Methods and sources

Orders of magnitude · energy absorbed by the ocean

The « Hiroshima bomb » analogy

1 Hiroshima bomb = 62.76 TJ (6.276 × 10¹³ J). Each « bomb » in this lab denotes a quantity of thermal energy absorbed by the ocean — not an explosion. The 62.76 TJ standard is the IAP/CAS convention for making zettajoules tangible.

The analogy is common in climate outreach (Lyman 2010, Hansen, Cheng, Abraham…) to make ocean warming zettajoules tangible.

From radiative imbalance (W/m²) to ZJ/yr

EEI (Earth Energy Imbalance) measures the net difference between absorbed solar energy and energy returned to space, in watts per square metre of Earth surface. It results from forcings (greenhouse gases, aerosols) minus the climate response; its recent rise also reflects less reflection by clouds and sea ice (Loeb et al. 2021). Multiplied by Earth's area (~5.1 × 10¹⁴ m²) and a year's duration, it gives total excess energy — of which about 91% is absorbed by the ocean (AR6, 1971–2018 inventory: ocean 91%, land 5%, ice 3%, atmosphere 1%).

Order of magnitude: EEI × area × seconds/year × 91% → ocean ZJ/yr. Table values below use published OHC reconstructions (IAP/CAS): they may differ slightly from pure EEI arithmetic (inventory, ENSO, gridding methods).

Example 2025: EEI over 2006–2025 ≈ 1.04 W/m² → ~15.2 ZJ/yr for the whole ocean by calculation (91%). IAP measures ≈ 11.7 ZJ/yr over 0–2,000 m and ~2.3 ZJ/yr deeper, i.e. ~14 ZJ/yr: within the EEI range (0.82–1.25 W/m², 12 to 18 ZJ/yr for the ocean).

Rate (ZJ/yr), not cumulative stock

The lab shows an annual absorption rate (extra energy absorbed each year), not total heat stored since 1960. 23 ZJ/yr in 2025 means the ocean absorbed 23 zettajoules of surplus that year — not that the historical total is 23 ZJ.

Reference table

* 2026: projection (not a published IAP observation). « EEI→ZJ model » = physical order of magnitude; « OHC » = lab anchor.

Monitor and dashboard formulas

• bombs/hour = ZJ/yr × 1,817.67
• bombs/second = bombs/hour ÷ 3,600
• joules/year = ZJ/yr × 10²¹

The unit selector on « Scale » and the dashboard applies these conversions to the curve without changing source data.

Do not confuse: ~90% of solar radiation reaching the ocean surface is absorbed there (albedo ~0.06). The ~91% above refers to climate surplus partitioning (radiative imbalance), not direct solar budget.

Reference sheet · from W/m² to bombs/s

One physical chain links the solar radiative budget, today's imbalance and the Hiroshima-equivalent pace. Values below are for 2025 (IAP observation or projection).

Energy chain

340 W/m² = mean solar input at equilibrium. Today's imbalance (~1.04 W/m²) is only a fraction — but the ocean absorbs ~91% of the surplus.

Compared to human consumption

In 2025, the ocean absorbs ~11.7 ZJ/yr of climate surplus — about 18× global primary energy consumption (~0.65 ZJ/yr, IEA/BP 2023). This is radiative surplus stored in water, not useful energy used by societies.

Consumption source: IEA Global Energy Review 2024-2025 — order of magnitude 650 EJ ≈ 0.65 ZJ. Aligned with the Bombastic calculation chain.

Radiative budget · Interactive monitor

OHC data (1980–2026)

Latest complete year: 2025. IAP/CAS estimates a gain of +23 ± 8 ZJ in the upper 2,000 m; the NOAA/NCEI annual series gives +22.17 ZJ between 2024 and 2025. Both confirm record ocean heat content in their respective reconstructions. Pan et al., 2026 · NOAA/NCEI annual data.

The main curve shows the 20-year rolling slope (least squares, same IAPv4.2 series each year): this smoothing highlights the long-term trend and attenuates El Niño / La Niña variability. A single-year gain remains a separate figure, sensitive to ENSO. 2026 is a projection: 12.2 ZJ/yr, not a measurement.

In 2025, the smoothed 20-year trend is 11.72 ZJ/yr (≈ 371 TW). The displayed series gives an annual gain of 22.9 ZJ; Pan et al. (2026) report about 23 ± 8 ZJ from 2024 to 2025. These figures describe an annual gain, distinct from the smoothed trend.

Across 2021–2025, the five IAP/CAS annual gains average 17.22 ZJ/yr. This short average remains influenced by ENSO and reconstruction revisions; the curve uses the 20-year slope to compare years without confusing fluctuations with the underlying acceleration.

Metric contract

Each number in the lab belongs to a precise measurement family. This table shows what can be updated immediately and what requires a homogeneous publication before changing the model.

Uncertainties

The monitor and dashboard show ± 8 ZJ for the increase in ocean heat content from 2024 to 2025 reported by IAP/CAS. This margin applies to that specific result; it is not extended to other annual changes, the rolling twenty-year trend or the 2026 projection.

What does the published ± 8 ZJ refer to?

Pan et al. (2026) report an increase of about 23 ± 8 ZJ in the upper 2,000 m between 2024 and 2025 according to IAP/CAS. OHC reconstructions use in situ temperature profiles and methods for spatial coverage and gridding. These challenges help explain measurement uncertainty; they do not establish a decomposition of the ± 8 ZJ that the article does not specify here.

• Incomplete spatial coverage: the Argo network is dense since ~2007, but polar regions, continental margins and depths > 2,000 m remain less well sampled; the pre-Argo period is sparser.
• Instrument bias and homogenisation: corrections to historical XBT/MBT probes, Argo calibration, choice of baseline (reference climatology).
• Gridding and infilling: different methods to fill ocean gaps (interpolation, empirical modes, reanalyses).
• Definition of the annual rate: OHC is a stock; the « ZJ/yr » shown here is the difference between two successive annual means from the same file (IAPv4.2, January 2026 release). Each new release revises past years: two releases are never mixed in one series.

IAP/CAS, NOAA/NCEI and Copernicus

This lab compares IAP/CAS, NOAA/NCEI and Copernicus products. They share some observations but differ in processing and coverage. The ± 8 ZJ value cited here comes from the IAP/CAS estimate of the 2024→2025 gain; it is neither a shared margin for all three catalogues nor a statistical combination of their results.

What this tool does

For 2025 only, the badge, bar and energy equivalents use the published ± 8 ZJ margin on the 2024→2025 gain. Other years and the 2026 projection do not display this margin.

No bar for another year means this page does not assign it the interval published for 2024→2025. It does not mean that other estimates have no uncertainty.

Do not confuse: CO₂ uncertainty (Mauna Loa curve on the dashboard) is negligible at this scale; « interpolated year » notes flag estimates between OHC anchors, not a ± ZJ margin.

Associated physical effects (2023+)

The monitor's « Associated physical effects » section does not show direct real-time measurements. It summarises expected physical effects when ocean heat storage accelerates strongly (2023 and beyond), including deoxygenation linked to stratification.

Thermosteric expansion

Heat-expanded water occupies more volume. Much of current sea-level rise comes from this mechanism, besides glacier and ice-sheet melt. High OHC surplus strengthens this signal.

Stratification and asphyxiation

The surface layer warms and stabilises above cold deep water. Vertical mixing decreases, limiting oxygen supply to the depths — a risk for marine life and biogeochemical cycles.

These signals chain together: more surface heat → thermal expansion and sea-level rise; stronger stratification → less oxygen at depth. The lab summarises them qualitatively from 2023 onward.

Labels « High » / « Strengthened » are qualitative and depend on the year selected on the slider (2023+ threshold).

Radiative budget (dedicated page)

Rounded pedagogical values in W/m², inspired by Stephens et al. (2012), CERES-EBAF and IPCC AR6 (FAQ 1.1).

Equilibrium: ~340 incoming ≈ ~100 reflected + ~239 IR to space. The ~240 W/m² absorbed warm the planet, which re-emits infrared until balance is restored.

CO₂ and layers: CO₂ is well mixed (~427 ppm in 2025, at all heights). The temperature effect differs by altitude: relative cooling in the stratosphere, warming in the troposphere and at the surface.

Review the radiative budget →

Projections & SSP scenarios (AR6)

The « Projections » page uses a 2-reservoir energy model (surface + ocean). The 2025 starting point is observed: GMST 1.39 °C (Forster et al. 2026), EEI 1.12 W/m² (2013–2025 mean), i.e. ~16.4 ZJ/yr for the whole ocean in the model.

SSP scenarios: radiative forcings by anchors (inspired by AR6 WG1 / ScenarioMIP). Forcings in 2050 and 2100 are fitted so that GMST reproduces AR6 Table SPM.1 best estimates for 2041–2060 (1.7 / 2.0 / 2.1 / 2.4 °C) and 2081–2100 (1.8 / 2.7 / 3.6 / 4.4 °C). The model uses published physical parameters (climate sensitivity 3 °C, AR6; deep-ocean coupling, Geoffroy et al. 2013), and the resulting 2100 forcings (2.8 / 4.9 / 7.2 / 9.0 W/m²) stay close to the scenarios' nominal levels. Intermediate trajectories, displayed EEI and OHC are 2-reservoir model orders of magnitude, not validated against ScenarioMIP.

ZEC scenario: anthropogenic CO₂ emissions are set to zero in 2025; forcing is then prescribed in the lab model. The panel compares its multi-decadal orders of magnitude with the ZECMIP synthesis (MacDougall et al. 2020) and the AR6 assessment. The model does not explicitly simulate the carbon cycle or other forcing agents; this comparison does not make the experiments identical.

What the model does not do

• No import of raw CMIP6 time series — pedagogical syntheses only: ZECMIP (ΔGMST percentiles) and ScenarioMIP/AR6 GMST markers (chart overlay).
• No interactive carbon cycle, aerosols, ENSO or ice sheets.
• « Deep ocean » = model variable, not an in situ measurement (Argo/IAP).

SSP5-8.5 remains an illustrative upper bound (AR6); CMIP7 scenarios will be integrated toward AR7 (~2029).

CO₂ & trends · toward 2050

Projected curves show an absorption rate (ZJ/yr), not cumulative stock. Three methods are offered (extended EEI, 2-reservoir model, recent extrapolation). The shaded illustrative range links a lower bound (SSP2-4.5, 2-reservoir) to an upper bound (linear 2019–2026 trend). It is distinct from the published ±8 ZJ interval for the 2024→2025 OHC gain. The slider does not go past 2026: only curves and the shaded band extend the display. Detailed thermal inertia (ZEC, surface/ocean lag) remains on the Projections page.

Timeline 1957–2025 · CO₂ & trends · Explore projections

Bathymetric strata

Cumulative warming distribution since 1960: 40% (0–300 m) · 23% (300–700 m) · 29% (700–2,000 m) · 8% (> 2,000 m).

The stratum simulation on the « Mechanisms » page applies a growing thermal penetration factor over time for deep layers (ocean inertia).

Ocean warming varies with depth. Circulation redistributes some surface heat into deeper layers over timescales of decades to centuries. Full adjustment of the ocean to the atmosphere can take centuries to millennia. The 700 m depth is a layer boundary used to analyse ocean change, not a universal transit time for heat. Ocean warming can continue after emissions decline; its magnitude depends on cumulative emissions and circulation. IPCC AR6, Chapter 1 · Chapter 9.

Two references, one divergence

Ocean heat content is not measured directly: it is reconstructed from probes, using mapping methods that differ between institutes. Two global references are authoritative, IAP/CAS and NOAA/NCEI. They do not give the same figures.

This table carries the main lesson of this lab: the two references diverge sharply on any single year, by up to nearly 10 ZJ, yet converge on the twenty-year trend, within about 7 % (same estimator on both sides: 2006–2025 slope). An annual variation is therefore not a climate signal: it is a measurement blurred by natural variability and by the reconstruction method. This is why the figure highlighted here is an average, not a record.

Sources: IAP/CAS through the Observatory calculation chain, and NOAA/NCEI, 0-2000 m heat content, global annual means (file h22-w0-2000m).

Limits of the analogy

The « bomb » equivalent quantifies stored or absorbed thermal energy, not an explosive event. The analogy aims at zettajoule readability; it does not predetermine geography, speed or how heat is distributed in the ocean.

Review the introduction on the choice of this pedagogical unit.