Storm Station 247

The Field Book/Vol. I, The Engine/FB-ENG-007

Radiation budget

The Earth takes in sunlight and sends the same energy back to space as its own invisible glow. The radiation budget is the account of that exchange: how much sunlight is reflected, how much is absorbed and where, and how the heat climbs back out through the air, which is why the surface is about 60 °F (33 °C) warmer than the Earth seen from space.

Plate FB-ENG-007RadiationRevision 1, 2026-09-25Status draftAlso called energy budget, earth's energy budget, heat budget, greenhouse effect, albedo, shortwave, longwave, outgoing longwave radiation, back radiation, Stefan Boltzmann law

Block diagram of the Earth's global mean energy budget in watts a square metre, each arrow as wide as its flow: 341.3 of sunlight arriving at the top of the atmosphere, 79 reflected by the air and clouds, 78 absorbed by the air, 184.3 reaching the surface, 23 reflected by the surface; the surface's glow, 356 absorbed by the air and 40 escaping through the window; 333 of back radiation from the air to the surface; 169 emitted to space by the air and 30 by clouds; and 17 carried up by thermals and 80 by evaporation.1122334455667788AABBCCDDEESTORM STATION 247THE FIELD BOOKPLATE FB-ENG-007-ATHE GLOBAL MEAN ENERGY BUDGET, 2000 TO 2004, EACH FLOW AN ARROW AS WIDE AS ITS FLUX; LAYER HEIGHTS NOT TO SCALEFIG. A WHERE THE ENERGY GOESTOP OF THE ATMOSPHERETHE SURFACECLOUDSSUNLIGHTINCOMING341.3REFLECTED BY AIR AND CLOUD79ABSORBED BY THE AIR78REACHING THE SURFACE184.3REFLECTED BY THE SURFACE23THE EARTH’S GLOWSURFACE, ABSORBED BY THE AIR356THROUGH THE WINDOW40BACK RADIATION333EMITTED BY THE AIR169EMITTED BY CLOUDS30CARRIED UPTHERMALS17EVAPORATION80EACH ARROW AS WIDE AS ITS FLOW, WATTS A SQUARE METRE; GLOBAL MEAN1234567TITLERadiation budget, where the energy goesVOL. I THE ENGINE · RADIATIONTYPEBLOCK DIAGRAMSCALEFLOW WIDTHS TO SCALE, HEIGHTS NTSREVREV 1 DRAFT SHEET 1 of 3DATE2026-09-25IDFB-ENG-007-ADRAWN AS linework on paperSOURCES AMS, Trenberth, Kopp
Fig. A Where the energy goes. The global mean energy budget, 2000 to 2004, each flow an arrow as wide as its flux; layer heights not to scale FLOW WIDTHS TO SCALE, HEIGHTS NTSMaximizeThe sheet, SVG, 11 by 17
  1. Sunlight arriving, 341.3
  2. Reflected by air and clouds, 79
  3. Reaching the surface, 184.3
  4. The surface's glow, absorbed by the air
  5. Back radiation, 333
  6. Emitted to space by the air, 169
  7. Evaporation, 80

What it is

Everything glows, and the hotter it is the more it glows and the shorter the waves it glows in. The sun, at 9,930 °F (5,772 K), glows mostly in visible light. The Earth, far colder, glows in the infrared, where the eye cannot see. The radiation budget is the account between the two: the sunlight coming in, and the Earth's own glow going out.

Averaged over the whole globe and the whole year, the two nearly balance. Fig. A draws the account in watts a square metre, each arrow as wide as its flow. Of 341.3 arriving at the top of the atmosphere, 101.9 is reflected straight back, 79 by the air and clouds and 23 by the surface. The air absorbs 78, and 161 is absorbed at the surface. To balance, the Earth sends 238.5 back to space as its glow. The last 0.9 is kept, and the Earth warms.

What it is not

It is not the same at every place or hour. The tropics take in more sunlight than they send out, and the poles send out more than they take in. The winds and ocean currents carry the difference toward the poles, and that carrying is the weather.

It is not the ozone hole. That is a thinning of ozone in the stratosphere, which lets through more ultraviolet light, a separate matter.

Lookalikes

Heat
Heat moves by radiation, by contact and by rising air; this plate follows all three but counts them in the radiation's units, watts a square metre.
The ozone hole
A thinning of stratospheric ozone that lets more ultraviolet through; a separate matter from the greenhouse effect.
Weather
The budget is a global average over years; weather is the budget out of balance from place to place and hour to hour.

The machine

Two kinds of light

Fig. B draws the two spectra. Sunlight peaks at 0.50 micrometres, in the middle of the visible band; the Earth's glow peaks near 11.4 micrometres. They barely overlap, parting near 4 micrometres, and so the budget divides cleanly: shortwave in, longwave out. The difference matters because the air treats them differently. It lets most sunlight through, but water vapour, carbon dioxide and clouds absorb most of the Earth's glow, Composition of air FB-ENG-002.

The Earth seen from space

The first equation below asks how warm the Earth would look to an instrument in space. The sun delivers 1,361 W m⁻² at the Earth's distance. About 30 per cent is reflected, and the rest, spread over the whole sphere, is 238 W m⁻². A black body that radiates that much is at 255 K, about −1 °F (−18 °C). The surface averages 59 °F (15 °C), about 60 °F (33 °C) warmer. That difference is the greenhouse effect.

Why the surface is warmer

The air absorbs the surface's glow and glows in turn, both upward and back down. Fig. A shows the result: the surface receives 333 W m⁻² from the air, about twice what it absorbs from the sun. The second equation below is the simplest model of it, one layer of air, drawn in Fig. C. A layer absorbing all the glow would warm the surface to 85 °F (30 °C); one absorbing 78 per cent gives 59 °F (15 °C), the observed mean. The real surface also loses heat without radiation: 17 W m⁻² in rising thermals and 80 in evaporation, which returns as heat when the vapour condenses in clouds.

Chart of two spectra against wavelength from 0.1 to 100 micrometres on a logarithmic scale, each the black body curve for its temperature and scaled to its own peak: sunlight at 9,930 degrees Fahrenheit (5,772 kelvin), peaking at 0.50 micrometres in the visible band; the Earth's glow at minus 1 degree Fahrenheit (255 kelvin), peaking near 11.4 micrometres in the infrared; the two barely overlapping, parting near 4 micrometres, so sunlight is called shortwave and the Earth's glow longwave.1122334455667788AABBCCDDEESTORM STATION 247THE FIELD BOOKPLATE FB-ENG-007-BTHE SPECTRUM OF SUNLIGHT AND OF THE EARTH'S GLOW, EACH THE PLANCK FUNCTION FOR ITS TEMPERATURE, ENERGY PER UNIT WAVELENGTH, EACH SCALED TO ITS OWN PEAKFIG. B SUNLIGHT AND THE EARTH’S GLOWVISIBLE0.10.20.5125102050100WAVELENGTH, MICROMETRESSUNLIGHT, 9,930 °F (5,772 K)THE EARTH, -1 °F (255 K)PEAK 0.50 MICROMETRESPEAK 11.4 MICROMETRESABOUT 4 MICROMETRES:SHORTWAVE LEFT,LONGWAVE RIGHTEACH CURVE SCALED TO ITS OWN PEAK: ENERGY PER UNIT WAVELENGTH1234TITLERadiation budget, sunlight and the earth's glowVOL. I THE ENGINE · RADIATIONTYPECLASSIFICATIONSCALEWAVELENGTH TO SCALE, LOGARITHMICREVREV 1 DRAFT SHEET 2 of 3DATE2026-09-25IDFB-ENG-007-BDRAWN AS linework on paperSOURCES AMS, Trenberth, Kopp
Fig. B Sunlight and the earth's glow. The spectrum of sunlight and of the Earth's glow, each the Planck function for its temperature, energy per unit wavelength, each scaled to its own peak WAVELENGTH TO SCALE, LOGARITHMICMaximizeThe sheet, SVG, 11 by 17
  1. Sunlight
  2. The visible band
  3. The Earth's glow
  4. Where they part, about 4 micrometres
Section of the one layer model of the greenhouse effect: sunlight passing through a single layer of air to the surface; the surface glowing up into the layer; the layer glowing both up to space and down to the surface; and a table of the surface temperature, minus 1 degree Fahrenheit (minus 18 degrees Celsius) with no layer, 85 degrees Fahrenheit (30 degrees Celsius) with a layer absorbing all the glow, and 59 degrees Fahrenheit (15 degrees Celsius), the observed mean, with a layer absorbing 78 per cent.1122334455667788AABBCCDDEESTORM STATION 247THE FIELD BOOKPLATE FB-ENG-007-CTHE ONE LAYER MODEL, A SINGLE LAYER OF AIR CLEAR TO SUNLIGHT AND ABSORBING THE SURFACE'S GLOW, WITH THE SURFACE TEMPERATURE WORKED FOR THREE CASESFIG. C THE GREENHOUSE EFFECT, ONE LAYERSPACEONE LAYER OF AIR: CLEAR TO SUNLIGHT, ABSORBING THE GLOWTHE SURFACESUNLIGHT ABSORBED, 238 W/m²THE SURFACE GLOWSTHE LAYER GLOWS UPAND DOWNTHE SHARE THE LAYER DOES NOT ABSORBTHE LAYERABSORBSSURFACENo layerNONE-1 °F (-18 °C)Absorbs all the glow185 °F (30 °C)Absorbs 78 per cent0.7859 °F (15 °C)Observed mean59 °F (15 °C)12345TITLERadiation budget, the greenhouse effect, one layerVOL. I THE ENGINE · RADIATIONTYPESECTIONSCALENOT TO SCALEREVREV 1 DRAFT SHEET 3 of 3DATE2026-09-25IDFB-ENG-007-CDRAWN AS linework on paperSOURCES AMS, Trenberth, Kopp
Fig. C The greenhouse effect, one layer. The one layer model, a single layer of air clear to sunlight and absorbing the surface's glow, with the surface temperature worked for three cases NOT TO SCALEMaximizeThe sheet, SVG, 11 by 17
  1. Sunlight, through the layer
  2. The surface's glow
  3. The layer's glow, up to space
  4. The layer's glow, down to the surface
  5. The surface temperature for a layer absorbing 78 per cent

Ingredients

  • Sunlight, most of its energy at short wavelengths the air lets through
  • The Earth's own glow, at long wavelengths the air's water vapour, carbon dioxide and clouds absorb
  • Clouds, snow and ice, which reflect sunlight straight back to space
  • Rising air and evaporation, which carry heat up from the surface without radiation

Scales

time
the budget balances over a year; each day and each season it runs a surplus or a deficit
horizontal
the whole planet; each place runs its own budget, in surplus near the equator and in deficit near the poles
vertical
the whole depth of the atmosphere, from the ground to the top of the atmosphere
orlanski
planetary

Equations

The Earth seen from space

σTe4=S0(1−α)4\sigma T_e^4 = \frac{S_0 (1 - \alpha)}{4}
44
the Earth intercepts sunlight on a disc and spreads it over a sphere four times the disc's area
σ\sigma
the Stefan Boltzmann constant, 5.67 × 10⁻⁸ W m⁻² K⁻⁴
TeT_e
the temperature of a black body that radiates what the Earth sends to space, K
S0S_0
the sunlight at the Earth's distance, 1,361 W m⁻²
α\alpha
the share of sunlight reflected, about 0.30

Assumes The whole Earth as one body in balance, radiating like a black body; the averages over the globe and the year.

Working form The Earth absorbs 1,361 × 0.70 ÷ 4 = 238 W m⁻² and sends 238.5 W m⁻² to space. A black body that radiates that much is at 255 K, about −1 °F (−18 °C). The surface averages 59 °F (15 °C), about 60 °F (33 °C) warmer: the greenhouse effect.

One layer of air

Ts=Te(22−ε)1/4T_s = T_e \left(\frac{2}{2 - \varepsilon}\right)^{1/4}
TsT_s
the surface temperature, K
TeT_e
the temperature the Earth shows to space, K
ε\varepsilon
the share of the surface's glow the layer absorbs, between 0 and 1

Assumes The textbook one layer model; the air as a single layer clear to sunlight, absorbing a share of the surface's glow and glowing up and down alike. It leaves out convection and evaporation, which carry heat up in the real atmosphere.

Working form With no layer the surface would be −1 °F (−18 °C). A layer absorbing all the glow gives 85 °F (30 °C); one absorbing 78 per cent gives 59 °F (15 °C), the observed mean.

Signatures

sounding
surface
the day's warming while the sun is up and the night's cooling after; clear; dry nights cooling most; cloudy; humid nights least
satellite
bright cloud and snow in visible images; reflecting sunlight; cold cloud tops in infrared images; glowing little to space
radar

The numbers

QuantityValue, and the kind of number it is
Total solar irradiance1,361 W m⁻², the sunlight on a surface facing the sun at the Earth's mean distanceTextbook, Kopp 2011
Global mean energy budget341.3 W m⁻² in; 101.9 reflected; 238.5 sent to space as the Earth's glow; 0.9 kept, warming the Earth, 2000 to 2004Textbook, Trenberth 2009
At the surface161 absorbed from the sun and 333 back radiation from the air in; 396 glow, 80 evaporation and 17 thermals out, W m⁻²Textbook, Trenberth 2009
AlbedoThe share of sunlight reflected; the Earth's is about 0.30Standard, Glossary of Meteorology
Greenhouse effectThe heating of the surface by the air's absorbing and re-emitting the surface's glowStandard, Glossary of Meteorology

How the station sees it

A station sees the budget of its own spot, hour by hour. By day the sun's side wins and the temperature climbs; after sunset the glow wins and it falls. Clouds change both sides: they reflect sunlight, so a cloudy day stays cooler, and they glow back down, so a cloudy night stays warmer. A clear, dry, calm night loses the most heat to space, and that is when frost and fog form, Fog types FB-WAT-020.

Satellites see the budget from above, Geostationary satellite FB-INS-006. Visible images show what is reflected; infrared images show the glow, cold cloud tops glowing least.

How it is warned

The budget is not warned. Its daily swing sits under every frost advisory, heat warning and fog forecast: each is a place where the budget has run far out of balance for a night or for a week.

See also

  • Atmosphere in section FB-ENG-001
  • Composition of air FB-ENG-002
  • Water vapour as a gas FB-ENG-011
  • Seasons FB-CLK-001
  • Sun and insolation FB-CLK-002
  • Day and night FB-CLK-004
  • Geostationary satellite FB-INS-006
  • Fog types FB-WAT-020

Sources

  1. American Meteorological Society. Glossary of Meteorology.
  2. Trenberth, K. E., J. T. Fasullo and J. Kiehl. Earth's Global Energy Budget, Bulletin of the American Meteorological Society 90 (2009).
  3. Kopp, G. and J. L. Lean. A new, lower value of total solar irradiance, Geophysical Research Letters 38 (2011).
  4. Wallace, J. M. and P. V. Hobbs. Atmospheric Science, An Introductory Survey, 2nd ed. (2006).

Definition after the Glossary of Meteorology. Plate FB-ENG-007, revision 1, 2026-09-25. The number is permanent; cite it.