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 heating of the atmosphere by MJO convection excites Rossby waves that reach the North Atlantic in one to two weeks. A positive NAO is more frequent about 10 to 15 days after the convection sits over the Indian Ocean (phases 3 and 4), a negative NAO after it has reached the western Pacific (phases 6 and 7) (Cassou, 2008; Lin et al., 2009). It is one of the few sources of predictability of European weather beyond ten days.

NAO difference, phases 3–4 minus 6–7 (days +10 to +15)

0.22

p = 0.004 (1000 circular shifts)

NAO after phases 3–4

0.38

877 winter days, 158 episodes

NAO after phases 6–7

0.16

843 winter days, 154 episodes

Period analysed

1991-01-01 → 2026-03-31

computed on Nov 6, 2026 · engine v1.0

Mean NAO in the days after the MJO (November to March)

Show the data as a table

Mean daily NAO 0 to 25 days after a day of active MJO in phases 3–4 (convection over the Indian Ocean) and in phases 6–7 (western Pacific), and after all winter days (reference). The test bears on days 10 to 15, fixed in advance after Cassou (2008).

NAO of days +10 to +15 by MJO phase

Phase	Inactive	1	2	3	4	5	6	7	8
Mean NAO	+0.23	+0.01	+0.33	+0.34	+0.43	+0.53	+0.26	+0.05	+0.11
Days · episodes	2056 · 137	388 · 69	428 · 77	466 · 78	411 · 80	353 · 73	427 · 78	416 · 76	433 · 71

Phases 1 and 2: convection over Africa and the western Indian Ocean; 3 and 4: Indian Ocean and Indonesia; 5 and 6: Maritime Continent and western Pacific; 7 and 8: central Pacific and Western Hemisphere. Red: NAO above the mean of all winter days (+0.25), blue: below it.

Aligned series (CSV)

Method and sources

MJO: OLR-based OMI index (NOAA PSL, 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. NAO: daily CPC index. MJO days of November to March. Fixed before the computation: the response is the mean NAO of days +10 to +15, the statistic the difference between the response after phases 3–4 and after phases 6–7. Significance: 1,000 circular shifts of the phase series (by one year to the length of the record minus one year), which keep its persistence and seasonality but break its link with the NAO; one-sided test. Successive days of one episode are not independent: the number of episodes is given next to the number of days.

Computation parameters

{
    "seed": 20261106,
    "phase": "OMI (NOAA PSL), x = PC2, y = −PC1, eight 45° sectors as RMM (Wheeler and Hendon 2004); inactive when amplitude < 1",
    "season": "MJO days of November to March",
    "response": "daily NAO index (NOAA CPC), mean of days +10 to +15",
    "statistic": "mean response after phases 3–4 minus mean response after phases 6–7",
    "significance": "1000 circular shifts of the phase series by 365 days to N − 365 days, one-sided"
}

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) · cpc.nao.daily (28,064 pts, run #31103)

Reading this result

The link shows: the NAO of days +10 to +15 averages +0.38 after phases 3–4 against +0.16 after phases 6–7, a difference of 0.22 that the circular shifts reach only 4 times in 1,000 (p = 0.004). The table refines the shape: the NAO peaks after phase 5 (+0.53) and is lowest after phases 7 and 1 (close to 0), a cycle shifted by about one phase from Cassou (2008). The effect is small against the daily variability of the NAO (standard deviation close to 1): it shifts the odds, it does not decide the weather. The mean NAO of the period is positive (about +0.2), hence values that are almost all positive. 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…
North Atlantic Oscillation, daily index (NOAA CPC, CDAS): NOAA CPC, daily North Atlantic Oscillation index: projection of the daily 500 hPa height anomalies of the CDAS reanalysis onto the NAO loading pattern, normalised (1950–). · source page ↗
Licence : U.S. Government work, public domain · retrieved on Nov 6, 2026 · SHA-256 46e257cd5ae5…
Cassou (2008): Cassou, C. (2008). Intraseasonal interaction between the Madden–Julian Oscillation and the North Atlantic Oscillation. Nature, 455(7212), 523–527. · doi:10.1038/nature07286
Licence : Published literature; cited
Lin et al. (2009): Lin, H., Brunet, G., & Derome, J. (2009). An observed connection between the North Atlantic Oscillation and the Madden–Julian Oscillation. Journal of Climate, 22(2), 364–380. · doi:10.1175/2008JCLI2515.1
Licence : Published literature; cited
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(5), 1697–1715. · doi:10.1175/MWR-D-13-00301.1
Licence : Published literature; cited

MJO and NAO When the tropical convection of the MJO passes over the Indian Ocean, does the North Atlantic Oscillation turn positive two weeks later?

What is linked, what is not

NAO of days +10 to +15 by MJO phase