Energy budget


There are two important sources of energy, the sun and the Earth itself.

The sun radiates energy at many wavelengths from the ultraviolet to the visible that impinges on the Earth's atmosphere. Some of this is absorbed by the Earth's atmosphere and surface and some of it is reflected back to outer space.

The Earth itself also radiates energy, but in the form of heat at infrared wavelengths. Some of this is absorbed by the atmosphere and some of it is radiated to outer space.

The major atmospheric gases (oxygen and nitrogen) are transparent to incoming sunlight, and are also transparent to outgoing thermal infrared. However, water vapor, carbon dioxide, methane, and other trace gases are opaque to many wavelengths of thermal infrared energy. The Earth's surface radiates the net equivalent of 17 percent of incoming solar energy as thermal infrared. However, the amount that directly escapes to space is only about 12 percent of incoming solar energy. The remaining fraction—a net 5-6 percent of incoming solar energy—is transferred to the atmosphere when greenhouse gas molecules absorb thermal infrared energy radiated by the surface.

Because greenhouse gas molecules radiate heat in all directions, some of it spreads downward and ultimately comes back into contact with the Earth’s surface, where it is absorbed. The temperature of the surface becomes warmer than it would be if it were heated only by direct solar heating. This supplemental heating of the Earth’s surface by the atmosphere is the natural greenhouse effect.

Energy budget current conditions IPCC AR5
Energy budget current conditions IPCC AR5


Terminology


The energy budget is calculated in terms of energy per unit of time per square meter or watts per square meter (W/m**2). A watt is an energy flow (power) of a joule of energy per second. 4.184 joules of heat energy (or one calorie) is required to raise the temperature of one gram of water from 0 to 1 degrees Celsius.

The energy budget of the Earth is broken down into contributions from sources of energy fluxes.

  • Incoming solar TOA (at the top of the atmosphere) = average solar radiation impinging on top of Earth's atmosphere
  • Solar reflected TOA = solar radiation reflected by Earth's atmosphere
  • Solar down surface = solar radiation hitting Earth's surface
  • Solar absorption surface = solar radiation absorbed by Earth's surface
  • Solar reflected surface = solar radiation reflected by Earth's surface
  • Thermal up surface = heat radiated by Earth's surface to atmosphere
  • Sensible heat = heat exchanged between Earth's surface and atmosphere due to convection
  • Thermal outgoing TOA = heat radiated from Earth'a atmosphere to space
  • Greenhouse gas effect = back radiation to the surface from heat retained on Earth's surface by greenhouse gases (CO2, CH4, N2O)
  • Evaporation = heat conveyed from Earth's surface to atmosphere by evaporation of water

Observed data


On average under current conditions 340 watts/square meter (W/m**2) of solar radiation hits the Earth's atmosphere.

Of this 100 W/m**2 of the incident energy is reflected. 76 W/m**2 is reflected from the atmosphere and clouds and 24 W/m**2 reflected from the ground (including land, water and ice).

The remaining 240 W/m**2 of the incident energy is absorbed: 161 W/m**2 is absorbed by land and water and 79 W/m**2 is absorbed by the atmosphere. Of the radiation absorbed by the surface, 84 W/m**2 is transferred into the atmosphere by the evaporation of water and 20 W/m**2 is transferred to the atmosphere by convection, called sensible heat.

The Earth's surface also radiates heat. The surface radiates 398 W/m**2 to the atmosphere. Much of this is captured by greenhouse gases which radiate 342 W/m**2 back to the Earth. The atmosphere radiates 239 W/m**2 of heat to outer space.

Global mean energy budget under present day climate conditions from AR5
Estimates of energy fluxes and uncertainties (W/m**2) adjusted within their uncertainty ranges to close the energy budgets.
ContributionFlux W/m**2LowHigh
Incoming solar TOA340340341
Solar reflected TOA10096100
Solar absorbed797491
Solar down surface 185179189
Solar reflected surface242226
Solar absorbed surface161154166
Evaporation847085
Sensible heat201525
Thermal outgoing TOA239236242
Thermal up surface398394400
Thermal down surface342338348
Imbalance0.60.21.0

Source: IPCC AR5 Chapter 2

Based on these radiation and heat fluxes we can calculate the energy balance for the atmosphere and the surface.

Atmosphere balance

The energy gain by the atmosphere due to solar radiation is the absorbed solar radiation (79 W/m**2) plus the energy gained from the surface by evaporation (84 W/m**2) plus the energy gained by sensible heat (20 W/m**2) for a total gain of 183 W/m**2.

With respect to thermal radiation the atmosphere gains 398 W/m**2 of heat radiated from the surface and loses 342 W/m**2 radiated back to the surface by greenhouse gases and 239 W/m**2 radiated to outer space for a net loss of 183 W/m**2.

For the atmosphere the two types of energy balance each other.

Surface balance

In the case of the surface, the energy gain from solar radiation is the absorbed solar radiation minus the energy lost to evaporation 84 W/m**2 and to sensible heat loss 20 W/m**2 for a net gain of 57 W/m**2.

The energy loss due to thermal radiation is 398 W/m**2 radiated to the atmosphere. But 342 W/m**2 is radiated back to the surface due to greenhouse gases. The net loss for thermal radiation is 56 W/m**2.

In this case there is an imbalance estimated to be 0.6 W/m**2. This represents the amount by which the solar energy absorbed by the surface exceeds the net thermal radiated heat and is the reason that the Earth is getting hotter.

Detailed calculations


Atmospheric energy balance

Gains = absorbed solar radiation - evaporation - sensible heat
= 79 + 84 + 20 = 183 W/m**2

Losses = heat radiated by surface - radiated back to surface - heat lost to space
= 398 - 342 - 239 = -183 W/m**2

Surface energy balance

Gains = absorbed solar radiation - evaporation - sensible heat
= 161 - 84 - 20 = 57 W/m**2

Losses = heat radiated by surface to atmosphere + back radiation from greenhouse gases
= -398 + 342 = -56 W/m**2

Surface imbalance

Net energy gain by surface = surface gain - surface losses
= 57 - 56 = 0.6 W/m**2