Correspondences

What is linked, what is not

Each arc joins two phenomena tested on this site. Green and animated: clear link (correlation significant at 5 % after correcting for autocorrelation, or a response outside chance in an event study). Grey: inconclusive test. A statistical link alone does not establish causation.

Clear link
Inconclusive

Hypotheses tested

Clear links

correlation p < 0.05 or epochs outside chance

Causation demonstrated

a correlation demonstrates none

Arc width from |r| of the stored result; several tests between the same phenomena are drawn as stacked arcs.

Hypothesis tested: The Madden–Julian oscillation (MJO) is an envelope of tropical convection that moves east, from the Indian Ocean to the Pacific, in 30 to 60 days. Where it is active, the mid-troposphere is moister, vorticity stronger and shear weaker: cyclones form there more often, and less often under its dry branch (Hall et al., 2001; Camargo et al., 2009; Klotzbach, 2010). The favourable phase should therefore advance from west to east with the basin.

Modulated basins

5 / 6

3,159 formations; Holm p < 0.05

Strongest contrast: North Indian Ocean

5.2 ×

phase 5: ×2.22, phase 8: ×0.43

All basins: highest ratio

1.21

lowest 0.87: the MJO moves more than it adds

Days of active MJO

56 %

OMI amplitude ≥ 1, 1991–2026

Period analysed

1991-01-01 → 2026-06-24

computed on Oct 26, 2026 · engine v1.0

Observed / expected formations, by basin and phase

Basin	Phase 1 Africa, Western Hemisphere	Phase 2 Western Indian Ocean	Phase 3 Eastern Indian Ocean	Phase 4 Maritime Continent	Phase 5 Maritime Continent, Australia	Phase 6 Western Pacific	Phase 7 Western and central Pacific	Phase 8 Western Hemisphere	Inactive	Favourable phase	p (Holm)
South Indian Ocean 596 formations, 84° E	×0.62 27 / 44	×0.92 43 / 46	×1.32 69 / 52	×1.68 75 / 45	×1.20 50 / 42	×0.92 44 / 48	×0.65 30 / 46	×0.50 24 / 48	×1.04	4.0	< 0,01
North Indian Ocean 186 formations, 80° E	×0.53 5 / 9	×0.58 8 / 14	×1.50 26 / 17	×2.09 21 / 10	×2.22 21 / 9	×1.16 17 / 15	×0.76 12 / 16	×0.43 5 / 12	×0.84	4.4	< 0,01
Western North Pacific 890 formations, 135° E	×0.84 37 / 44	×0.68 55 / 80	×0.58 35 / 60	×0.58 19 / 33	×1.03 57 / 55	×1.41 108 / 77	×1.58 97 / 61	×1.30 55 / 42	×0.98	6.9	< 0,01
South Pacific 359 formations, 167° E	×0.93 25 / 27	×0.75 21 / 28	×0.53 17 / 32	×0.57 16 / 28	×0.98 25 / 26	×1.30 37 / 28	×1.71 49 / 29	×1.33 40 / 30	×0.98	7.1	< 0,01
Eastern North Pacific 605 formations, 246° E	×1.76 51 / 29	×1.00 56 / 56	×0.75 29 / 38	×0.41 8 / 20	×0.49 19 / 38	×0.70 37 / 53	×1.50 60 / 40	×1.23 32 / 26	×1.03	8.4	< 0,01
North Atlantic 523 formations, 298° E	×1.10 24 / 22	×1.11 53 / 48	×1.23 43 / 35	×0.91 14 / 15	×0.65 20 / 31	×0.87 38 / 44	×0.78 27 / 34	×0.74 16 / 22	×1.06	2.2	0.16

Each cell: ratio of observed to expected formations (day-of-year climatology), then observed / expected. Orange: more formations than expected; blue: fewer. In bold, the most favourable phase. Longitude: circular mean of the formation points. Under each phase, the region where MJO convection is strongest. Basins are ordered from west to east.

Ratio of observed to expected formations by phase

Show the data as a table

A ratio of 1 means as many formations as the season would lead to expect. Dashed: all basins together. The maxima move towards higher phases from west to east, then return to phases 1 to 3 for the eastern Pacific and the Atlantic.

Aligned series (CSV)

Method and sources

Formation: first six-hourly IBTrACS fix at 34 knots or more (1-minute wind of NHC, CPHC and JTWC, otherwise that of the WMO agency). Phase: NOAA PSL OMI index, based on outgoing long-wave radiation (Kiladis et al., 2014), plotted as RMM (x = PC2, y = −PC1) and cut into eight 45° sectors (Wheeler and Hendon, 2004); amplitude below 1: inactive MJO. Over 1991–2024, the OMI phase so defined falls in the same phase as the Australian Bureau of Meteorology RMM, or a neighbouring one, on 91 % of active days.

Expected: for each basin, sum over the days of the phase of the climatological formation rate for that day of the year (±15-day window): seasons cannot pass for phases. Test: χ² distance between observed and expected formations over the eight active phases, against 1,000 circular shifts of the MJO series (by one year to N − 1 years: same persistence, link broken); Holm correction over the six basins. Favourable phase: direction of the sum of departures (ratio − 1) placed at the centre of each sector of the phase plane.

Computation parameters

{
    "null": {
        "seed": 20261025,
        "draws": 1000,
        "method": "circular shift of the MJO series by 365 to N − 365 days"
    },
    "phase": "OMI (NOAA PSL), x = PC2, y = −PC1, eight 45° sectors as RMM (Wheeler and Hendon 2004); inactive when amplitude < 1",
    "genesis": "first six-hourly IBTrACS fix with a wind of 34 kt or more (USA_WIND, else WMO)",
    "expected": "sum over the days of each phase of the basin genesis rate for that day of the year (±15 days)",
    "statistic": "Σ (observed − expected)² / expected over the eight active phases",
    "multiple_testing": "Holm over 6 basins"
}

Inputs : psl.mjo.omi.pc1.daily (12,959 pts, run #3733) · psl.mjo.omi.pc2.daily (12,959 pts, run #3733) · psl.mjo.omi.amplitude.daily (12,959 pts, run #3733) · ibtracs.storms.global.yearly (46 pts, run #3650)

Reading this result

Five basins out of six are clearly modulated, and the favourable phase moves east with the basin: around 4 for the Indian Ocean (convection over the eastern Indian Ocean), around 7 for the western and South Pacific, around 8 to 1 for the eastern Pacific; this is the signature of a propagating wave, not an artefact. Over the whole tropics the ratio stays close to 1: the MJO moves cyclone formation around more than it adds to it. The North Atlantic leans towards phases 1 to 3, as in Klotzbach (2010), but does not reach the threshold here (the MJO acts there mostly on intensification, and the OMI, built on convection alone, captures it less well than the RMM). The OMI index is published about four months late: this test describes the past, it is not a forecast. Correlation is not causation: common factors (seasons, cycles, trends) or coincidence can produce it. The p-values account for autocorrelation (effective n) but not for preprocessing choices; the confidence interval comes from a block bootstrap. The limits of the source data apply.

SOURCES OF THIS PAGE

Madden–Julian Oscillation, OMI index (NOAA PSL): Kiladis, G. N., Dias, J., Straub, K. H., Wheeler, M. C., Tulich, S. N., Kikuchi, K., Weickmann, K. M. and Ventrice, M. J. (2014). A comparison of OLR and circulation-based indices for tracking the MJO. Monthly Weather Review, 142, 1697–1715. · doi:10.1175/MWR-D-13-00301.1 · source page ↗
Licence : U.S. Government work, public domain; cite Kiladis et al. (2014) · retrieved on Oct 25, 2026 · SHA-256 52b5d504eb59…
IBTrACS v04, International Best Track Archive for Climate Stewardship (NOAA NCEI): Knapp, K. R., Kruk, M. C., Levinson, D. H., Diamond, H. J., Neumann, C. J. (2010). The International Best Track Archive for Climate Stewardship (IBTrACS). BAMS 91, 363–376; Gahtan, J., et al. (2024). IBTrACS Project, Version 4r01. NOAA NCEI. · doi:10.25921/82ty-9e16 · source page ↗
Licence : U.S. Government work, public domain (NOAA NCEI); cite Knapp et al. (2010) · retrieved on Oct 25, 2026 · SHA-256 9c00ce8a7cc3…
Kiladis et al. (2014): Kiladis, G. N., Dias, J., Straub, K. H., Wheeler, M. C., Tulich, S. N., Kikuchi, K., Weickmann, K. M., & Ventrice, M. J. (2014). A comparison of OLR and circulation-based indices for tracking the MJO. Monthly Weather Review, 142, 1697–1715. · doi:10.1175/MWR-D-13-00301.1
Licence : Published literature; cited
Wheeler et al. (2004): Wheeler, M. C., & Hendon, H. H. (2004). An all-season real-time multivariate MJO index: development of an index for monitoring and prediction. Monthly Weather Review, 132, 1917–1932. · doi:10.1175/1520-0493(2004)132<1917:AARMMI>2.0.CO;2
Licence : Published literature; cited
Hall et al. (2001): Hall, J. D., Matthews, A. J., & Karoly, D. J. (2001). The modulation of tropical cyclone activity in the Australian region by the Madden–Julian oscillation. Monthly Weather Review, 129, 2970–2982. · doi:10.1175/1520-0493(2001)129<2970:TMOTCA>2.0.CO;2
Licence : Published literature; cited
Camargo et al. (2009): Camargo, S. J., Wheeler, M. C., & Sobel, A. H. (2009). Diagnosis of the MJO modulation of tropical cyclogenesis using an empirical index. Journal of the Atmospheric Sciences, 66, 3061–3074. · doi:10.1175/2009JAS3101.1
Licence : Published literature; cited
Klotzbach (2010): Klotzbach, P. J. (2010). On the Madden–Julian oscillation–Atlantic hurricane relationship. Journal of Climate, 23, 282–293. · doi:10.1175/2009JCLI2978.1
Licence : Published literature; cited
Maloney et al. (2000): Maloney, E. D., & Hartmann, D. L. (2000). Modulation of eastern North Pacific hurricanes by the Madden–Julian oscillation. Journal of Climate, 13, 1451–1460. · doi:10.1175/1520-0442(2000)013<1451:MOENPH>2.0.CO;2
Licence : Published literature; cited

Madden–Julian oscillation and cyclone formation A wave of convection that circles the tropics in 30 to 60 days

What is linked, what is not

Observed / expected formations, by basin and phase