Multivariate Time Series Analysis
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Transcript of Multivariate Time Series Analysis
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Multivariate Time Series Analysis
Charles D. Camp
MSRI
July 18, 2008
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PCA: 2 variable example
Weakly Correlated Variables Strongly Correlated Variables
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PCA algorithm
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PCA algorithm, cont.
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PCA algorithm, cont.
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An example using Column Ozone Data
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Brewer-Dobson circulation and Planetary Waves
Upwelling planetary waves break in shaded region
Drives the Brewer-Dobson circulation
Transports heat to the polar vortex
Effect on the strength of the polar night vortex
Courtesy of M. Salby
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2D CTM Model
The Caltech/JPL two-dimensional chemistry and transport model (2D CTM) is used to investigate interannual variability of the total ozone column.
Forced by the monthly mean meridional circulation (isentropic circulation) and eddy diffusivity calculated from the NCEP/DOE Reanalysis2 data (NCEP2).
Compared to the MOD observations.
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Isentropic Mass Stream FunctionSeasonal Cycle derived from NCEP
Units: 109 kg/s
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Part II: TOMS and MOD data sets
TOMS: 1°×1.25° lat-lon grid, Nov.1978 - Apr.1993, monthly means
Merged Ozone Data (MOD) combines TOMS and SBUV data: 5°×10° lat-lon grid; Nov.1978 - Dec.2000, monthly means
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MOD decomposition & PCA
data is deseasonalized: mean for each month removed
then detrended: linear trend removed. Anomaly field is spectrally filtered to remove
intra-annual variability. Principal Component Analysis (PCA) is
performed to get EOF patterns and PC time series.
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MOD EOF patterns and PC time series
42%
75%
90%
93%
EOFs PCs Amplitude SpectraCumul. Var.
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MOD EOF 1: QBO (and Decadal)
Captures 42% of the interannual variance.
R=0.80 ( 1% )
<= 0
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MOD EOF2: Decadal and QBO
Captures 33% of the interannual variance.
R= -0.73 ( 5% )
<= 0
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Filtered PCs 1 & 2: Separating the QBO and Decadal signals
PC1
PC2
[15, 72] mo. [72, max] mo.
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Linear Combinations of EOFs 1 & 2:Patterns for QBO and Decadal Signals
Using the standard deviations of the filtered PCs as weights, take weighted sum and difference of EOFs 1 & 2. (Zonal averages shown)
EOF 1
EOF2sum => QBO
diff => decadal
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EOF 3: interaction between QBO and annual cycles (QBO-annual beat)
Captures 15% of the interannual variance.
<= 0
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QBO-annual beat(analysis with intra-annual variability)
Quadratic nonlinearity between the QBO and annual cycles creates signals with periods of 20 and 8.6 months (for a average QBO period of 30 months):
tttt 212111 sinsinsinsin2
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EOF 4: ENSO
Captures 3% of the interannual variance.
R=0.71 ( < 0.1% )
<= 0
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ENSO in TOMS
R=0.76 ( 0.1% )
<= 0