The radiative energy balance of Earth, the natural greenhouse effect, the enhanced greenhouse effect from increased greenhouse gas concentrations, climate feedbacks, and the physics of climate change mitigation

What this dot point is asking

VCAA wants you to apply physics (radiation, energy balance, Stefan-Boltzmann) to Earth's climate. The dot point synthesises thermodynamics, the greenhouse effect, and the physics of climate change.

Earth's energy balance

Earth's climate is determined by the balance between incoming solar radiation and outgoing thermal (infrared) radiation.

Solar constant

Approximately 1370 W m$^{-2}$ at Earth's mean orbital distance. This is the energy flux through a surface perpendicular to the sun at the top of the atmosphere.

Average flux at Earth's surface

Earth intercepts solar power on a cross-section $\pi R^2$ but distributes it over a surface area $4 \pi R^2$. So the average flux at the surface (before atmospheric effects) is $1370 / 4 \approx 342$ W m$^{-2}$.

Planetary albedo

Earth reflects about 30 percent of incoming solar radiation (clouds, ice, deserts). Albedo $\approx 0.30$. The absorbed fraction is $0.70$, giving about 240 W m$^{-2}$.

Radiative equilibrium

In equilibrium, Earth emits as much energy as it absorbs. Use Stefan-Boltzmann ($P/A = \sigma T^4$) to find the effective radiating temperature: $T_{\text{eff}} \approx 255$ K (or $-18$ degrees C).

The natural greenhouse effect

The actual average surface temperature of Earth is about $+15$ degrees C ($288$ K), 33 K warmer than the $-18$ degrees C equilibrium prediction. The difference is the natural greenhouse effect.

How it works:

1. Earth's surface, at about 15 degrees C, emits thermal radiation (infrared, peak wavelength about 10 micrometres).
2. Greenhouse gases in the atmosphere (water vapour, CO2, methane, ozone, N2O) absorb some of this infrared.
3. The absorbing gases re-emit infrared in all directions; some travels down to the surface and is reabsorbed.
4. The net effect: surface temperature is higher than radiative equilibrium would predict.

The greenhouse effect is essential for life. Without it, Earth would be frozen.

The enhanced greenhouse effect

Human activities have increased atmospheric greenhouse gas concentrations:

• CO2. Pre-industrial: about 280 ppm. 2024: over 420 ppm. Source: fossil fuel burning, deforestation, cement production.
• CH4 (methane). Pre-industrial: about 700 ppb. 2024: over 1900 ppb. Source: agriculture (cattle, rice paddies), fossil fuel extraction, waste decomposition.
• N2O. Industrial agriculture, particularly fertilisers.
• CFCs and HFCs. Industrial gases (now restricted by the Montreal Protocol 1987, then Kigali Amendment 2016).

Increased concentrations absorb more outgoing infrared, leading to:

• Higher surface temperature.
• Changes in atmospheric and ocean circulation.
• Sea level rise (thermal expansion, ice melt).
• Changes in precipitation patterns.
• Ocean acidification (CO2 dissolving in seawater).

Observed warming since pre-industrial: approximately 1.2 degrees C (2024).

Climate feedbacks

Climate response to forcing is amplified or dampened by feedbacks:

Positive feedbacks (amplifying).

• Water vapour feedback. Warmer atmosphere holds more water vapour, which is a greenhouse gas. Roughly doubles the direct CO2 forcing.
• Ice-albedo feedback. Less sea ice means less reflection of sunlight, more absorption, more warming, more melting.
• Permafrost feedback. Thawing permafrost releases methane.

Negative feedbacks (dampening).

• Stefan-Boltzmann. Warmer surface emits more radiation ($T^4$ scaling), tending toward equilibrium.
• Cloud feedbacks. Mixed; some clouds reflect more sunlight (cooling), others trap more infrared (warming). Sign uncertain.

Net of feedbacks: positive overall. Climate sensitivity (warming per CO2 doubling) is approximately 2.5 to 4 degrees C.

Physics of renewable energy

Mitigation requires shifting from fossil fuel to lower-carbon energy sources:

Solar

Photovoltaic (PV) cells convert sunlight directly to electricity (photoelectric effect at semiconductor band gaps). Efficiency 15 to 25 percent for commercial silicon PV.

Wind

Kinetic energy of wind converted by turbines. Power $\propto \rho A v^3$ (proportional to cube of wind speed). Wind farms produce 20 to 50 percent of theoretical maximum (Betz limit 59 percent).

Hydro

Gravitational potential energy of water converted by turbines.

Nuclear (fission)

Already discussed. Low CO2 emissions but waste and safety concerns.

Geothermal

Earth's internal heat (largely from radioactive decay in mantle).

Battery storage

Critical for intermittent renewables. Lithium-ion is current dominant technology.

Each technology has physics that determines its limits and efficiency. The Unit 1 framework introduces these concepts; later units and degrees develop them further.

Examples in context

Example 1. Melbourne urban heat island and local forcing. The Melbourne CBD averages $1.5$-$2.5^\circ$C warmer than the western suburbs at night because dark bitumen and concrete absorb solar radiation by day and release infrared at night. This local effect is layered on top of global greenhouse forcing. A roof at $50^\circ$C ($323$ K) radiates $\sigma T^4 = 5.67 \times 10^{-8} \times (323)^4 = 617$ W m$^{-2}$ versus a cool roof at $30^\circ$C ($303$ K) radiating $478$ W m$^{-2}$. The City of Melbourne's cool-roof policy increases urban albedo from $0.15$ to $0.65$, reducing absorbed solar by $50$% on treated roofs and locally cutting summer peak temperatures by up to $4^\circ$C.

Example 2. Loy Yang closure pathway and cumulative emissions. Loy Yang A is scheduled to close by 2035. Until then, its $19$ Mt CO$_2$ per year, integrated over the remaining decade, contributes approximately $190$ Mt to atmospheric CO$_2$. Globally this raises CO$_2$ by about $24$ ppb, producing a forcing of $5.35 \ln(C_2/C_1) \approx 3 \times 10^{-4}$ W m$^{-2}$. By comparison, replacing Loy Yang with Snowy 2.0 plus the Hornsdale-class batteries avoids that emissions pulse and delivers the same firm capacity, illustrating why dispatchable storage and pumped hydro are central to Victoria's transition plan.

Try this

Q1. Distinguish between the natural and the enhanced greenhouse effect. [2 marks]

• Cue. Natural maintains $288$ K via baseline gas concentrations; enhanced is the additional warming from human-driven increases in CO$_2$, CH$_4$ and other gases.

Q2. A planet with surface temperature $290$ K has albedo $0.30$. Calculate (a) the power per square metre radiated by the surface, and (b) the absorbed solar power per square metre if the solar constant is $1361$ W m$^{-2}$. [4 marks]

• Cue. (a) $\sigma T^4 = 5.67 \times 10^{-8} \times 7.07 \times 10^9 = 401$ W m$^{-2}$. (b) Absorbed = $(1-0.30) \times 1361/4 = 238$ W m$^{-2}$.

Q3. Refer to the Melbourne urban heat island. (a) Outline the role of albedo in surface temperature. (b) Calculate the increase in radiated power per square metre when a roof warms from $30^\circ$C to $50^\circ$C. (c) Evaluate the effectiveness of cool roofs as a local mitigation measure. [2+2+2 marks]

• Cue. (a) Higher albedo reflects more solar; surface warms less. (b) $617 - 478 = 139$ W m$^{-2}$. (c) Cool roofs work locally but do not address global CO$_2$ forcing; useful in combination with emissions cuts.