Apply the energy balance of the Earth-atmosphere system to model the enhanced greenhouse effect, including the role of greenhouse gases and the radiative forcing concept

What this dot point is asking

VCAA wants you to model the Earth's surface temperature as the result of a radiation balance, to identify the natural and anthropogenic greenhouse effects, and to apply the radiative forcing concept to climate change.

The Earth's energy balance

Energy in: $1361$ W m$^{-2}$ of solar irradiance at the top of the atmosphere, spread over the Earth's cross-section (a disc), then averaged over the full sphere (a factor of $4$), gives an average of $340$ W m$^{-2}$ at the top of the atmosphere.

Of this, about $30$% is reflected back to space by clouds, atmosphere, and surface (the Earth's albedo). About $70$% is absorbed by the Earth-atmosphere system, then re-emitted at infrared wavelengths.

The natural greenhouse effect

Without an atmosphere, the Earth's equilibrium temperature would be about $255$ K ($-18$°C). Stefan-Boltzmann gives this from $(1 - \alpha) S / 4 = \sigma T^4$ with albedo $\alpha = 0.30$ and solar constant $S = 1361$ W m$^{-2}$.

With its atmosphere, the Earth's actual mean surface temperature is about $288$ K ($15$°C). The $33$ K difference is the natural greenhouse effect.

The mechanism: short-wavelength visible sunlight reaches the surface (the atmosphere is mostly transparent to visible). The warm surface re-emits in the infrared. Greenhouse gases (water vapour, CO$_2$, methane, nitrous oxide) absorb infrared photons and re-emit them in all directions, including downward (back-radiation). The surface stays warmer than it would otherwise.

Greenhouse gases work because their molecular vibrations and rotations match infrared photon energies. Diatomic gases of identical atoms (N$_2$, O$_2$) are nearly transparent to infrared.

The enhanced greenhouse effect

Pre-industrial atmospheric CO$_2$ was approximately $280$ ppm. By 2023 it exceeded $420$ ppm. Methane has more than doubled. These increases trace to fossil-fuel combustion, deforestation and agriculture since 1750.

The result is radiative forcing: the change in net incoming minus outgoing radiation at the top of the atmosphere. CO$_2$ at $420$ ppm produces a forcing of approximately $2.1$ W m$^{-2}$ relative to pre-industrial; total anthropogenic forcing (including other greenhouse gases, aerosols, land-use changes) is approximately $2.7$ W m$^{-2}$.

This forcing raises the equilibrium surface temperature. With climate sensitivity of approximately $3$°C per doubling of CO$_2$, a doubling produces $3$°C warming. Observed warming (about $1.2$°C since the pre-industrial baseline) is broadly consistent with the radiative-forcing model plus thermal inertia in the oceans.

Feedbacks

Water vapour feedback (positive)

Warmer air holds more water vapour, which is itself a greenhouse gas, amplifying warming.

Ice-albedo feedback (positive)

Melting sea ice exposes darker ocean, which absorbs more sunlight, accelerating warming.

Cloud feedback (uncertain)

Different cloud types either warm or cool.

These feedbacks make precise climate sensitivity estimates challenging; the IPCC's likely range is $2.5$-$4.0$°C per doubling.

VCAA exam style

VCE Year 11 SAC tasks typically include:

• Calculating outgoing radiation per unit area with Stefan-Boltzmann.
• Comparing equilibrium temperatures with and without atmosphere.
• Explaining the mechanism of the greenhouse effect at molecular level.
• Distinguishing natural and enhanced greenhouse effects.

Common traps

Confusing greenhouse effect with ozone hole

Different physics, different gases, different consequences.

Treating "greenhouse" as a literal greenhouse

Real glass greenhouses warm mainly by preventing convective heat loss, not by re-radiating infrared. The atmospheric greenhouse mechanism is dominated by the radiation effect.

Forgetting that all radiation must obey energy balance

At equilibrium, the rate of energy input equals the rate of energy output. Climate change is a non-equilibrium response to a forcing.

In one sentence

The Earth's surface temperature reflects a radiation balance: incoming solar energy at $340$ W m$^{-2}$ (top of atmosphere average) minus albedo reflection equals outgoing infrared radiation via Stefan-Boltzmann, with greenhouse gases (water vapour, CO$_2$, methane) raising the surface temperature by about $33$ K above the no-atmosphere case; anthropogenic emissions since 1750 have raised CO$_2$ from $280$ to over $420$ ppm, producing approximately $2.7$ W m$^{-2}$ of radiative forcing and the observed warming of roughly $1.2$°C above pre-industrial levels.

Examples in context

Example 1. Loy Yang A power station radiative forcing contribution. Loy Yang A in the Latrobe Valley burns brown coal and emits roughly $19$ Mt of CO$_2$ each year, about $4\%$ of Australia's total. Spread over Earth's surface area $5.1 \times 10^{14}$ m$^2$, one year of Loy Yang emissions adds about $0.037$ ppm to global atmospheric CO$_2$. Using a forcing factor of $5.35 \ln(C/C_0)$ W m$^{-2}$, an increase from $420.000$ ppm to $420.037$ ppm produces a tiny additional radiative forcing of $4.7 \times 10^{-4}$ W m$^{-2}$, illustrating why mitigation requires aggregation of many sources rather than focus on any single plant.

Example 2. Snowy 2.0 displacement of fossil generation. Snowy 2.0 pumped hydro will provide $2200$ MW of dispatchable power and $350$ GWh of storage. If it displaces gas peakers at $0.40$ kg CO$_2$ per kWh, full annual cycling avoids approximately $1.4$ Mt of CO$_2$ per year. Modelled over a $100$ year lifetime, the cumulative avoided forcing is small ($\approx 10^{-3}$ W m$^{-2}$), but combined with rooftop solar and the AGL Hornsdale battery, the Australian National Electricity Market is shifting from a $0.7$ kg CO$_2$ per kWh emissions intensity toward $0.2$ kg per kWh by 2035.

Try this

Q1. Define radiative forcing and state the approximate present-day anthropogenic value in W m$^{-2}$. [2 marks]

• Cue. Net change in incoming minus outgoing radiation at the top of the atmosphere due to a perturbation. Present forcing approximately $2.7$ W m$^{-2}$.

Q2. A planet of albedo $0.25$ orbits a star delivering $1700$ W m$^{-2}$ of irradiance at the top of its atmosphere. Calculate the no-atmosphere equilibrium temperature. [4 marks]

• Cue. Apply $(1-\alpha)S/4 = \sigma T^4$. Solve $T = [(0.75 \times 1700)/(4 \times 5.67 \times 10^{-8})]^{1/4} \approx 261$ K.

Q3. Refer to Loy Yang A. (a) Outline two ways in which the combustion of brown coal contributes to the enhanced greenhouse effect. (b) Calculate the energy radiated per square metre per second by a surface at $300$ K. (c) Explain one positive feedback in the climate system that amplifies the warming caused by such emissions. [2+2+2 marks]

• Cue. (a) CO$_2$ release plus albedo reduction from land use. (b) $\sigma T^4 = 5.67 \times 10^{-8} \times 8.1 \times 10^9 = 459$ W m$^{-2}$. (c) Water-vapour feedback or ice-albedo feedback with one-line mechanism.