# Earth's energy budget **Earth's energy budget** is the accounting of the [[Energy|energy]] that arrives at the planet as [[Sunlight|sunlight]], the fraction that is turned straight back to space, the fraction that is absorbed, and the [[Thermal_radiation|thermal radiation]] by which all of it is eventually returned. Because the Sun is hot and the Earth is cold, the two streams sit in different parts of the spectrum: at 5,780 K the solar peak lies near 0.5 µm, while a surface at 287 K peaks near 10 µm, so the budget can be kept as two nearly separate ledgers, shortwave in and longwave out.[^ochsner-12-1] Over the long run the two must balance, and the [[Temperature|temperature]] of the planet is whatever makes them balance. In the microsim below the reader moves three controls — the [[Albedo|albedo]] α from 0.05 to 0.9, the solar constant S, and the [[Emissivity|emissivity]] of a single absorbing atmospheric layer — and watches the planet's radiating temperature follow `T_e = [(1 - alpha) S/(4 sigma)]^(1/4)`, with σ = 5.67×10⁻⁸ W m⁻² K⁻⁴.[^ochsner-12-2] A second panel drops from the whole planet to one field: the surface balance `Rn = (1 - alpha) Rs + Rli - Rlo = LE + H + G` is drawn across a measured Iowa day whose net radiation runs from about −50 W/m² at night to +300 W/m² near noon, and a third shows the top-of-atmosphere partition 25 / 5 / 14 / 3 / 31 / 22 %.[^ochsner-12-3][^ochsner-iowa][^ochsner-partition] On the [[Energy]] flagship this article is the child of Part IV — Scientific use, section *Earth sciences* (row E26). It is the planetary-scale counterpart of the engine bookkeeping in Part V: the same first-law accounting, but with a radiative boundary instead of a boiler, and with [[Earth's_internal_heat_budget|Earth's own internal heat]] entering as a term small enough to be neglected at the top of the atmosphere and impossible to neglect underground. ## Definition The budget is a statement of conservation applied to a chosen boundary. The usual boundary is the top of the atmosphere, where the only exchanges with the rest of the universe are radiative: shortwave energy arriving from the Sun, shortwave energy reflected back, and longwave energy emitted by the planet and its air. Nothing else crosses in any quantity that matters — the mass flux is negligible, and the heat conducted up from the interior is three orders of magnitude smaller than the solar term. Two units are in circulation and the difference between them is a factor of four. The solar constant is the flux on a surface held perpendicular to the beam at Earth's distance; the book's own worked construction, from a solar radius of 6.96×10⁸ m, an emitting temperature of 5,780 K and an orbital distance of 1.50×10¹¹ m, gives 1,349 W/m² (computed).[^ochsner-solar-const] But the planet intercepts sunlight over a disc of area πR² and radiates over a sphere of area 4πR², so the globally averaged incoming flux is a quarter of that, about 337 W/m² (derived). Every figure quoted below as a global mean carries this disc-to-sphere factor; every figure quoted for a field or an instrument does not. Confusing the two is the commonest arithmetic error in the subject, and it is why the sim prints both. ## Earth's energy flows The flows divide into three groups: the shortwave stream in, the longwave stream out, and the internal transfers that move energy around inside the system without changing the total. The first two are large and nearly equal; the third is what makes weather, ocean circulation and life. About 44 % of the solar stream arrives as visible light and roughly 7 % as ultraviolet, of which UVC is blocked entirely, UVB mostly, and UVA largely passes.[^patrich-uv] ### Incoming solar energy (shortwave radiation) Of the sunlight arriving at the top of the atmosphere, clouds reflect about 25 % and the air itself about 5 %, so roughly 30 % leaves again without ever being absorbed; the air absorbs about 14 % and clouds about 3 %; and about 53 % reaches the ground, 31 % as direct beam and 22 % as diffuse [[Black-body_radiation|sky radiation]].[^ochsner-partition] That 30 % is the planetary albedo, and it is the single number the microsim's first slider controls. What the slider then changes is the temperature at which the planet must radiate to balance its books. Setting absorbed shortwave equal to emitted longwave over the whole sphere gives T_e = [(1 − α)·S/(4σ)]^(1/4). At α = 0.3 and S = 1,349 W/m² the absorbed flux is 236 W/m² and T_e = 254 K (derived) — about 33 K colder than the observed surface. The gap is the [[Greenhouse_effect|greenhouse effect]], and the sim closes it with the crudest possible device: one atmospheric layer, transparent to sunlight and grey in the infrared with emissivity ε, for which T_s⁴ = T_e⁴ · 2/(2 − ε). Reproducing the book's 287 K surface needs ε ≈ 0.77 (derived). ILLUSTRATIVE: a real atmosphere is neither one layer nor grey, and the fitted ε absorbs everything the model leaves out — [[Convection|convection]], the vertical temperature profile, the wavelength dependence of absorption, and cloud. The number should be read as a tuning knob, not as a measured property of air. Albedo itself varies more than any other term. Fresh snow reflects up to about 0.9, open water less than 0.1 and more at low sun angles, and soils and vegetation fall between 0.1 and 0.4, the moist and organic-rich soils being darkest; the FAO reference grass surface is fixed at 0.23.[^ochsner-albedo][^ochsner-fao] Pushing the slider to 0.9 drives the sim's modelled noon net radiation to −4.5 W/m² (computed): a snowfield loses energy at midday and so preserves itself, which is the feedback that makes the shortwave ledger the least linear part of the budget. ### Outgoing longwave radiation The outgoing stream obeys the Stefan–Boltzmann law, `Jt = eps sigma T^4`, with emissivities that are high and narrowly spread for natural surfaces: snow and ice about 0.99, water 0.98–0.99, vegetation 0.95–0.98, and soil 0.86–0.96, rising with water content.[^ochsner-12-2] Taking ε_s = 0.95 at 287 K gives 384.7 W/m² leaving the ground (computed) — far more than the 236 W/m² the planet absorbs, which is only possible because most of it does not escape. What intercepts it is the atmosphere, whose own emissivity is the loose term in the whole budget: it runs from about 0.5 in cold dry air to nearly 1 under thick cloud, rising with water vapour and cloud cover.[^ochsner-emis] The downward longwave flux Rli that results is what keeps a clear desert night from being far colder than it is. The trace gases matter out of all proportion to their abundance because they absorb where water vapour does not: molecule for molecule, methane traps about 23 times as much as carbon dioxide and CFC-12 about 10,600 times, and methane now stands at roughly two and a half times its natural level while carbon dioxide is up by more than 35 %.[^patrich-ghg] ### Earth's internal heat sources and other minor effects Geothermal [[Heat_transfer|heat transfer]] out of the interior, tidal dissipation, and the waste heat of human energy use are all present in the budget and all negligible at the top of the atmosphere: together they amount to well under a thousandth of the absorbed solar flux. They are treated in [[Earth's_internal_heat_budget|Earth's internal heat budget]], where the same watts are the dominant term because the boundary has moved to the base of the crust. Photosynthesis diverts a similarly small share of the shortwave stream, and the residence of that share in [[Biomass|biomass]] and fossil carbon is what makes it interesting rather than its size.[^internal-external] ## Budget analysis Analysis means choosing a boundary and then insisting that what enters equals what leaves plus what accumulates. At the top of the atmosphere, accumulation is the imbalance; at the land surface, it is the heat stored in soil; in the ocean, it is the change in heat content of a column of [[Water|water]]. The equations below are the same conservation statement written at three scales. ### Internal flow analysis At the surface the budget splits in two. Net radiation is the radiative part, `Rn = (1 - alpha) Rs + Rli - Rlo`, counted positive toward the surface; the non-radiative part is `Rn = LE + H + G`, where LE is the [[Latent_heat|latent]] flux carried by [[Evaporation|evaporation]] (LE = L·ET), H the sensible flux carried by turbulence, and G the [[Thermal_conduction|conduction]] into the ground, all counted positive away from the surface.[^ochsner-12-3][^ochsner-12-4] The sign conventions reverse at night, and getting them wrong is the standard bug. The microsim's second panel plays a measured diurnal cycle over corn residue in Iowa: Rn runs from about −50 W/m² before dawn to about +300 W/m² near solar noon, H peaks near +200 W/m², and LE and G stay at or below +100 W/m².[^ochsner-iowa] Calibrating the model to those endpoints (computed) requires an atmospheric emissivity of 0.82, comfortably inside the observed range, and a peak incoming shortwave of 455 W/m² at α = 0.23. The partition of Rn among LE, H and G is drawn only as an illustrative stacked area, because net radiation does not determine that split — soil moisture does. A wet surface spends nearly all of Rn on LE and stays cool; a dry one spends it on H and gets hot. LE goes to zero at night and turns negative when dew forms.[^ochsner-12-4] ### Heat storage reservoirs Almost all of the energy that accumulates in the Earth system goes into the ocean, because [[Ocean_current|seawater]] has both an enormous [[Heat_capacity|heat capacity]] and a mixed layer that is stirred to tens of metres. The comparison is worth doing in numbers. A year is 3.16×10⁷ s, so a steady 1 W/m² delivers 3.16×10⁷ J/m² over that year.[^murphy-year] Spread through a 70 m mixed layer at 1,000 kg/m³ with c_p = 4.181 kJ/(kg·K), the column's heat capacity is 2.9×10⁸ J/(m²·K) and the warming is 0.11 K (derived).[^yan-cp] Delivered instead to the whole atmospheric column — about 1.0×10⁴ kg/m², since column mass is surface pressure divided by g, at c_p ≈ 1.0 kJ/(kg·K) — the same energy raises the air by 3.0 K (derived), roughly thirty times as much. That ratio is why the ocean is the reservoir that matters and the air is the reservoir that is noticed. Land is a poor reservoir by comparison: in soil, conduction dominates heat transfer, and conduction is slow, so the daily wave of G penetrates a few tens of centimetres and the annual wave a few metres.[^ochsner-soil] [[Ice|Ice]] is a reservoir of a different kind, storing energy as [[Latent_heat|latent heat]] at constant temperature, which is why melting buffers warming without showing up on a thermometer. ### Heating/cooling rate analysis Dividing an accumulated energy by a reservoir's heat capacity converts watts into degrees per decade, and the answer differs by orders of magnitude between reservoirs receiving the same flux. The same arithmetic run backwards is how a measured warming rate is converted into an implied imbalance. Because the ocean takes the overwhelming majority of the accumulation, the planet's heating rate is essentially an ocean heat-content question, and the atmosphere's temperature is a fast, noisy indicator of a slow, quiet integral. Rate analysis is also the honest way to state uncertainty: a flux known to ±2 W/m² and a flux known to ±0.1 W/m² produce very different confidence in the same decadal trend. ## Earth's energy imbalance (EEI) The imbalance is the difference between absorbed shortwave and outgoing longwave at the top of the atmosphere. It is a small residue of two large numbers — of order one watt per square metre against an absorbed 236 W/m² — and the ratio is the whole methodological problem: a residue of 0.4 % cannot be recovered by subtracting two fluxes whose absolute calibration is uncertain at the percent level (derived).[^theis-climate] The consequence is that no instrument measures the imbalance directly. Each of the methods below measures something larger and better conditioned and infers the residue from it: an accumulation of heat in a reservoir, a change in sea level, a difference of two [[Power_(physics)|power]] time series whose common calibration error cancels. The three are largely independent, which is why agreement between them is the argument rather than the precision of any one. The sim makes the same point from the other direction: change α by 0.01 and the absorbed flux moves by 3.4 W/m² (derived), several times the imbalance itself, so a budget that is stable to a watt is a budget whose reflective properties are stable to a fraction of a percent. ### Energy inventory assessments The inventory method adds up where the energy went rather than watching it arrive. Ocean heat content from profiling floats dominates the sum; ice melt, land heat storage and atmospheric warming complete it. Dividing the total accumulation over a period by the period and by Earth's surface area gives the imbalance directly in W/m², and the method's strength is that it integrates, so short-term noise in any single flux averages away. ### Measurements at top of atmosphere (TOA) Broadband radiometers on satellites measure reflected shortwave and emitted longwave with excellent precision and much poorer absolute accuracy. The standard practice is therefore to use the satellite record for the variation of the imbalance in time and space, and to anchor its absolute level to the inventory estimate. The result is a hybrid: the shape of the curve is radiometric, the offset is oceanographic. ### Geodetic and hydrographic surveys Two independent checks come from geometry rather than radiation. Satellite altimetry measures total sea-level rise, and satellite gravimetry measures the part of it due to added mass; the difference is thermal expansion, which is a direct measure of ocean heat uptake. Hydrographic sections measure the same quantity by profiling temperature and salinity from ships. ### Importance as a climate change metric The imbalance is the most direct statement of whether the planet is accumulating energy, and unlike surface temperature it is not confounded by internal redistribution between ocean and atmosphere. A temperature record can pause while the imbalance holds steady, because the energy is going somewhere that is not the [[Atmosphere_of_Earth|air]]. As a diagnostic it also closes the loop with the sim: every term the reader adjusts — albedo, layer emissivity, the solar constant — moves the balance point, and the imbalance is what the planet shows while it travels from one balance point to the next.[^theis-climate] ## See also - [[Solar_irradiance]] - [[Albedo]] - [[Greenhouse_effect]] - [[Earth's_internal_heat_budget]] - [[Stefan–Boltzmann_law]] - [[Wien's_displacement_law]] - [[Earth_system_science]] - [[Emissivity]] ## References [^ochsner-12-1]: Ochsner, Tyson E. (2019). *Rain or Shine: An Introduction to Soil Physical Properties and Processes*. Chapter 12 "Surface Energy Balance and Evapotranspiration", p. 278 (Wien's law, Eq. 12-1, with b = 2,900 µm·K) and p. 279 (the solar peak near 0.5 µm at 5,780 K and the terrestrial peak near 10 µm at 287 K). Portal Book 119, https://open.umn.edu/opentextbooks/textbooks/rain-or-shine [^ochsner-12-2]: Ochsner (2019), *Rain or Shine*, Chapter 12, p. 279 (the Stefan–Boltzmann law, Eq. 12-2, σ = 5.67×10⁻⁸ W m⁻² K⁻⁴, and the emissivity table: snow and ice ≈ 0.99, water 0.98–0.99, vegetation 0.95–0.98, soil 0.86–0.96 rising with water content). Portal Book 119. The equation displays were lost in text extraction; sub-manual 10 §5.1 supplies them in standard form. [^ochsner-12-3]: Ochsner (2019), *Rain or Shine*, Chapter 12, p. 292 (net radiation, Eq. 12-3, positive toward the surface). Portal Book 119; display supplied in standard form by sub-manual 10 §5.2. [^ochsner-12-4]: Ochsner (2019), *Rain or Shine*, Chapter 12, p. 293 (the surface energy balance, Eq. 12-4, with LE, H and G positive away from the surface; LE = L·ET; the signs reverse at night and LE can be negative with dew). Portal Book 119. [^ochsner-partition]: Ochsner (2019), *Rain or Shine*, Chapter 12, p. 280 (the top-of-atmosphere partition: 25 % reflected by clouds, 5 % by air, 14 % absorbed by air, 3 % by clouds, 31 % direct and 22 % diffuse at the surface, so ≈ 53 % reaches the ground). Portal Book 119. [^ochsner-albedo]: Ochsner (2019), *Rain or Shine*, Chapter 12, p. 290 (albedo: fresh snow up to ≈ 0.9; water < 0.1 and higher at low sun; soils and vegetation 0.1–0.4, moist and organic-rich soils darkest). Portal Book 119. [^ochsner-fao]: Ochsner (2019), *Rain or Shine*, Chapter 12, p. 288 (the FAO reference surface albedo of 0.23). Portal Book 119. [^ochsner-emis]: Ochsner (2019), *Rain or Shine*, Chapter 12, pp. 291–292 (atmospheric emissivity from 0.5 to nearly 1, rising with cloud and water vapour). Portal Book 119. [^ochsner-iowa]: Ochsner (2019), *Rain or Shine*, Chapter 12, p. 295 (the measured Iowa diurnal cycle over corn residue: Rn from about −50 W/m² at night to +300 W/m² near noon, H peaking near +200 W/m², LE and G ≤ +100 W/m²). Portal Book 119. The calibration values quoted here (ε_atm = 0.82, peak Rs = 455 W/m², and the −4.5 W/m² noon Rn at α = 0.9) are computed in sub-manual 10 §5.2 from these endpoints, not printed in the book. [^ochsner-soil]: Ochsner (2019), *Rain or Shine*, Chapter 12, p. 294 (conduction dominates heat transfer in soil). Portal Book 119. [^ochsner-solar-const]: Ochsner (2019), *Rain or Shine*, Chapter 12, p. 283 (unworked problems). The value 1,349 W/m² is computed in sub-manual 10 §5.1 from the book's own inputs: ε = 0.990 at 5,780 K gives 6.27×10⁷ W/m² at the solar surface, 3.81×10²⁶ W over a radius of 6.96×10⁸ m, and 1,349 W/m² at 1.50×10¹¹ m. Portal Book 119. [^murphy-year]: Murphy, Thomas W. (2021). *Energy and Human Ambitions on a Finite Planet*. Chapter 5 (energy and power units), p. 95 (1 yr ≈ 3.16×10⁷ s, the "π × 10⁷" rule). Portal Book 097, https://open.umn.edu/opentextbooks/textbooks/energy-and-human-ambitions-on-a-finite-planet [^yan-cp]: Yan, Claire Yu (2022). *Introduction to Engineering Thermodynamics*. Chapter 6 "Entropy and the Second Law of Thermodynamics", p. 275 (c_p of water = 4.181 kJ/(kg·K), used in the book's warmed-lake example). The printed water density was lost in text extraction; 1,000 kg/m³ is a supplied standard value per sub-manual 10 §2.3. Portal Book 115, https://open.umn.edu/opentextbooks/textbooks/introduction-to-engineering-thermodynamics [^patrich-uv]: Patrich, Jeremy (2020). *Physical Geography — Version 1*. Unit 5 "Earth–Sun Relationships: Reasons for the Seasons", pp. 69, 71 (about 44 % of sunlight visible and ≈ 7 % ultraviolet; UVC fully blocked, UVB mostly, UVA largely transmitted). Portal Book 125, https://open.umn.edu/opentextbooks/textbooks/physical-geography [^patrich-ghg]: Patrich (2020), *Physical Geography — Version 1*, Unit 5, p. 72 (one CH₄ molecule traps 23 times the heat of one CO₂ molecule and one CFC-12 molecule 10,600 times; CH₄ ≈ 2½ times its natural level and CO₂ up more than 35 %). Portal Book 125. [^theis-climate]: Theis, Tom; Tomkin, Jonathan, eds. (2015). *Sustainability: A Comprehensive Foundation*. Chapter "Climate and Global Change" (page to pin; the chapters index for this book records the chapter without a usable page range). Portal Book 098, https://open.umn.edu/opentextbooks/textbooks/sustainability-a-comprehensive-foundation — the numerical value of the present imbalance is external to the sub-manuals and is stated here only as an order of magnitude. [^internal-external]: The present global geothermal heat flow and the waste-heat term are external to sub-manual 10 and are stated here only as an order-of-magnitude comparison; see [[Earth's_internal_heat_budget]], where the same quantity is the leading term (page to pin). ## External links - [Rain or Shine](https://open.umn.edu/opentextbooks/textbooks/rain-or-shine), Ochsner (2019) — Portal Book 119, Chapter 12 is the surface energy balance used throughout this page - [Physical Geography — Version 1](https://open.umn.edu/opentextbooks/textbooks/physical-geography), Patrich (2020) — Portal Book 125, Unit 5 for the solar spectrum and the trace gases - [Sustainability: A Comprehensive Foundation](https://open.umn.edu/opentextbooks/textbooks/sustainability-a-comprehensive-foundation), Theis and Tomkin (2015) — Portal Book 098 - The Wikipedia pair's external links list the satellite and ocean-inventory datasets <!-- MATTERSIM:BEGIN g24 — Matter & Energy Cluster microsim (framework build, specs/sims/Earth's_energy_budget.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework), pending deploy:** *Earth's energy budget* will play here once `https://wikitube-3d-microsims.netlify.app/matter/Earth's_energy_budget.html` is live. <!-- pending: <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Earth's_energy_budget.html" data-title="Earth's energy budget"></div> --> <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Earth's_energy_budget) : [Wikitube](https://en.wikitube.io/wiki/Earth's_energy_budget) · pinned revision [1374065966](https://en.wikipedia.org/w/index.php?oldid=1374065966) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Energy]]. --- *Matter & Energy Cluster child articles, wave 1 · 2026-09-11 · drafted · Energy row E26 · sim pending (matter/Earth's_energy_budget).*