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Earth's Energy Budget

The Earth's energy budget (also called the Earth's radiation budget or the planetary energy balance) is the accounting of the energy that enters the Earth system, moves within it, and leaves it.

The Earth's energy budget (also called the Earth's radiation budget or the planetary energy balance) is the accounting of the energy that enters the Earth system, moves within it, and leaves it. It rests on the first law of thermodynamics (conservation of energy) and on the physics of radiative transfer. The climate depends on the balance between incoming shortwave solar radiation that is absorbed and the outgoing longwave infrared radiation that the planet emits to space.

Over multi-decadal to geological timescales, the global mean temperature is stable only if the net radiative flux at the top of the atmosphere (TOA) is close to zero, so that absorbed solar radiation equals outgoing thermal emission. This is a steady state of radiative balance and not thermodynamic equilibrium, because the Earth system is an open system that receives energy at a high effective temperature (the Sun) and radiates it at a much lower one. Energy absorbed unevenly across latitudes, and between the surface and the atmosphere, is redistributed vertically by convection, latent heat release, and sensible heat transfer, and horizontally by atmospheric circulation and ocean currents. If an external perturbation, such as a change in solar irradiance, volcanic aerosols, or greenhouse gases, disturbs the balance, the planet gains or loses energy. This difference is the Earth's energy imbalance (EEI). Most of the energy is stored in the oceans, and smaller amounts go into the cryosphere, the land, and the atmosphere, until a change in temperature restores balance. In the 2000s to the 2020s the imbalance has been positive, of the order of 1 W/m2, and it is the most direct measure of the rate at which the planet is accumulating heat.

History of the concept

The idea that the atmosphere affects the temperature of the surface goes back to Joseph Fourier, who argued in the 1820s that the Earth would be colder without its atmosphere. John Tyndall measured in 1859 that water vapor and carbon dioxide absorb infrared radiation, and Svante Arrhenius calculated in 1896 how the surface temperature would change if the concentration of carbon dioxide changed. Early estimates of the solar constant were made by Claude Pouillet in the 1830s. Milutin Milanković related ice ages to changes in the orbital distribution of sunlight in the 1920s to 1940s.

Measurements from space began with the Earth Radiation Budget Experiment (ERBE) in the 1980s. The Clouds and the Earth's Radiant Energy System (CERES), on several satellites since 1997, now provides a continuous record. Global energy budget diagrams, such as those of Kiehl and Trenberth (1997), Trenberth and colleagues (2009), Stephens and colleagues (2012), Wild and colleagues (2013, 2015), and Loeb and colleagues (2018), combine satellite measurements, surface radiation networks, and models. The values in this article are rounded averages of such estimates, and individual components of the budget are uncertain by several watts per square meter.

Simple models

Radiative equilibrium temperature

If the Earth is treated as a single body that absorbs sunlight and emits as a black body, balance requires that absorbed solar power equals emitted power. With solar constant S0, planetary albedo αp, and the Stefan-Boltzmann constant σ, the effective emission temperature Te satisfies:

(S0 / 4)(1 − αp) = σ Te4 so that Te = [ S0 (1 − αp) / (4_σ_) ]1/4

For S0 = 1,361 W/m2 and αp = 0.293, the result is Te ≈ 255 K (about −18 °C). The observed global mean near-surface temperature is about 288 K (about 15 °C), so the atmosphere warms the surface by about 33 K. The difference is the greenhouse effect, discussed below.

A single absorbing layer

In a model in which the atmosphere is one layer that absorbs all upwelling infrared radiation and emits equally upward and downward, the surface must balance both the absorbed sunlight and the downward emission of the layer. This gives a surface temperature Ts = 21/4 Te ≈ 303 K. This is higher than the observed value because the real atmosphere is partly transparent in the infrared window, because convection and latent heat transport carry energy from the surface to the atmosphere by non-radiative means, and because the emission is spread over many altitudes with different temperatures. The model illustrates the principle, and it does not give a quantitative prediction.

Incoming solar radiation

Nearly all of the energy that drives the climate system comes from nuclear fusion by the proton-proton chain in the core of the Sun. Geothermal heat, from radioactive decay and the primordial heat of formation, supplies a heat flux of about 0.09 W/m2 (about 47 terawatts), which is about 0.03 percent of the incident sunlight.

Solar spectrum

The solar photosphere radiates approximately as a black body with an effective temperature of T☉ ≈ 5,772 K. The wavelength of peak emission follows Wien's displacement law:

λmax = b / T☉ ≈ 2,897.8 μm·K / 5,772 K ≈ 0.50 μm

Solar radiation is therefore classified as shortwave radiation, and most of its energy lies between 0.15 and 4 μm. At the top of the atmosphere, roughly 8 percent of the energy is in the ultraviolet, about 43 to 47 percent is in the visible spectrum (which includes photosynthetically active radiation), and the remainder, about 45 to 49 percent, is in the near-infrared. The exact fractions depend on the reference spectrum.

Total solar irradiance and geometry

The total solar irradiance (TSI), or solar constant S0, is the radiant flux perpendicular to the Sun's rays at a distance of one astronomical unit (1.496 × 1011 m). Spaceborne cavity radiometers, such as SORCE/TIM and TSIS-1, give a value of about 1,361 W/m2 (1,360.8 ± 0.5 W/m2 at solar minimum). The Earth, with a mean radius RE of about 6,371 km, intercepts sunlight over a disk of area π RE2, so that the total intercepted solar power is:

Pin = S0 π RE2 ≈ 1.74 × 1017 W (about 174 petawatts)

Rotation spreads this over the entire surface area 4_π_ RE2, so the global mean incident flux is:

ITOA = S0 / 4 ≈ 340 W/m2

Three effects cause variation of the incident sunlight:

  • Orbital eccentricity. The Earth is closest to the Sun (perihelion) in early January and farthest (aphelion) in early July. With an eccentricity of about 0.0167, the irradiance varies by about ±3.3 percent (about ±45 W/m2), so the global mean incident flux is about 7 percent higher in January than in July.
  • The solar cycle. Over the 11-year solar cycle, the TSI varies by about 0.1 percent (about 1 W/m2 from minimum to maximum), mainly because of the balance of dark sunspots and bright faculae. This is equivalent to about 0.25 W/m2 averaged over the globe.
  • Orbital cycles. The distribution of sunlight by latitude and season changes over 104 to 105 years because of variations in eccentricity, axial tilt, and precession (Milankovitch cycles).

Reflection of sunlight

About 29 percent of the incident sunlight is reflected or scattered back to space without being absorbed. The albedo α of a surface or of the planet is the fraction of incident shortwave radiation that is reflected:

α = FSW,↑ / FSW,↓

CERES measurements give a planetary albedo αp of about 0.29 to 0.30 (0.293 in many estimates), which corresponds to a reflected flux of about 100 W/m2. About three quarters of this is reflected by the atmosphere and clouds, and about a quarter by the surface.

Clouds, aerosols, and scattering

In clear skies, the reflected flux is about 53 W/m2, which includes reflection by the surface and scattering by air molecules and aerosols. Clouds add to this, and the shortwave cloud radiative effect is about −47 W/m2, so that the total reflected flux is about 100 W/m2. Clouds are the largest single factor that changes the planetary albedo. The optical depth τc of a liquid cloud is approximately proportional to its liquid water path (LWP) and inversely proportional to the effective radius re of the droplets:

τc ≈ 3 LWP / (2 ρw re)

where ρw is the density of liquid water. Thick, low marine stratocumulus clouds over the eastern subtropical oceans have albedos of about 0.5 to 0.8. They cool the planet because they reflect much sunlight while emitting infrared radiation at a temperature close to that of the surface.

Two other processes contribute to atmospheric reflection:

  • Rayleigh scattering by air molecules is much stronger at short wavelengths (the scattering cross-section is proportional to λ−4). It scatters blue light both downward as diffuse skylight and upward to space.
  • Aerosols, including sea salt, mineral dust, sulfates, and organic particles, scatter sunlight directly. They also act as cloud condensation nuclei. At a fixed liquid water path, more nuclei produce more and smaller droplets and increase cloud reflectivity (the Twomey effect). Some aerosols, such as black carbon, absorb sunlight.

Surface albedo

The global mean surface albedo is about 0.12 to 0.13. The incident surface flux is about 185 W/m2, so about 24 W/m2 is reflected. Typical values for different surfaces are:

  • Snow and ice. Fresh snow has an albedo of about 0.8 to 0.9, and old or melting snow has a lower value (about 0.5 to 0.7). Bare glacier ice has about 0.3 to 0.5, and bare sea ice has about 0.4 to 0.7. Melt ponds on sea ice can lower the albedo to about 0.2 to 0.4.
  • Land. Deserts reflect about 0.3 to 0.4, grasslands and crops about 0.18 to 0.25, deciduous forests about 0.15 to 0.18, and dark coniferous boreal forests about 0.08 to 0.13. Healthy vegetation absorbs most visible light through chlorophyll and reflects much more near-infrared light, a sharp change at about 0.7 μm called the red edge.
  • Oceans. Open water has an albedo of 0.03 to 0.06 when the Sun is high, and it increases at large zenith angles according to the Fresnel equations (the refractive index of seawater is about 1.33). Averaged over the globe, ocean albedo is about 0.06.

The contrast between bright ice and snow (about 0.6 to 0.85) and dark ocean or soil (about 0.06 to 0.15) produces the ice-albedo feedback. A warming climate melts ice and snow, exposes darker surfaces, increases the absorption of sunlight, and causes more warming. The feedback parameter is positive, with a best estimate of about +0.35 W·m−2·K−1 and a wide uncertainty range. It is a major contributor to Arctic amplification.

Absorption of sunlight

Subtracting the reflected flux from the incident flux gives the absorbed solar radiation (ASR):

ASR = (S0 / 4)(1 − αp) ≈ 240 W/m2

This is about 70 percent of the incident sunlight. Roughly one third of it is absorbed in the atmosphere, and about two thirds is absorbed at the surface.

Absorption in the atmosphere

The atmosphere absorbs about 75 to 80 W/m2 (about 23 percent of the incident sunlight). The main absorbers are:

  • Ozone and oxygen. Molecular oxygen absorbs extreme ultraviolet radiation at the top of the atmosphere, and ozone in the stratosphere absorbs the shortwave ultraviolet (UV-C and most of UV-B, in the Hartley and Huggins bands) and some visible light (the Chappuis band). This absorption heats the stratosphere and creates the temperature inversion above the tropopause. It involves a small fraction of the total energy, of order 10 W/m2.
  • Water vapor, clouds, and aerosols. Water vapor has vibrational and rotational bands in the near-infrared (centered near 0.94, 1.14, 1.38, 1.87, and 2.7 μm) and is responsible for most of the absorption in the troposphere. Liquid water and ice in clouds, the oxygen bands at 0.69 and 0.76 μm, and light-absorbing aerosols such as black carbon add to this.

Absorption at the surface

The surface absorbs about 160 W/m2, which is the difference between the incident flux of about 185 W/m2 and the reflected flux of about 24 W/m2. Most of this is absorbed in the upper layers of the oceans and in the topmost soil and vegetation canopy of land. It is accompanied by about 342 W/m2 of downward longwave radiation from the atmosphere, so that the total radiative input at the surface is about 500 W/m2.

Surface energy balance

The net radiation at the surface Rn is the sum of net shortwave and net longwave fluxes. Using the values of the table below:

Rn = (FSW,↓ − FSW,↑) + (FLW,↓ − FLW,↑) ≈ 161 + (342 − 398) ≈ 105 W/m2

At the surface, this net radiation is balanced by the turbulent fluxes of latent heat QLH and sensible heat QSH, and by the heat flux into the subsurface G (the oceans, soils, and ice):

Rn = QLH + QSH + G

Radiation alone could not remove this surplus without a very large temperature difference between the surface and the air. Calculations of radiative equilibrium without convection give a much warmer, unstable lower atmosphere, so that convection and evaporation remove much of the heat.

Latent and sensible heat fluxes

  • Latent heat flux (about 80 to 90 W/m2, with 84 W/m2 used here) is the largest non-radiative term. Absorbed energy evaporates water from the oceans and from land and plants (evapotranspiration). Each kilogram of evaporated water carries about 2.45 × 106 J. The global mean flux therefore corresponds to a mean evaporation rate (equal to the precipitation rate) of:
E = QLH / Lv ≈ 84 / (2.45 × 106) ≈ 3.4 × 10−5 kg m−2 s−1
This is about 3 mm per day, or roughly 1,050 to 1,100 mm per year. The energy is released in the atmosphere where the vapor condenses, mostly in the free troposphere. This links the energy budget to the water cycle.
  • Sensible heat flux (about 20 W/m2) is the transfer of heat by conduction through a thin layer next to the surface, followed by transport in turbulent eddies and thermals. In terms of the turbulent covariance of vertical wind _w_′ and temperature _T_′, it is QSH = ρa cp ⟨_w_′_T_′⟩, where ρa is the air density and cp is the specific heat of air.

Bowen ratio

The partition of the available energy between sensible and latent heat is described by the Bowen ratio B = QSH / QLH. Typical values are about 0.1 over the oceans (as low as about 0.05 in the tropics), about 0.1 to 0.3 over wet tropical forests and irrigated land, about 0.4 to 0.8 over temperate forests and grasslands, and above 5 (and up to 10 or more) over deserts and drought-stricken land. In dry conditions, the stomata of plants close and soil moisture is depleted, so that nearly all the available energy goes into sensible heat.

Outgoing longwave radiation and the greenhouse effect

Emission by the surface and to space

The Earth's surface and atmosphere are much cooler than the Sun, so they emit in the thermal infrared. For a temperature of about 288 K, Wien's displacement law gives a peak near 10 μm, and most of the emission is at wavelengths of about 4 to 100 μm (wavenumbers of 100 to 2,500 cm−1). This is called longwave radiation.

The surface emits upward according to the Stefan-Boltzmann law, with an emissivity ε of about 0.98 to 0.99:

FLW,↑ = ε σ Ts4

The global mean of this flux is about 398 W/m2. This value is not obtained by inserting the global mean temperature into the formula. Because emission depends on the fourth power of temperature, the mean of _σ_T4 over the surface and over time is larger than σ times the fourth power of the mean temperature (an application of Jensen's inequality). For example, two equal areas at 278 K and 298 K have a mean temperature of 288 K, but their mean blackbody emission is about 393 W/m2, which is about 3 W/m2 more than the emission at 288 K. The real distribution of temperatures in space and time is wider than this example, which explains the larger value.

The outgoing longwave radiation (OLR) measured at the top of the atmosphere is only about 239 to 240 W/m2. It corresponds to an effective emission temperature of Te = (OLR / σ)1/4 ≈ 255 K. The difference between the surface emission and the OLR is a measure of the strength of the greenhouse effect G:

G = FLW,↑,surf − OLR ≈ 398 − 239 = 159 W/m2

The normalized greenhouse factor g = G / FLW,↑,surf is about 0.40.

Absorption and emission by greenhouse gases

Nitrogen (78 percent of dry air) and oxygen (21 percent) are essentially transparent to thermal infrared radiation, because their molecules have no permanent dipole moment. The radiatively active gases are water vapor (absorbing at about 6.3 μm and in the rotational band at wavelengths above about 12 μm), carbon dioxide (the strong 15 μm bending band), ozone (9.6 μm), methane (7.66 μm), nitrous oxide (about 7.8 and 17 μm), and halocarbons. Clouds also absorb and emit strongly in the infrared.

Only a part of the surface emission, about 20 W/m2 under average cloudy conditions and up to about 40 W/m2 in clear skies, escapes directly to space through the infrared atmospheric window at wavelengths of about 8 to 12 μm. The remainder is absorbed in the troposphere. Near sea level, the time between molecular collisions is about 10−10 s, while the radiative lifetime of an excited CO2 bending-mode vibration is of the order of a second. An absorbed photon is therefore almost always converted into thermal motion of the surrounding gas before it can be re-emitted. As a result, the gas is in local thermodynamic equilibrium up to an altitude of about 60 km, and its emission is determined by its temperature, as described by Planck's law.

The atmosphere emits infrared radiation in all directions:

  • Downwelling longwave radiation at the surface (DLR, about 342 W/m2) comes mainly from the warm, moist lowest kilometers of the troposphere and from cloud bases. It is more than twice the solar radiation absorbed at the surface.
  • Upward emission to space comes from a range of altitudes. A simple description is that radiation escapes from an effective emission level at which the overlying optical depth is about 1. For the global mean OLR, this level is near 5 km in the troposphere, where the temperature is about 255 K, consistent with a lapse rate of about 6.5 K/km. The emission level depends on wavelength. It is higher, in the stratosphere, near the center of the CO2 band, and lower in the window.

Adding greenhouse gases raises the effective emission level to a higher and colder altitude. Colder air emits less radiation, so the OLR decreases for a given surface temperature. This imbalance is the basis of the radiative forcing of greenhouse gases. The increase of CO2 has a particularly clear effect in the wings of the 15 μm band, where the emission level rises most.

Cloud radiative effects

Clouds affect both parts of the budget. Their reflection of sunlight reduces ASR by about 47 W/m2 (the shortwave cloud radiative effect). Their absorption of surface and atmospheric emission and re-emission at lower temperatures reduces OLR by about 27 to 28 W/m2 (the longwave effect). The net effect of present-day clouds is a cooling of about 19 to 20 W/m2. High, thin cirrus clouds warm the climate on balance, whereas low, thick clouds cool it. The response of clouds to warming is the largest uncertainty in the climate feedbacks.

Global mean budget

The following table summarizes a typical annual global mean budget, rounded from combinations of CERES observations, surface radiation networks, and reanalyses. Fluxes in W/m2 are positive when they add energy to the specified domain, and the individual terms are uncertain by about 2 to 10 W/m2. For this reason, quoted budgets do not close exactly, and the TOA imbalance is adjusted to agree with measurements of ocean heat content.

DomainShortwave and non-radiative fluxesLongwave fluxesBalance
Top of the atmosphereIncident solar: +340. Reflected: −100. Absorbed (ASR): about +240.5.OLR: about −239.7 (including about −20 from the surface through the window).Net imbalance N = ASR − OLR ≈ +0.8, a mean for the 2000s to the 2010s. Recent values are higher.
AtmosphereAbsorbed solar: about +79. Latent heat from the surface: about +84. Sensible heat from the surface: about +20.Absorbed from the surface: about +376 (398 minus the 22 that passes through the window). Emitted to space: about −218. Emitted to the surface (DLR): about −342.The net radiative loss of the atmosphere is about 184 W/m2 (218 + 342 − 376). It is balanced by the gains of 79 + 84 + 20 ≈ 183 W/m2.
SurfaceIncident solar: about +185. Reflected: about −24. Net solar: about +161. Turbulent heat loss: about −104.DLR: about +342. Emitted by the surface: about −398. Net longwave: about −56.Rn ≈ 105. After turbulent fluxes of 104, about 1 W/m2 remains (G), mostly stored in the oceans.

The table shows several features of the budget. The atmosphere is cooled radiatively, and it is heated by absorbed sunlight and by turbulent fluxes from the surface, mostly the latent heat released in clouds. The net longwave flux at the surface (−56 W/m2) is much smaller than the surface emission, because the surface receives a large flux of downward infrared radiation.

Spatial and temporal variation

The global mean budget hides large regional differences:

  • Latitude. The tropics absorb much more sunlight than the polar regions, because of the larger angle of incidence at high latitudes and the high albedo of ice and snow. The OLR varies less with latitude than ASR. The result is a surplus of net radiation at latitudes below about 35 to 40° and a deficit at higher latitudes. The atmosphere and oceans move energy poleward to balance this. The total poleward transport at its maximum is about 5 to 6 petawatts in each hemisphere, with the atmosphere carrying most of it at mid-latitudes and the oceans carrying a larger share at low latitudes.
  • Season and hemisphere. The seasonal cycle of insolation, and the difference between the land-dominated Northern Hemisphere and the ocean-dominated Southern Hemisphere, produce seasonal variations in the global mean ASR, OLR, and net flux. The global mean incident flux is highest in January.
  • Regional processes. Persistent cloud decks, deserts, monsoon systems, and the intertropical convergence zone have distinctive cloud effects and OLR. Deep convective clouds have strong, partly canceling shortwave and longwave effects.
  • Short-term variability. El Niño and La Niña events, volcanic eruptions, and changes in aerosols and clouds produce changes in the imbalance of a few tenths of a W/m2 from year to year.

Minor terms

Several other energy fluxes are small compared to the radiative terms:

TermApproximate powerEquivalent flux over the Earth's surface
Geothermal heat flowAbout 47 TWAbout 0.09 W/m2
Tidal dissipation in the Earth-Moon systemAbout 3.7 TWAbout 0.007 W/m2
Global human primary energy use (2020s)About 19 to 20 TWAbout 0.04 W/m2
Energy stored by photosynthesis (net primary production)About 100 TWAbout 0.2 W/m2, or about 0.1 percent of ASR

The direct heating by human energy use is therefore about 25 times smaller than the present imbalance. Warming results from changes in the atmosphere's radiative properties and not from the waste heat of energy use.

Earth's energy imbalance

Forcing, feedback, and the energy equation

Before the industrial era, the long-term mean of ASR and OLR were nearly equal. Since 1750, human activities have increased the concentrations of well-mixed greenhouse gases: CO2 from about 278 ppm to above 420 ppm, CH4 from about 730 ppb to about 1,900 ppb, and N2O from about 270 ppb to about 337 ppb, together with synthetic halocarbons. This has reduced the OLR at a given surface temperature. The change in net flux caused by a perturbation, after the stratosphere and troposphere have adjusted, is the effective radiative forcing (ERF), ΔF. For CO2, the dependence on concentration C is approximately logarithmic:

ΔF ≈ 5.35 ln(C / C0) W/m2

For example, for an increase from 280 to 420 ppm, ΔF ≈ 5.35 × ln 1.5 ≈ 2.2 W/m2, and for a doubling the result is about 3.7 W/m2 (a more recent assessment gives about 3.9 W/m2). The total anthropogenic ERF assessed for 2019 in the Sixth Assessment Report of the Intergovernmental Panel on Climate Change was about 2.7 W/m2 (about 1.96 to 3.48 W/m2), including a cooling effect of aerosols of about −1.3 W/m2. The value for the mid-2020s is probably somewhat higher, as greenhouse gases have continued to increase and aerosol emissions have fallen in some regions.

The oceans have a large heat capacity, so the surface temperature cannot change at once to its equilibrium value. The difference between ASR and OLR at the top of the atmosphere is the energy imbalance N, which is given by:

N = ASR − OLR = ΔF + λ ΔTs

where ΔTs is the change in global mean surface temperature and λ is the net climate feedback parameter, which is negative for a stable climate. Its value is of the order of −1 to −1.3 W·m−2·K−1, with an uncertainty range that depends on the assessment. It is the sum of the strongly stabilizing Planck feedback (about −3.2 W·m−2·K−1) and the positive feedbacks of water vapor, surface albedo, and (on balance) clouds, together with the lapse rate feedback. The equilibrium warming for a constant forcing is ΔTeq = −_ΔF_ / λ, which is the basis for climate sensitivity estimates. As long as ΔTs is smaller than −_ΔF_ / λ, N remains positive and the planet continues to accumulate heat, which is why further warming is expected even if concentrations are stabilized.

The Planck response

For a black body at Te = 255 K, the increase of emission with temperature is:

d(_σ_T4) / d_T_ = 4_σ_ T3 ≈ 3.8 W·m−2·K−1

The Planck feedback of about 3.2 W·m−2·K−1 from climate models is of the same order, with the difference arising from the vertical structure of temperature change. Without any other feedback, a forcing of 3.7 W/m2 for a doubling of CO2 would warm the surface by about 3.7 / 3.2 ≈ 1.2 K. Positive feedbacks amplify this value.

Response time

If the heat capacity per unit area is C, the response of ΔTs to a step forcing has a time constant of τ = C / |_λ_|. For an ocean mixed layer of 70 m, C = ρw cp,w h ≈ 1,000 × 4,186 × 70 ≈ 2.9 × 108 J m−2 K−1, and with |_λ_| = 1.2 W·m−2·K−1 the time constant is about 2.4 × 108 s, or roughly 8 years. Mixing of heat into the deeper ocean adds a second, much longer timescale of centuries, so the full response takes a very long time.

Observation of the imbalance

The imbalance is a small difference between two large fluxes of about 240 W/m2 each. The absolute calibration of satellite radiometers is not accurate enough to measure it directly, because the absolute uncertainty of CERES fluxes is a few W/m2. Instead, the satellite instruments are very stable, with changes of only a few tenths of a W/m2 per decade, and they measure changes in the imbalance well. The absolute value is fixed by estimates of the heat taken up by the climate system, mostly the ocean heat content:

OHC(t) = ∭ ρw cp,w _T_(x, y, z, t) d_x_ d_y_ d_z_

The main source of ocean data since about 2005 is the Argo array of nearly 4,000 autonomous profiling floats, which measure temperature and salinity from the surface to 2,000 m, with Deep Argo floats extending to 4,000 to 6,000 m. Other sources include ship-based measurements, satellite altimetry, and the gravity measurements of GRACE and GRACE-FO, which are combined in sea-level budget estimates.

An imbalance of 1 W/m2 over the surface area of the Earth (5.1 × 1014 m2) is about 510 terawatts, or about 16 zettajoules (1021 J) per year. The Sixth Assessment Report of the IPCC gave an average imbalance of about 0.50 W/m2 (0.32 to 0.69) for 1971 to 2006 and about 0.79 W/m2 (0.52 to 1.06) for 2006 to 2018, and the energy taken up from 1971 to 2018 was about 380 zettajoules. Analyses of CERES data showed that the imbalance approximately doubled between the early 2000s and 2019, to about 1 W/m2. Some analyses report values of about 1.5 W/m2 or more for 2023 and 2024, partly because of short-term variability. Current values should be checked against the latest CERES data releases and assessments.

The recent increase is mostly due to an increase of absorbed solar radiation (a decrease of planetary albedo) and not only to a decrease of OLR. The causes of the albedo change are debated. Proposed contributors are the decline of aerosol emissions in Europe, North America, East Asia, and shipping (including the 2020 reduction of the sulfur content of marine fuel), reductions of low cloud cover and sea ice, and natural variability in ocean temperature patterns. Their relative contributions are still under study.

Where the heat goes

Different reservoirs of the Earth system hold the excess energy in very different proportions. In the assessment of the IPCC for 1971 to 2018, about 91 percent of the heat went into the ocean, about 5 percent into warming the land, about 3 percent into melting ice, and about 1 percent into warming the atmosphere.

  • Oceans. Roughly half to 60 percent of the ocean heat gain is in the upper 700 m, about a quarter to a third is between 700 and 2,000 m, and a smaller share (of the order of 10 percent) is below 2,000 m. The heat uptake raises sea surface temperatures, intensifies marine heatwaves, strengthens ocean stratification, and reduces the oxygen concentration (ocean deoxygenation). It also causes thermal expansion of seawater, which accounts for roughly 40 percent of recent sea level rise, the remainder coming mostly from the melting of land ice and from changes in land water storage.
  • Land. About 5 percent of the excess heat warms soils and rock, and it penetrates slowly downward. It contributes to the thawing of permafrost.
  • Cryosphere. About 3 percent of the energy is used as the latent heat of fusion (Lf = 3.34 × 105 J/kg) to melt glaciers, the Greenland ice sheet, the Antarctic ice sheet, and sea ice. Melting of land ice raises sea level, and melting of floating sea ice does not.
  • Atmosphere. The atmosphere has a mass of about 5.15 × 1018 kg and a small heat capacity, so about 1 percent of the energy is sufficient to warm it. Its warming increases the water vapor content by about 7 percent per kelvin, as described by the Clausius-Clapeyron relation. The global mean surface temperature has risen by roughly 1.2 to 1.5 °C since 1850 to 1900.

Uncertainties and open questions

Several issues limit the precision of the budget and its interpretation:

  • Absolute values of individual fluxes, especially surface fluxes and the latent heat flux, are uncertain by several W/m2, and different data sets disagree. Surface budgets are harder to measure than the budget at the top of the atmosphere.
  • The response of clouds and aerosols to warming, and the effect of aerosol-cloud interactions on the forcing, are the largest sources of uncertainty in the feedbacks and the forcing.
  • Pattern effects, in which the global feedback depends on the spatial pattern of surface warming, mean that the feedback parameter inferred from recent observations may not equal the one that applies to the long-term response.
  • Heat uptake in the deep ocean and under ice shelves is sampled sparsely.
  • Natural variability on timescales of years to decades can alter the imbalance and make short-term trends hard to interpret.

See also

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