
ROOT
MEAN
SQUARE
VALUES
OF
DRIFT
AND
DIFFUSION
COEFFICIENT
.
57
8.2
PDF
AND
MID
OF
THE
FOKKER-PLANCK
EQ
.
59
8.2.1
CALCULATING
THE
STATIONARY
SOLUTION
OF
THE
FOKKER-PLANCK
EQ
.
59
8.2.2
STATIONARY
SOLUTION
AND
MID
FOR
THE
GCM
DATA
.
59
9
AN
EMPIRICAL
FIT
OF
THE
GENERAL
LANGEVIN
EQ.
63
9.1
SDES
AND
AUTOCORRELATION
FUNCTION
(ACF)
.
63
9.1.1
EQUIVALENCE
OF
ITO
AND
STRATONOVITCH
SDE
.
64
9.1.2
STOCHASTICALLY
EQUIVALENT
PROCESSES
.
64
9.1.3
NUMERICAL
INTEGRATION
OF
SDES
.
65
VI
9.1.4
SENSITIVITY
OF
NUMERICAL
RESULTS
.
65
9.1.5
THE
PROBABILITY
DENSITY
FUNCTION
OF
THE
SDE
.
66
9.1.6
THE
AUTOCORRELATION
FUNCTION
OF
THE
SDE
.
67
9.2
LOCAL
TEMPORAL
BEHAVIOR
.
68
9.2.1
LINKING
DRIFT
AND
DIFFUSION
TO
PREDICTION
AND
PREDICTABILITY
.
68
9.2.2
LOCAL
TEMPORAL
BEHAVIOR
OF
THE
GCM
.
69
9.2.3
DISCUSSION
.
70
10
THE
PLANE
SPANNED
BY
EOF1
AND
EOFIO
80
10.1
PROBABILITY
DENSITY
FUNCTIONS
AND
MEAN
TENDENCIES
.
80
10.2
DRIFT
AND
DIFFUSION
COEFFICIENTS
OF
THE
GCM
DATA
.
86
10.3
RMS
VALUES
OF
KRAMERS-MOYAL
EXPANSION
COEFFICIENTS
.
87
10.4
STATIONARY
SOLUTION
AND
MID
FOR
THE
GCM
DATA
.
87
10.5
PROBABILITY
DENSITY
AND
AUTOCORRELATION
OF
THE
SDE
.
87
10.6
LOCAL
TEMPORAL
BEHAVIOR
.
88
10.7
DISCUSSION
.
88
11
DISCUSSION
99
11.1
WHY
TOO
SMALL
TIME
LAGS
FAIL
.
99
11.2
WHY
TOO
LARGE
TIME
LAGS
FAIL
.
100
11.3
OPTIMAL
TIME
LAG
.
100
11.4
INTERPRETATION
USING
THE
FLUCTUATION-DISSIPATION
RELATION
.
101
11.5
MAGNITUDES
OF
DRIFT
AND
DIFFUSION
COEFFICIENTS
.
102
12
SIMPLIFIED
MODELS
107
12.1
DETERMINISTIC
PART
AND
NOISE
AMPLITUDE
.
108
12.2
TWO
DIFFERENT
SDES
WITH
THE
SAME
DRIFT
AND
DIFFUSION
.
110
12.3
SIMPLIFIED
MODELS
.
ILL
12.4
DISCUSSION
.
113
VII
13
NONLINEAR
SIGNATURES
IN
HIGHER
DIMENSIONS
115
13.1
NON-NORMALITY
AND
SWIRLINESS
IN
3D
AND
4D
.
115
13.2
FOKKER-PLANCK
EQUATION,
SDE
AND
AND
ACF
IN
3D
.
117
13.3
FOKKER-PLANCK
EQUATION,
SDE
AND
AND
ACF
IN
4D
.
122
14
SUMMARY
AND
CONCLUSIONS
127
A
FINITE-DIFFERENCE
ERROR
CORRECTION
131
A.L
FINITE-DIFFERENCE
APPROXIMATION
.
131
A.
2
FINITE-DIFFERENCE
ERROR
CORRECTION
.
134
B
PLOT
APPENDIX
135
ACKNOWLEDGEMENTS
157
VIII |
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| id | DE-604.BV017283708 |
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| indexdate | 2024-08-13T00:12:37Z |
| institution | BVB |
| isbn | 3537878583 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010416836 |
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| physical | VIII, 157 S. Ill., graph. Darst. : 30 cm |
| publishDate | 2003 |
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| series | Bonner meteorologische Abhandlungen |
| series2 | Bonner meteorologische Abhandlungen |
| spelling | Berner, Judith Verfasser aut Detection and stochastic modeling of nonlinear signatures in the geopotential height field of an atmospheric general circulation model Judith Berner Sankt Augustin Asgard-Verl. 2003 VIII, 157 S. Ill., graph. Darst. : 30 cm txt rdacontent n rdamedia nc rdacarrier Bonner meteorologische Abhandlungen 58 Zugl.: Bonn, Univ., Diss., 2003 Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Potenzialfeld (DE-588)4126347-9 gnd rswk-swf General circulation model (DE-588)4466088-1 gnd rswk-swf Geopotential (DE-588)4020255-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content General circulation model (DE-588)4466088-1 s Geopotential (DE-588)4020255-0 s Potenzialfeld (DE-588)4126347-9 s Nichtlineare Dynamik (DE-588)4126141-0 s Stochastisches Modell (DE-588)4057633-4 s DE-604 Bonner meteorologische Abhandlungen 58 (DE-604)BV000002255 58 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010416836&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berner, Judith Detection and stochastic modeling of nonlinear signatures in the geopotential height field of an atmospheric general circulation model Bonner meteorologische Abhandlungen Nichtlineare Dynamik (DE-588)4126141-0 gnd Stochastisches Modell (DE-588)4057633-4 gnd Potenzialfeld (DE-588)4126347-9 gnd General circulation model (DE-588)4466088-1 gnd Geopotential (DE-588)4020255-0 gnd |
| subject_GND | (DE-588)4126141-0 (DE-588)4057633-4 (DE-588)4126347-9 (DE-588)4466088-1 (DE-588)4020255-0 (DE-588)4113937-9 |
| title | Detection and stochastic modeling of nonlinear signatures in the geopotential height field of an atmospheric general circulation model |
| title_auth | Detection and stochastic modeling of nonlinear signatures in the geopotential height field of an atmospheric general circulation model |
| title_exact_search | Detection and stochastic modeling of nonlinear signatures in the geopotential height field of an atmospheric general circulation model |
| title_full | Detection and stochastic modeling of nonlinear signatures in the geopotential height field of an atmospheric general circulation model Judith Berner |
| title_fullStr | Detection and stochastic modeling of nonlinear signatures in the geopotential height field of an atmospheric general circulation model Judith Berner |
| title_full_unstemmed | Detection and stochastic modeling of nonlinear signatures in the geopotential height field of an atmospheric general circulation model Judith Berner |
| title_short | Detection and stochastic modeling of nonlinear signatures in the geopotential height field of an atmospheric general circulation model |
| title_sort | detection and stochastic modeling of nonlinear signatures in the geopotential height field of an atmospheric general circulation model |
| topic | Nichtlineare Dynamik (DE-588)4126141-0 gnd Stochastisches Modell (DE-588)4057633-4 gnd Potenzialfeld (DE-588)4126347-9 gnd General circulation model (DE-588)4466088-1 gnd Geopotential (DE-588)4020255-0 gnd |
| topic_facet | Nichtlineare Dynamik Stochastisches Modell Potenzialfeld General circulation model Geopotential Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010416836&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002255 |
| work_keys_str_mv | AT bernerjudith detectionandstochasticmodelingofnonlinearsignaturesinthegeopotentialheightfieldofanatmosphericgeneralcirculationmodel |