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|
The realtime Multivariate Index for tropical Intraseasonal oscillations.
|Projection of 9 day running average anomalies onto the daily spatial multivariate EOFs of 20-96 day eastward filtered OLR, U850 and U200. Anomalies are calculated by first subtracting the previous 40 day mean. The running average is tapered as the target date is approached.||RMII values|
The Rotated EOFs OLR Madden Julian Index.
|Projection of 20-96 day filtered OLR, including all eastward and westward wave numbers onto the rotated daily spatial EOF patterns of 30-96 day eastward filtered OLR. EOFs are calculated using OLR from 1979-2012. PCs are calculated from 1979-2022. EOFs are rotated to reduce noise and potential degeneracy issues as detailed in Weidman et al., 2022.||REOMI values|
The Koopman Real-time MultiVariate Madden Julian Index
|Calculated following the Wheeler-Hendon RMM, but using Koopman spectral analysis to compute eigenfunctions. The leading mode of intraseasonal variability is rotated to maximize correlation with the standard RMM. See link to Lintner et al. 2023 for further discussion of the Koopman spectral analysis and methodological details.||KRMM 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. For the REOMI, code is in the same repository. using the parameter eofs_postprocessing_type="eof_rotation" in the main method for calculating EOFs: omi.omi_calculator.calc_eofs_from_olr(). No other changes should be necessary from the standard OMI calculation. 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)The rMII code and MII values are available upon request from the lead author (Shuguang Wang: email@example.com). For more information for all indices other than the VPM and rMII, 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.:
Python routines to calculate OMI
MATLAB routines to calculate KRMM
|FMO Spatial EOFs|
rMII was computed using OLR and 850hPa and 200hPa zonal winds from ERA5. PC signs are consistent with the RMM index for the phase plots.