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Cross-spectral Analysis

Cross-spectral Analysis. Investigates the dependence or relationship between two time series. Begin by reviewing cross-correlation function – how similar two time series x , y are. L = lag N = # of elements in time series. Covariance or cross-covariance. Cross-correlation.

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Cross-spectral Analysis

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  1. Cross-spectral Analysis Investigates the dependence or relationship between two time series. Begin by reviewing cross-correlation function – how similar two time series x , y are L = lag N = # of elements in time series Covariance or cross-covariance Cross-correlation -1 <ψxy< 1

  2. Ensenada de la Paz

  3. Current velocity in Ensenada de La Paz Year Day

  4. Current velocity and water level (red) in Ensenada de La Paz Year Day

  5. Cross-correlation between current velocity and water level in Ensenada de La Paz

  6. Cross-correlation between current velocity and water level in Ensenada de La Paz

  7. A generalization of: Complex Cross-correlation * is the complex conjugate

  8. Complex Cross-correlation between vectors at 2 depths in Ensenada de La Paz  w1w2 L

  9. Complex Cross-correlation between vectors at 2 depths in Ensenada de La Paz

  10. Complex Cross-correlation between vectors at 2 depths in Ensenada de La Paz

  11. Coherence spectrum (coherency) < > = running mean X is the Fourier Transform  = 0.1, 0.05, 0.01

  12. Current velocity and water level (red) in Ensenada de La Paz Year Day

  13. Coherence squared window size= 2 cpd  = 0.1, 0.05, 0.01

  14.  = 0.1, 0.05, 0.01

  15. JAMES RIVER DATA

  16. 99% Coherence 2 95% Window size= 10 Phase (deg)

  17. Coherence 2 99% 95% Window size= 24 Phase (deg)

  18. 99% Coherence 2 95% Window size= 10 Phase (deg)

  19. 99% Coherence 2 95% Window size= 10 Phase (deg)

  20. Coherence 2 99% 95% Window size= 24 Phase (deg)

  21. Coherence 2 99% 95% Window size= 24 Phase (deg)

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