24.4 Earth's Energy Budget

What is Earth's Energy Budget?

Earth's energy budget describes the balance between the incoming solar radiation (shortwave) received from the Sun and the outgoing thermal radiation (longwave infrared) emitted by Earth back into space.

For a stable climate, these two fluxes must be equal. Any persistent imbalance drives warming or cooling.

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Incoming Solar Radiation

The Sun emits radiation predominantly as visible light and near-infrared (shortwave). Of the total solar energy reaching the top of the atmosphere:

Earth's average albedo is approximately 0.30 (30% reflected).

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Outgoing Terrestrial Radiation

Earth's surface, warmed by absorbed solar energy, re-emits energy as longwave infrared radiation. The rate of emission is governed by the Stefan-Boltzmann Law:

$P=\sigma A{T}^4$

where:

• $P$ = power radiated (W)
• $\sigma =5.67\times 10^{-8}{\text{W m}}^{-2}{\text{K}}^{-4}$ (Stefan-Boltzmann constant)
• $A$ = surface area (m²)
• $T$ = absolute temperature (K)

Because Earth is much cooler than the Sun (~288 K vs ~5778 K), it radiates at much longer wavelengths (infrared), consistent with Wien's Displacement Law.

Effective Radiating Temperature

At equilibrium, power absorbed = power emitted:

$\frac{L_{\odot }(1-a)}{4}=\sigma T_{\text{eff}}^4$

where $a$ is albedo and $L_{\odot }/4$ is the average solar flux at Earth's surface. This gives $T_{\text{eff}}\approx 255\text{K}$ (−18 °C) — Earth's actual average surface temperature (~288 K) is higher due to the greenhouse effect.

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The Greenhouse Effect and the Energy Budget

Greenhouse gases (${\text{CO}}_2$, ${\text{CH}}_4$, ${\text{H}}_2\text{O}$ vapour) are largely transparent to incoming shortwave solar radiation but absorb outgoing longwave infrared radiation emitted by Earth's surface. They then re-emit this energy in all directions — including back toward the surface — effectively trapping heat in the lower atmosphere.

This raises Earth's equilibrium surface temperature from ~255 K to ~288 K (~15 °C), making the planet habitable.

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Earth's Energy Imbalance (EEI)

Earth's Energy Imbalance (EEI) is the net difference between absorbed solar energy and emitted infrared radiation:

$\text{EEI}=E_{\text{in}}-E_{\text{out}}$

• EEI > 0 (Positive): Earth absorbs more than it emits → net warming (global warming). The excess energy is stored mainly in the oceans (~90%).
• EEI = 0: Climate equilibrium.
• EEI < 0 (Negative): Earth emits more than it absorbs → net cooling.

The current measured EEI is approximately +0.3 to +0.9 W m⁻², indicating ongoing planetary warming driven by enhanced greenhouse forcing.

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Radiative Forcing and Climate

Radiative forcing quantifies how a factor (e.g., increased ${\text{CO}}_2$, changed albedo) perturbs the energy budget:

• A positive radiative forcing (e.g., increased greenhouse gases) reduces outgoing radiation → warming tendency.
• A negative radiative forcing (e.g., increased albedo from volcanic aerosols) increases reflected radiation → cooling tendency.

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Summary: Energy Budget Numbers

$\underset{\text{Incoming solar}}{\underbrace{\sim 340{\text{W m}}^{-2}}}\stackrel{\text{albedo 30\%}}{\to }\underset{\text{Absorbed by Earth}}{\underbrace{\sim 240{\text{W m}}^{-2}}}\approx \underset{\text{Emitted as IR (equilibrium)}}{\underbrace{\sim 240{\text{W m}}^{-2}}}$

Any deviation from this balance constitutes the Earth's Energy Imbalance.