MJO Indices

Daily Timeseries | Composite Maps | Animations | ASCII EOF's | Other MJO Indices and Information

PSL is creating a set of MJO timeseries that quantify current and historic MJO activity.
The links and descriptions are below as well as links to some other MJO timeseries created at other institutions.
A description of the timeseries format is available.

NOTE: OMI has been updated through May 16 2021. These PC amplitudes will differ slightly from the previous version since the sample used for the 20-96 day filter is longer (1979-2021), resulting in slightly different values for the filtered OLR used to calculate OMI. In some cases this may also result in a phase difference (by one phase) from the previous versions. The EOFs used are still from 1979-2012 (see below). The previous (1979-2012) version of OMI can be obtained here.

NOTE: When comparing OMI directly with RMM, to obtain the proper phase the sign of OMI PC1 and the PC ordering should be reversed, so that OMI(PC2) is analogous to RMM(PC1) and -OMI(PC1) is analogous to RMM (PC2).

Daily MJO index time series from 1979.

IndexDescriptionObtain timeseries
The OLR MJO Index
Projection of 20-96 day filtered OLR, including all eastward and westward wave numbers onto the daily spatial EOF patterns of 30-96 day eastward filtered OLR.OMI values
The Original OLR MJO Index
Projection of 30-96 day eastward only filtered OLR onto the spatial EOF patterns of 30-96 day eastward filtered OLR. This results in a smoother index than OMI due to more restrictive filtering.OOMI values
The Real-time OLR MJO Index
Projection of 9 day running average OLR anomalies onto the daily spatial EOF patterns of 30-96 day eastward filtered OLR. OLR anomalies are calculated by first subtracting the previous 40 day mean OLR. The running average is tapered as the target date is approached.ROMI values
The Filtered OLR MJO index.
Univariate EOF of normalized 20-96 day filtered OLR averaged from 15S-15N, by longitude. The same spatial EOF pattern is used for the entire year (see below).FMO values
The Velocity Potential MJO index.
Calculated in the same way as the Wheeler-Hendon RMM, except using 200 hPa Velocity Potential instead of OLR, along with U200 and U850 in a combined EOF (see link to Ventrice et al. 2013 below).VPM values
A python routine to calculate the OMI has been developed for use on real-time and model data, and can be accessed via GitHub at: https://github.com/cghoffmann/mjoindices and also at Zenodo: https://doi.org/10.5281/zenodo.3613752 Details of the implementation of this software are outlined in the journal article: Hoffmann CG, Kiladis GN, Gehne M, von Savigny C 2021 A Python Package to Calculate the OLR-Based Index of the Madden-Julian-Oscillation (OMI) in Climate Science and Weather Forecasting. Journal of Open Research Software, 9:9. DOI: https://doi.org/10.5334/jors.331/ (PDF)

For more information for all indices other than the VPM, please read the article "A comparison of OLR and circulation based indices for tracking the MJO". We ask that if you use the timeseries in you research that, please cite that paper, e.g.:
Kiladis G.N., J. Dias, K.H. Straub, M.C Wheeler, S.N. Tulich, K. Kikuchi, K.M. Weickmann, M.J. Ventrice. A comparison of OLR and circulation based indices for tracking the MJO. Monthly Weather Review, May 2014, 142 1697-1715.
For the VPM, please cite:
Ventrice et al. A Modified Multivariate Madden-Julian Oscillation Index Using Velocity Potential. Monthly Weather Review, December 2013, 141, p. 4197-4120.

Python routines to calculate OMI

Composite streamfunction and OLR patterns for RMM and OMI based on the events that exceed 1 standard deviation for each phase of the PC combination.

These are based on data from 1979 through 2012, and the number of events in each composite is given as "N= " at the bottom of each plot. Blue shading denotes negative OLR anomalies (regions of convection) and red positive (suppressed), with two levels of shading at +- 10 and +- 6 W/m**2. Streamfunction contour interval is 5 X 10**5 m**2/s at 200 hPa, and 2 X 10**5 m**2/s at 850 hPa. To facilitate comparison with RMM, these composites are constructed by reversing the sign of OMI PC1 and the OMI PC ordering, so that OMI(PC2) is analogous to RMM(PC1) and -OMI(PC1) is analogous to RMM(PC2), as described in Kiladis et al. 2014.

  1. 200mb OMI DJF
  2. 200mb OMI JJA
  3. 200mb RMM DJF
  4. 200mb RMM JJA
  5. 850mb OMI DJF
  6. 850mb OMI JJA
  7. 850mb RMM DJF
  8. 850mb RMM JJA

MJO EOF Patterns

OMI EOF patterns.

OMI EOF Animations

VPM EOF patterns.

FMO EOF patterns.

Phase Diagrams

  • ROMI phase diagram for the latest 90 days.

    To plot the diagram in the same phase space as the Wheeler-Hendon RMM index, the sign of ROMI PC1 is reversed and the PC ordering is switched, so that ROMI(PC2) is analogous to RMM(PC1) and -ROMI(PC1) is analogous to RMM(PC2). See Kiladis et al. 2014, available above, and the RMM home page linked below for details.

ROMI phase plot
  • VPM phase diagram for the latest 90 days.

    The VPM index was computed using zonal wind and velocity potential based on the NCEP/NCAR Reanalysis Version 1. The VPM PC signs were adjusted to match the RMM index signs for the phase plot.

VPM phase plot

Other MJO indices and MJO information.