Are EOF-based descriptions of the MJO relevant to its role in ENSO?

Several ways of extracting a large-scale, eastward-propagating "MJO" are explored and compared. Input fields were pentad OLR (1979-98) and ECMWF 10 m winds (1985-99).

The fields were bandpassed using complex demodulation, with central periods of 40 and 60 days. The half-power points were 28 to 72 days and 42 to 108 days, respectively.

SVD analysis (Bretherton et al 1992) was used to decompose bandpassed fields reconstructed from complex demodulation. Using an idea of Mike Wallace's, a second time series was formed by shifting the dates of the original by 15 days (1/4 period). The original and shifted time series were decomposed by SVD. The results give eigenvectors in quadrature pairs that represent propagating variability.

From another point of view, the eastward-propagating variability was extracted by successively time-shifting the band-passed fields (in x,t) so the eastward propagation became simultaneous. Then the fields were smoothed in x, then the shifting was reversed. The results are not restricted to EOF modes, but show ALL the eastward-propagating large-scale intraseasonal signals.

Figures on this page compare results from these analyses.

This page is old. The paper has been published (J.Clim. 2001)

New page for figures made during revision of this paper

• Figures as in paper (but color): Figure 1   Figure 2   Figure 3  Figure 3 (2-panel)

• Amplitude of intraseasonal OLR and Zonal Wind along the equator from CdMod  40 days  60 days
• SVD spatial patterns for bandpassed 40-day OLR: Mode pair 1    Amplitude along equator (60 days)    Eigenvalues    Eigenvalues and the North et al (1982) criteria    Mode pair 1 for EC zonal wind
• Eastward-propagating signals extracted by time-shifting:  OLR   Zonal wind    Overlay SVD contours:  OLR   Zonal wind
• Examples of SVD and eastward-propagating signals: Bandpass, EPP and SVD:  (1991-93)  (1986-88).  EPP and SVD sums:  (1991-93)  (1986-88)  (1991-93 including difference)
• Examples of BP, SVD and EPP in 2-year chunks:  79-80  81-82  83-84  85-86  87-88  89-90  91-92  93-94  95-96  97-98
  Add EPP-SVD difference:  79-80  81-82  83-84  85-86  87-88  89-90  91-92  93-94  95-96  96-97
  91-93 EC wind example:  91-93
• Amplitude along equator: OLR Cdmod Amp, SVD Recon, E-ward
• Compare RMS fields:  40 days: OLR    Zonal wind   OLR CdMod Amp, SVD and E-ward RMS   OLR SVD, EPP and difference  60-day OLR   
• Compare RMS fields from higher SVD modes:  OLR modes 2 and 3  OLR mode sums 1+2, 1+2+3  OLR mode sum 1+2+3+4  Zonal wind modes 2 and 3  Zonal wind mode sums  
  Compare running RMS (SVD and EPP) and SOI at specific longitudes:
• OLR:  180°  175°E  170°E  170°E (V2)  165°E   Zonal motion of the eastward edge (4 W/m2 contour)   Version 2   Overlay SST
• Zonal Wind:  180°  175°E  170°E  170°E (V2)  165°E  165°W  
• OLR and Zonal Wind RMS:  180°  175°E  170°E  165°E  
  Running RMS and SOI at specific longitudes for higher SVD modes: 
  
• OLR:   Modes 2 and 3: 180°  170°E  Mode sums: 180°  170°E  
  Zonal wind:   Modes 2 and 3: 180°  170°E  Mode sums: 180°  170°E
• (Scaled) Time series at various longitudes overlaid: SVD  EPP

• Global average MJO activity and the SOI

  Correlations (some are old):
  

• Running RMS of indices with the SOI along the equator    Significance    From SVD mode sums
• Correlations among the interannual timeseries (SVD and E-ward): Correlations   Degrees of freedom   95% sig correlations
• Correlations among the unfiltered timeseries (SVD and Eastward): Correlations   90% sig correlations
• Auto-correlations among the interannual timeseries (SVD and Eastward): Correlations   90% sig correlations (old)
• Correlations with SOI along the equator: c=5.5 m/s, different smoothings Overlay 95% significance 90%
• Redone correlations with SOI and Niño-3 SST: SOI, 12-month  SOI, 5-month  Nino-3, 12-month  Nino-3, 5-month  95% significance
• Lag correlations: SOI, 12-month  SOI, 5-month  Nino-3, 12-month  Nino-3, 5-month  
• Lag correlations for SOI with SVD and EOF for higher mode pairs: 1-4  5-8  9-12

• Compare SVD and EOF representations (OLR):
  EOF mode pair 1 spatial pattern
  Compare EOF and SVD interannual patterns along equator
  Temporal coefficients of EOF and SVD modes 1 and 2 (1991-92 example)
  Compare EOF and SVD interannual reconstructions: 80°E   150°E   180°
• SVD and EOF spatial mode pair 1  SVD and EOF spatial modes 1-6
    SVD and EOF reconstructions from mode pairs 1-4

  Comparisons with different speeds and smoothings:
  

• Variance as a function of speed: nsm=21  nsm=31  nsm=41  nsm=61  nsm=87  nsm=143  All overlaid
• Comparisons time series at 0°,170°E (Fig 3): Original Fig 3  c=5.5, Nsm=21  Nsm=31  Original and c=5.5, nsm=21 and 41
• Compare E-ward part along equator (Fig 2): c=5.5 m/s, nsm=21 and 41
• Fig 2 with c=5.5 m/s and nsm=21
  CdMod smoothing comparisons (with extended time to 12-Jul-98):
  
• x-t sections: Eastward part  SVD
• Versions of Fig 3 (0°,170°W): Original Fig 3  nsm=0  nsm=999  nsm=0 (180°)  nsm=999 (180°)
• Compare correlations. Original and nsm=999

• SST: Reynolds SST anomalies along the equator  Overlay OLR RMS  Reynolds SST and OLR RMS at 0°,180°  COADS SST at 0°,180°  

• Some windspeed time series: ECMWF and TAO at 0°, 160°E    EC 3-yr RM and remainder    Zonal and meridional components at 0°, 160°E