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Multivariate Time Series Analysis

Multivariate Time Series Analysis. Charles D. Camp MSRI July 18, 2008. PCA: 2 variable example. Weakly Correlated Variables. Strongly Correlated Variables. PCA algorithm. PCA algorithm, cont. PCA algorithm, cont. An example using Column Ozone Data.

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Multivariate Time Series Analysis

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  1. Multivariate Time Series Analysis Charles D. Camp MSRI July 18, 2008

  2. PCA: 2 variable example Weakly Correlated Variables Strongly Correlated Variables

  3. PCA algorithm

  4. PCA algorithm, cont.

  5. PCA algorithm, cont.

  6. An example using Column Ozone Data

  7. 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

  8. 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.

  9. Isentropic Mass Stream FunctionSeasonal Cycle derived from NCEP Units: 109 kg/s

  10. 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

  11. 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.

  12. MOD EOF patterns and PC time series Cumul. Var. Amplitude Spectra EOFs PCs 42% 75% 90% 93%

  13. MOD EOF 1: QBO (and Decadal) <= 0 R=0.80 ( 1% ) Captures 42% of the interannual variance.

  14. MOD EOF2: Decadal and QBO <= 0 R= -0.73 ( 5% ) Captures 33% of the interannual variance.

  15. Filtered PCs 1 & 2: Separating the QBO and Decadal signals [15, 72] mo. [72, max] mo. PC1 PC2

  16. 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) diff => decadal EOF 1 EOF2 sum => QBO

  17. EOF 3: interaction between QBO and annual cycles (QBO-annual beat) <= 0 Captures 15% of the interannual variance.

  18. 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):

  19. EOF 4: ENSO <= 0 R=0.71 ( < 0.1% ) Captures 3% of the interannual variance.

  20. ENSO in TOMS <= 0 R=0.76 ( 0.1% )

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