2) Radiation & The Greenhouse Effect

Radiation Laws

• Warmer objects emit more intensely than cold objects. (Stefan-Boltzmann Law)

• Warmer objects emit a higher proportion of their energy at short wavelengths than cold objects. (Wien’s Law)

Why does effective temperature have small changes year to year?

• The system is in equilibrium: the energy inputs must be balanced approximately by energy losses.

• It has increased due to industrial activity

• Natural fluctuations due to El Niño

Calculation for incoming solar radiation

Incoming = (1-α) x S₀ x A

Incoming = 1361 x πr_e²

Where:

• S₀ = solar constant (W/m²)

• A = area

• α = albedo

Calculation for outgoing radiation

Outgoing = σT⁴ × 4πr_e²

Where:

• T = Temperature (K)

• σ = Stefan-Boltzmann constant (5.67 x 10^-8 W m^-2 K^-4).

• 4πr_e² = Surface area of Earth

Describe the atmosphere’s transmission characteristics

• Atmosphere is nearly transparent to shortwave radiation but almost opaque to the earth’s ‘longwave’ radiation

• These characteristics explain how the atmosphere absorbs, emits and transmits radiation

• The trapping of the ‘longwave’ radiation by the atmosphere is the ‘greenhouse effect’

Describes what happens to the incoming solar radiation

• Albedo means 30% reflected.

• Of the 70% absorbed:

  • 51% is absorbed by land/water

    • Some (15%) is absorbed and then re-radiated by the Earth as IR radiation.

    • Some (16%) is absorbed and re-radiated by the atmosphere as longwave IR radiation. 

    • This radiation is absorbed and re-radiated by greenhouse gases. This leads to a warming the atmosphere (troposphere) and the earth.

  • 19% is absorbed by the atmosphere & clouds

Describe the water vapour feedback

• Positive

• Warming → more evaporation → more water vapour → more warming

Describe the ice-albedo feedback

• Positive

• Ice melts → albedo drops → more absorption → more warming

Describe the lapse rate feedback

• Negative

• Warmer air emits more IR → increased radiation loss → cooling

Describe cloud feedback

• Mixed

• Negative caused by low-level clouds (e.g. stratocumulus)

  • As temperatures rise, more low clouds can form

  • These reflect more incoming solar radiation → dampening the warming

• Positive caused by high-level clouds (e.g. cirrus clouds)

  • With warming, the atmosphere can hold more moisture → more high clouds

  • These trap more outgoing radiation → further warming

Describe the carbon cycle feedback

• Positive

• Warming → permafrost melts → CO₂ & CH₄ release → more warming

What is effective radiative forcing?

• Change in Earth’s energy balance after fast (days-months) atmospheric adjustments but before full surface temperature response.

• ERF accounts for short-term feedbacks (e.g., cloud and stratospheric changes).

What is equilibrium climate sensitivity (ECS)?

• Long-term temperature change from a doubling of CO₂ after the climate system reaches equilibrium

• Includes slow feedbacks like ice sheet response and deep ocean warming

• Estimated: ~1.5–4.5°C

• Important for long-term climate risk projections

• Not directly observable, inferred from palaeoclimate records, models, and energy balance approaches

What is transient climate response (TCR)?

• TCR is the global temperature increase at the time of CO₂ doubling, assuming it increases 1% per year (which takes ~70 years).

• Captures shorter-term warming with less involvement of slow-acting feedbacks.

• Estimated range: ~1.0–2.5°C

• More relevant for policy decisions over the next 50–100 years

• Observationally constrained

Describe the relationship between TCR and ECS?

• TCR < ECS, because ECS includes slow components that don’t respond immediately

• ECS is what we expect eventually, TCR is what we see within a century