B.2 Greenhouse effect

Track every pathway

Incoming solar radiation can be reflected by the planet–atmosphere system, absorbed by the atmosphere or surface, and later emitted as infrared radiation. The energy balance concerns the total absorbed input and total emitted output, not just one arrow in the diagram.

Interpret imbalance

If absorbed power exceeds emitted power, the system’s internal energy and average temperature tend to increase. If emitted power exceeds absorbed power, they tend to decrease. Equal rates mean no net long-term energy accumulation.

Use the radiation equation

For a surface of area A,

$$P=\varepsilon\sigma AT^4$$

Use T in kelvin. A black body has $$\varepsilon=1$$; real surfaces have emissivity less than or equal to 1 in this model.

What emissivity is not

Emissivity is not the fraction of incoming sunlight reflected; that is albedo. Emissivity concerns emission of thermal radiation by a surface at its temperature.

Worked example from the mapped local textbook

A planet has surface temperature $-63\,^{\circ}\mathrm{C}=210\,\mathrm{K}$, area $1.4\times10^{14}\,\mathrm{m^2}$ and luminosity $1.3\times10^{16}\,\mathrm{W}$.

$$\varepsilon=\frac{P/A}{\sigma T^4}=\frac{(1.3\times10^{16})/(1.4\times10^{14})}{(5.67\times10^{-8})(210)^4}=0.84$$

Emissivity is dimensionless, and the kelvin conversion is required by the fourth-power law.

Interpret the value

An albedo near 0 means most incident energy is absorbed; an albedo near 1 means most is reflected. It has no units and is often reported as a decimal or percentage.

Use ratios safely

Calculate each albedo from reflected divided by incident power before comparing surfaces. A snow surface can have a higher albedo than concrete because it reflects a larger fraction of the same incoming intensity.

Worked example from the mapped local textbook

Radiation of intensity $610\,\mathrm{W\,m^{-2}}$ reaches water with albedo $a=0.18$. The absorbed fraction is $1-a=0.82$, so

$$I_{\mathrm{absorbed}}=(1-a)I_{\mathrm{incident}}=(0.82)(610)=5.0\times10^2\,\mathrm{W\,m^{-2}}$$

About $110\,\mathrm{W\,m^{-2}}$ is reflected; the absorbed and reflected intensities add back to the incident intensity, within rounding.

Daily variation

Cloud cover changes with weather and the position of the Sun changes during the day. Both alter the fraction of incident radiation reflected by a region.

Latitude and incidence angle

At different latitudes, sunlight arrives at different angles to the surface normal. The effective surface and reflected fraction therefore vary; snow, ice, ocean, land and clouds also contribute different albedos.

It is not the global mean

The solar constant describes the incident intensity on a surface facing the Sun. A planet’s spherical geometry spreads the intercepted power over a larger total surface, so the planet-wide mean incoming intensity is smaller.

Use it as an input

In an energy-balance problem, S is the incoming solar intensity before accounting for the planet’s projected area, albedo, atmospheric absorption or averaging over the whole sphere.

Mean incoming intensity

If the solar constant is S,

$$\overline I=\frac{S\pi r^2}{4\pi r^2}=\frac S4$$

This is the mean intensity before accounting for reflection or atmospheric absorption.

Add albedo when required

If the planetary albedo is a, the globally averaged absorbed intensity is

$$I_{\mathrm{abs}}=(1-a)\frac S4$$

provided the problem’s model treats the planet as a uniform system.

Worked example from local Question Bank row 30218

For $S=1400\,\mathrm{W\,m^{-2}}$ and atmospheric albedo $a=0.30$, the transmitted incident intensity is

$$I=(1-a)S=(0.70)(1400)=980\,\mathrm{W\,m^{-2}}$$

Averaging the intercepted power over the full sphere gives

$$\overline I=\frac{980}{4}=245\,\mathrm{W\,m^{-2}}$$

This result combines reflection with geometry: $(1-a)S/4$.

Natural and human origins

Each of these gases has natural sources and sources affected by human activity. For example, water vapour participates in the natural water cycle, while combustion, agriculture and land-use changes can alter atmospheric concentrations of several greenhouse gases.

Abundance is not the only factor

A gas’s contribution depends on both its atmospheric abundance and how strongly it absorbs infrared radiation. Do not rank gases using concentration alone.

Re-emit in all directions

The excited molecule soon returns to a lower energy state and emits infrared radiation. The emission is in random directions, so some radiation continues upward and some is directed back toward the surface.

Why Earth’s radiation matters

The cooler Earth emits mainly longer-wavelength infrared radiation. Greenhouse gases absorb part of this outgoing radiation; they are less likely to absorb most of the Sun’s shorter-wavelength incoming radiation.

Model boundary from local Question Bank row 30018

Mars's atmosphere is mainly carbon dioxide, but its pressure is less than $1\%$ of Earth's. The low pressure means far fewer absorbing molecules per unit volume, so much less outgoing infrared radiation is absorbed and re-emitted toward the surface.

The presence of a greenhouse-gas species alone does not determine the size of the effect; the amount of gas also matters.

Molecular energy-level model

The same absorption can be described as a photon whose energy matches the gap between molecular energy levels. The molecule is excited, then returns to a lower level and emits infrared radiation.

Complete mechanism

Earth’s surface emits long-wave infrared radiation. Greenhouse gases absorb part of it and re-emit radiation in random directions; some is directed back toward the surface, raising the surface temperature compared with an atmosphere-free model.

Frequency test from local Question Bank row 31337

If a carbon dioxide vibration has period $5\times10^{-14}\,\mathrm{s}$, its natural frequency is

$$f_0=\frac1T=\frac1{5\times10^{-14}}=2\times10^{13}\,\mathrm{Hz}=20\,\mathrm{THz}$$

Earth's outgoing infrared is around $30\,\mathrm{THz}$, much closer to this molecular frequency than the cited solar infrared near $300\,\mathrm{THz}$. The resonance model therefore predicts stronger absorption of part of Earth's outgoing infrared; the energy-level model describes the same selectivity as matched photon-energy gaps.

Enhanced greenhouse effect

The enhanced greenhouse effect is the augmentation of that effect due to human activity. Increased concentrations of greenhouse gases can increase absorption and downward re-radiation of infrared energy.

Primary cause in the syllabus

Burning fossil fuels is identified as a primary cause because it increases atmospheric carbon dioxide and contributes to changes in the Earth–atmosphere energy balance. Other human activities can affect greenhouse-gas concentrations too.