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
35
Clear links
24
Causation demonstrated
0
Arc width from |r| of the stored result; several tests between the same phenomena are drawn as stacked arcs.
Hypothesis tested: The ocean takes about 90 % of the excess energy the Earth receives (von Schuckmann et al., 2023): the net flux measured by satellite at the top of the atmosphere should show up, roughly, in the heat gained by the ocean, on average, in trend and from year to year.
Pearson correlation r (lag 0 year(s))
-0.13
95% interval [-0.46; 0.27] (block bootstrap)
Aligned points
19
effective n ≈ 19 (autocorrelation)
p-value
0.597
two-sided, Fisher z transform, effective n
Mean imbalance (CERES)
0.99 W/m²
ocean 0–2000 m: 0.65 W/m², i.e. 66 % (partly by construction, see the method)
Trend of the imbalance (per decade)
0.45 W/m²
± 0.16 (standard error corrected for autocorrelation)
Trend of the ocean heat gain (per decade)
0.15 W/m²
± 0.16; difference between the two trends: p = 0.18
Period analysed
2006 → 2024
computed on Oct 27, 2026 · engine v1.0
Aligned series (standard deviations, after preprocessing)
Show the data as a table
Method and sources
Net flux at the top of the atmosphere: CERES EBAF-TOA, mean of each complete year. Heat gained by the ocean: NOAA NCEI 0–2000 m heat content (Levitus et al., 2012, updated), centred difference (H(y+1) − H(y−1)) / 2 for year y, converted to W/m² over the whole surface of the Earth (10²² J per year = 0.62 W/m²).
Three comparisons. Means: they agree partly by construction, as the EBAF net flux is anchored to the ocean heating measured by Argo over 2005–2015. Trends: independent, least-squares lines, standard error corrected for the autocorrelation of the residuals; difference of the two trends against their uncertainty. Year-to-year variations: correlation of the two detrended series, effective size from the autocorrelation, 2-year block bootstrap interval; it gives the verdict of the page.
Computation parameters
{
"r": "Pearson correlation of the detrended yearly values; effective size n(1 − r1x r1y)/(1 + r1x r1y); block bootstrap (2 years)",
"ohc": "NCEI ocean heat content 0–2000 m (yearly), centred difference (OHC(y+1) − OHC(y−1)) / 2, × 0.6213 W m⁻² per 10²² J/yr (whole Earth surface)",
"toa": "CERES EBAF-TOA net flux, yearly mean of the 12 months of each year",
"trend": "least squares, standard error inflated for the lag-1 autocorrelation of the residuals, per decade",
"caveat": "EBAF net flux adjusted to the 2005–2015 ocean heating: the means are not independent, the trends and yearly variations are"
}Inputs : ceres.toa.net.monthly (318 pts, run #7258) · ncei.ohc.2000m.yearly (21 pts, run #33)
Reading this result
The satellite sees the Earth’s heating accelerate: the imbalance has nearly doubled in twenty years, mainly because the planet reflects less sunlight (fewer low clouds and less ice: Loeb et al., 2021). The ocean stores most of this surplus (a little over half to two thirds here for the upper 2000 m alone, the rest going deeper, into ice, land and the atmosphere). From one year to the next, however, the two measurements do not vary together: the yearly heat gain of the ocean is very noisy (Argo sampling, exchanges with deep layers), and El Niño moves heat between ocean and atmosphere without changing the total. It takes several years for the two budgets to meet. 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
- CERES EBAF-TOA, Earth's radiation budget at the top of the atmosphere, monthly global means (NASA LaRC)
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Loeb, N. G., Doelling, D. R., Wang, H., Su, W., Nguyen, C., Corbett, J. G., Liang, L., Mitrescu, C., Rose, F. G., & Kato, S. (2018). Clouds and the Earth's Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) top-of-atmosphere (TOA) Edition-4.0 data product. Journal of Climate, 31, 895–918. NASA/LARC/SD/ASDC, CERES EBAF-TOA Edition 4.2.1, doi:10.5067/TERRA-AQUA-NOAA20/CERES/EBAF-TOA_L3B004.2.1.
· doi:10.1175/JCLI-D-17-0208.1 · source page ↗
Licence : NASA open data, no restriction; Earthdata login required; cite Loeb et al. (2018) and the data DOI · retrieved on Oct 27, 2026 · SHA-256 0136ab1f3b02… - Global ocean heat content 0–2000 m, yearly (NOAA NCEI)
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Levitus, S., et al. (2012). World ocean heat content and thermosteric sea level change (0–2000 m), 1955–2010. Geophysical Research Letters, 39, L10603. Updated yearly series (0–2000 m, Argo era), NOAA NCEI.
· doi:10.1029/2012GL051106 · source page ↗
Licence : U.S. Government work, public domain; cite Levitus et al. (2012) · retrieved on Oct 23, 2026 · SHA-256 5b0fabf106dc… - Loeb et al. (2018)
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Loeb, N. G., Doelling, D. R., Wang, H., Su, W., Nguyen, C., Corbett, J. G., Liang, L., Mitrescu, C., Rose, F. G., & Kato, S. (2018). Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) top-of-atmosphere (TOA) Edition-4.0 data product. Journal of Climate, 31(2), 895–918.
· doi:10.1175/JCLI-D-17-0208.1
Licence : Published literature; cited - Loeb et al. (2021)
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Loeb, N. G., Johnson, G. C., Thorsen, T. J., Lyman, J. M., Rose, F. G., & Kato, S. (2021). Satellite and ocean data reveal marked increase in Earth’s heating rate. Geophysical Research Letters, 48(13), e2021GL093047.
· doi:10.1029/2021GL093047
Licence : Published literature; cited - Johnson et al. (2016)
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Johnson, G. C., Lyman, J. M., & Loeb, N. G. (2016). Improving estimates of Earth’s energy imbalance. Nature Climate Change, 6, 639–640.
· doi:10.1038/nclimate3043
Licence : Published literature; cited - von Schuckmann et al. (2023)
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von Schuckmann, K., Minière, A., Gues, F., Cuesta-Valero, F. J., Kirchengast, G., et al. (2023). Heat stored in the Earth system 1960–2020: where does the energy go? Earth System Science Data, 15(4), 1675–1709.
· doi:10.5194/essd-15-1675-2023
Licence : Published literature; cited - Levitus (2012)
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Levitus, S., et al. (2012). World ocean heat content and thermosteric sea level change (0–2000 m), 1955–2010. Geophysical Research Letters, 39, L10603.
· doi:10.1029/2012GL051106
Licence : Published literature; cited