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: During El Niño the tropical Pacific releases heat to the atmosphere; global temperature peaks about three months after the index (Trenberth et al., 2002).

Pearson correlation r (lag 2 month(s))

0.49

95% interval [0.38; 0.57] (block bootstrap)

Aligned points

918

effective n ≈ 215 (autocorrelation)

p-value

0.00000

two-sided, Fisher z transform, effective n

Period analysed

1950-01 → 2026-08

computed on Oct 23, 2026 · engine v1.0

Aligned series (standard deviations, after preprocessing)

Show the data as a table

Both series are drawn in standard-deviation units (z) after removing the seasonal cycle and slow variations, to compare their fluctuations; original values are in the table and the CSV export.

Correlation by lag (month(s))

Show the data as a table

Pearson coefficient for each lag; a positive lag means the second series follows the first. The table gives n, effective n and p for each lag.

Aligned series (CSV)

Method and sources

Monthly series deseasonalised then high-pass filtered over 10 years (running mean removed), so that long-term warming does not create an artificial correlation. Pearson correlation for lags of −12 to +12 months, effective sample size from Bretherton et al. (1999), interval from a block bootstrap with 12-month blocks.

Computation parameters

{
    "max_lag": 12,
    "bootstrap": {
        "seed": 20261023,
        "block": 12,
        "draws": 1000
    },
    "statistic": "pearson",
    "deseasonalize": "monthly climatology",
    "high_pass_months": 120
}

Inputs : cpc.oni.monthly (920 pts, run #13) · gistemp.global.monthly (1,761 pts, run #14)

Reading this result

The link is one of the best established in climate; it explains much of the record years (1998, 2016, 2024). It says nothing about the underlying trend, removed by the filter. 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

Oceanic Niño Index (NOAA CPC): NOAA CPC, Oceanic Niño Index (ONI): 3-month running mean of ERSSTv5 SST anomalies in the Niño 3.4 region, centred 30-year base periods updated every 5 years. · source page ↗
Licence : U.S. Government work, public domain · retrieved on Oct 23, 2026 · SHA-256 5d6fa3a2f857…
GISTEMP v4 global land-ocean temperature anomaly: GISTEMP Team (2026). GISS Surface Temperature Analysis (GISTEMP), version 4. NASA Goddard Institute for Space Studies; Lenssen et al. (2024). · doi:10.1029/2023JD040179 · source page ↗
Licence : NASA data, public domain; cite GISTEMP Team and Lenssen et al. (2024) · retrieved on Oct 23, 2026 · SHA-256 4c64eda288bc…
Trenberth et al. (2002): Trenberth, K. E., Caron, J. M., Stepaniak, D. P., & Worley, S. (2002). Evolution of El Niño–Southern Oscillation and global atmospheric surface temperatures. Journal of Geophysical Research, 107(D8), 4065. · doi:10.1029/2000JD000298
Licence : Published literature; cited

El Niño and global temperature The planet warms a few months later

What is linked, what is not