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: Large explosive eruptions inject sulphate aerosols into the stratosphere and cool the surface by a few tenths of a degree for one to two years (Robock, 2000).

Pearson correlation r (lag 10 month(s))

-0.27

95% interval [-0.36; -0.15] (block bootstrap)

Aligned points

1,583

effective n ≈ 380 (autocorrelation)

p-value

0.00000

two-sided, Fisher z transform, effective n

Events used

minimum composite anomaly -0.06 °C

Period analysed

1880-01 → 2012-09

computed on Oct 23, 2026 · engine v1.0

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.

Superposed epochs

Show the data as a table

Mean anomaly around the 14 events (1883 Krakatau, 1886 Okataina, 1902 Santa Maria, 1907 Ksudach, 1912 Novarupta, 1916 Azul, Cerro, 1933 Kharimkotan, 1955 Bezymianny, 1963 Agung, 1980 St. Helens, 1982 Chichon, El, 1991 Pinatubo, 2011 Puyehue-Cordon Caulle, 2021 Hunga Tonga-Hunga Ha'apai), relative to the mean of the years before each event; dashed lines are the 5th and 95th percentiles of composites built on randomly drawn events (Monte-Carlo).

Aligned series (CSV)

Method and sources

Superposed epochs: yearly GISTEMP anomaly around each confirmed VEI ≥ 5 eruption (GVP, since 1880), relative to the mean of the five preceding years, averaged over events; Monte-Carlo band (2000 draws of random years). Lag correlation: monthly optical depth (GISS, 1850–2012) against the monthly GISTEMP anomaly, seasonal cycle and variations longer than ten years removed; lags from −36 to +36 months; confidence interval from a 24-month block bootstrap.

Computation parameters

{
    "sea": {
        "after": 5,
        "draws": 2000,
        "before": 5,
        "min_vei": 5,
        "from_year": 1880
    },
    "max_lag": 36,
    "bootstrap": {
        "seed": 20261023,
        "block": 24,
        "draws": 1000
    },
    "deseasonalize": "monthly climatology",
    "high_pass_months": 120
}

Inputs : gistemp.global.monthly (1,761 pts, run #14) · giss.aod550.global.monthly (1,953 pts, run #15) · gvp.eruptions.vei5.yearly (527 pts, run #114)

Reading this result

The composite mixes eruptions of very different size (VEI 5 to 7) and years in which El Niño masks or reinforces the signal; the negative correlation with optical depth (aerosols leading by several months) is expected but modest because optical depth does not capture the whole forcing. 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

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…
NASA GISS stratospheric aerosol optical depth (Sato et al., updated to 2012): Sato, M., Hansen, J. E., McCormick, M. P., & Pollack, J. B. (1993). Stratospheric aerosol optical depths, 1850–1990. J. Geophys. Res., 98, 22987–22994; updated through 2012 by NASA GISS. · doi:10.1029/93JD02553 · source page ↗
Licence : NASA data, public domain; cite Sato et al. (1993) · retrieved on Oct 23, 2026 · SHA-256 40b245c8fc87…
Smithsonian Global Volcanism Program, Holocene eruptions (Volcanoes of the World): Global Volcanism Program (2024). Volcanoes of the World (v. 5.2.x). Distributed by Smithsonian Institution, compiled by Venzke, E. · doi:10.5479/si.GVP.VOTW5-2024.5.2 · source page ↗
Licence : Smithsonian GVP data, free for non-commercial use with citation; redistribution of the database requires permission · retrieved on Oct 23, 2026 · SHA-256 5290b8ce1693…
Robock (2000): Robock, A. (2000). Volcanic eruptions and climate. Reviews of Geophysics, 38(2), 191–219. · doi:10.1029/1998RG000054
Licence : Published literature; cited

Volcanoes and temperature Cooling after large eruptions

What is linked, what is not